The correct answer is the volume of water (in liters) pumped in during the first minute is 7.766 liters.
Given a pump is delivering water into a tank at a rate of r (t) 3t2+5 liters/minute where t is the time in minutes since the pump was turned on. Using a left Riemann sum with n 5 subdivisions to estimate the volume of water pumped in during the first minute.
We need to calculate the left Riemann sum first.
Let's find the width of each subdivision first: ∆t=(b-a)/n where a=0, b=1, and n=5.
∆t= (1-0)/5=0.2
Next, let's calculate the height of each subdivision using left endpoints: r(0)
= 3(0)^2 + 5
= 5r(0.2)
= 3(0.2)^2 + 5
= 5.24r(0.4)
= 3(0.4)^2 + 5
= 6.4r(0.6)
= 3(0.6)^2 + 5
= 7.8r(0.8)
= 3(0.8)^2 + 5
= 9.4
We have the width and height of each subdivision, so now we can calculate the left Riemann sum:
LRS = f(a)∆t + f(a + ∆t)∆t + f(a + 2∆t)∆t + f(a + 3∆t)∆t + f(a + 4∆t)∆t where a=0, ∆t=0.2
LRS = r(0)∆t + r(0.2)∆t + r(0.4)∆t + r(0.6)∆t + r(0.8)∆t
= 5(0.2) + 5.24(0.2) + 6.4(0.2) + 7.8(0.2) + 9.4(0.2)
= 1 + 1.048 + 1.28 + 1.56 + 1.88
= 7.766 litres
Therefore, the volume of water (in liters) pumped in during the first minute is 7.766 liters.
know more about left Riemann sum
https://brainly.com/question/30763921
#SPJ11
Which linear equality will not have a shared solution set with the graphed linear inequality? y > two-fifthsx 2 y < negative five-halvesx – 7 y > negative two-fifthsx – 5 y < five-halvesx 2
The linear equality that will not have a shared solution set with the graphed linear inequality is y > 2/5x + 2. So, option A is the correct answer.
To determine which linear equality will not have a shared solution set with the graphed linear inequality, we need to compare the slopes and intercepts of the inequalities.
The given graphed linear inequality is y > -5/2x - 3.
Let's analyze each option:
A. y > 2/5x + 2:
The slope of this inequality is 2/5, which is different from -5/2, the slope of the graphed inequality. Therefore, option A will not have a shared solution set.
B. y < -5/2x - 7:
The slope of this inequality is -5/2, which is the same as the slope of the graphed inequality. However, the intercept of -7 is different from -3, the intercept of the graphed inequality. Therefore, option B will have a shared solution set.
C. y > -2/5x - 5:
The slope of this inequality is -2/5, which is different from -5/2, the slope of the graphed inequality. Therefore, option C will not have a shared solution set.
D. y < 5/2x + 2:
The slope of this inequality is 5/2, which is different from -5/2, the slope of the graphed inequality. Therefore, option D will not have a shared solution set.
Based on the analysis, the linear inequality that will not have a shared solution set with the graphed linear inequality is option A: y > 2/5x + 2.
The question should be:
Which linear equality will not have a shared solution set with the graphed linear inequality?
graphed linear equation: y>-5/2x-3 (greater then or equal to)
A. y >2/5 x + 2
B. y <-5/2 x – 7
C. y >-2/5 x – 5
D. y <5/2 x + 2
To learn more about linear inequality: https://brainly.com/question/23093488
#SPJ11
Answer:
b
Step-by-step explanation:
y<-5/2x - 7
Find the scalar tangent and normal components of acceleration, at(t) and an(t) respectively, for the parametrized curve r = t2, 6, t3 .
The scalar normal component of acceleration an(t) is given by the magnitude of the rejection of a(t) from the velocity vector v(t) is |(-8t² - 36t⁴, 0, -6t³)|.
To find the scalar tangent and normal components of acceleration, we need to differentiate the parametric equation twice with respect to time (t).
Given the parametrized curve r = t², 6, t³, we can find the velocity vector v(t) and acceleration vector a(t) by differentiating r with respect to t.
First, let's find the velocity vector v(t):
v(t) = dr/dt = (d(t²)/dt, d(6)/dt, d(t³)/dt)
= (2t, 0, 3t²)
Next, let's find the acceleration vector a(t):
a(t) = dv/dt = (d(2t)/dt, d(0)/dt, d(3t²)/dt)
= (2, 0, 6t)
The scalar tangent component of acceleration at(t) is given by the magnitude of the projection of a(t) onto the velocity vector v(t):
at(t) = |a(t) · v(t)| / |v(t)|
= |(2, 0, 6t) · (2t, 0, 3t²)| / |(2t, 0, 3t²)|
= |4t + 18t³| / √(4t² + 9t⁴)
The scalar normal component of acceleration an(t) is given by the magnitude of the rejection of a(t) from the velocity vector v(t):
an(t) = |a(t) - at(t) * v(t)|
= |(2, 0, 6t) - (4t + 18t³) * (2t, 0, 3t²)|
= |(2, 0, 6t) - (8t² + 36t⁴, 0, 12t³)|
= |(-8t² - 36t⁴, 0, -6t³)|
To know more about scalar tangent visit:
https://brainly.com/question/32524644
#SPJ11
Solve the initial value problem: y"+4y'=64sin(4t)+256cos(4t) with y(0)=9 and y'(0)=7.
The solution to the initial value problem is y = 1 + 8[tex]e^{-4t}[/tex] - 4cos(4t) - 20sin(4t). It satisfies the given initial conditions y(0) = 9 and y'(0) = 7.
To solve the initial value problem, we can use the method of undetermined coefficients. First, we find the general solution to the homogeneous equation y"+4y'=0.
The characteristic equation is[tex]r^{2}[/tex]+4r=0, which gives us the characteristic roots r=0 and r=-4. Therefore, the general solution to the homogeneous equation is y_h=c1[tex]e^{0t}[/tex]+c2[tex]e^{-4t}[/tex]=c1+c2[tex]e^{-4t}[/tex].
Next, we find a particular solution to the non-homogeneous equation y"+4y'=64sin(4t)+256cos(4t). Since the right-hand side is a combination of sine and cosine functions, we assume a particular solution of the form y_p=Acos(4t)+Bsin(4t).
Taking the derivatives, we have y_p'=-4Asin(4t)+4Bcos(4t) and y_p"=-16Acos(4t)-16Bsin(4t).
Substituting these expressions into the original differential equation, we get -16Acos(4t)-16Bsin(4t)+4(-4Asin(4t)+4Bcos(4t))=64sin(4t)+256cos(4t). Equating the coefficients of the sine and cosine terms, we have -16A+16B=256 and -16B-16A=64. Solving these equations, we find A=-4 and B=-20.
Therefore, the particular solution is y_p=-4cos(4t)-20sin(4t). The general solution to the non-homogeneous equation is y=y_h+y_p=c1+c2[tex]e^{-4t}[/tex])-4cos(4t)-20sin(4t).
To find the specific solution that satisfies the initial conditions, we substitute y(0)=9 and y'(0)=7 into the general solution. From y(0)=9, we have c1+c2=9, and from y'(0)=7, we have -4c2+16+80=7. Solving these equations, we find c1=1 and c2=8.
Therefore, the solution to the initial value problem is y=1+8[tex]e^{-4t}[/tex]-4cos(4t)-20sin(4t).
Learn more about initial value here:
https://brainly.com/question/30503609
#SPJ11
Having trouble:
Find the surface area or a cube with side length of 8
inches
The surface area of a cube with a side length of 8 inches is 384 square inches.
A cube is a three-dimensional object with six congruent square faces. If the side length of the cube is 8 inches, then each face has an area of 8 x 8 = 64 square inches.
To find the total surface area of the cube, we need to add up the areas of all six faces. Since all six faces have the same area, we can simply multiply the area of one face by 6 to get the total surface area.
Total surface area = 6 x area of one face
= 6 x 64 square inches
= 384 square inches
Therefore, the surface area of a cube with a side length of 8 inches is 384 square inches.
Learn more about " total surface area" : https://brainly.com/question/28178861
#SPJ11
A train was scheduled to arrive at 7:45, but arrived at 8:10. How long was the delay?
Answer:
25 minutes.
Step-by-step explanation:
From 7:45 to 8:00 is 15 minutes.
From 8:00 to 8:10 is 10 minutes.
15 + 10 = 25
15 minutes + 10 minutes = 25 minutes,
(1 point) If we simplify \[ \left(x^{2}\right)^{10} \] as \( x^{A} \), what is the value of \( A \) ?
The value of [tex]\( A \)[/tex] when simplifying [tex]\( \left(x^{2}\right)^{10} \)[/tex] as [tex]\( x^{A} \)[/tex] is 20. This is because raising a power to another power involves multiplying the exponents, resulting in [tex]\( 2 \times 10 = 20 \)[/tex]. Therefore, we can simplify [tex]\( \left(x^{2}\right)^{10} \)[/tex] as [tex]\( x^{20} \)[/tex].
When we raise a power to another power, we multiply the exponents. In this case, we have the base [tex]\( x^2 \)[/tex] raised to the power of 10. Multiplying the exponents, we get [tex]\( 2 \times 10 = 20 \)[/tex]. Therefore, we can simplify [tex]\( \left(x^{2}\right)^{10} \)[/tex] as [tex]\( x^{20} \)[/tex].
This can be understood by considering the repeated multiplication of [tex]\( x^2 \)[/tex]. Each time we raise [tex]\( x^2 \)[/tex] to the power of 10, we are essentially multiplying it by itself 10 times. Since [tex]\( x^2 \)[/tex] multiplied by itself 10 times results in [tex]\( x^{20} \)[/tex], we can simplify [tex]\( \left(x^{2}\right)^{10} \)[/tex] as [tex]\( x^{20} \)[/tex].
To summarize, when simplifying [tex]\( \left(x^{2}\right)^{10} \)[/tex] as [tex]\( x^{A} \)[/tex], the value of [tex]\( A \)[/tex] is 20.
To learn more about Exponents, visit:
https://brainly.com/question/847241
#SPJ11
Use a change of variables to evaluate the following indefinite integral. ∫x 5
(x 6
+18) 4
dx Determine a change of variables from x to u. Choose the correct answer below. A. u=x 6
+18 B. u=(x 6
+18) 4
C. u=x 6
D. u=6x 5
Write the integral in terms of u. ∫x 5
(x 6
+18) 4
dx=∫du Evaluate the integral. ∫x 5
(x 6
+18) 4
dx=
Answer:
The correct answer is: ∫x^5(x^6+18)^4 dx = (1/6) * (x^6 + 18)^5 / 5 + C.
Step-by-step explanation:
To evaluate the given integral ∫x^5(x^6+18)^4 dx, we can make a change of variables to simplify the expression. Let's determine the appropriate change of variables:
Let u = x^6 + 18.
Now, we need to find dx in terms of du to rewrite the integral. To do this, we can differentiate both sides of the equation u = x^6 + 18 with respect to x:
du/dx = d/dx(x^6 + 18)
du/dx = 6x^5
Solving for dx, we find:
dx = du / (6x^5)
Now, let's rewrite the integral in terms of u:
∫x^5(x^6+18)^4 dx = ∫x^5(u)^4 (du / (6x^5))
Canceling out x^5 in the numerator and denominator, the integral simplifies to:
∫(u^4) (du / 6)
Finally, we can evaluate this integral:
∫x^5(x^6+18)^4 dx = ∫(u^4) (du / 6)
= (1/6) ∫u^4 du
Integrating u^4 with respect to u, we get:
(1/6) ∫u^4 du = (1/6) * (u^5 / 5) + C
Therefore, the evaluated integral is:
∫x^5(x^6+18)^4 dx = (1/6) * (x^6 + 18)^5 / 5 + C
So, the correct answer is: ∫x^5(x^6+18)^4 dx = (1/6) * (x^6 + 18)^5 / 5 + C.
Learn more about Integral:https://brainly.com/question/30094386
#SPJ11
Let F=⟨0, z
x
,e −xyz
⟩ and let S be the portion of the paraboloid z=2−x 2
−y 2
,z≥−2, oriented upward. Use Stokes' Theorem to evaluate
Stokes' Theorem states that the line integral of a vector field F around a simple closed curve C is equal to the surface integral of the curl of F over the surface S bounded by C. In other words:
∮C F · dr = ∬S curl(F) · dS
In this case, the surface S is the portion of the paraboloid z = 2 - x^2 - y^2 for z ≥ -2, oriented upward. The boundary curve C of this surface is the circle x^2 + y^2 = 4 in the plane z = -2.
The curl of a vector field F = ⟨P, Q, R⟩ is given by:
curl(F) = ⟨Ry - Qz, Pz - Rx, Qx - Py⟩
For the vector field F = ⟨0, z/x, e^(-xyz)⟩, we have:
P = 0
Q = z/x
R = e^(-xyz)
Taking the partial derivatives of P, Q, and R with respect to x, y, and z, we get:
Px = 0
Py = 0
Pz = 0
Qx = -z/x^2
Qy = 0
Qz = 1/x
Rx = -yze^(-xyz)
Ry = -xze^(-xyz)
Rz = -xye^(-xyz)
Substituting these partial derivatives into the formula for curl(F), we get:
curl(F) = ⟨Ry - Qz, Pz - Rx, Qx - Py⟩
= ⟨-xze^(-xyz) - 1/x, 0 - (-yze^(-xyz)), -z/x^2 - 0⟩
= ⟨-xze^(-xyz) - 1/x, yze^(-xyz), -z/x^2⟩
To evaluate the surface integral of curl(F) over S using Stokes' Theorem, we need to parameterize the boundary curve C. Since C is the circle x^2 + y^2 = 4 in the plane z = -2, we can parameterize it as follows:
r(t) = ⟨2cos(t), 2sin(t), -2⟩ for 0 ≤ t ≤ 2π
The line integral of F around C is then given by:
∮C F · dr
= ∫(from t=0 to 2π) F(r(t)) · r'(t) dt
= ∫(from t=0 to 2π) ⟨0, (-2)/(2cos(t)), e^(4cos(t)sin(t))⟩ · ⟨-2sin(t), 2cos(t), 0⟩ dt
= ∫(from t=0 to 2π) [0*(-2sin(t)) + ((-2)/(2cos(t)))*(2cos(t)) + e^(4cos(t)sin(t))*0] dt
= ∫(from t=0 to 2π) (-4 + 0 + 0) dt
= ∫(from t=0 to 2π) (-4) dt
= [-4t] (from t=0 to 2π)
= **-8π**
Therefore, by Stokes' Theorem, the surface integral of curl(F) over S is equal to **-8π**.
learn more about stokes
https://brainly.com/question/30402683
#SPJ11
Each of the followingintegrals represents the volume of either a hemisphere or a cone integral 0 20 pi(4-y/5)^2dy
The integrals represents the volume of either a hemisphere or a cone integra of the integral is [tex]\frac{35\pi }{5}[/tex], that represent the volume of a cone.
To determine whether the given integral represents the volume of a hemisphere or a cone, let's evaluate the integral and analyze the result.
Given integral: ∫₀²₀ π(4 - [tex]\frac{y}{5}[/tex])² dy
To simplify the integral, let's expand the squared term:
∫₀²₀ π(16 - 2(4)[tex]\frac{y}{5}[/tex] + ([tex]\frac{y}{5}[/tex])²) dy
∫₀²₀ π(16 - ([tex]\frac{8y}{5}[/tex]) + [tex]\frac{y^ 2}{25}[/tex] dy
Now, integrate each term separately:
∫₀²₀ 16π dy - ∫₀²₀ ([tex]\frac{8\pi }{5}[/tex]) dy + ∫₀²₀ ([tex]\frac{\pi y^{2} }{25}[/tex]) dy
Evaluating each integral:
[16πy]₀²₀ - [([tex]\frac{8\pi y^{2} }{10}[/tex]) ]₀²₀ + [([tex]\frac{\pi y^{3} x}{75}[/tex])]₀²₀
Simplifying further:
(16π(20) - 8π([tex]\frac{20^{2} }{10}[/tex]) + π([tex]\frac{20^{3} }{75}[/tex])) - (16π(0) - 8π([tex]\frac{0^{2} }{10}[/tex]) + π([tex]\frac{0^{3} }{75}[/tex]))
This simplifies to:
(320π - 320π + [tex]\frac{800\pi }{75}[/tex]) - (0 - 0 + [tex]\frac{0}{75}[/tex])
([tex]\frac{480\pi }{75}[/tex]) - (0)
([tex]\frac{32\pi }{5}[/tex])
Since the result of the integral is ([tex]\frac{32\pi }{5}[/tex]), we can conclude that the given integral represents the volume of a cone.
To know more about hemisphere visit:
https://brainly.com/question/30065978
#SPJ11
The given integral i.e., [tex]\int\limits^{20}_0 \pi(4 - \frac{y}{5})^2 dy[/tex] does not represent the volume of either a hemisphere or a cone.
To determine which shape it represents, let's analyze the integral:
[tex]\int\limits^{20}_0 \pi(4 - \frac{y}{5})^2 dy[/tex]
To better understand this integral, let's break it down into its components:
1. The limits of integration are from 0 to 20, indicating that we are integrating with respect to y over this interval.
2. The expression inside the integral, [tex](4 - \frac{y}{5})^2[/tex], represents the radius squared. This suggests that we are dealing with a shape that has a varying radius.
To find the shape, let's simplify the integral:
[tex]= \int\limits^{20}_0 \pi(16 - \frac{8y}{5} + \frac{y^2}{25}) dy[/tex]
[tex]=> \pi\int\limits^{20}_0(16 - \frac{8y}{5} + \frac{y^2}{25}) dy[/tex]
[tex]=> \pi[16y - \frac{4y^2}{5} + \frac{y^3}{75}]_0^{20}[/tex]
Now, let's evaluate the integral at the upper and lower limits:
[tex]\pi[16(20) - \frac{4(20^2)}{5} + \frac{20^3}{75}] - \pi[16(0) - \frac{4(0^2)}{5} + \frac{0^3}{75}][/tex]
[tex]= \pi[320 - 320 + 0] - \pi[0 - 0 + 0][/tex]
[tex]= 0[/tex]
Based on the result, we can conclude that the integral evaluates to 0. This means that the volume represented by the integral is zero, indicating that it does not correspond to either a hemisphere or a cone.
In conclusion, the given integral does not represent the volume of either a hemisphere or a cone.
Learn more about cone from the given link:
https://brainly.com/question/29424374
#SPJ11
If the general solution of a differential equation is \( y(t)=C e^{-3 t}+9 \), what is the solution that satisfies the initial condition \( y(0)=4 \) ? \[ y(t)= \]
The solution that satisfies the initial condition [tex]\(y(0) = 4\)[/tex] for the differential equation is [tex]\(y(t) = -5e^{-3t} + 9\)[/tex].
To find the solution that satisfies the initial condition [tex]\(y(0) = 4\)[/tex] for the differential equation [tex]\(y(t) = Ce^{-3t} + 9\)[/tex], we substitute the initial condition into the general solution and solve for the constant [tex]\(C\)[/tex].
Given: [tex]\(y(t) = Ce^{-3t} + 9\)[/tex]
Substituting [tex]\(t = 0\)[/tex] and [tex]\(y(0) = 4\)[/tex]:
[tex]\[4 = Ce^{-3 \cdot 0} + 9\][/tex]
[tex]\[4 = C + 9\][/tex]
Solving for [tex]\(C\)[/tex]:
[tex]\[C = 4 - 9\][/tex]
[tex]\[C = -5\][/tex]
Now we substitute the value of [tex]\(C\)[/tex] back into the general solution:
[tex]\[y(t) = -5e^{-3t} + 9\][/tex]
Therefore, the solution that satisfies the initial condition [tex]\(y(0) = 4\)[/tex] for the differential equation is:
[tex]\[y(t) = -5e^{-3t} + 9\][/tex]
To know more about differential equation, refer here:
https://brainly.com/question/32645495
#SPJ4
Find (a) the number of subsets and (b) the number of proper subsets of the following set. \( \{h, i, j, k, l, m\} \). a. The number of subsets is (Type a whole number.)
In the set {h, i, j, k, l, m},
(a) The number of subsets is 64
(b) The number of proper subsets is 63
To find the number of subsets and the number of proper subsets of the set {h, i, j, k, l, m},
(a) The number of subsets
To find the number of subsets of a given set, we can use the formula which is 2^n, where n is the number of elements in the set.
Hence, the number of subsets of the given set {h, i, j, k, l, m} is 2^6 = 64
Therefore, the number of subsets of the set is 64.
(b) The number of proper subsets
A proper subset of a set is a subset that does not include all of the elements of the set.
To find the number of proper subsets of a set, we can use the formula which is 2^n - 1, where n is the number of elements in the set.
Hence, the number of proper subsets of the given set {h, i, j, k, l, m} is:2^6 - 1 = 63
To learn more about proper subsets visit:
https://brainly.com/question/28705656
#SPJ11
the provider orders a prescription for ampicillin 500mgs p.o. bid x10 days. how many capsules will be dispensed by the pharmacy?
The pharmacy will dispense 20 capsules of ampicillin 500mg each for a prescription of ampicillin 500mg PO BID for 10 days.
In the prescription, "500mgs p.o. bid x10 days" indicates that the patient should take 500mg of ampicillin orally (p.o.) two times a day (bid) for a duration of 10 days. To calculate the total number of capsules required, we need to determine the number of capsules needed per day and then multiply it by the number of days.
Since the patient needs to take 500mg of ampicillin twice a day, the total daily dose is 1000mg (500mg x 2). To determine the number of capsules needed per day, we divide the total daily dose by the strength of each capsule, which is 500mg. So, 1000mg ÷ 500mg = 2 capsules per day.
To find the total number of capsules for the entire prescription period, we multiply the number of capsules per day (2) by the number of days (10). Therefore, 2 capsules/day x 10 days = 20 capsules.
Hence, the pharmacy will dispense 20 capsules of ampicillin, each containing 500mg, for the prescription of ampicillin 500mg PO BID for 10 days.
Learn more about multiply here: https://brainly.com/question/30875464
#SPJ11
If z = 2x2 - 3y with u = x2 siny and v= 2y cosx, determine expressions for dz/du and dz/dv
The expressions for dz/du and dz/dv are as follows:
dz/du = 4x siny
dz/dv = -6y cosx
To find the expressions for dz/du and dz/dv, we need to differentiate the given function z = 2x^2 - 3y with respect to u and v, respectively.
1. dz/du:
Since u = x^2 siny, we can express z in terms of u by substituting x^2 siny for u in the original function:
z = 2u - 3y
Now, we differentiate z with respect to u while treating y as a constant:
dz/du = d/dx (2u - 3y)
= 2(d/dx (x^2 siny)) - 0 (since y is constant)
= 2(2x siny)
= 4x siny
Therefore, dz/du = 4x siny.
2. dz/dv:
Similarly, we express z in terms of v by substituting 2y cosx for v in the original function:
z = 2x^2 - 3v
Now, we differentiate z with respect to v while treating x as a constant:
dz/dv = d/dy (2x^2 - 3v)
= 0 (since x^2 is constant) - 3(d/dy (2y cosx))
= -6y cosx
Therefore, dz/dv = -6y cosx.
In summary, the expressions for dz/du and dz/dv are dz/du = 4x siny and dz/dv = -6y cosx, respectively.
To learn more about expressions, click here: brainly.com/question/4344214
#SPJ11
Use the disc method to find the volume of the solid obtained by rotating about the x-axis the region bounded by the curves y=2x^3,y=0,x=0 and x=1.
To find the volume of the solid obtained by rotating the region bounded by the curves y=[tex]2x^3[/tex], y=0, x=0, and x=1 about the x-axis, we can use the disc method. The resulting volume is (32/15)π cubic units.
The disc method involves slicing the region into thin vertical strips and rotating each strip around the x-axis to form a disc. The volume of each disc is then calculated and added together to obtain the total volume. In this case, we integrate along the x-axis from x=0 to x=1.
The radius of each disc is given by the y-coordinate of the function y=[tex]2x^3[/tex], which is 2x^3. The differential thickness of each disc is dx. Therefore, the volume of each disc is given by the formula V = [tex]\pi (radius)^2(differential thickness) = \pi (2x^3)^2(dx) = 4\pi x^6(dx)[/tex].
To find the total volume, we integrate this expression from x=0 to x=1:
V = ∫[0,1] [tex]4\pi x^6[/tex] dx.
Evaluating this integral gives us [tex](4\pi /7)x^7[/tex] evaluated from x=0 to x=1, which simplifies to [tex](4\pi /7)(1^7 - 0^7) = (4\pi /7)(1 - 0) = 4\pi /7[/tex].
Therefore, the volume of the solid obtained by rotating the region about the x-axis is (4π/7) cubic units. Simplifying further, we get the volume as (32/15)π cubic units.
Learn more about volume here:
https://brainly.com/question/28058531
#SPJ11
A factory produces cans costing $240,000 per month and costs $0.05 per can, where C is the total cost and x is the quantity produced. c(x)=0.05x+240000 Express, using functional notation, what quantity makes the total cost $300,000 ? 1,200,000C(x)=300,000⊙C(x)=1,200,000∘C(300,000)∘C(300,000)=255,000∘C(1,200,000) What is the value returned from that function (what is x )?
The value returned from the function C(1,200,000) is $300,000. This means that producing 1,200,000 cans will result in a total cost of $300,000.
To find the quantity that makes the total cost $300,000, we can set the total cost function equal to $300,000 and solve for x:
C(x) = 0.05x + 240,000
$300,000 = 0.05x + 240,000
$60,000 = 0.05x
x = $60,000 / 0.05
x = 1,200,000
Therefore, the quantity that makes the total cost $300,000 is 1,200,000 cans.
To find the value returned from the function C(1,200,000), we can substitute x = 1,200,000 into the total cost function:
C(1,200,000) = 0.05(1,200,000) + 240,000
C(1,200,000) = 60,000 + 240,000
C(1,200,000) = $300,000
Therefore, the value returned from the function C(1,200,000) is $300,000. This means that producing 1,200,000 cans will result in a total cost of $300,000.
Learn more about " cost function" : https://brainly.com/question/2292799
#SPJ11
Solve each quadratic equation by completing the square. 2x² - (1/2)x = 1/8.
By completing the square, the quadratic equation 2x² - (1/2)x = 1/8 can be solved to find the values of x.
To solve the given quadratic equation, we can use the method of completing the square. First, we rewrite the equation in the form ax² + bx + c = 0, where a = 2, b = -(1/2), and c = -1/8.
Step 1: Divide the entire equation by the coefficient of x² to make the coefficient 1. This gives us x² - (1/4)x = 1/16. Step 2: Move the constant term (c) to the other side of the equation. x² - (1/4)x - 1/16 = 0.
Step 3: Take half of the coefficient of x, square it, and add it to both sides of the equation. In this case, we have (1/4) ÷ 2 = 1/8. Squaring 1/8 gives us 1/64. Adding 1/64 to both sides, we get x² - (1/4)x + 1/64 = 1/16 + 1/64. Step 4: Simplify the equation. The left side of the equation can be written as (x - 1/8)² = 5/64.
Step 5: Take the square root of both sides of the equation. This yields x - 1/8 = ±√(5/64). Step 6: Solve for x by adding 1/8 to both sides. We have two solutions: x = 1/8 ± √(5/64).
Therefore, the solutions to the quadratic equation 2x² - (1/2)x = 1/8, obtained by completing the square, are x = 1/8 + √(5/64) and x = 1/8 - √(5/64).
Learn more about quadratic equation here:
https://brainly.com/question/29269455
#SPJ11
Two tirequality experts examine stacks of tires and assign quality ratingsto each tire on a three-point scale. Let X denote the grade givenbe each expert A and Y denote the grade given by B. The followingtable gives the joint distribution for X and Y.
y
_F(x,y) 1 2 3___
1 0.10 0.05 0.02
x 2 0.10 0.35 0.05
3 0.03 0.10 0.20
Find μx and μy.
please show all steps to solve
The means μx and μy are 2.16 and 2.19, respectively.
To find the means μx and μy, we need to calculate the expected values for X and Y using the joint distribution.
The expected value of a discrete random variable is calculated as the sum of the product of each possible value and its corresponding probability. In this case, we have a joint distribution table, so we need to multiply each value of X and Y by their respective probabilities and sum them up.
The formula for calculating the expected value is:
E(X) = ∑ (x * P(X = x))
E(Y) = ∑ (y * P(Y = y))
Let's calculate μx:
E(X) = (1 * P(X = 1, Y = 1)) + (2 * P(X = 2, Y = 1)) + (3 * P(X = 3, Y = 1))
+ (1 * P(X = 1, Y = 2)) + (2 * P(X = 2, Y = 2)) + (3 * P(X = 3, Y = 2))
+ (1 * P(X = 1, Y = 3)) + (2 * P(X = 2, Y = 3)) + (3 * P(X = 3, Y = 3))
Substituting the values from the joint distribution table:
E(X) = (1 * 0.10) + (2 * 0.10) + (3 * 0.03)
+ (1 * 0.05) + (2 * 0.35) + (3 * 0.10)
+ (1 * 0.02) + (2 * 0.05) + (3 * 0.20)
Simplifying the expression:
E(X) = 0.10 + 0.20 + 0.09 + 0.05 + 0.70 + 0.30 + 0.02 + 0.10 + 0.60
= 2.16
Therefore, μx = E(X) = 2.16.
Now let's calculate μy:
E(Y) = (1 * P(X = 1, Y = 1)) + (2 * P(X = 1, Y = 2)) + (3 * P(X = 1, Y = 3))
+ (1 * P(X = 2, Y = 1)) + (2 * P(X = 2, Y = 2)) + (3 * P(X = 2, Y = 3))
+ (1 * P(X = 3, Y = 1)) + (2 * P(X = 3, Y = 2)) + (3 * P(X = 3, Y = 3))
Substituting the values from the joint distribution table:
E(Y) = (1 * 0.10) + (2 * 0.05) + (3 * 0.02)
+ (1 * 0.10) + (2 * 0.35) + (3 * 0.10)
+ (1 * 0.03) + (2 * 0.10) + (3 * 0.20)
Simplifying the expression:
E(Y) = 0.10 + 0.10 + 0.06 + 0.10 + 0.70 + 0.30 + 0.03 + 0.20 + 0.60
= 2.19
Therefore, μy = E(Y) = 2.19.
Learn more about discrete random variable here:brainly.com/question/17217746
#SPJ11
Find the area of the given region analytically. Common interior of r = 3 - 2 sine and r -3 + 2 sine
The area of region R is found to be 4 square units. We have used the polar coordinate system and double integrals to solve for the area of the given region analytically.
The region that we need to find the area for can be enclosed by two circles:
r = 3 - 2sinθ (let this be circle A)r = 3 + 2sinθ (let this be circle B)
We can use the polar coordinate system to solve this problem: let θ range from 0 to 2π. Then the region R is defined by the two curves:
R = {(r,θ)| 3+2sinθ ≤ r ≤ 3-2sinθ, 0 ≤ θ ≤ 2π}
So, we can use double integrals to solve for the area of R. The integral would be as follows:
∬R dA = ∫_0^(2π)∫_(3+2sinθ)^(3-2sinθ) r drdθ
In the above formula, we take the integral over the region R and dA refers to an area element of the polar coordinate system. We use the polar coordinate system since the region is enclosed by two circles that have equations in the polar coordinate system.
From here, we can simplify the integral:
∬R dA = ∫_0^(2π)∫_(3+2sinθ)^(3-2sinθ) r drdθ
= ∫_0^(2π) [1/2 r^2]_(3+2sinθ)^(3-2sinθ) dθ
= ∫_0^(2π) 1/2 [(3-2sinθ)^2 - (3+2sinθ)^2] dθ
= ∫_0^(2π) 1/2 [(-4sinθ)(2)] dθ
= ∫_0^(2π) [-4sinθ] dθ
= [-4cosθ]_(0)^(2π)
= 0 - (-4)
= 4
Therefore, we have used the polar coordinate system and double integrals to solve for the area of the given region analytically. The area of region R is found to be 4 square units.
To know more about the double integrals, visit:
brainly.com/question/27360126
#SPJ11
Suppose that you estimate that lohi corp. will skip its next three annual dividends, but then resume paying a dividend, with the first dividend paid to be equal to $1.00. if all subsequent dividends will grow at a constant rate of 6 percent per year and the required rate of return on lohi is 14 percent per year, what should be its price? a. $6.35 b. $8.44 c. $10.37 d. $12.50 continuing the previous problem, what is lohi's expected capital gains yield over the next year? a. 10.34% b. 11.85% c. 12.08% d. 14.00%
Lohi Corp.'s expected capital gains yield over the next year is 0.48%.
To determine the price of lohi corp., we need to calculate the present value of its future dividends. First, we estimate that the company will skip the next three annual dividends. This means that we will start receiving dividends from the fourth year. The first dividend to be paid is $1.00, and subsequent dividends will grow at a constant rate of 6 percent per year. The required rate of return on lohi corp. is 14 percent per year. This is the rate of return that investors expect to earn from investing in the company.
To calculate the price of Lohi Corp., we need to use the dividend discount model (DDM). The DDM formula is:
Price = Dividend / (Required rate of return - Dividend growth rate)
In this case, we know that Lohi Corp. will skip its next three annual dividends and then resume paying a dividend of $1.00. The dividend growth rate is 6% per year, and the required rate of return is 14% per year.
First, let's calculate the present value of the future dividends:
PV = (1 / (1 + Required rate of return))^1 + (1 / (1 + Required rate of return))^2 + (1 / (1 + Required rate of return))^3
PV = (1 / (1 + 0.14))^1 + (1 / (1 + 0.14))^2 + (1 / (1 + 0.14))^3
PV = 0.877 + 0.769 + 0.675
PV = 2.321
Next, let's calculate the price:
Price = (Dividend / (Required rate of return - Dividend growth rate)) + PV
Price = (1 / (0.14 - 0.06)) + 2.321
Price = (1 / 0.08) + 2.321
Price = 12.5
Therefore, the price of Lohi Corp. should be $12.50.
To calculate the expected capital gains yield over the next year, we need to use the formula:
Capital gains yield = (Dividend growth rate) / (Price)
Capital gins yield = 0.06 / 12.5
Capital gains yield = 0.0048
Convert to percentage:
Capital gains yield = 0.0048 * 100
Capital gains yield = 0.48%
Therefore, Lohi Corp.'s expected capital gains yield over the next year is 0.48%.
Know more about DDM formula
https://brainly.com/question/32370691
#SPJ11
Lohi Corp.'s expected capital gains yield over the next year is 0.48%.
To determine the price of lohi corp., we need to calculate the present value of its future dividends. First, we estimate that the company will skip the next three annual dividends. This means that we will start receiving dividends from the fourth year. The first dividend to be paid is $1.00, and subsequent dividends will grow at a constant rate of 6 percent per year. The required rate of return on lohi corp. is 14 percent per year. This is the rate of return that investors expect to earn from investing in the company.
To calculate the price of Lohi Corp., we need to use the dividend discount model (DDM). The DDM formula is:
[tex]Price = Dividend / (Required rate of return - Dividend growth rate)[/tex]
In this case, we know that Lohi Corp. will skip its next three annual dividends and then resume paying a dividend of $1.00. The dividend growth rate is 6% per year, and the required rate of return is 14% per year.
First, let's calculate the present value of the future dividends:
[tex]PV = (1 / (1 + Required rate of return))^1 + (1 / (1 + Required rate of return))^2 + (1 / (1 + Required rate of return))^3[/tex]
[tex]PV = (1 / (1 + 0.14))^1 + (1 / (1 + 0.14))^2 + (1 / (1 + 0.14))^3[/tex]
[tex]PV = 0.877 + 0.769 + 0.675[/tex]
PV = 2.321
Next, let's calculate the price:
[tex]Price = (Dividend / (Required rate of return - Dividend growth rate)) + PV[/tex]
[tex]Price = (1 / (0.14 - 0.06)) + 2.321[/tex]
Price = (1 / 0.08) + 2.321
Price = 12.5
Therefore, the price of Lohi Corp. should be $12.50.
To calculate the expected capital gains yield over the next year, we need to use the formula:
[tex]Capital gains yield = (Dividend growth rate) / (Price)[/tex]
[tex]Capital gins yied = 0.06 / 12.5[/tex]
Capital gains yield = 0.0048
Convert to percentage:
Capital gains yield = 0.0048 * 100
Capital gains yield = 0.48%
Therefore, Lohi Corp.'s expected capital gains yield over the next year is 0.48%.
Know more about DDM formula
brainly.com/question/32370691
#SPJ11
Assume that X is a Poisson random variable with μ 4, Calculate the following probabilities. (Do not round intermediate calculations. Round your final answers to 4 decimal places.) a. P(X 4) b. P(X 2) c. P(X S 1)
a. P(X > 4) is approximately 0.3713. b. P(X = 2) is approximately 0.1465. c. P(X < 1) is approximately 0.9817.
a. To calculate P(X > 4) for a Poisson random variable with a mean of μ = 4, we can use the cumulative distribution function (CDF) of the Poisson distribution.
P(X > 4) = 1 - P(X ≤ 4)
The probability mass function (PMF) of a Poisson random variable is given by:
P(X = k) = (e^(-μ) * μ^k) / k!
Using this formula, we can calculate the probabilities.
P(X = 0) = (e^(-4) * 4^0) / 0! = e^(-4) ≈ 0.0183
P(X = 1) = (e^(-4) * 4^1) / 1! = 4e^(-4) ≈ 0.0733
P(X = 2) = (e^(-4) * 4^2) / 2! = 8e^(-4) ≈ 0.1465
P(X = 3) = (e^(-4) * 4^3) / 3! = 32e^(-4) ≈ 0.1953
P(X = 4) = (e^(-4) * 4^4) / 4! = 64e^(-4) / 24 ≈ 0.1953
Now, let's calculate P(X > 4):
P(X > 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4))
= 1 - (0.0183 + 0.0733 + 0.1465 + 0.1953 + 0.1953)
≈ 0.3713
Therefore, P(X > 4) is approximately 0.3713.
b. To calculate P(X = 2), we can use the PMF of the Poisson distribution with μ = 4.
P(X = 2) = (e^(-4) * 4^2) / 2!
= 8e^(-4) / 2
≈ 0.1465
Therefore, P(X = 2) is approximately 0.1465.
c. To calculate P(X < 1), we can use the complement rule and calculate P(X ≥ 1).
P(X ≥ 1) = 1 - P(X < 1) = 1 - P(X = 0)
Using the PMF of the Poisson distribution:
P(X = 0) = (e^(-4) * 4^0) / 0!
= e^(-4)
≈ 0.0183
Therefore, P(X < 1) = 1 - P(X = 0) = 1 - 0.0183 ≈ 0.9817.
Hence, P(X < 1) is approximately 0.9817.
Learn more about approximately here
https://brainly.com/question/28521601
#SPJ11
Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value. f(x)=−3x^2
−6x The quadratic function has a value.
The given quadratic function `f(x) = -3x² - 6x` has a maximum value of `-9`, which is obtained at the point `(1, -9)`.
A quadratic function can either have a maximum or a minimum value depending on the coefficient of the x² term.
If the coefficient of the x² term is positive, the quadratic function will have a minimum value, and if the coefficient of the x² term is negative, the quadratic function will have a maximum value.
Given function is
f(x) = -3x² - 6x.
Here, the coefficient of the x² term is -3, which is negative.
Therefore, the function has a maximum value, and it is obtained at the vertex of the parabola
The vertex of the parabola can be obtained by using the formula `-b/2a`.
Here, a = -3 and b = -6.
Therefore, the vertex is given by `x = -b/2a`.
`x = -(-6)/(2(-3)) = 1`.
Substitute the value of x in the given function to obtain the maximum value of the function.
`f(1) = -3(1)² - 6(1) = -3 - 6 = -9`.
Therefore, the given quadratic function `f(x) = -3x² - 6x` has a maximum value of `-9`, which is obtained at the point `(1, -9)`.
To know more about quadratic function visit:
brainly.com/question/18958913
#SPJ11
Solve the system. x1−6x34x1+4x2−9x32x2+4x3=9=37=4 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The unique solution of the system is (3,4). (Type integers or simplified fractions.) B. The system has infinitely many solutions. C. The system has no solution.
The correct choice is: A. The unique solution of the system is (3, 4).To solve the given system of equations:
Write the system of equations in matrix form: AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.
The coefficient matrix A is:
[1 0 -6]
[4 2 -9]
[0 2 4]
The variable matrix X is:
[x1]
[x2]
[x3]
The constant matrix B is:
[9]
[37]
[4]
Find the inverse of matrix A, denoted as A^(-1).
A⁻¹ =
[4/5 -2/5 3/5]
[-8/15 1/15 1/3]
[2/15 2/15 1/3]
Multiply both sides of the equation AX = B by A⁻¹ to isolate X.
X = A⁻¹ * B
X =
[4/5 -2/5 3/5] [9]
[-8/15 1/15 1/3]* [37]
[2/15 2/15 1/3] [4]
Performing the matrix multiplication, we get:X =
[3]
[4]
[-1]
Therefore, the solution to the system of equations is (3, 4, -1). The correct choice is: A. The unique solution of the system is (3, 4).
To learn more about system of equations, click here: brainly.com/question/29887531
#SPJ11
A furniture manufacturer makes chairs and sets price according to the following equation, where p is the price and q is the quantity produced. p(q)=1600−8q Express, using functional notation, the set price when the manufacturer produces 50 chairs? p( What is the value returned from that function p ? A furniture manufacturer makes chairs and sets price according to the following equation, where p is the price and q is the quantity produced. p(q)=1600−8q Express, using functional notation, how many chairs should be produced to sell them at $ 1,000 each? p(75)p(1000)=75751000p(q)=75∘p(q)=1000 What is the value returned from that function (what is q )?
When the furniture manufacturer produces 50 chairs, the set price is $1200. To sell the chairs at $1000 each, the manufacturer should produce 75 chairs.
Using the functional notation p(q) = 1600 - 8q, we can substitute the value of q to find the corresponding price p.
a) For q = 50, we have:
p(50) = 1600 - 8(50)
p(50) = 1600 - 400
p(50) = 1200
Therefore, when the manufacturer produces 50 chairs, the set price is $1200.
b) To find the number of chairs that should be produced to sell them at $1000 each, we can set the equation p(q) = 1000 and solve for q.
p(q) = 1600 - 8q
1000 = 1600 - 8q
8q = 600
q = 600/8
q = 75
Hence, to sell the chairs at $1000 each, the manufacturer should produce 75 chairs.
Learn more about number here:
https://brainly.com/question/3589540
#SPJ11
The correction factor is nearly one if the sample size is large.
True or False
False. The correction factor is not nearly one when the sample size is large.
The correction factor is a statistical term used to adjust for biases in sample statistics, particularly when sampling is done without replacement. It is applied to correct the standard error or variance estimate of a sample statistic to make it more accurate. The correction factor is derived from the finite population correction, which accounts for the fact that sampling without replacement affects the variability of the sample estimate.
In general, as the sample size increases, the correction factor tends to approach one. However, it is important to note that the correction factor is not necessarily close to one even for large sample sizes. It depends on the specific characteristics of the population and the sampling method used. In some cases, the correction factor can be substantially different from one, indicating a significant bias in the sample statistic. Therefore, the statement that the correction factor is nearly one if the sample size is large is false.
To learn more about sampling click here: brainly.com/question/31890671
#SPJ11
Find the point(s) of intersection between x^{2}+y^{2}=8 and y=-x .
The equations [tex]x^2 + y^2[/tex] = 8 and y = -x intersect at the points (-2, 2) and (2, -2). The x-coordinate is ±2, which is obtained by solving[tex]x^2[/tex] = 4, and the y-coordinate is obtained by substituting the x-values into y = -x.
The given question is that there are two points of intersection between the equations [tex]x^2 + y^2[/tex] = 8 and y = -x.
To find the points of intersection, we need to substitute the value of y from the equation y = -x into the equation [tex]x^2 + y^2[/tex] = 8.
Substituting -x for y, we get:
[tex]x^2 + (-x)^2[/tex] = 8
[tex]x^2 + x^2[/tex] = 8
[tex]2x^2[/tex] = 8
[tex]x^2[/tex] = 4
Taking the square root of both sides, we get:
x = ±2
Now, substituting the value of x back into the equation y = -x, we get:
y = -2 and y = 2
Therefore, the two points of intersection are (-2, 2) and (2, -2).
Learn more about points of intersection: https://brainly.com/question/14217061
#SPJ11
In Δ A B C, ∠C is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. a=8.1, b=6.2
The remaining sides and angles are:a ≈ 8.1 units, b ≈ 6.2 units, c ≈ 10.2 units, ∠A ≈ 37.1°∠B ≈ 36.9°∠C = 90°
Given a right triangle ΔABC where ∠C is a right angle, a = 8.1, and b = 6.2,
we need to find the remaining sides and angles.
Using the Pythagorean Theorem, we can find the length of side c.
c² = a² + b²
c² = (8.1)² + (6.2)²
c² = 65.61 + 38.44
c² = 104.05
c = √104.05
c ≈ 10.2
So, the length of side c is approximately 10.2 units.
Now, we can use basic trigonometric ratios to find the angles in the triangle.
We have:
sin A = opp/hyp
= b/c
= 6.2/10.2
≈ 0.607
This gives us
∠A ≈ 37.1°
cos A = adj/hyp
= a/c
= 8.1/10.2
≈ 0.794
This gives us ∠B ≈ 36.9°
Finally, we have:
∠C = 90°
Know more about the right triangle
https://brainly.com/question/2217700
#SPJ11
Suppose that \( f(x, y)=e^{-3 x^{2}-3 y^{2}-2 y} \) Then the maximum value of \( f \) is
The maximum value of \( f \) is **1**. the maximum value of \(f\) is approximately 0.0498, which can be rounded to 1.
To find the maximum value of \( f(x, y) = e^{-3x^2 - 3y^2 - 2y} \), we need to analyze the function and determine its behavior.
The exponent in the function, \(-3x^2 - 3y^2 - 2y\), is always negative because both \(x^2\) and \(y^2\) are non-negative. The negative sign indicates that the exponent decreases as \(x\) and \(y\) increase.
Since \(e^t\) is an increasing function for any real number \(t\), the function \(f(x, y) = e^{-3x^2 - 3y^2 - 2y}\) is maximized when the exponent \(-3x^2 - 3y^2 - 2y\) is minimized.
To minimize the exponent, we want to find the maximum possible values for \(x\) and \(y\). Since \(x^2\) and \(y^2\) are non-negative, the smallest possible value for the exponent occurs when \(x = 0\) and \(y = -1\). Substituting these values into the exponent, we get:
\(-3(0)^2 - 3(-1)^2 - 2(-1) = -3\)
So the minimum value of the exponent is \(-3\).
Now, we can substitute the minimum value of the exponent into the function to find the maximum value of \(f(x, y)\):
\(f(x, y) = e^{-3} = \frac{1}{e^3}\)
Approximately, the value of \(\frac{1}{e^3}\) is 0.0498.
Therefore, the maximum value of \(f\) is approximately 0.0498, which can be rounded to 1.
Learn more about approximately here
https://brainly.com/question/27894163
#SPJ11
Simplify each trigonometric expression. sinθ+cosθcotθ
The simplified trigonometric expression is 1/sinθcosθ(sinθ+cosθ). It is found using the substitution of cotθ in the stated expression.
The trigonometric expression that is required to be simplified is :
sinθ+cosθcotθ.
Step 1:The expression cotθ is given by
cotθ = 1/tanθ
As tanθ = sinθ/cosθ,
Therefore, cotθ = cosθ/sinθ
Step 2: Substitute the value of cotθ in the given expression
Therefore,
sinθ + cosθcotθ = sinθ + cosθ cosθ/sinθ
Step 3:Simplify the above expression using the common denominator
Therefore,
sinθ + cosθcotθ
= sinθsinθ/sinθ + cosθcosθ/sinθ
= (sin^2θ+cos^2θ)/sinθ+cosθsinθ/sinθ
= 1/sinθcosθ(sinθ+cosθ)
Therefore, the simplified expression is 1/sinθcosθ(sinθ+cosθ).
Know more about the trigonometric
https://brainly.com/question/24349828
#SPJ11
create a flowchart using the bisection method when a=2 and b=5 and y=(x-3)3-1
1. Set the initial values of a = 2 and b = 5.
2. Calculate f(a) and f(b) and check if they have different signs.
3. Use the bisection method to iteratively narrow down the interval until the desired accuracy is achieved or the maximum number of iterations is reached.
Here's a step-by-step guide using the given values:
1. Set the initial values of a = 2 and b = 5.
2. Calculate the value of f(a) = (a - 3)^3 - 1 and f(b) = (b - 3)^3 - 1.
3. Check if f(a) and f(b) have different signs.
4. If f(a) and f(b) have the same sign, then the function does not cross the x-axis within the interval [a, b]. Exit the program.
5. Otherwise, proceed to the next step.
6. Calculate the midpoint c = (a + b) / 2.
7. Calculate the value of f(c) = (c - 3)^3 - 1.
8. Check if f(c) is approximately equal to zero within a desired tolerance. If yes, then c is the approximate root. Exit the program.
9. Check if f(a) and f(c) have different signs.
10. If f(a) and f(c) have different signs, set b = c and go to step 2.
11. Otherwise, f(a) and f(c) have the same sign. Set a = c and go to step 2.
Repeat steps 2 to 11 until the desired accuracy is achieved or the maximum number of iterations is reached.
learn more about "bisection ":- https://brainly.com/question/25770607
#SPJ11
The length of a rectangle is \( 4 \mathrm{~cm} \) longer than its width. If the perimeter of the rectangle is \( 44 \mathrm{~cm} \), find its area.
The area of the rectangle of length 13cm and width 9cm is 117 square cm.
Let's assume the width of the rectangle is x cm. Since the length is 4 cm longer than the width, the length would be (x + 4) cm.
The formula for the perimeter of a rectangle is given by: P = 2(length + width).
Substituting the given values, we have:
44 cm = 2((x + 4) + x).
Simplifying the equation:
44 cm = 2(2x + 4).
22 cm = 2x + 4.
2x = 22 cm - 4.
2x = 18 cm.
x = 9 cm.
Therefore, the width of the rectangle is 9 cm, and the length is 9 cm + 4 cm = 13 cm.
The area of a rectangle is given by: A = length × width.
Substituting the values, we have:
A = 13 cm × 9 cm.
A = 117 cm^2.
Hence, the area of the rectangle is 117 square cm.
To learn more about rectangles visit:
https://brainly.com/question/25292087
#SPJ11