Answer:
15
Step-by-step explanation:
Answer: 15
Step-by-step explanation: (9-6) + 12
(3) + 12
15
Consider the following. x = 6 sin y , 0 ≤ y ≤ π, x = 0; about y = 4
(a) Set up an integral for the volume V of the solid obtained by rotating the region bounded by the given curve about the specified axis.
(b) Use your calculator to evaluate the integral correct to four decimal places.
Answer:
12pi(8-pi), or
183.158 to third decimal place
Step-by-step explanation:
The geometry is indicated in the attached figure.
A. by integration
We will find the volume of the solid by the method of shells, i.e. we will integrate strips parallel to the axis of rotation to form many thin shells, then integrate to get the sum of all these shells.
For each shell, of thickness dy, we integrate strips of length located at y
L(x) = y(x)
and area
L(x)dy
Each strip is at a distance of (4-y) from
for which the volume of each shell equals
dV = 2*pi*(4-y)*L(x)dy = 2*pi*(4-y)*y(x) dy
The total volume of the solid can be obtained by integrating y from 0 to pi
integral( dV ) from 0 to pi
= integral (2*pi*(4-y)*y(x) dy) for y from 0 to pi
= 12*pi(-sin(y)+y*cos(y)-4*cos(y)) for y from 0 to pi
=12(8-pi)*pi
= 183.158
B. Using Pappus theorem
Pappus theorem simplifies the calculation of volume of revolution by multiplying the area of the rotating region by 2pi times the distance between the centroid and the rotation axis.
Here the area of the figure is A=2*6=12, (2 is the area under the sine curve from 0 to pi), or
A = integral (6sin(x))dx, x from 0 to pi
= 6 cos(x), x from 0 to pi
= 6(1- (-1))
= 12
Distance from centroid to axis of rotation = (4-pi/2)
Volume = 2*pi*A*(4-pi/2) = 2*pi*12*(4-pi/2)
= 12pi(8-pi)
=183.158 as before
What are
are the types of algebric
expression?
Answer:
Step-by-step explanation:
monomial, polynomial, binomial, trinomial and multinomial are the different types of algebraic expressions.
plz mark as brainliest!!!!!!!
Find the side of a cube with surface area of 150cm square
Anyone that answers my question I will mark as brilliant
Answer:
5cm for each side
Answer:
5 cmsolution,
Surface area= 150 cm^2
Side of a cube(a)=?
Now,
[tex]surface \: area \: of \: cube = 6 {a}^{2} \\ or \: 150 = 6 {a}^{2} \\ or \: {a}^{2} = \frac{150}{6} \\ or \: {a}^{2} = 25 \\ or \: a = \sqrt{25} \\ or \: a = \sqrt{ {(5)}^{2} } \\ a = 5 \: cm[/tex]
Hope this helps...
Good luck on your assignment..
What is the area of rectangle ABCD given the information below?
Answer: Area is 1840units²
Step-by-step explanation:
From the given information,
Firstly, area of a rectangle is given as
A = l × b ie, length multiply by the breadth.
One of the side of the rectangle is known , AD = 16 , now to calculate the other side, we need some calculations.Since FE = 23 and
FD = DE ,,therefore,
DE = 23/2.
From the information, DE = 1/10 of DC. We now find DC the required side for finding the area of the rectangle by simple equation. Since DE = 23/2 , the equation now looks like this to get DC
23/2 = DC/10. Now , solving this
2DC = 23 × 10
2DC = 230
DC = 230/2
= 115.
Now the area of the rectangle will be
A = 16 × 115
= 1840units²
PLEASE HELP!! 2. Helen and Stephen both simplify the exponential expression .
Helen:
Stephen:
Unfortunately, they both made an error. Identify where each person made his or her error and explain in words what he or she did wrong. Then, correctly simplify the expression.
Answer:
We start with the expression:
exp( (4/3)*ln(2) - 1)
Here we can use that:
exp(ln(x)) = x.
and e^(a + b) = e^a*e^b.
the first step here is:
e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)
So the first step of Stephen is correct, but the first step of helen is not, you can not simplify the expression in that way.
now, we have that:
a*ln(x) = ln(x^a)
then we can write:
(4/3)*ln(2) = ln(2^(4/3))
and e^(ln(2^(4/3)) = 2^(4/3)
then we have:
e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e
now we can write this as:
∛(2^4)/e
here is where stephen makes the mistake, he uses the 4 in the rooth and the 3 in the power.
so the expression actually is:
∛(16)/e
Select all the correct equations.
Which equations have no real solution but have two complex solutions? PLZ 20 POINTS
Answer:
You did not post the options, but i will try to answer this in a general way.
Because we have two solutions, i know that we are talking about quadratic equations, of the form of:
0 = a*x^2 + b*x + c.
There are two easy ways to see if the solutions of this equation are real or not.
1) look at the graph, if the graph touches the x-axis, then we have real solutions (if the graph does not touch the x-axis, we have complex solutions).
2) look at the determinant.
The determinant of a quadratic equation is:
D = b^2 - 4*a*c.
if D > 0, we have two real solutions.
if D = 0, we have one real solution (or two real solutions that are equal)
if D < 0, we have two complex solutions.
Answer:
This was for 5 points. not 20 my dude. Also the first answer is correct.
Step-by-step explanation:
45 points! Yay An investment may earn interest using a simple interest rate or a compound interest rate. This expression can be used to find the value of an investment that is earning simple interest: P(1+rt) This expression can be used to find the value of an investment that is earning compound interest: P(1+r)t Use the drop-down menus to complete the statements about simple and compound interest. For an investment earning(simple interest,compound interest) , the interest is applied each year to the principal and to any interest that already accrued. For an investment earning(simple interest, compojnd interest) , the interest is applied each year only to the principal. Please help I'm literally the dumbest person i know •,-,•
Answer:
1. Compound Interest
2. Simple Interest
Step-by-step explanation:
Simple Interest multiplies the interest rate on the principal rate by the number of days.
Compound Interest multiplies the interest rate on the principal rate and existing rate by periods.
Answer:
:)
Step-by-step explanation:
the expression7(b+3) is equivalent to which expression? A.7b+3, B.7+b+c, C.7b+10, D.7b+21
Answer:
7b+21
Step-by-step explanation:
7(b+3)
Distribute
7*b + 7*3
7b+21
[tex]\frac{8-i}{3-2i}[/tex] If the expression above is rewritten in the form a+bi, where a and b are real numbers, what is the value of a? (Note: [tex]i=\sqrt{-1}[/tex]
Answer:
a = 2 , b = 1
Step-by-step explanation:
[tex]\frac{8-i}{3-2i}*\frac{3+2i}{3+2i}[/tex]
=> [tex]\frac{(8-i)(3+2i)}{9+4}[/tex]
=> [tex]\frac{24+13i-2i^2}{13}[/tex]
=> [tex]\frac{26+13i}{13}[/tex]
Comparing it with a+bi
a = 26/13 , b = 13/13
a = 2, b = 1
Answer:
a = 2
b = 1
Step-by-step explanation:
[tex]\frac{8-i}{3-2i}[/tex]
Write the fraction in this form:
[tex]\frac{a+bi}{c+di}\:=\:\frac{\left(c-di\right)\left(a+bi\right)}{\left(c-di\right)\left(c+di\right)}=\:\frac{\left(ac+bd\right)+\left(bc-ad\right)i}{c^2+d^2}[/tex]
[tex]\frac{\left(8(3)+-1(-2)\right)+\left(-1(3)-8(-2)\right)i}{3^2+-2^2}[/tex]
Evaluate.
[tex]\frac{26+13i}{13}[/tex]
Factor the numerator.
[tex]\frac{13\left(2+i\right)}{13}[/tex]
[tex]2+1i[/tex]
How do we write this as a power? [tex]4(\sqrt{7})x^{3[/tex]
Answer:
It might be 4 * [tex]7^{1/2}[/tex] * [tex]x^{3}[/tex]
What is the area of the triangle?
9 4 12
Answer:
13.636
Step-by-step explanation:
The area can be found using Heron's formula:
A = √(s(s-a)(s-b)(s-c))
where s=(a+b+c)/2.
For the given triangle, ...
a=9, b=4, c=12, s=(9+4+12)/2 = 12.5
A = √(12.5(3.5)(8.5)(0.5)) = √185.9375 ≈ 13.636
The area of the triangle is about 13.636 square units.
Answer:
24 units\
Step-by-step explanation:
PLEASE HELP I’LL MARK BRAINLIEST If 1 equals 1 2/3 how much does 1 1/2 equal?
Answer:
0.9 (9/10)
Step-by-step explanation:
(see picture)
Write two point-slope equations for the line passing through the points (6, 5) and (3, 1). Show your work.
Answer:
y=-4/3x-3
Step-by-step explanation:
You look for the slope using the the slope formula (m=y2-y1/x2-x1)
You will end up with (m=1-5/3-6)
Simplify to end up with (-4/3) as your slope.
Then, pick a coordinate point. Your choices are (6,5) and (3,1). You will us it to plug into the equation.
I am picking (3,1) The y-value here is 1 and the x-value is 3.
Your equation to find b, or the y-intercept is going to be (1=-4/3(3)+b)
You will have to simplify.
1=-4/3(3)+b
You will multiply -4/3 and -3 and end up with 4 so it looks like...
1=4+b
You subtract 4 on both sides and then end up with....
-3=b
So, the final answer is: y=-4/3x-3
In a random sample of cars driven at low altitudes, of them exceeded a standard of grams of particulate pollution per gallon of fuel consumed. In an independent random sample of cars driven at high altitudes, of them exceeded the standard. Can you conclude that the proportion of high-altitude vehicles exceeding the standard is less than the proportion of low-altitude vehicles exceeding the standard
Complete question is;
In a random sample of 370 cars driven at low altitudes, 43 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 80 cars driven at high altitudes, 23 of them exceeded the standard. Can you conclude that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard at an level of significance? Group of answer choices
Answer:
Yes we can conclude that there is enough evidence to support the claim that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard (P-value = 0.00005).
Step-by-step explanation:
This is a hypothesis test for the difference between the proportions.
The claim is that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.
Then, the null and alternative hypothesis are:
H0 ; π1 - π2 = 0
H1 ; π1 - π2 < 0
The significance level would be established in 0.01.
The random sample 1 (low altitudes), of size n1 = 370 has a proportion of;
p1 = x1/n1
p1 = 43/370
p1 = 0.116
The random sample 2 (high altitudes), of size n2 = 80 has a proportion of;
p2 = x2/n2
p2 = 23/80
p2 = 0.288
The difference between proportions is pd = (p1-p2);
pd = p1 - p2 = 0.116 - 0.288
pd = -0.171
The pooled proportion, we need to calculate the standard error, is:
p = (x1 + x2)/(n1 + n2)
p = (43 + 23)/(370 + 80)
p = 66/450
p = 0.147
The estimated standard error of the difference between means is computed using the formula:
S_(p1-p2) = √[((p(1 - p)/n1) + ((p(1 - p)/n2)]
1 - p = 1 - 0.147 = 0.853
Thus;
S_(p1-p2) = √[((0.147 × 0.853)/370) + ((0.147 × 0.853)/80)]
S_(p1-p2) = 0.044
Now, we can use the formula for z-statistics as;
z = (pd - (π1 - π2))/S_(p1-p2)
z = (-0.171 - 0)/0.044
z = -3.89
Using z-distribution table, we have the p-value = 0.00005
Since the P-value of (0.00005) is smaller than the significance level (0.01), then the effect is significant.
We conclude that The null hypothesis is rejected.
Thus, there is enough evidence to support the claim that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.
PLEASE HELP ME OUT
Move point b to different locations in the coordinate plane. What do you notice about the relationship between BG and GF? Explain in terms of <BGF
Answer:
BG is always perpendicular to GF. The measure of angle BGF is always 90 degree
Step-by-step explanation:
Answer:
is always perpendicular to . The measure of is always 90°.
Step-by-step explanation:
Plato Awnser
A swimming pool is being drained at a constant rate of 3 inches (depth of the water) per hour. The depth of the water after 5 hours is 32 inches. Write the equation for this function in point slope form
Answer:
The equation in point slope form is [tex]y - 47\,in = \left(-3\,\frac{in}{h}\right)\cdot (t-0\,h)[/tex]
Step-by-step explanation:
Since the swimming pool is being drained at a constant rate, the equation of the process must be a first-order polynomial (linear function), where depth of water decrease as time goes by. The form of the expression is:
[tex]y = m \cdot t + b[/tex]
Where:
[tex]t[/tex] - Time, measured in hours.
[tex]b[/tex] - Initial depth of the water in swimming pool (slope), measured in inches.
[tex]m[/tex] - Draining rate, measured in inches per hour.
[tex]y[/tex] - Current depth of the water in swimming pool (x-Intercept), measured in inches.
If [tex]m = -3\,\frac{in}{h}[/tex] and [tex]y (5\,h) = 32\,in[/tex], the initial depth of the water in swimming pool is:
[tex]b = y - m\cdot t[/tex]
[tex]b = 32\,in -\left(-3\,\frac{in}{h} \right)\cdot (5\,h)[/tex]
[tex]b = 47\,in[/tex]
The equation in point slope form is:
[tex]y-y_{o} = m \cdot (t-t_{o})[/tex]
Where [tex]y_{o}[/tex] and [tex]t_{o}[/tex] are initial depth of the water in swimming pool and initial time, respectively. Then, the equation in point slope form is:
[tex]y - 47\,in = \left(-3\,\frac{in}{h}\right)\cdot (t-0\,h)[/tex]
calculate the force acting on a man of mass 600g running to a tree through a distance of 20m
120N
f= mgh
=o. 6x10x20
= 120N
Step-by-step explanation:
given,
mass ( m)=0.6kg
gravity=9.8 m/s^2
by the formula of force,
f= ma
=0.6×9.8
therefore force is 5.88 n.
What value of x is in the solution set of 4x – 12 5 16 + 8x?
-10
-9
-8
-7
Answer:
[tex] 4x-12= 16 +8x[/tex]
And we can subtract 4x in both sides and we got:
[tex] -12 = 16 +4x[/tex]
Now we can subtract in both sides 16 and we got:
[tex] -28 = 4x[/tex]
And if we divide both sides by 4 we got:
[tex] x = -7[/tex]
And the best solution would be:
-7
Step-by-step explanation:
For this case we assume the following equation:
[tex] 4x-12= 16 +8x[/tex]
And we can subtract 4x in both sides and we got:
[tex] -12 = 16 +4x[/tex]
Now we can subtract in both sides 16 and we got:
[tex] -28 = 4x[/tex]
And if we divide both sides by 4 we got:
[tex] x = -7[/tex]
And the best solution would be:
-7
help me pls help me pls
Answer:
It should be D if not Than A
Answer:
it should be D
Step-by-step explanation:
Which of the following is parallel to
2Y = 6X + 4?
A. Y = -3X + 3
B. Y = 3X + 4
C. Y = x + 3
D. Y = -2X - 3
E. Y= 1/2 X + 3
Answer:
B. y = 3x + 4
Step-by-step explanation:
Step 1: Find slope-intercept form of 1st equation
2y = 6x + 4
2y/2 = 6x/2 + 4/2
y = 3x + 2
A parallel line has the same slope but different y-intercept:
y = -3x + 3 (No, different slope)
y = 3x + 4 (Yes, same slope, different y-int)
y = x + 3 (No, different slope)
y = -2x - 3 (No, different slope)
y = 1/2x + 3 (No, different slope)
What is the inverse of 520/2 = 260?
260/520 = .5
260 * 2 = 520
2/520 = .004
260 * 520 = 135,200
Answer:
The answer is 260 * 2 = 520
Step-by-step explanation:
520/2 = 260
Multiply both sides by 2
We have
260 × 2 = 560
Hope this helps
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
The non-even numbers are 1, 3, and 5 on the dice.
3 numbers out of 6.
3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
Total sides of 6-sided die = 6
Numbers not even = 3
Probability of not getting an even = 3/6
=> 1/2
The four-member math team at Pecanridge Middle School is chosen from the math club, which has three girls and five boys. How many different teams made up of two girls and two boys could be chosen?
Answer:
30 ways
Step-by-step explanation:
Given the following :
Number of boys in school (n1) = 5
Number of girls in school (n2) = 3
Total number of team members to be selected = 4
Number of boys required in team(r1) = 2
Number of girls required in team(r2) = 2
How many different teams made up of two girls and two boys could be chosen?
= (2 boys from 5) * (2 girls from 3)
Using combination :
5C2 * 3C2
Recall :
nCr = n! ÷ (n-r)! r!
5C2 = 5! ÷ (5-2)! 2!
5C2 = 5! ÷ 3!2!
5C2 = (5*4) / 2 * 1 = 10ways
3C2 = 3! ÷ (3-2)! 2!
3C2 = 3! ÷ 1!2!
3C2 = (3) / 1 = 3ways
3C2 = 3/1 = 3ways
10 * 3 = 30 ways
EXPONENTIAL FUNCTIONS HELP Write the function for each graph described below. the graph of f(x) = 2x reflected across the x-axis. The graph of f(x)= 1/3x translated up 5 units. The graph of f(x) = 3x left 2 units, and down 3. The graph of f(x) = 1/2x translated down 2 units. The graph of f(x) = 4x stretched horizontally by a factor of 3. The graph of f(x) = 2x up 4 units, right 3.
Answer:
-2^x(1/3)^x +53^(x +2) -3(1/2)^x -24^(x/3)2^(x -3) +4Step-by-step explanation:
In general, the transformation ...
g(x) = f(x -h) +k
translates f(x) right h units and up k units.
The transformation ...
g(x) = f(x/a)
stretches the graph horizontally by a factor of "a".
The transformation ...
g(x) = -f(x)
causes the graph to be reflected over the x-axis.
___
Applying the above, we have ...
f(x) = 2^x reflected over x is g(x) = -2^x
f(x) = (1/3)^x translated up 5 is g(x) = (1/3)^x +5
f(x) = 3^x translated by (-2, -3) is g(x) = 3^(x +2) -3
f(x) = (1/2)^x translated down 2 is g(x) = (1/2)^x -2
f(x) = 4^x stretched horizontally by a factor of 3 is g(x) = 4^(x/3)
f(x) = 2^x translated by (3, 4) is g(x) = 2^(x -3) +4
Answer:
-2^x
(1/3)^x +5
3^(x +2) -3
(1/2)^x -2
4^(x/3)
2^(x -3) +4
Step-by-step explanation:
In general, the transformation ...
g(x) = f(x -h) +k
translates f(x) right h units and up k units.
The transformation ...
g(x) = f(x/a)
stretches the graph horizontally by a factor of "a".
The transformation ...
g(x) = -f(x)
causes the graph to be reflected over the x-axis.
___
Applying the above, we have ...
f(x) = 2^x reflected over x is g(x) = -2^x
f(x) = (1/3)^x translated up 5 is g(x) = (1/3)^x +5
f(x) = 3^x translated by (-2, -3) is g(x) = 3^(x +2) -3
f(x) = (1/2)^x translated down 2 is g(x) = (1/2)^x -2
f(x) = 4^x stretched horizontally by a factor of 3 is g(x) = 4^(x/3)
f(x) = 2^x translated by (3, 4) is g(x) = 2^(x -3) +4
Frequency table help
Answer: 1) 21-25
2) III
3) II
4) 8
5) 4
Step-by-step explanation:
Question 1: Which numbers are missing?
The previous interval ends at 20 the following interval starts at 26.
The missing interval is 21 - 25
Question 2: How many tally marks to draw?
The frequency is given as 3, so draw three tally marks: III
Question 3: How many tally marks to draw?
The frequency is given as 2, so draw two tally marks: II
Question 4: What is the frequency?
There are eight tally marks so the frequency is 8.
Question 5: What is the frequency?
There are four tally marks so the frequency is 4.
Pls cam someone help me
Extremely confused with both if poss xxxx
Answer:
1. Red red blue blue
2. Red blue red blue
Step-by-step explanation:
A 50 percent chance
Brainliest to whoever gets this correct! Does this graph show a function? Explain how you know.A.No; there are y-values that have more than one x-value.B.No; the graph fails the vertical line test.C.Yes; the graph passes the vertical line test.D.Yes; there are no y-values that have more than one x-value.
Answer:
B. No; the graph fails the vertical line test.
Step-by-step explanation:
If you hold a pencil up to the graph, the parabola would technically touch the pencil at more than one point. That means it failed the test, and therefore it is not a function.
hope this helped :)
5. Calculate, in terms of it, the total surface
area of a solid cylinder of radius 3cm and
height 4cm
Answer:
131.88 cm²
Step-by-step explanation:
At = 2×Acircle + Arectangle
= 2×π·r² + w×h
w = 2π·r = 2·3.14·3 = 18.84 cm
At = 2·3.14·9cm² + 18.84cm·4cm
= 56.52cm² + 75.36cm²
= 131.88 cm²
Find the measure of ∠2.
Answer:
∠[tex]2=131[/tex]°
Step-by-step explanation:
We know that ∠[tex]4[/tex] is ≅ ∠[tex]1[/tex].
This means that ∠ [tex]1=49[/tex]°
Therefore, [tex]49+49=98[/tex]°
We know that a trapezoid is [tex]360[/tex]°.
To find ∠[tex]2[/tex] ,which is congruent to ∠[tex]3\\[/tex], we will have to subtract [tex]360[/tex]° from [tex]98[/tex]°.
[tex]360-98=262[/tex]°.
Because ∠[tex]2[/tex]≅∠[tex]3[/tex], we will have to divide [tex]262[/tex] by [tex]2[/tex] to see their measurement.
So,
[tex]\frac{262}{2}=131[/tex].
Hence, ∠[tex]2=131[/tex]°.
I really hope this helps:D
-Jazz
a manufacturer of bicycle parts requires that a bicycle chain have a width of 0.3 inch with an absolute deviation of at most 0.0003 inch. write and solve an absolute value inequality that represents the acceptable widths.
Answer:
[tex] |w-0.3| \leq 0.0003[/tex]
And solving we got:
[tex] -0.0003 \leq w-0.3 \leq 0.0003[/tex]
[tex]0.3-0.0003 \leq w \leq 0.3+0.0003[/tex]
[tex] 0.2997 \leq w \leq 0.3003[/tex]
Step-by-step explanation:
For this case we can define the following notation:
[tex] W[/tex] represent the width
And we want a maximum error of 0.0003 so we can set up the following equation:
[tex] |w-0.3| \leq 0.0003[/tex]
And solving we got:
[tex] -0.0003 \leq w-0.3 \leq 0.0003[/tex]
[tex]0.3-0.0003 \leq w \leq 0.3+0.0003[/tex]
[tex] 0.2997 \leq w \leq 0.3003[/tex]