Answer:
[tex](a)[/tex]
[tex]Maximum\ Error = 27[/tex]
[tex]Relative\ Error = 0.008[/tex]
[tex]Percentage\ Error = 0.8\%[/tex]
[tex](b)[/tex]
[tex]Maximum\ Error = 36[/tex]
[tex]Relative\ Error = 0.0267[/tex]
[tex]Percentage\ Error = 2.67\%[/tex]
Step-by-step explanation:
Given
[tex]x = 15[/tex] -- edge length
[tex]\triangle x = 0.2[/tex] -- possible error
Solving (a): Errors in volume
The volume of a cube is:
[tex]V(x) = x^3[/tex]
Differentiate
[tex]\frac{dV}{dx} = 3x^2[/tex]
Make dV the subject
[tex]dV =3x^2dx[/tex]
Rewrite as:
[tex]\triangle V = 3x^2 \triangle x[/tex]
Substitute values for x and [tex]\triangle x[/tex]
[tex]\triangle V = 3 * 15^2 * 0.2^2[/tex]
[tex]\triangle V = 27[/tex]
Hence:
[tex]Maximum\ Error = 27[/tex]
The relative error is then calculated as:
[tex]Relative\ Error = \frac{Maximum\ Error}{Volume}[/tex]
[tex]Relative\ Error = \frac{27}{x^3}[/tex]
[tex]Relative\ Error = \frac{27}{15^3}[/tex]
[tex]Relative\ Error = \frac{27}{3375}[/tex]
[tex]Relative\ Error = 0.008[/tex]
The percentage error is:
[tex]Percentage\ Error = Relative\ Error * 100\%[/tex]
[tex]Percentage\ Error = 0.008 * 100\%[/tex]
[tex]Percentage\ Error = 0.8\%[/tex]
Solving (a): Errors in Surface Area
The volume of a cube is:
[tex]A(x) =6x^2[/tex]
Differentiate
[tex]\frac{dA}{dx} =12x[/tex]
Make dA the subject
[tex]dA = 12xdx[/tex]
Rewrite as:
[tex]\triangle A =12x\triangle x[/tex]
Substitute values for x and [tex]\triangle x[/tex]
[tex]\triangle A =12 *15 * 0.2[/tex]
[tex]\triangle A =36[/tex]
Hence:
[tex]Maximum\ Error = 36[/tex]
The relative error is then calculated as:
[tex]Relative\ Error = \frac{Maximum\ Error}{Surface\ Area}[/tex]
[tex]Relative\ Error = \frac{36}{6x^2}[/tex]
[tex]Relative\ Error = \frac{36}{6*15^2}[/tex]
[tex]Relative\ Error = \frac{36}{1350}[/tex]
[tex]Relative\ Error = 0.0267[/tex]
The percentage error is:
[tex]Percentage\ Error = Relative\ Error * 100\%[/tex]
[tex]Percentage\ Error = 0.0267* 100\%[/tex]
[tex]Percentage\ Error = 2.67\%[/tex]
Assume that theta is a positive acute angle.
Given: sin theta=40/41
Find: cos2theta
SHOW YOUR WORK. First correct answer gets Brainliest.
By utilizing trigonometric identities,we got cos 2θ = -1519/1681.
Given that sin θ = 40/41 and θ is a positive acute angle, we can find cos θ using the Pythagorean identity sin²θ + cos²θ = 1. Rearranging the equation, we have cos²θ = 1 - sin²θ.
Substituting the given value, we get cos²θ = 1 - (40/41)² = 1 - 1600/1681 = 81/1681.
Now, we can find cos 2θ using the double-angle identity cos 2θ = cos²θ - sin²θ.
Substituting the known values, we have
cos 2θ = (81/1681) - (40/41)² = 81/1681 - 1600/1681 = -1519/1681.
Therefore, cos 2θ = -1519/1681.
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l
Marie left her briefcase at home and had to return to get it. State which point represents when she
turned back around to go home and explain how you arrived at that conclusion.
Evaluating function rules
f(x)= -3x^2
f(x)=(1+x)^2
Answer:
4x^+2x+1=0
Step-by-step explanation:
Tell me if this is right
Answer:
what I'm bored
Step-by-step explanation:
what's u need help with anything I'
the average length of a female dophin is 234 inches
what is the answer in feet and inches
Answer:
in feet its 19
In inches it would be 4
Create an equivalent expression for 9(5x - 4) by using the distributive property.
Answer:
3(15x-12)
Step-by-step explanation:
Customers are charged a late fee of 20% of their bill. This person is a week late on a bill of $200.00. What should we charge for the late fee?"
Answer:
$40
Step-by-step explanation:
Leo baseball team scored 180 home runs they only have 50 games how many home runs did they score per game
HELP ME QUICKLY PLEASE IM GIVING BRAINLIEST!!!
Answer:
its the second one
Step-by-step explanation:
Help me plz will mark branialist
Answer:
8
Step-by-step explanation:
What are the zeros of the polynomial function f(x) = x3 - 2x2 - 24x? (1 point)
1) -6, 0, 4
2) 6, 0, -4
3) -6, 0, -4
4) 6,0, 4
f(x) = x³ - 2x² - 24x
x³ - 2x² - 24x = 0
x(x² - 2x - 24) = 0
x = 0
x² - 2x - 24 = 0
a = 1, b = -2, c = -24
Delta = (-2)² - 4 * 1 * (-24) = 4 + 96 = 100
x = (-(-2) - 10)/(2 * 1) = -8/2 = -4
x = (-(-2) + 10)/(2 * 1) = 12/2 = 6
Answer: 2)
A store is having a sale on trail mix and jelly beans. For 5 pounds of trail mix and 3 pounds of jelly beans, the total cost is $18. For 2 pounds of trail mix and 12 pounds of jelly beans, the total cost is $45. Find the cost for each pound of trail mix and each pound of jelly beans.
The cost for each pound of trail mix is $1.5 and each pound of jelly beans is $3.5 .
What is elimination method?The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.
According to the question
A store is having a sale on trail mix and jelly beans .
Let trail mix = T
and jelly beans = J
For 5 pounds of trail mix and 3 pounds of jelly beans, the total cost is $18.
i.e
5T + 3J = 18 -------------------------- (1)
For 2 pounds of trail mix and 12 pounds of jelly beans, the total cost is $45.
i.e
2T + 12J = 45 -------------------------------(2)
Now,
multiplying eq (1) from 4
20T + 12J = 72 -----------------(3)
Solving equation (3) and (2) the equation by elimination method
20T + 12J = 72 -----------------(3)
2T + 12J = 45 -------------------------(2)
subtracting equation (2) from (3)
18T = 27
T = 1.5
substituting the value of T in equation 1
5T + 3J = 18
5*1.5 + 3J = 18
7.5 + 3J = 18
3J = 18 - 7.5
3J = 10.5
J = 3.5
Hence, the cost for each pound of trail mix is $1.5 and each pound of jelly beans is $3.5 .
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7) At what interest rate would a deposit of $50,000 grow to $111,277 in 25 years with continuous compounding?
A) 3.2%
B) 6.2%
C) 1.2%
D) 4.2%
Helpppppp hurry and no links
Step-by-step explanation:
6.3%
that is the correct answer
plsss help mee xoxox
Answer:
length is 20, so width would be 16
Step-by-step explanation:
In ΔCDE, the measure of ∠E=90°, the measure of ∠C=43°, and CD = 95 feet. Find the length of EC to the nearest tenth of a foot
Answer:
69.5 FT
Step-by-step explanation:
\cos C = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{x}{95}
cosC=
hypotenuse
adjacent
=
95
x
\cos 43=\frac{x}{95}
cos43=
95
x
95\cos 43=x
95cos43=x
Cross multiply.
x=69.4786\approx \mathbf{69.5}\text{ feet}
x=69.4786≈69.5 feet
Consider the function f(x)=-3x2+12x-5. What is the location of the vertex? Write your answer as an ordered pair.
Answer:
The (x,y) point of the vertex is usually labelled as:
Vertex = (h, k)
h = -b / 2a
k = ah^2 + bh + c
f(x) = -3x^2 + 12x -5
a = -3 b=12 c=-5
h = -12 / -6 therefore h = 2
k = -3*2^2 + 12*2 -5
k = -12 + 24 -5 therefore k = 7
Vertex (2, 7)
Source: http://www.1728.org/quadr3.htm
Step-by-step explanation:
What is the volume of this composite solid
A rectangular prism has a length of 18 feet, a height of 14 feet, and a width of 2 feet.
What is its volume, in cubic feet?
feet3
Answer:
504ft3
Step-by-step explanation:
V=Bh
V=(18x2) 14
V=36x14
V= 504
Answer:
volume = height × length ×width
volume =18×14×2
volume =504ft³
Help help help help plz
Which expression represents the circumference of a circle when r is the radius and d is the diameter of the circle?
Hey so can someone do my delta math for me
like i give u the questions and u answer yeah ok thanks
Please help me on question 1 :)
A student graphed an ordered pair on a coordinate plane that was located on the y axis and was 5 units above the origin. Write the ordered pair that the student graphed with these characteristics.
Given the equation Square root of 2x plus 1 = 3, solve for x and identify if it is an extraneous solution
Can y’all tell me which one is a function and which ones is not ?
the ones with straight lines are functions the ones that are curved is not a function
Answer:
Ones that have 2 values of y for a single value of x
(vertical line, sideways v shape are not functions)
Step-by-step explanation:
In a function, each input (x) can have only one output (y)
There cannot be two ys for one x
PLS ANSWER GIVING 15 POINTS!!!
Answer:
Instead of adding the exponents of 2 to get four you should just leave the exponent as two in the final answer.
Write the equation and solve:
I. You and three friends go to the town carnival. You have a coupon for $20 off that will
save your group money! If the total bill to get into the carnival was $100, how much does one
regular price ticket cost?
Write the equation and solve:
Answer:
The regular cost of each ticket is $30
Step-by-step explanation:
Hi,
You and three friends means there was a total of 4 people. Your equation is...
4x - 20 = 100
Remember to add the -20 since there was a coupon that saved you $20.
Now solve...
4x - 20 = 100
+ 20 on both sides
4x = 120
Divide by 4 on both sides
x = 30
The regular cost of each ticket is $30
Hope this helps :)
Answer:
e it's really first question re want to make this
each ticket would be $25 a regular
Step-by-step explanation:
The circumference of a circle is 124 inches. Determine the radius. Round to the nearest tenthC = 2πr
124 = 2(3.14)r
Answer:
radius:19.73521 Diamiter:39.47042 Area:1223.583
Step-by-step explanation:
Select all the expressions that are equivalent to 4x+2.
A 8x+48 x plus 4
B 12(8x+4)1 half times open paren 8 x plus 4 close paren
C 12(2x+1)1 half times open paren 2 x plus 1 close paren
D 2(2x+1)2 times open paren 2 x plus 1 close paren
E 2x+2x+1+1
and one brainleiss