MATHEMATICS MIDDLE SCHOOL

[CALCULUS] [HELP PLEASE]7. The edge of a cube was found to have a length of 50 cm with a possible error in measurement of 0.1 cm. Based on the measurement, you determine that the volume is 125,000 cm^3. Use tangent line approximation to estimate the percentage error in volume.

0.6%
0.9%
1.2%
1.5%
1.8%

A point on a damped spring has motion given by s(t)=2e^(-1.5t) s in(2(pi)t), where s is measured in centimeters and t is measured in seconds. Choose which of these is the graph for the velocity function for 0 < or equal to t < or equal to 4

Answers

Answer 1

Answer:

Answer:

(7)

error percentage is 0.6%

(8)

Graph-C

Step-by-step explanation:

(7)

we are given cube

Let's assume edge of cube =x

so, volume of cube will be

$V(x)=x^3$

we are given

V=125000

so, we can find 'x'

$125000=x^3$

$x=50$

So,

$a=50$

now, we can use linear approximation formula

$L(x)=V(a)+(x-a)V'(a)$

$L(x)=V(a)+(\Delta x)V'(a)$

we have

$\Delta x=0.1$

we can plug a=50

$L(x)=V(50)+(0.1)V'(50)$

$V(x)=x^3$

we can find derivative

$V'(x)=3x^2$

now, we can plug x=50

$V'(50)=3(50)^2$

$V'(50)=7500$

now, we can plug these values

and we get

$L(x)=V(50)+(0.1)* 7500$

$L(x)=V(50)+750$

$L(x)-V(50)=750$

so, error is

$error=750$

now, we can find percentage error

Percentage is

$=(750)/(125000)* 100$

=0.6%

so, error percentage is 0.6%

(8)

we are given

$s(t)=2e^(-1.5t)sin(2\pi t)$

We will find derivative

To get velocity , we will find derivative

$s'(t)=(d)/(dt)\left(2e^(-1.5t)\sin \left(2\pi t\right)\right)$

we can use product rule

and we get

$s'(t)=-3e^(-1.5t)sin(2\pi t)+4\pi e^(-1.5t) sin(2\pi t)$

so, we get velocity equation as

$v(t)=-3e^(-1.5t)sin(2\pi t)+4\pi e^(-1.5t) sin(2\pi t)$

now, we can draw graph

we can see that firstly , we get maxima and then minima

so, our graph would be

graph-C........Answer

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Answers

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SOLVE THE EQUATION
−9(x + 6) + 60 = 13 − 10x

Answers

Answer:

x=7

Step-by-step explanation:

−9(x + 6) + 60 = 13 − 10x

Distribute

−9x -54 + 60 = 13 − 10x

Combine like terms

-9x +6 = 13 -10x

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A trapezoid has an area of 13.5 square inches. If the bases are 3 and 6 inches what is the height?

Answers

well the formula is : b1+b2/2 (h)

so the height would be solved as :
13.5 = 3+6/2 (h)
13.5 = 9/2 (h)
h = (13.5)/(9/2)
h = (13.5) x (2/9) *reciprocal*
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Answers

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Hope that helped! =)

The statement is true on apex, just took the test so I know.

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Answers

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Answers

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