MATHEMATICS COLLEGE

The edge of a cube was found to be 30 cm with a possible error in measurement of 0.5 cm. Use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (Round your answers to four decimal places.) My Notes Ask Your Teacher (a) the volume of the cube maximum possible error relative error percentage error cm
(b) the surface area of the cube maximum possible error relative error percentage error cm Need Help? ReadTalk to Tuter

Answers

Answer 1

Answer:

Answer with Step-by-step explanation:

We are given that

Side of cube, x=30 cm

Error in measurement of edge, $\delta x=0.5$ cm

(a)

Volume of cube, $V=x^3$

Using differential

$dV=3x^2dx$

Substitute the values

$dV=3(30)^2(0.5)$

$dV=1350 cm^3$

Hence, the maximum possible error in computing the volume of the cube

= $1350 cm^3$

Volume of cube, $V=(30)^3=27000 cm^3$

Relative error= $(dV)/(V)=(1350)/(2700)$

Relative error=0.05

Percentage error= $0.05* 100=5$ %

Hence, relative error in computing the volume of the cube=0.05 and

percentage error in computing the volume of the cube=5%

(b)

Surface area of cube, $A=6x^2$

$dA=12xdx$

$dA=12(30)(0.5)$

$dA=180cm^2$

The maximum possible error in computing the volume of the cube= $180cm^2$

$A=6(30)^2=5400cm^2$

Relative error= $(dA)/(A)=(180)/(5400)$

Relative error in computing the volume of the cube=0.033

The percentage error in computing the volume of the cube= $0.033* 100=3.3$ %

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Answers

Answer:

Step-by-step explanation:

I need the right answers pls and tysmmm

Answers

Answer:

It's 21, you are correct!!

Step-by-step explanation:

1. Write the equation for each of the following:- Slope Intercept:
- Point-Slope:
- Standard Form:

Answers

Answer:

Slope Intercept:y=mx+b

Point-slope:

y-y1=m(x-x1)

Standard form:Ax+By=C

The value of a particular rookie baseball card was $2.00 when it was first printed. Five years later, when the player was at his peak, the card was valued at $25.00. Ten years after printing, the card was valued at $8.00. Model the above scenario, showing the value of the card, y, with respect to years since it was printed, x. Write the equation in standard form, y = ax2 + bx + c, where a, b, and c are real numbers rounded to the nearest tenth.

Answers

Let t be the time passed in years and y be the value of baseball card.

You know that

when x=0, then y=2;
when x=5, then y=25;
when x=10, y=8.

The equation in standard form is $y=ax^2+bx+c.$ Substitute given data into the equation:

$a\cdot 0^2+b\cdot 0+c=2,\n\na\cdot 5^2+b\cdot 5+c=25,\n\na\cdot 10^2+b\cdot 10+c=8.$

Solve the system of equations:

$\left\{\begin{array}{l}c=2\n25a+5b+c=25\n100a+10b+c=8\end{array}\right.\Rightarrow \left\{\begin{array}{l}c=2\n25a+5b=23\n100a+10b=6\end{array}\right.\Rightarrow$