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3 years ago

The volume of a cube is 1 cubic meter. What is the length of of each side of the cube

1 answer:

4 0

1 Metre is the length of each side of the cube.

To example, here is the Volume Of Cube Equation:

V = a^3

We are given the value for V, so just take the cube root of 1, which equates to 1.

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For the function y=3x2: (a) Find the average rate of change of y with respect to x over the interval [3,6]. (b) Find the instant

nirvana33 [79]

Answer:

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

Step-by-step explanation:

a) Geometrically speaking, the average rate of change of $y$ with respect to $x$ over the interval by definition of secant line:

$r = \frac{y(b) -y(a)}{b-a}$ (1)

Where:

$a$ , $b$ - Lower and upper bounds of the interval.

$y(a)$ , $y(b)$ - Function exaluated at lower and upper bounds of the interval.

If we know that $y = 3\cdot x^{2}$ , $a = 3$ and $b = 6$ , then the average rate of change of $y$ with respect to $x$ over the interval is:

$r = \frac{3\cdot (6)^{2}-3\cdot (3)^{2}}{6-3}$

$r = 27$

The average rate of change of $y$ with respect to $x$ over the interval $[3,6]$ is 27.

b) The instantaneous rate of change can be determined by the following definition:

$y' = \lim_{h \to 0}\frac{y(x+h)-y(x)}{h}$ (2)

Where:

$h$ - Change rate.

$y(x)$ , $y(x+h)$ - Function evaluated at $x$ and $x+h$ .

If we know that $x = 3$ and $y = 3\cdot x^{2}$ , then the instantaneous rate of change of $y$ with respect to $x$ is:

$y' = \lim_{h \to 0} \frac{3\cdot (x+h)^{2}-3\cdot x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{(x+h)^{2}-x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{2\cdot h\cdot x +h^{2}}{h}$

$y' = 6\cdot \lim_{h \to 0} x +3\cdot \lim_{h \to 0} h$

$y' = 6\cdot x$

$y' = 6\cdot (3)$

$y' = 18$

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

5 0

3 years ago

Brian's gross earnings for the week of July 8, 2019, are $1227.38. His deductions comprise 23% of his total compensation.

artcher [175]

Question is Incomplete;Complete question is given below;

Brian's gross earnings for the week of July 8, 2019, are $1227.38. His deductions comprise 23% of his total compensation.

What is his net pay?

Enter the answer to the nearest hundredth, such as $1234.56.

Answer:

Brian's Net pay is $945.08.

Step-by-step explanation:

Given:

Gross earnings for the week = $1227.38

Deductions = 23%

We need to find the net pay.

Solution:

First we will find the amount deducted.

amount deducted is equal to Deductions on Gross pay.

framing in equation form we get;

amount deducted = $\frac{23}{100}\times 1227.38 = \$282.2974$

Now we can say that;

Net pay is equal to Gross earnings minus amount deducted in tax.

framing in equation form we get;

Net pay = $1227.38-282.2974 = \$945.0826$

Rounding to nearest hundred we get;

Net pay = $945.08

Hence Brian's Net pay is $945.08.

6 0

3 years ago

There is a bag filled with 2 blue, 4 red and 3 green marbles.

NISA [10]

Answer:

5 out of 9

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

the pie factory sells an apple pie with a diameter of 16 in. for $10.99. What's the approximate cost per square inch of surface

AURORKA [14]

I'm going to assume the crust covered by the dosenot matter because the total surface area cannot be found without the depth of the pie.

So the surface are is the area of the top of the pie, the top of the pie is circular and is equal to 2 $\pi$ r²

The diameter is the sum of 2 radii, hence r=8

D=12
= 2r =12
r=8

With the raduis the area can be found
A= 2 $\pi$ r²
A=2 $\pi$ 8²
A=2(64) $\pi$
A=128 $\pi$

If the pie cost 10.99, the cost per inch can be found by dividing the area by cost

cost/inch =128 $\pi$ /10.99
cost/inch =11.64 $\pi$
= 11.64(3.14)
= 36.57

The pie costs 36 cents per square inch

5 0

3 years ago

1/2 × 2 1/3 can u help

lawyer [7]

Thats easy its 7/6 hope this helps

7 0

3 years ago

Read 2 more answers