Calculate the change in GPE stored when a 15 kg post driver is lifted by 70 cm

How many 1/ 4-inch cubes does it take to fill a box with width 2 1/ 4 inches, length 2 1/ 2 inches, and height 1 3/ 4 inches?

lys-0071 [83]

Answer:

630.

Step-by-step explanation:

<u>Given the following data;</u>

Dimensions for cube = ¼ inches

$Volume \; of \; cube = \frac {1}{4} * \frac {1}{4} * \frac {1}{4}$

Volume = 1/64 cubic inches.

For rectangular box;

Length = 2½ = 5/2 inches.

Width = 2¼ = 9/4 inches.

Height = 1¾ = 7/4 inches.

$Volume \; of \; cube = \frac {5}{2} * \frac {9}{4} * \frac {7}{4}$

Volume = 315/32 inches

Therefore, to find the amount of cubes;

$Number \; of \; cubes = \frac {Volume \; of \; box}{Volume \; of \; cube}$

Substituting into the equation, we have;

$Number \; of \; cubes = \frac {\frac {315}{32}} {\frac {1}{64}}$

$Number \; of \; cubes = \frac {315}{32} * 64$

$Number \; of \; cubes = 315 * 2$

Number of cubes = 630

6 0

3 years ago

Read 2 more answers

Consider the inequality x + 7 < 9. Select all the true statements.

alex41 [277]

Answer:

Step-by-step explanation:

here you go mate

step 1

x + 7 < 9 equation

step 2

x + 7 < 9 subtract -7

x+7(-7)<9(-7)

answer

x<2

3 0

3 years ago

This figure represents a small brick that is to be covered on all sides with a striped fabric. How much fabric is needed to cove

kati45 [8]

For a question like this you need to find the surface area
The formula is :
b x w x h (base x width x height)

So you multiply 3 1/2 x 6 x 5 1/2 = 22.5

Answers 22.5

7 0

2 years ago

Read 2 more answers

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do n

aliya0001 [1]

Answer:

$f(x)=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}$

Step-by-step explanation:

The Maclaurin series of a function f(x) is the Taylor series of the function of the series around zero which is given by

$f(x)=f(0)+f^{\prime}(0)x+f^{\prime \prime}(0)\dfrac{x^2}{2!}+ ...+f^{(n)}(0)\dfrac{x^n}{n!}+...$

We first compute the n-th derivative of $f(x)=\ln(1+2x)$ , note that

$f^{\prime}(x)= 2 \cdot (1+2x)^{-1}\\f^{\prime \prime}(x)= 2^2\cdot (-1) \cdot (1+2x)^{-2}\\f^{\prime \prime}(x)= 2^3\cdot (-1)^2\cdot 2 \cdot (1+2x)^{-3}\\...\\\\f^{n}(x)= 2^n\cdot (-1)^{(n-1)}\cdot (n-1)! \cdot (1+2x)^{-n}\\$

Now, if we compute the n-th derivative at 0 we get

$f(0)=\ln(1+2\cdot 0)=\ln(1)=0\\\\f^{\prime}(0)=2 \cdot 1 =2\\\\f^{(2)}(0)=2^{2}\cdot(-1)\\\\f^{(3)}(0)=2^{3}\cdot (-1)^2\cdot 2\\\\...\\\\f^{(n)}(0)=2^n\cdot(-1)^{(n-1)}\cdot (n-1)!$

and so the Maclaurin series for f(x)=ln(1+2x) is given by

$f(x)=0+2x-2^2\dfrac{x^2}{2!}+2^3\cdot 2! \dfrac{x^3}{3!}+...+(-1)^{(n-1)}(n-1)!\cdot 2^n\dfrac{x^n}{n!}+...\\\\= 0 + 2x -2^2 \dfrac{x^2}{2!}+2^3\dfrac{x^3}{3!}+...+(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}+...\\\\=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^n\dfrac{x^n}{n}$

3 0

3 years ago

Can someone explain how to solve for x?

alina1380 [7]

Answer:

x=11

Step-by-step explanation:

Notice that the first diagram is similar with the second diagram with ratio 1:2

Ex: Side length of JK is 6 and NP being 12, 6:12→1:2

You can conclude that x:22 needs to follow the ratio of 1:2

Thus, x=11

8 0

3 years ago