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2 years ago

What is the volume of the right rectangular prism below?

Mathematics

1 answer:

Vesnalui [34]2 years ago

7 0

Answer:

Volume of right rectangular prism = 3.75 in³

Step-by-step explanation:

Given:

First side of rectangular prism = 2 inches

Second side of rectangular prism = 1 $\frac{1}{2}$ = 1.5 inches

Third side of rectangular prism = 1 $\frac{1}{4}$ = 1.25 inches

Find:

Volume of right rectangular prism:

Computation:

$Volume\ of\ right\ rectangular\ prism=lbh\\\\Volume\ of\ right\ rectangular\ prism=(2)(1.5)(1.25)\\\\ Volume\ of\ right\ rectangular\ prism= 3.75 in^3$

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GaryK [48]

Answer:

$B_2=4\pi r^2$

see the explanation

Step-by-step explanation:

we know that

The area of the base of a cylinder is given by the formula

$B=\pi r^{2}$

where

r is the radius of the circular base

If the radius is doubled

then

$r=2r$

The new base area is

$B_2=\pi (2r)^{2}$

$B_2=4\pi r^2$

$B_2=4B$

therefore

The new area of the base is 4 times the area of the original base

7 0

3 years ago

− 1/2 (−3y+10) how do i work it out?

ehidna [41]

Answer:

3/2y -5

Step-by-step explanation:

− 1/2 (−3y+10)

Distribute

-1/2 * -3y + -1/2(10)

3/2y -5

3 0

2 years ago

Place the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of

victus00 [196]

Answer:

g(x), f(x) and h(x)

Step-by-step explanation:

Given

Interval: (0,3)

See attachment for functions f(x), g(x) and h(x)

Required

Order from fastest to slowest decreasing average rate of change

The average rate of change is calculated as:

$Rate = \frac{f(b) - f(a)}{b - a}$

In this case:

$(a,b) = (0,3)$

i.e.

$a = 0\\b=3$

For f(x)

$f(x) = 16(\frac{1}{2})^x$

$Rate = \frac{f(b) - f(a)}{b - a}$

$Rate = \frac{f(3) - f(0)}{3 - 0}$

$Rate = \frac{f(3) - f(0)}{3}$

Calculate f(3) and f(0)

$f(x) = 16(\frac{1}{2})^x$

$f(3) = 16(\frac{1}{2})^3 = 16 * \frac{1}{8} = 2$

$f(0) = 16(\frac{1}{2})^0 = 16 * 1 = 16$

So:

$Rate = \frac{f(3) - f(0)}{3}$

$Rate = \frac{2 - 16}{3}$

$Rate = -\frac{14}{3}$

For g(x)

$Rate = \frac{g(b) - g(a)}{b - a}$

$Rate = \frac{g(3) - g(0)}{3 - 0}$

$Rate = \frac{g(3) - g(0)}{3}$

From the table of g(x)

$g(3) = 1$

$g(1) = 27$

So:

$Rate = \frac{1 - 27}{3}$

$Rate = -\frac{26}{3}$

For h(x)

$Rate = \frac{h(b) - h(a)}{b - a}$

$Rate = \frac{h(3) - h(0)}{3 - 0}$

$Rate = \frac{h(3) - h(0)}{3}$

From the graph of h(x)

$h(3) = -3$

$h(0) = 4$

So:

$Rate = \frac{-3 - 4}{3}$

$Rate = -\frac{7}{3}$

So, the calculated rates of change are:

$f(x) = -\frac{14}{3}$ $= -4.67$

$g(x) = -\frac{26}{3}$ $=-8.67$

$h(x) = -\frac{7}{3}$ $=-2.33$

By comparison:

From the fastest decreasing to slowest, the order is: g(x), f(x) and h(x)

4 0

2 years ago

A rescue helicopter flew from its home base for 35 kilometers on a course of 330 degrees to pick up an accident victim. It then

artcher [175]

I've drawn a triangle to represent the journey (see attached.

The angle from Home to Victim to Hospital is:

a = $90 - (360 - 330) = 90- 30 = 60^o$

Using the cos rule, we can solve for the length x:

$a^2 = b^2 +c^2 - 2bccosA
\\x^2 = 35^2+25^2-2(35)(25)cos60
\\x^2 = 1850 - 875
\\x^2 = 975
\\x = \sqrt{975}
\\x = 31.2249...$

Using the cos rule, we can solve for angle b:

$a^2 = b^2 +c^2 - 2bccosA
\\35^2 = 31.22...^2+25^2-2(31.22...)(25)cosb
\\1225 = 975 + 625 - 1561.249...cosb
\\-375 = -1561.249...cosb
\\b = cos^{-1}( \frac{-375}{-1561.249...}) 
\\b = 76.1...$

So the bearing the helicopter has to travel is:

270 - 76.1 = 193.9 degrees (1 dp)

And the distance it travels is 31.2 km (1 dp)

5 0

3 years ago

Maria is ordering copy paper for her office. The office is low on white paper and on blue paper. She will play 3.50 per ream of

m_a_m_a [10]

So we know that the decimal place will move one right. Well basically let's assume she could have bought these expressions:

x 10 x 3.50 = 35.00
x 9 x 3.50 = 31.50 + 3.75 = 35.25
x 8 x 3.5 = 28 + 3.75 x 2 = 35.5
x 7 x 3.5 = 24.5 + 3.75 x 35.75

We know that there is a pattern. See how the cents goes .25 up each time. So we know she'd buy 6 reams of white because (6 x 3.5 = 21) + (4 x 3.75 = 15) = 36.

8 0

3 years ago

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