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3 years ago

15

The volume of a single layer in a rectangular prism is 18 cubic centimeters. There are 5 layers in this rectangular prism. What

is the volume, on cubic centimeters, of this rectangular prism?

1 answer:

sweet [91]3 years ago

8 0

Answer: $90cm^3$

Step-by-step explanation:

A rectangular prism is a three-dimensional solid.

A rectangular prism has six faces (each one of these faces are rectangles), eight vertices and twelve edges.

You know that this rectangular prism has 5 layers and the volume of one of these layers is 18 cubic centimeters ( $18cm^3$ ).

Assuming that all these layers are equal, the volume of this rectangular prism can be calculated with:

$V_{prism}=5*V_1$

Where $V_1$ is the volume of one layer.

Substituting, you get:

$V_{prism}=(5)(18cm^3)\\\\V_{prism}=90cm^3$

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Financial advisors counsel young people to start saving early for their retirement. Explain why an early start is important.

Inessa05 [86]

Answer:

The more money you invest and the earlier you start means your retirement savings will have that much more time and potential to grow and investing early you can be able to take advantage of compound earnings.

Step-by-step explanation:

5 0

3 years ago

The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep

Alchen [17]

Ooh, fun

geometric sequences can be represented as
$a_n=a(r)^{n-1}$
so the first 3 terms are
$a_1=a$
$a_2=a(r)$
$a_2=a(r)^2$

the sum is -7/10
$\frac{-7}{10}=a+ar+ar^2$
and their product is -1/125
$\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3$

from the 2nd equation we can take the cube root of both sides to get
$\frac{-1}{5}=ar$
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
$\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r$
subsituting -1/5 for ar
$\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r$
which simplifies to
$\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}$
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for $ax^2+bx+c=0$
$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$
so
for 2r²-5r+2=0
a=2
b=-5
c=2

$r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}$
$r=\frac{5 \pm \sqrt{25-16}}{4}$
$r=\frac{5 \pm \sqrt{9}}{4}$
$r=\frac{5 \pm 3}{4}$
so
$r=\frac{5+3}{4}=\frac{8}{4}=2$ or $r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}$

use them to solve for the value of a
$\frac{-1}{5}=ar$
$\frac{-1}{5r}=a$
try for r=2 and 1/2
$a=\frac{-1}{10}$ or $a=\frac{-2}{5}$

test each
for a=-1/10 and r=2
a+ar+ar²= $\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}$
it works

for a=-2/5 and r=1/2
a+ar+ar²= $\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}$
it works

both have the same terms but one is simplified

the 3 numbers are $\frac{-2}{5}$ , $\frac{-1}{5}$ , and $\frac{-1}{10}$

6 0

4 years ago

What is the slope intercept of 4X plus Y equals eight?

viva [34]

Y= -4x+8.... all u had to do is subtract 4x to the other side and get that answer

3 0

3 years ago

What is 20% of 9 no remanders or link

sergij07 [2.7K]

Answer:

1.8

Step-by-step explanation:

Your answer would be 1.8 because you would have to do 0.20x 9 and that gives you 1.8

Hope I was able to help!

4 0

3 years ago

Read 2 more answers

In 9 and 10, order the decimals from greatest to least. 9. 878.403, 887.304,887.043

Katena32 [7]

Answer:

Greatest to least: 887.304, 887.043, 878.403

Step-by-step explanation:

7 0

3 years ago