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3 years ago

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Each cube in this rectangular prism is 1 cm3. What is the volume of the rectangular prism? A. 9 cm3 B. 20 cm3 C. 40 cm3 D. 48 cm

3

2 answers:

snow_tiger [21]3 years ago

7 0

Did this test its c. 40

Dafna1 [17]3 years ago

6 0

It's C HOPE IT HELPS

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Erin spent $15.30 on ingredients for cookies she’s making for the school bake sale. How many cookies must she sell at $0.35 a pi

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How many square yards of cement are needed to create the walkway around the rectangular pool?

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The base of a solid is the region enclosed by the graphs of y=e^x, y=0, x=0, and x = 1. If each cross-section perpendicular to t

yanalaym [24]

Answer:

A

Step-by-step explanation:

The base of a solid in the region enclosed by the graphs of <em>y</em> = eˣ, <em>y</em> = 0, <em>x </em>= 0, and <em>x</em> = 1. Each cross-section perpendicular to the <em>x</em>-axis is an equilateral triangle. We want to find the volume of the solid.

Please refer to the graph below. We are concerned with the red region.

In order to find the volume, we essentially sum up the area of the figure at each <em>x</em> value. So, we integrate from <em>x </em> = 0 to <em>x </em>= 1.

The area for an equilateral triangle is given by:

$\displaystyle A=\frac{\sqrt{3}}{4}s^2$

Where <em>s</em> is the side length of the triangle.

Since the triangle lies perpendicular on the region, the side length of the triangle at <em>x</em> is simply <em>y</em>, which is eˣ.

Therefore, our volume is:

$\displaystyle V=\int_0^1\frac{\sqrt3}{4}(y)^2\, dx$

Substitute:

$\displaystyle V=\int_0^1\frac{\sqrt3}{4}(e^x)^2\, dx$

Evaluate the integral. Simplify:

$\displaystyle V=\frac{\sqrt3}{4}\int_0^1e^{2x}\, dx$

Integrate using u-substitution:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^{2x}\Big|_0^1\right)$

Evaluate:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^{2(1)}-e^{2(0)} \right)$

Therefore, the volume of the solid is:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^2-1\right)$

Our answer is A.

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3 years ago

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Find the measure of the exterior angle. *

MatroZZZ [7]

Step-by-step explanation:

✧ $\underline{ \underline{ \large{ \tt{S \: O \: L \: U \: T \: I \: O \: N}}} }:$

Set up an equation and solve for x :

⋆ $\large{ \bf{(4x + 9) \degree = 2x \degree + (3x - 12) \degree}}$ [ Exterior angle is always equal to the sum of two non - adjacent interior angles ]

~Remove the unnecessary brackets

⟶ $\large{ \bf{4x \degree + 9 \degree = 2x \degree + 3x \degree - 12 \degree}}$

~Add the like terms : 2x ° & 3x°

⟶ $\large{ \bf{4x \degree + 9 \degree = 5x \degree - 12 \degree}}$

~Move 4x to right hand side and change it's sign

~Similarly move 12 to left hand side and change it's sign

⟶ $\large{ \bf{9 \degree + 12 \degree = 5x \degree - 4x \degree}}$

⟶ $\large{ \bf{21 \degree = x \degree}}$

⟶ ${ \large{ \bf{x = 21 \degree}}}$

Now , Substituting the value of x in (4x+9)° [ Exterior angle ]

⤿ $\large{ \bf{4 \times 21 \degree + 9 \degree}} = \boxed{93 \degree}$

☥ $\boxed{ \boxed{ \large{ \tt{Our \: Final \: Answer : \boxed{ \underline { \tt{93\degree}}}}}}}$

Hope I helped ! ツ

Have a wonderful day / night ! ♡

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3 years ago

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