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vichka [17]
4 years ago
15

Eloise’s rabbit cage is shape like a rectangular prism. The cage has a height of 28 inches and a volume of 8,680 cubic inches. E

loise bought a plastic mat for the bottom of the cage. The plastic mat fits the bottom of the cage perfectly. What is the area of the plastic mat on the bottom of the cage?
Mathematics
1 answer:
Neporo4naja [7]4 years ago
7 0

Answer:

310 inches²

Step-by-step explanation:

Given: A rectangular prism cage has a height of 28 inches.

           Volume of prism is 8680 cubic inches.

           

We know the area of base of rectangular prism is equal to the area of rectangle.

∴ Lets find out the lenght and width of rectangular prism.

Volume of rectangular prism= w\times l\times h

Where, w is width

             l is length

             h is height.

Now, putting the value in the formula of volume.

⇒ 8,680= w\times l\times 28

cross multiplying

⇒ wl= \frac{8680}{28}

∴ wl= 310 inches²

As we need to find the area of the plastic mat on the bottom of the cage, which is rectangle in shape.

Area of rectangle= wl

∴ Area of rectangle= 310 inches²

Hence,  310 inches² is the area of the plastic mat on the bottom of the cage.

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PLEASE HELP ME I'M GIVING 20PTS AND MARKING BRAINLIEST!!!!
pishuonlain [190]

Using a trigonometric identity, it is found that the values of the cosine and the tangent of the angle are given by:

  • \cos{\theta} = \pm \frac{2\sqrt{2}}{3}
  • \tan{\theta} = \pm \frac{\sqrt{2}}{4}

<h3>What is the trigonometric identity using in this problem?</h3>

The identity that relates the sine squared and the cosine squared of the angle, as follows:

\sin^{2}{\theta} + \cos^{2}{\theta} = 1

In this problem, we have that the sine is given by:

\sin{\theta} = \frac{1}{3}

Hence, applying the identity, the cosine is given as follows:

\cos^2{\theta} = 1 - \sin^2{\theta}

\cos^2{\theta} = 1 - \left(\frac{1}{3}\right)^2

\cos^2{\theta} = 1 - \frac{1}{9}

\cos^2{\theta} = \frac{8}{9}

\cos{\theta} = \pm \sqrt{\frac{8}{9}}

\cos{\theta} = \pm \frac{2\sqrt{2}}{3}

The tangent is given by the sine divided by the cosine, hence:

\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}

\tan{\theta} = \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}

\tan{\theta} = \pm \frac{1}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}

\tan{\theta} = \pm \frac{\sqrt{2}}{4}

More can be learned about trigonometric identities at brainly.com/question/24496175

#SPJ1

5 0
2 years ago
A coin is tossed 5 times. Find the probability that none are heads. Find the probability that at most 2 are heads.
kiruha [24]
1- the answer is 1/32


each time we flip a coin the whole probabilities are 2
if we flip it 5 times
2*2*2*2*2=32

6 0
3 years ago
Which of the following lines is perpendicular to the x-axis and contains the point (-11.4, 12.8)
sergejj [24]

The line x = -11.4 is perpendicular to the x-axis and contains point

(-11.4 , 12.8)

Step-by-step explanation:

Let us revise the equations of the vertical lines and horizontal lines

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  • The x-coordinates of all points lie on the line are equal
  • The equation of the vertical line basses through point (a , b) is x = a
  • The horizontal line is a line parallel to x-axis
  • The y-coordinates of all points lie on the line are equal
  • The equation of the horizontal line passes through point (a , b) is y = b
  • The vertical line and the horizontal line are perpendicular to each other when intersect each other

∵ The line is perpendicular to the x-axis

∴ The line is a vertical line

∴ The equation of the line is x = a, where a is the x-coordinate

   of any point lies on the line

∵ The line contains point (-11.4 , 12.8)

∵ The x-coordinate of the point is -11.4

∴ a = -11.4

∴ The equation of the line is x = -11.4

The line x = -11.4 is perpendicular to the x-axis and contains point

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Learn more:

You can learn more about the linear equation in brainly.com/question/13168205

#LearnwithBrainly

7 0
3 years ago
Select the correct comparison
seropon [69]

Answer:

pretty sure its d

Step-by-step explanation:

Because a has spread out dots and b has them all towered and neat so d

5 0
3 years ago
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n200080 [17]
K can be 10,11,14,25

Work
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(2x+6)(X+2)
(2x+2)(X+6)
(2x+1)(X+12)
(2x+12)(X+1)
6 0
4 years ago
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