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GREYUIT [131]
3 years ago
13

For her presentation on the Wonders of the World, Mary baked a square pyramid-shaped cake as pictured below. The slant height of

the cake is 10 inches. Each edge of the square-shaped base is 8 inches. Find the volume of Mary's cake. Round your answer to the nearest cubic inch.

Mathematics
1 answer:
mihalych1998 [28]3 years ago
4 0

Answer:

V=196in^3

Step-by-step explanation:

The volume of a pyramid is:

V=\frac{A_{b}h}{3}

where A_{b} is the area of the base and h is the height (the perpendicular measurement between base and highest point, not the slant height)

Since the base is a square, the area is given by:

A_{b}=l^2

where l is the length of the side: l=8in, thus:

A_{b}=(8in)^2\\A_{b}=64in^2

Now we need to find the height, for this we use the right triangle that forms with half of a square side (8in/2 = 4in), the slant height (10in), and the height.

In this right triangle, the slant height is the hypotenuse, the leg 1 is the unknown height, and leg 2 is half of the square side.

Using pythagoras:

hypotenuse^2=leg1^2+leg2^2

substituting our values, and indicating that leg 1 is height h:

(10in)^2=h^2+(4in)^2

100in^2=h^2+16in^2

and solving for the height:

h^2=100in^2-16in^2\\h^2=84in^2\\h=\sqrt{84in^2}\\ h=9.165in

and finally we calculate the volume using this height and the area of the base:

V=\frac{A_{b}h}{3}

V=\frac{(64in^2)(9.165in)}{3} \\V=195.5in^3

rounding to the nearest cubic inch: V=196in^3

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An official playing field (including end zones) for the Indoor Football League has a length 29 yd longer than its width. The per
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An official playing field (including end zones) for the Indoor Football League has a length 29 yd longer than its width. The perimeter of the rectangular field is 158 yd. Find the length and width of the field

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What is the solution (pls help ASAP )
Zarrin [17]

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Step-by-step explanation:

4 0
2 years ago
Imani spent half of her weekly allowance playing mini-golf. To earn more money, her parents let her wash the car for $4. What is
joja [24]

Answer:

$16

Step-by-step explanation:

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6 0
2 years ago
Find , , and if and terminates in quadrant .
ioda

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

STEP - BY - STEP EXPLANATION

What to find?

• sin2x

,

• cos2x

,

• tan2x

Given:

tanx = 2/3 = opposite / adjacent

We need to first make a sketch of the given problem.

Let h be the hypotenuse.

We need to find sinx and cos x, but to find sinx and cosx, first determine the value of h.

Using the Pythagoras theorem;

hypotenuse² = opposite² + adjacent²

h² = 2² + 3²

h² = 4 + 9

h² =13

Take the square root of both-side of the equation.

h =√13

This implies that hypotenuse = √13

We can now proceed to find the values of ainx and cosx.

Using the trigonometric ratio;

\sin x=\frac{opposite}{\text{hypotenuse}}=\frac{2}{\sqrt[]{13}}\cos x=\frac{adjacent}{\text{hypotenuse}}=\frac{3}{\sqrt[]{13}}

And we know that tanx =2/3

From the trigonometric identity;

sin 2x = 2sinxcosx

Substitute the value of sinx , cosx and then simplify.

\sin 2x=2(\frac{2}{\sqrt[]{13}})(\frac{3}{\sqrt[]{13}})=\frac{12}{13}

Hence, sin2x = 12/13

cos2x = cos²x - sin²x

Substitute the value of cosx, sinx and simplify.

\begin{gathered} \cos 2x=(\frac{3}{\sqrt[]{13}})^2-(\frac{2}{\sqrt[]{13}})^2 \\  \\ =\frac{9}{13}-\frac{4}{13} \\ =\frac{5}{13} \end{gathered}

Hence, cos2x = 5/13

tan2x = 2tanx / 1- tan²x

\tan 2x=\frac{2\tan x}{1-\tan ^2x}=\frac{2(\frac{2}{3})}{1-(\frac{2}{3})^2}=\frac{\frac{4}{3}}{1-\frac{4}{9}}=\frac{\frac{4}{3}}{\frac{9-4}{9}}=\frac{\frac{4}{3}}{\frac{5}{9}}=\frac{4}{3}\times\frac{9}{5}=\frac{4}{1}\times\frac{3}{5}=\frac{12}{5}

OR

\tan 2x=\frac{\sin 2x}{\cos 2x}=\frac{\frac{12}{13}}{\frac{5}{13}}=\frac{12}{5}

Hence, tan2x = 12/5

Therefore,

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

3 0
1 year ago
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