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3 years ago

Given a cube with a volume of 27 cm3, what is the volume of a square pyramid that can fit perfectly inside the cube?

Mathematics

1 answer:

VARVARA [1.3K]3 years ago

3 0

27/3 = 9 cm3
the pyramid is 1/3 the volume of the cube because it fits exactly inside it

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Find the values of x and y. Pls helpI’m helpless at math

Svetradugi [14.3K]

Answer:

x = 1

$y=\frac{\sqrt{3}}{2}$

Step-by-step explanation:

From the given right-angle triangle

The angle = ∠60°

The adjacent to the angle ∠60° is 1/2.

The opposite to the angle ∠60° is y.

The hypotenuse = x

Determining the value of x:

Using the trigonometric ratio

cos 60° = adjacent / hypotenuse

substituting adjacent = 1/2 and hypotenuse = x

$cos\:60^{\circ }=\:\:\frac{\frac{1}{2}}{x}$

$\cos \left(60^{\circ \:}\right)=\frac{1}{2x}$

$\frac{1}{2}=\frac{1}{2x}$ ∵ cos (60°) = 1/2

$2x=2$

Dividing both sides by 2

$\frac{2x}{2}=\frac{2}{2}$

Simplify

$x=1$

Thus, the value of hypotenuse x is:

x = 1

Determining the value of y:

Using the trigonometric ratio

sin 60° = opposite / hypotenuse

As we have already determined the value of hypotenuse x = 1

substituting opposite = y and hypotenuse = 1

sin 60° = y/1

y = 1 × sin 60°

$y=\frac{\sqrt{3}}{2}$ ∵ $\sin \left(60^{\circ \:}\right)=\frac{\sqrt{3}}{2}$

Therefore, the value of y is:

$y=\frac{\sqrt{3}}{2}$

Summary:

x = 1

$y=\frac{\sqrt{3}}{2}$

5 0

3 years ago

(3x5)-1 expression word

pshichka [43]

Answer:

Subtract the result of three times five with 1.

Step-by-step explanation:

$(3 \times 5)-1$

$15-1$

$14$

Subtract the result of three times five with 1.

4 0

3 years ago

Select the equivalent expression. A, B or C?

Alina [70]

Answer:

Step-by-step explanation:

The relevant rules of exponents are ...

(a^b)^c = a^(bc)

a^-b = 1/a^b

$\left(\dfrac{2^{-10}}{4^2}\right)^7=\dfrac{2^{(-10)(7)}}{4^{(2)(7)}}=\dfrac{2^{-70}}{4^{14}}\\\\=\boxed{\dfrac{1}{2^{70}\cdot 4^{14}}}$

6 0

4 years ago

Today, everything at store is on sale. The store offers a 20% discount. Which of these expressions could be used to

MArishka [77]

Answer:

2. 0.2x

Step-by-step explanation:

6 0

3 years ago

The hypotenuse of a right triangle is 7 feet long. One leg is 4 feet longer than the other. Find the lengths of the legs, Round

Andrews [41]

Answer:

Shorter leg = 2.5 ft.

Longer leg = 6.5 ft.

Step-by-step explanation:

a^2 + b^2 = c^2

Because the hypotenuse = 7 ft, a^2 + b^2 = 49

To represent the two legs, we can use x and x+4.

x^2 + (x+4)^2 = 49

Simplifying this equation using FOIL gives us 2x^2 + 8x - 33 = 0.

Then, using the quadratic formula, we find that x = 2.5.

Thus, the shorter leg is 2.5 ft. and, when 4 is added, the longer leg is 6.5 ft.

5 0

3 years ago