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1 year ago

X is directly proportional to w²

Mathematics

1 answer:

umka21 [38]1 year ago

3 0

The formula for x in terms of w is x = 3w² and the formula for y in terms of x is y = (1/112)x³

<h3>Variation</h3>

x = k × w²

w = 4, x = 48

48 = k × 4²

48 = k × 16

48 = 16k

k = 48/16

k = 3

So,

x = k × w²

x = 3 × w²

x = 3w²

y = k/x³

x = 2, y = 14

14 = k / 2³

14 × 2³ = k

14 × 8 = k

112 = k

So,

y = k/x³

y = 112/x³

y = (1/112)x³

Learn more about variation:

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1 year ago

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC =16 and DC=5 what is the length of BC in the simplest ra

Nana76 [90]

The length of BC is $4 \sqrt{5}$ .

Solution:

Given ABC is a right triangle.

AC is the hypotenuse and BD is the altitude.

AB and BC are legs of the triangle ABC.

AC = 16 and DC = 5

<u>Leg rule of geometric mean theorem:</u>

$\frac{\text { hypotenuse }}{\text { leg }}=\frac{\text { leg }}{\text { part }}$

$\Rightarrow \frac{AC}{BC}=\frac{BC}{DC}$

$\Rightarrow \frac{16}{x}=\frac{x}{5}$

Do cross multiplication.

$\Rightarrow 16\times 5 = x\times x$

$\Rightarrow 80= x^2$

$\Rightarrow 16\times 5= x^2$

Taking square root on both sides.

$\Rightarrow \sqrt{16\times 5} = \sqrt{x^2}$

$\Rightarrow \sqrt{4^2\times 5} = \sqrt{x^2}$

square and square roots get canceled, we get

$\Rightarrow 4\sqrt{ 5} = x$

The length of BC is $4 \sqrt{5}$ .

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2 years ago

what power can you write to represent the volume of the cube shown? write the power as an expression with a base and an exponent

sergiy2304 [10]

Answer:

The power for the volume of the cube is '3'.

Exponent form of the volume is $(\frac{1}{3})^3$

Volume of the cube is $\frac{1}{27}$ inch³.

Step-by-step explanation:

We are given,

A cube with side equal to $\frac{1}{3}$ inches.

As we know,

Volume of a cube = $side^{3}$

Thus, we get,

Volume of the given cube is,

Volume = $(\frac{1}{3})^3$

i.e. Volume = $\frac{1}{27}$ inch³

Thus, we have,

The power for the volume of the cube is '3'.

Exponent form of the volume is $(\frac{1}{3})^3$

Volume of the cube is $\frac{1}{27}$ inch³.

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