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3 years ago

A point G is 40m away from a building, which is 15m high. What is the angle of elevation to the top of the building from G?

1 answer:

8 0

Ф is the angle of elevation to the topo of the building from G.
length of leg adyacent to angle Ф=40m
length of leg opposite to angle Ф=15 m
tan Ф=leg opposite / leg adyacent=15/40=0.375
Ф=arctan 0.375=20.56º

The angle of elevation to the top of the building from G is 20.56º.

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Henry knows that the circumference of a circle is 56.52 inches. What is the area of the circle? (Use 3.14 for and round to the

ahrayia [7]

The area of circle is 254.34 square inches, if the circumference of a circle is 56.52 inches.

Step-by-step explanation:

The given is,

Circumference of a circle is 56.52 inches.

$\pi =3.14$

Step:1

Formula for circumference of circle is,

$Circumference, C = 2\pi r$ ........................(1)

Where, r - Radius of circle

From the given,

C = 56.52 inches

Equation (1) becomes,

56.52 = 2 $\pi$ (r)

56.52 = (2) (3.14) (r)

56.52 = 6.28 (r)

$r = \frac{56.52}{6.28}$

r = 9 inches

Step:2

Formula for area of circle,

$Area,A = \pi r^{2}$ ............................(2)

Where, r - Radius of circle

From the given,

r = 9 inches

Equation (2) becomes,

$A = \pi (9)^{2}$

= (3.14) (81)

= 254.34

Area of circle, A = 254.34 square inches

Result:

The area of circle is 254.34 square inches, if the circumference of a circle is 56.52 inches.

3 0

2 years ago

Using the digits 5, 6, 7, 8, 9 and repetition is allowed how many options are there to

just olya [345]

Answer:

250 options to create an even number

375 options to create an odd number

8 0

3 years ago

WILL MARK BRAINLIEST <br><br> what is the domain of (f/g) (x)?

tatyana61 [14]

Given that $f(x) = \sqrt{7-x}$ and $g(x) = \sqrt{x + 2}$ , we can say the following:

$\Bigg(\dfrac{f}{g}\Bigg)(x) = \dfrac{f (x)}{g(x)} = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}$

Now, remember what happens if we have a negative square root: it becomes an imaginary number. We don't want this, so we want to make sure whatever is under a square root is greater than 0 (given we are talking about real numbers only).

Thus, let's set what is under both square roots to be greater than 0:

$\sqrt{7 - x} \Rightarrow 7 - x \geq 0 \Rightarrow x \leq 7$

$\sqrt{x + 2} \Rightarrow x + 2 \geq 0 \Rightarrow x \geq -2$

Since both of the square roots are in the same function, we want to take the union of the domains of the individual square roots to find the domain of the overall function.

$x \leq 7 \,\,\cup x \geq -2 = \boxed{-2 \leq x \leq 7}$

Now, let's look back at the function entirely, which is:

$\Bigg( \dfrac{f}{g} \Bigg)(x) = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}$

Since $\sqrt{x + 2}$ is on the bottom of the fraction, we must say that $\sqrt{x + 2} \neq 0$ , since the denominator can't equal 0. Thus, we must exclude $\sqrt{x + 2} = 0 \Rightarrow x + 2 = 0 \Rightarrow x = -2$ from the domain.

Thus, our answer is Choice C, or $\boxed{ \{ x | -2 < x \leq 7 \}}$ .

<em>If you are wondering why the choices begin with the $x |$ symbol, it is because this is a way of representing that $x$ lies within a particular set.</em>