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2 years ago

Correct answers only please!

Mathematics

1 answer:

Semmy [17]2 years ago

5 0

Answer:

62.7°

Step-by-step explanation:

9 = Hypotenuse

8 = Opposite

In this question we have to use some trigonometry to work out angle EFG. The first thing we need to identify is will formula will we use out of the following:

Sin⁻¹ = Opposite ÷ Hypotenuse

Tan⁻¹ = Opposite ÷ Adjacent

Cos⁻¹ = Adjacent ÷ Hypotenuse

We know which formula to use because the length won't be in the triangle for example we will be using the Sin triangle because we don't have an adjacent. If we don't have an adjacent then the other formula's won't work.

Now we substitute in the values

Sin⁻¹ = Opposite ÷ Hypotenuse

Sin⁻¹ = 8 ÷ 9

The value of angle EFG is 62.73395555

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F(x) = x^2 and g(x) = 2x-3 What is the value of g(4) + f(-3)?

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Answer: 66

Step-by-step explanation:see attachment.

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2 years ago

A cylinder has a base diameter of 14m and a height of 10m. What is its volume in cubic m, to the nearest tenths place?

VARVARA [1.3K]

Answer:

1539 cubic meters

Step-by-step explanation:

Hello, I can help you with this

to solve need we will need these two equations

Step one

Remember

area of a circle

$Area=\pi *\frac{diameter^{2} }{4}\\$

Also, the volume of the cylinder

Volume= area of the circle * height

$Volume=\pi *\frac{diameter^{2} }{4} *height\\$

Step 2

put the values into the equation

Let

diameter= 14 m

height = 10 m

$Volume=\pi *\frac{diameter^{2} }{4} *height\\\\Volume=\pi *\frac{(14\ m)^{2} }{4} *10\ m \\\\Volume=\pi *49\ m^{2} *10\ m\\Volume=1539.38\ cubic\ meters$

I hope it helps,have a great day.

3 0

2 years ago

What is the equation of the quadratic graph with a focus of (4, −3) and a directrix of y = −6?

Artyom0805 [142]

Answer:

$y=\frac{1}{6} (x-4)-\frac{9}{2}$

Step-by-step explanation:

∵ The quadratic equation form is :

y = [1/2(b - k)] (x - a)² + (b + k)/2

Where (a , b) is the focus and directrix y = k

∵ The focus is (4 , -3) and directix is y = -6

∵ $y=\frac{1}{2(-3-(-6))} (x-4)^{2}+\frac{(-3)+(-6)}{2}$

∴ $y=\frac{1}{6} (x - 4)^{2}+\frac{-9}{2}$

∴ $y=\frac{1}{6} (x-4)-\frac{9}{2}$

another way:

Assume that (x , y) is the general point on the parabola

∵ The distance between the directrix and (x , y) = the distance between the focus and (x , y)

By using the distance rule:

∵ (y - -6)² = (x - 4)² + (y - -3)² ⇒ (y + 6)² = (x - 4)² + (y + 3)

∴ y² + 12y + 36 = (x - 4)² + y² + 6y + 9

∴ 12y - 6y = (x - 4)² + 9 - 36

∴ 6y = (x - 4)² - 27 ⇒ ÷ 6

∴ y = 1/6 (x - 4)² - 9/2

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2 years ago

A circle has a center of (5,-5) and goes through (6,-2). What is the radius?

Fittoniya [83]

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