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2 years ago

Calculate DE to the hundredths place.

Mathematics

1 answer:

kompoz [17]2 years ago

5 0

<h3>Answer: 9.03</h3>

=====================================================

Explanation:

For now, focus solely on triangle HGF.

We'll need to find the measure of angle F.

Use the law of cosines

f^2 = g^2 + h^2 - 2*g*h*cos(F)

(4.25)^2 = 8^2 + 6^2 - 2*8*6*cos(F)

18.0625 = 100 - 96*cos(F)

18.0625-100 = -96*cos(F)

-81.9375 = -96*cos(F)

cos(F) = (-81.9375)/(-96)

cos(F) = 0.853515625

F = arccos(0.853515625)

F = 31.403868 degrees approximately

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Now we can move our attention to triangle DEF.

We'll use the angle F we just found to find the length of the opposite side DE, aka side f.

Once again, we use the law of cosines.

f^2 = d^2 + e^2 - 2*d*e*cos(F)

f^2 = (4.75+8)^2 + (11+6)^2 - 2*(4.75+8)*(11+6)*cos(31.403868)

f^2 = 81.563478

f = sqrt(81.563478)

f = 9.031250 approximately

Rounding to two decimal places means we get the final answer of DE = 9.03

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What is the area of a circle whose equation is (x-3)² + (y + 1) ² =81?

kupik [55]

Okay, first, given the equation, we need to find out what the radius of the circle is. Let us state the general equation of a circle:

$\frac{(x-x_{1})^2}{r^2}+ \frac{(y-y_{1})_^2}{r^2}=1$

Where $(x_{1}, y_{1})$ is the centre of the circle. In this case, we don't need to know the centre. Just the radius.

Let us start by converting the equation into standard for, which I typed above. Divide both sides by 81.

$\frac{(x-3)^2}{81}+ \frac{(y+1)^2}{81}=1$

Great! We now know the radius of the circle. It is $\sqrt{81}$ because it is the bottom fraction. Now we know that the radius is 9.

So now lets input this into the area of circle formula:

$A=πr^2$

Now we insert our radius.

$A=9^2π$

$=A=81π$

You can convert that into a decimal if you wish.

Hope this helped!

~Cam943, Moderator

4 0

3 years ago

Which statements are true regarding the area of circle

Pavlova-9 [17]

Question:

Which statements are true regarding the area of circle D? Select two options.

The area of the circle depends on the square of the radius.

The area of circle D is 36Pi centimeters squared.

The area of circle D is 324Pi centimetres squared

The area of the circle depends on the square of pi.

The area of the circle depends on the central angle.

Answer:

The following statements are true regarding the area of circle D:

The area of the circle depends on the square of the radius
The area of circle D is 324Pi centimeters

Step-By-Step Explanation:

As we know, the formula for area of the circle is given by,

$A=\pi r^{2}$

Where, r = radius of the circle. In figure, CD = radius = 18 cm

So, the circle area can be measured as

$A=\pi(18)^{2}=324 \pi \mathrm{cm}^{2}$

From this, concluding that the circle area depends on radius square and its value is $324 \pi \mathrm{cm}^{2}$ . Hence, the statement given in option A and C are correct (reveals that option B is incorrect).

As the Pi is constant, the circle radius cannot depend on Pi value and Option D also incorrect. The area of sector of circle only depends on ratio of central angle to entire circle (So option E also incorrect).