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krok68 [10]
3 years ago
11

Find the polar equation of the conic with the focus at the pole, directrix y = -6, and eccentricity 4 (picture provided)

Mathematics
1 answer:
Keith_Richards [23]3 years ago
5 0

Answer:

Choice B is correct

Step-by-step explanation:

The eccentricity of the conic section is given as 4 and thus the conic section is a hyperbola. Hyperbolas are the only conic sections with an eccentricity greater than 1.

Next, the directrix of this hyperbola is located at y = -6 implying that the hyperbola will be opening upwards. Consequently, the polar equation of this hyperbola will be of the form;

r=\frac{k}{1-4sin(theta)}

The value of k in the numerator is the product of eccentricity and the absolute value of the directrix;

k= 4*6 = 24

The polar equation is thus given by alternative B

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What is the measurement of BC to the nearest centimeter?
77julia77 [94]

Answer:

a   8

Step-by-step explanation:

You are given two sides and the included angle. Since you don't have any side and the opposite angle, you must use the law of cosines.

a^2 = b^2 + c^2 - 2bc\cos A

a^2 = 5^2 + 11^2 - 2(5)(11)\cos 39^\circ

a^2 = 25 + 121 - 110\cos 39^\circ

a^2 = 60.51

a = 7.779

Answer: a = 8 cm

7 0
3 years ago
A function is a rule that assigns each value of the independent variable to exactly one value of the dependent variable. True or
vesna_86 [32]
<span>The answer is true
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 Dependent variable: y
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 </span>y = (- 1) ^ 2 = 1 &#10;
<span> For x = 1:
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3 0
3 years ago
Read 2 more answers
Find the volume.<br> Area = 16.4 cm²<br> 8.1 cm<br> cm³
Tasya [4]

Answer:

132.84 is the answer as volume is area times length

6 0
2 years ago
Translate this sentence into an equation.
Andrew [12]

Step-by-step explanation:

"product" means multiplication. the same as "times".

so,

135 = r×9

3 0
3 years ago
What is f–1(8)??<br><br> Please select the best answer
notka56 [123]

Answer:

f^{-1}(8)=\frac{3}{2}

Step-by-step explanation:

Given f(x)=2x+5

We have to find f^{-1}(8)

In order to find f^{-1}(x) we have to make x as the subject of the formula

Let us assume f(x)=y

⇒2x+5=y

Subtracting both sides by 5

2x+5-5=y-5

2x=y-5

Dividing both sides by 2

\frac{2x}{2}=\frac{y-5}{2}

⇒x=\frac{y-5}{2}

Now substituting y with x

we have f^{-1}(x)=\frac{x-5}{2}

Now f^{-1}(8)=\frac{8-5}{2}

=\frac{3}{2}

So option (ii) is correct


5 0
3 years ago
Read 2 more answers
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