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3 years ago

What is the equation of a circle with center -4, 7 and radius 6

Mathematics

1 answer:

Kitty [74]3 years ago

4 0

Answer:

$( x + 4 )^2 + ( y - 7 )^2 = 36$

Step-by-step explanation:

Use the circle equation, $( x - h )^2 + ( y - k )^2 = r^2$

Plug in the center and radius:

$( x + 4 )^2 + ( y - 7 )^2 = 6^2$

Simplify:

$( x + 4 )^2 + ( y - 7 )^2 = 36$

So, the equation is $( x + 4 )^2 + ( y - 7 )^2 = 36$

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An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression. To the nearest foot, how far is the boa

Yuri [45]

Answer:

407.22 foot is the boat from the base of the lighthouse

Step-by-step explanation:

Given the statement: An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression.

Let x foot be the distance of the object(boat) from the base of the lighthouse

Angle of depression = $7^{\circ}$

$\angle CAB = \angle DCA = 7^{\circ}$ [Alternate angle]

In triangle CAB:

To find AB = x foot.

Using tangent ratio:

$\tan (\theta) = \frac{Opposite side}{Adjacent Base}$

$\tan (\angle CAB) = \frac{BC}{AB}$

Here, BC = 50 foot and $\angle CAB =7^{\circ}$

then;

$\tan (7^{\circ}) = \frac{50}{x}$

$x = \frac{50}{\tan 7^{\circ}}$

$x = \frac{50}{0.1227845609}$

Simplify:

AB = x = 407.217321 foot

Therefore, the boat from the base of the light house is, 407.22'

5 0

3 years ago

Sociologists say the percentage of the classic music lovers is about 5%. From the survey, we know that only 83 out of 2000 peopl

disa [49]

Answer:

p value from chi square = 0.081

Step-by-step explanation:

Given that sociologists say the percentage of the classic music lovers is about 5%. From the survey, we know that only 83 out of 2000 people listen to the classic music. Let denote the proportion of the classic music lovers. The hypotheses are H0: p=0.05 vs Ha: p≠0.05

p value = 0.09

Instead of this if we do chi square

H0: Proportion of music lovers is 5% and non music lovers is 95%

Ha: Proportions are not as per the estimate

(Two tailed chi square test)

Observed 83 1917 2000

Expected 100 1900 2000

O-E -17 17 0

chi square

(O-E)^2/E 2.89 0.1521 3.0421

df =1

p value from chi square = 0.081

Though p value is not exactly the same, the conclusion in both tests are the same

5 0

3 years ago

A disco ball is shaped like a sphere with a diameter of 16 inches. To the nearest square inch, what is the surface of the disco

Mademuasel [1]

If the diameter is 16 inches, then its radius is half that, r = 8.

$\bf \textit{surface area of a sphere}\\\\
A=4\pi r^2\quad 
\begin{cases}
r=radius\\
-----\\
r=8
\end{cases}\implies A=4\pi 8^2$

5 0

3 years ago

How do u do 6x32 and 7x29 using distribuative property to solve

Rufina [12.5K]

Answer:

use multiple the numbers to get the co rrect

Step-by-step explanation:

32×6

=192

29×7=203

4 0

3 years ago

Read 2 more answers

-. In Ms. Nice's class of 9 students, the average

frutty [35]

Answer: 94.5

Step-by-step explanation:

If average of 9 students is 94, their total will be 94x 9 = 846

If the 10th student scores 99, the new total is 846 + 99 = 945

So, the new average will be

945/10 = 94.5

6 0

3 years ago