which table represents a function

Question:

A lighthouse is located on an island 3 miles from the closest point on a straight shoreline. If the lighthouse light rotates clockwise at a constant rate of 9 revolutions per minute, how fast does the beam of light move towards the point on the shore closest to the island when it is 52 miles from that point

Answer:

The beam of light moves at [tex]16278\pi[/tex] miles/min

Step-by-step explanation:

This question is illustrated with the attached image

Taking the instructions in the question, one at a time.

A revolution of 9 per minute implies that:

[tex]\frac{d\theta}{dt} = \frac{9 * 2\pi\ rad}{1\ min}[/tex]

[tex]\frac{d\theta}{dt} = 18\pi \frac{rad}{min}[/tex]

Take tan of the angle in the attachment:

[tex]tan(\theta) =\frac{52}{3}[/tex]

Differentiate both sides with respect to time

[tex]\frac{d\ tan(\theta)}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]

Rewrite as:

[tex]\frac{d\ tan(\theta)}{d\theta} * \frac{d\theta}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]

In calculus:

[tex]sec^2(\theta) =\frac{d\ tan(\theta)}{d\theta}[/tex] -- Chain rule

So:

[tex]sec^2(\theta) *\frac{d\theta}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]

In trigonometry:

[tex]sec^2(\theta) = tan^2(\theta) + 1[/tex]

So:

[tex](tan^2(\theta) + 1)\frac{d\theta}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]

Recall that:

[tex]tan(\theta) =\frac{x}{3}[/tex]

[tex]((\frac{52}{3})^2 + 1)\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]

[tex](\frac{52^2}{9} + 1)\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]

[tex](\frac{2704}{9} + 1)\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]

[tex](\frac{2704+9}{9})\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]

[tex](\frac{2713}{9})\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]

Recall that: [tex]\frac{d\theta}{dt} = 18\pi \frac{rad}{min}[/tex]

[tex](\frac{2713}{9}) * 18\pi =\frac{1}{3} * \frac{dx}{dt}[/tex]

[tex]2713 * 2\pi =\frac{1}{3} * \frac{dx}{dt}[/tex]

Multiply both sides by 3

[tex]3 * 2713 * 2\pi =\frac{1}{3} * \frac{dx}{dt} * 3[/tex]

[tex]3 * 2713 * 2\pi =\frac{dx}{dt}[/tex]

[tex]16278\pi =\frac{dx}{dt}[/tex]

[tex]\frac{dx}{dt} = 16278\pi[/tex] miles/min

Hence:

The beam of light moves at [tex]16278\pi[/tex] miles/min

Answer:

Step-by-step explanation:

NO SPEAK ENGLISH SORRYYYY

The inequality explains the value of -4°C is greater than -9°C

It is known as inequality when both sides of a mathematical statement contain mathematical signs that are either less than or larger than one another.

It is given that,

-4°C >  -9°C

We utilize the "Greater than or equal to" sign in linear inequalities when the value of a variable is greater than or equal to a certain value. The "greater than" symbol (>), which has a sleeping line beneath it, is used to denote it. It is represented by the character (≥). 

Thus, the inequality explains the value of -4°C is greater than -9°C.

Learn more about inequality here:

brainly.com/question/19491153

#SPJ2

Answer:

100 times

Step-by-step explanation:

doesn't matter if the number is in the same place value so, the answer is 100 times.

Answer:

Ava's

Step-by-step explanation:

To find whose plot of land is smaller, compare the sizes of their plots.

Jason's is 2/5 of an acre, while Ava's is 2/8 of an acre.

Because they have the same numerator, we can look at the denominator to see which is smaller.

The number with the larger denominator will be smaller. So, this means 2/8 is smaller than 2/5.

So, Ava's plot of land is smaller

Answer:

14

Step-by-step explanation:

126/9=14

Answer:

option 4, complementary angles total 90°

Step-by-step explanation:

Answer:

13 weeks because he loses 3 pounds per week

Step-by-step explanation:

269-251=39

39 divided by 3 = 13

13 weeks is your answer!

please mark brainliest please!!!

Answer:

NO you only got 70 percent

Step-by-step explanation:

Answer:

62.857142857143%

Step-by-step explanation:

Answer:

2 (3x - 2)

Step-by-step explanation:

It means your multiplying two to each number.

Answer:

  c) parabola and circle: 0, 1, 2, 3, 4 times

  d) parabola and hyperbola: 1, 2, 3 times

Step-by-step explanation:

c. A parabola can miss a circle, be tangent to it in 1 or 2 places, intersect it 2 places and be tangent at a 3rd, or intersect in 4 places.

__

d. A parabola must intersect a hyperbola in at least one place, but cannot intersect in more than 3 places. If the parabola is tangent to the hyperbola, the number of intersections will be 2.

If the parabola or the hyperbola are "off-axis", then the number of intersections may be 0 or 4 as well. Those cases seem to be excluded in this problem statement.

Answer: m=3

Step-by-step explanation:

This could be written as m+5=8

You would then do the inverse to 'undo' the equation. So instead of adding 5 you would take away 5 from 8.

8-5=3

Hope this helps :)

Answer:

C

Step-by-step explanation:

All you are doing is multiplying the 3 sides that appear since its volume. length times height times width.

Answer:

D

Step-by-step explanation: Snap Add?

1. Volume of rectangle

V = L*W*H

Now: V = L*2W*H

2. Plug in numbers

V = 24.5*2(12.5)*10

V = 6125 cm^3

Answer:

-1 and -3

(n+7)(n-8)

Step-by-step explanation:

1. Find the Zeros

[tex]f(x)=x^{2} +4x+3[/tex]

[tex]f(x)=\left(x+1\right)\left(x+3\right)[/tex]

[tex]x+1=0\\x=-1\\x+3=0\\x=-3[/tex]

2. Factoring Trinomials

[tex]f(x)=n^{2} -n-56[/tex]

[tex]f(x)=\left(n+7\right)\left(n-8\right)[/tex]

[tex]n+7=0\\n=-7\\n-8=0\\n=8[/tex]

Answer:

4 m

Step-by-step explanation:

hope you have a great day

Answer:

Step-by-step explanation:

yes that is correct!-2

[tex]330in^{3}[/tex]

I'm pretty sure that's the answer

Answer:

I dont see the question...

Step-by-step explanation:

Answer: 8

Step-by-step explanation: np:)

Answer: The Vertex is at (-1,25)

Axis of symmetry X=-1

Left x intercept (-6,0)

Right x intercept (4,0)

I’m not to sure about the set of all real numbers or the range but i hope this helped

Step-by-step explanation:

Graph on Desmos

Answer:

confess and believe are the two main words.

Step-by-step explanation:

Just got this right :')

Answer:

Just multiply 9.6*4.9 which is 47.04 m^2.

You can basically cut the shape in half, then put the shapes back together to look like a rectangle. The area formula is bh, or 9.6*4.9. Ignore the 11 m.

Answer:

45/11.25 is 4.

4*25=100

This tells us that the jeans are discounted at 75%.

Answer:

yes, they are by SSS

Step-by-step explanation:

EF=AB

ED=BC

DF=AC

therefore, both triangles are congruent

Answer:

True

Step-by-step explanation:

It is true because the graph of [tex]y=x-12[/tex] passes through the point [tex](16,4)[/tex]

x = 16

y = 4

Substitute

4 = 16 - 12

4 = 4

Therefore, the answer is true.