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zvonat [6]
3 years ago
13

A rotating beacon is located 1 kilometer off a straight shoreline. If the beacon rotates at a rate of 3 revolutions per minute,

how fast (in kilometers per hour) does the beam of light appear to be moving to a viewer who is 1/2 kilometer down the shoreline?
Mathematics
1 answer:
Valentin [98]3 years ago
5 0
Find the radius of the circle by finding the distance between the viewer and the beacon. 
then find the circumference by using 2πr2

this will be the distance the light covers over 1 revolution.
then using dimensional analysis:
3 rev/min (7.037 km/rev) (60 min/1 hr) = 1266.7 km/hr
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A prism with a base area of 5 ft² and a height of 10 ft is dilated by a factor of 65 . What is the volume of the dilated prism?
mina [271]

Answer:

The volume of the dilated prism is 86.4ft^3.

Step-by-step explanation:

The original prism has base area 5ft^2 and a height of 10ft.

The volume of the original prism is v=5\times 10=50ft^3.

The prism is dilated by a scale factor of k=\frac{6}{5}.

To find the volume of the dilated prism, we multiply the volume of the original prism by k^3=\frac{216}{125}.

V=\frac{216}{125} \times 50ft^3

\Rightarrow V=86.4ft^3

3 0
2 years ago
Creat an equation for a cubic function, in standard form, that has x- intercept given by the set {-3,1,7} and which passes throu
prohojiy [21]

Given :

Set of x-intercepts {-3,1,7},

point through which it passes (-2,54)

Now,

Step 1: Substitute value of x intercepts in equation, y=a(x-p)(x-q)(x-r), we get,

y=a(x-(-3))(x-1)(x-7)

y= a(x+3)(x-1)(x-7)               ... equation (1)

Step 2: substitute x an y with the point through which it passes,

54=a((-2)+3)((-2)-1)((-2)-7)

54 = 27a

∴ a=2

Step 3: Now, substituting value of a in equation (1), we have

y=(2x+6)(x^{2} -8x+7)

y=2x^{3}-10x^{2}  -34x +42   (Requited cubic equation)

   

6 0
3 years ago
Use the x-coordinates A and C to calculate AC without counting
alexandr1967 [171]
21 its 21 because it is 21
3 0
2 years ago
Explain how you know that 7/12 is greater than 1/3 but less than 2/3
PtichkaEL [24]
Or this question you should know that:
1/3 = (1*4)/(3*4) = 4/12 
and 
2/3 = (2*4)/(3*4) = 8/12 
so you can see that 7/12 is greater than 4/12 which is 1/3 and less than 8/12 which is 2/3 :))))
i hope this is helpful
have a nice day
7 0
3 years ago
Read 2 more answers
PLEASE HELP ME!!
Step2247 [10]

Answer:

A = $10,441.68

A = P + I where

P (principal) = $10,400.00

I (interest) = $41.68

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 0.02/100

r = 0.0002 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 10,400.00(1 + 0.0002/2)(2)(20)

A = 10,400.00(1 + 0.0001)(40)

A = $10,441.68

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $10,400.00 at a rate of 0.02% per year compounded 2 times per year over 20 years is $10,441.68.

8 0
2 years ago
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