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mariarad [96]
3 years ago
10

Could you help me with theses 4 questions thanks <3

Mathematics
2 answers:
Marina CMI [18]3 years ago
8 0
You have to find the area of the base which is a circle and that's pier^2 and then get that and multiply it by the height
Vesnalui [34]3 years ago
8 0
1. 1339.56pi mm^3
2. 11,304 mm^3
3. 5.1 cm
4. 288pi ft^3
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A balloon rises at the rate of 10 ft/sec from a point on the ground 100 feet from an observer. Find the rate of change of the an
lubasha [3.4K]

The rate of change of the angle of elevation of the balloon from the observer when the balloon is 100 feet above the ground is  1/20 degree/sec.

<h3>What is angle of elevation?</h3>

It is described as a relationship between an oblique line from the observer's eye to an item above his eye and the horizontal plane. This angle eventually develops above the surface. The angle of elevation is made in such a way that it is above the observer's eye, as the name suggests.

Calculation for the rate of change of angle of elevation-

According to the question,

A balloon rises at the rate of 10 ft/sec from a point on the ground 100 feet from an observer.

The balloon is 100 feet above the ground.

Let the height of the balloon be 'h' ft.

Then tanØ = h/100

h = 100tanØ

Differentiate the above equation with respect to time.

dh/dt = 100 sec² Ø (dØ/dt)

We know dh/dt = 10 ft/sec.

when h = 100

tanØ = 100/100 = 1/1

tanØ = Perpendicular/Base

On comparing above two equations,

Perpendicular = 1; Base = 1.

By Pythagoras the hypotenuse is,

H² = P² + B²

    = 1² + 1²

    = 2

H = √2

Now, calculate the value of cosØ.

cosØ = B/H = 1/√2

Squaring both side

cos² Ø = 1/2

sec² Ø = 1/cos² Ø

sec² Ø = 2

The main equation was,

dh/dt = 100 sec² Ø (dØ/dt)

Substitute the values,

dØ/dt = (dh/dt )/100 sec² Ø

         = (10)/(100×2)

dØ/dt = 1/20 degree/sec.

Therefore, the rate of change of the angle of elevation of the balloon from the observer is  1/20 degree/sec.

To know more about the angle of elevation, here

brainly.com/question/9817377

#SPJ4

8 0
1 year ago
The organizers of a 5k race surveyed runners about their finishing times (f) and the number of previous races they had run (n).
Rzqust [24]
Let's interpret this equation. If we have that a runner has 0 races under his belt, he completes the race in 38.1 min. We have that the slope is -1.2 min/race and the intercept at n=0 is 38.1 min. Hence, for every race, the duration of the run decreases by 1.2 min (or increases by -1.2 min).
Lets derive that. Suppose a runner that has run n races, runs once more.
The difference of times is:
(-1.2(n+1)+38.1)-(-1.2n+38.1)=-1.2(n+1)-(-1.2n)= -1.2n-1.2+1.2n=1.2 minutes.
Hence, the correct answer is the first.
5 0
3 years ago
Read 2 more answers
Why is 6/8 greater than 5/8 but less than 7/8
marta [7]
Because 6/8 means, dividing 6 by 8. If you divide 7 by 8 eight you will get a greater number then 6/8 because 7 is greater than 6. And if you divide 5 by 8 you will get a smaller number than 6/8 because 5 is less than 6. I hope its not confusing.
6 0
3 years ago
Read 2 more answers
Which system of equations below has exactly one solution?
marysya [2.9K]

That is the third choice.

If we add the 2 equations we get

2y = -12 so y = -6

substituting in one of the equations we get x = 0

4 0
3 years ago
Read 2 more answers
HELPPPP PLSSS........
shepuryov [24]
They earned 500 for a bonus and she earns 250 each week for 12 weeks multiply 250x12 then add 500 so in this case they earned $3,500
3 0
3 years ago
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