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SpyIntel [72]
3 years ago
12

A)Chris and Alex Were Building a sand Castle. They Decided to make it into a cone shape. After some time, the diameter of the th

e sand shaped cone was 12in and the height was 7in. What is the exact volume of the sand cone?
B) the kids kept adding sand, ten minutes later the volume of the sand cone had increased by 30%. what is the exact volume of the sand cone now?
Mathematics
1 answer:
Nesterboy [21]3 years ago
3 0

Answer:

A.) 84π | B.) 546π/5

Step-by-step explanation:

A.)

V(Cone) = πr²(h/3) where r = radius and h = height.

r = d/2 where d = diameter.

r = 12/2 = 6

V(Cone) = π(6)²(7/3) = π(36)(7/3) = 84π

B.)

84π · 0.3 = 126π/5

84π + 126π/5 = 546π/5  

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a person stands on top of a 200 ft building and spots a person on the ground below. the angle of depression from where the perso
PolarNik [594]

Answer:

246.979 ft

Step-by-step explanation:

When we draw our picture, we should be able to see that the angle of depression from the point of view is equal to the angle of elevation from the ground. We also know the height, and we are trying to find horizontal <em>x</em>. We must use tan∅ to solve:

tan39° = 200/x

xtan39° = 200

x = 200/tan39°

x = 246.979

6 0
3 years ago
if you double the input of a function and it results in twice the output and if you triple the input and it result in three time
bearhunter [10]

A function behaving as you state is a linear function, which means that the output varies directly with the input.

So, there exists some constant k \in \mathbb{R} such that your function is in the form

f(x) = kx

In fact, if you double the input, you have

f(2x) = k\cdot(2x) = 2\cdot (kx) = 2f(x)

And similarly

f(3x) = k\cdot(3x) = 3\cdot (kx) = 3f(x)

Note that this is a guess, it may happen that output doubles (triples) if you double (triple) the input, and still the function is not like y=kx.

For example, the function

f(x) = \dfrac{x^3}{3} - 2x^2 + \dfrac{14}{3}x -2

is such that

f(1) = 1,\ f(2) = 2,\ f(3) = 3

So, it may seems that doubling and tripling the input doubles and triples the output, but this is not true for every input, for example,

f(2) = 2,\ f(4) = 6

And so doubling the input didn't double the output.

8 0
3 years ago
Read 2 more answers
In a police on the interstate, the suspect's car reached a speed of 88 miles per hour for the total 15 minutes. In the time, how
miss Akunina [59]

As always, distance = rate times time. Here, distance is unknown, but we have the speed 88 mph and the time 0.25 hour. Thus,

distance traveled during chase = (88 mph)(0.25 hr) = 22 miles.

7 0
3 years ago
Read 2 more answers
Please help im very confused
joja [24]
Download the app photo math, it will give u all the answers for those and shows the work
7 0
3 years ago
In ∆MNP, m∠N = 90º, NH – altitude, m∠P = 21º, PM = 4 cm. Find MH.
Sveta_85 [38]

Answer:

0.51 cm

Step-by-step explanation:

In right triangle MNP, MP = 4 cm, m∠N = 90°, m∠P = 21°

By the sine definition,

\sin \angle P=\dfrac{\text{Opposite leg}}{\text{Hypotenuse}}=\dfrac{MN}{MP}\\ \\MN=MP\sin \angle P\\ \\MN=4\sin 21^{\circ}\approx 1.43\ cm

Now, consider right triangle HMN (it is right because NH is an altitude). By the cosine definition,

\cos \angle M=\dfrac{\text{Adjacent leg}}{\text{Hypotenuse}}=\dfrac{MH}{MN}\\ \\MH=MN\cos \angle M

In the right triangle, two acute angles are always complementary, so

m\angle M=90^{\circ}-m\angle P=90^{\circ}-21^{\circ}=69^{\circ}

Thus,

MH=1.43\cos 69^{\circ}\approx 0.51\ cm

7 0
3 years ago
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