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Ainat [17]
3 years ago
14

Find the volume of the cone, read the directions carefully!!​

Mathematics
1 answer:
luda_lava [24]3 years ago
8 0

Answer:

300 units^3 or 96π

Step-by-step explanation:

Volume of the cone would be:

Because the formula of finding the volume of cone is

V = πr^2 * h/3

r is the radius of the base

h is the height of the cone

π is Pi, approximately 3.142 and it is the circumference of any circle divided by its diameter

V is volume

So in this case:

V = πr^2 * h/3

V = π * 6^2 * 8/3

V = π * 36 * 8/3

V = 96π or 301.44 and round it up to 300 units^3

Hope this help :3

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Two trains leave New York at the same time heading in opposite directions. Train A travels at 4/5 the speed of train one. After
grandymaker [24]
<h3>Answer:  </h3><h3>speed of train A = 44 mph</h3>

=============================================

Work Shown:

x = speed of train A

y = speed of train B

"train A travels 4/5 the speed of train B" (I'm assuming "train one" is supposed to read "train B"). So this means x = (4/5)y

distance = rate*time

d = x*7

d = (4/5)y*7 = (28/5)y represents the distance train A travels

d = y*7 = 7y represents the distance train B travels

summing those distances will give us 693

(28/5)y + 7y = 693

5*(  (28/5)y + 7y ) = 5*693

28y + 35y = 3465

63y = 3465

y = 3465/63

y = 55

Train B's speed is 55 mph

4/5 of that is (4/5)y = (4/5)*55 = 4*11 = 44 mph

Train A's speed is 44 mph

8 0
3 years ago
You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along
sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}

Then, the time (speed divided by distance) is:

t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1

To optimize this function we have to derive and equal to zero:

\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\  \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\

x

As d_b=x, the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0
3 years ago
The length of a rectangle is 5 inches less than 4 times the width. The perimeter is 110 inches. Find the length and the width.
nataly862011 [7]

Answer:

  • Length = 43 inches
  • Width = 12 inches

Step-by-step explanation:

Perimeter of a rectangle = 2 * ( L + W)

The length of a rectangle is 5 inches less than 4 times the width.

Assume the width is x. Length is:

4x - 5

Equation is therefore:

2 * (4x - 5 + x) = 110

4x - 5 + x = 110/2

5x - 5 = 55

5x = 55 + 5

x = 60/5

x = 12 inches

If width is 12 inches, then length is:

= 4x - 5

= 4 * 12 -5

= 43 inches

6 0
3 years ago
I need help..... I don't understand at all
cluponka [151]
I think you have to estimate to a whole so 2 1/2 would be 3
8 0
3 years ago
Read 2 more answers
Please help asap!!!!!
emmasim [6.3K]
43 maybe? And if I’m wrong in advance-Sorry
3 0
3 years ago
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