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3 years ago

13

of the 400 vehicles that passed the intersection, 98 are buses, what percent of the vehicles that passed the intersection are bu

sses

1 answer:

frutty [35]3 years ago

5 0

It should be 24.5%. If you divide 98 by 400 it's .245. Then multiply it by 100, you get 24.5%.

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A canister is dropped from a helicopter 500m above the ground. Its parachute does not open, but the canister has been designed t

solmaris [256]

Answer:

The impact speed 98.995 m/s is less than 100 m/s and the canister will not burst.

Step-by-step explanation:

A function<em> F</em> is called an antiderivative of <em>f</em> on an interval <em>I</em> if $F'(x) = f(x)$ for all x in <em>I.</em>

Recall that if the object has position function $s=f(t)$ , then the velocity function is $v(t)=s'(t)$ . This means that the position function is an antiderivative of the velocity function. Likewise, the acceleration function is $a(t)=v'(t)$ , so the velocity function is an antiderivative of the acceleration.

An object near the surface of the earth is subject to a gravitational force that produces a downward acceleration denoted by $g$ . For motion close to the ground we may assume that $g$ is constant, its value being about $9.8 \:{\frac{m}{s^2}}$ .

We know that the acceleration due to gravity is given by

$a(t)=-9.8$

and the antiderivative is velocity

$v(t)=\int a(t)\,dt\\v(t)=\int -9.8\,dt\\v(t)=-9.8t +C$

We know that the canister was dropped, so the initial velocity at t = 0 is zero, this fact let us know the value of C.

$v(0)=9.8(0)+C\\C=0$

The antiderivative of velocity is the position

$s(t)=\int v(t) \, dt\\s(t)=\int -9.8t \, dt\\s(t)=-4.9t^2+C$

To find the value of the constant C, we know that the height was 500 m at t = 0, this means $s(0)=500$

$500=-4.9(0)^2+C\\C=500$

$s(t)=-4.9t^2+500$

Using the fact that at the time of impact the height s(t) is zero we can compute the total time of the fall:

$s(t)=-4.9t^2+500=0\\\\-4.9t^2=-500\\\\t^2=\frac{5000}{49}\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\t=\sqrt{\frac{5000}{49}},\:t=-\sqrt{\frac{5000}{49}}$

A negative time does not make sense, so we only take as a possible solution

$t=\sqrt{\frac{5000}{49}}=\frac{50\sqrt{2}}{7}\approx 10.102$

Now the final velocity is

$v(\frac{50\sqrt{2}}{7})=-9.8(\frac{50\sqrt{2}}{7})\approx -98.995$

The impact speed 98.995 m/s is less than 100 m/s and the canister will not burst.

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4 years ago

William has a fish tank that has a volume of 3,825 cubic inches. The base has a width of 12.5 inches and a length of 24 inches.

andre [41]

Answer:

12.75

Step-by-step explanation:

3,825 / 12.5 / 24 = 12.75

3 0

3 years ago

Does 8,6,4 contain numbers that are less than 10

raketka [301]

Yessssssssssssssssss

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3 years ago

Mrs. Lewis received her paycheck this week in the amount of $535.75. She spent $76.98 on groceries, she paid her $59.95 phone bi

SIZIF [17.4K]

Answer:

376.37

Step-by-step explanation:

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3 years ago

Read 2 more answers

Can someone help me solve this matrix

liraira [26]

Answer:

You cant add a negative number.

Step-by-step explanation:

If you add a negative number you will not have a full answer.

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3 years ago