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nevsk [136]
2 years ago
7

A man runs at the speed of 10 km/hr. How much time will he take to cover 2000 meters?

Mathematics
1 answer:
LUCKY_DIMON [66]2 years ago
4 0
200 hours.

It’s 10km for every one hour
Divide 2000 by 10 and you will be left with the number of km for every one hour.
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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.

5 0
3 years ago
Please help .<br> From the equation, what is the value of the radius, r ? x2 + y2 = 144
ale4655 [162]

Answer:

should be 12 if the x and y are squared. If you meant 2x and 2y than 12 is incorrect.

Step-by-step explanation: 144=r^2.

3 0
3 years ago
Given the following functions, evaluate each of the following:
Olegator [25]

Answer:

1. -6

Step-by-step explanation:

f(x)=x²-9

g(x)= x-3

1. (f+g)(2) =

(2²-9)+(2-3) = (4-9)+(2-3) = (-5)+(-1)= -6

8 0
2 years ago
The index number representing the price level changes from 109 to 113 in one year. The inflation rate during the year is _____ p
Dima020 [189]

First, get the difference between the price level changes.

113-109=4

Then, divide it by the initial price level, which is 109.

\frac{4}{109}=0.0367

Multiply by 100 to get its percent.

0.0367\times100=3.67

Thefore, the inflation rate during the year is 3.67 percent.

8 0
1 year ago
What is the next term of the geometric sequence. 135,45,15​
WINSTONCH [101]

Answer:

5

Step-by-step explanation:

Each term is 1/3 of the preceding term

135 / 3 = 45

45 / 3 = 15

15 / 3 = 5

5 0
3 years ago
Read 2 more answers
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