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3 years ago

How to solve (5/6-1/6)-1/12

1 answer:

6 0

First, find the equivalent fractions of 5/6 and 1/6 with a denominator of 12: 10/12 and 2/12. Then begin the equation. 10/12-2/12 is 8/12. 8/12-1/12 is 7/12

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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 F is called an antiderivative of f on an interval I if $F'(x) = f(x)$ for all x in I.

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

4 years ago

The length of a rectangular garden is 10 yards and it’s width is 10 feet. What is the perimeter of the garden in feet

ollegr [7]

Answer: 80 feet

Step-by-step explanation:

10 yard= 30 feet

2[l + b]

2{30+10}

8 0

3 years ago

Solve for all values of x by factoring. x^2- 3x = 4x

Alona [7]

Answer: x=0,7

Step-by-step explanation:

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3 years ago

Read 2 more answers

Two less than the sum of twice a number and forty

DiKsa [7]

Answer: 2-(2x+40) or (2x+40)-2

Step-by-step explanation: If you wanted to solve the problem, you have to do the stuff in the parentheses before you do the stuff out of the parentheses. In the parentheses, you will have to solve 2x before you do anything else. When you solve 2x, the answer to that, add it to 40. Then the answer in the parentheses, subtract it by 2 and you can get the answer.

6 0

3 years ago

Use cross products to determine whether the pair of ratios 4/6 and 14/21 form a proportion. Write yes or no. *SHOW WORK*

Dafna1 [17]

4/6 can reduce to 2/3. (divide each by 2)
14/21 can reduce to 2/3 by dividing the nume/denominator by 7.
in this case, they are proportional.

3 0

3 years ago