Which of the binomials below is a factor of this expression 9x2 + 48xy + 64y2?

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

Calculate the amount of air in a room 6m long, 5m wide and 3mm high.

kherson [118]

Answer:

90.000 m³

Step-by-step explanation:

L = 6 m
W = 5 m
H = 3 mm = 3.000 m

V = L × W × H

V = 6 × 5 × 3.000

V = 30 × 3.000

V = 90.000 m³

4 0

2 years ago

Read 2 more answers

If it's possible to tell, decide if a and b are positive or negative: a-3>b-3 and b>4

Svetllana [295]

Answer:

a and b are positive

Step-by-step explanation:

We are given that

$a-3>b-3$

$b>4$

We have to find that a and b are positive or negative.

We have

$b>4$

It means b is positive and greater than 4.

$a-3>b-3$

Adding 3 on both sides

$a-3+3>b-3+3$

$a>b>4$

$\implies a>4$

Hence, a is positive and greater than 4.

Therefore, a and b are positive

6 0

2 years ago

Find the equation of the line that passes through the given points

uranmaximum [27]

First you need to figure out the slope:
y2-y1/x2-x1=(1+5)/(-5-7)=-1/2

y+5=-1/2(x-7)
y=-1/2x-3/2

6 0

3 years ago

Someone please help me !

Leni [432]

Answer:

Can't tell if it went through...

1. Shop A = 2x

2. Shop B = 2x - 580

3. Total = Shop A + Shop B

1949 = 2x + 2x - 580

4. Combine like terms

2x + 2x = 4x

1949 = 4x - 580

5. Add 580 to both sides (to remove -580 from right side)

1949 + 580 = 4x - 580 + 580

2529 = 4x

6. Divide both sides by 4 (to get x)

2529 / 4 = 4x / 4

632.25 = x

7. Shop A = 2x

2 * 632.25 = 1264.50

Shop A = 1264.50

8. Shop B = 2x - 580

2 * 632.25 - 580 = 684.50

Shop B = 684.50

Check: Shop A + Shop B = 1949

1264.50 + 684.50 = 1949

Shop A = 1264.50

Shop B = 684.50

Step-by-step explanation:

8 0

3 years ago