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3 years ago

Given that 2 x − 2 y = 23 Find x when y = 9

Mathematics

2 answers:

saveliy_v [14]3 years ago

7 0

Answer:

20.5

Step-by-step explanation:

2x - 2y = 23

2x - 2(9) = 23

2x - 18 = 23

2x = 23 + 18

2x = 41

x = 20.5

gulaghasi [49]3 years ago

4 0

Answer:

$x=41/2=20.5$

Step-by-step explanation:

So we have the equation:

$2x-2y=23$

And we want to find x when y is 9.

So, substitute y for 9 and solve for x:

$2x-2(9)=23$

Multiply:

$2x-18=23$

Add 18 to both sides:

$2x=41$

Divide both sides by 2:

$x=41/2=20.5$

So, our answer is 20.5

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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 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

2. Find the mzBDC. E B 120° 60°

timofeeve [1]

Sorry dude got no idea

6 0

2 years ago

For every pizza Eric's family ate, eric ate2 of the 8 pieces. If Eric's family bought 2 pizzas, write the ratio of the total num

soldier1979 [14.2K]

Answer:

4 over sixteen, or 4/16 is your answer.

Step-by-step explanation:

There are 2 pizzas, each of which contain 8 pieces. So, in all, there were 8 pieces. Eric ate two pieces from each pizza. So, 2+2=4. Thus, he ate four out of the 16 pieces. That brings us to our answer, 4/16.

I hope this helps you, have a wonderful day!

4 0

3 years ago

Moesha needs $79 for a class trip. She already has $22 and she can earn the rest by babysitting for 8 hours. If h represents her

elena55 [62]

Answer:

79-22=8h

Step-by-step explanation:

She can earn the rest by babysitting for only 8 hours,

so take 22 from 79, divide the total by 8 and that is how much she gets per hour (8h)

6 0

3 years ago

Read 2 more answers

Simplify (-8.5) (-5) (-2).

Ber [7]

Answer:

-85

Step-by-step explanation:

(-8.5)(-5)(-2)

=(-8.5)(10)

=-85

8 0

3 years ago