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3 years ago

HELP ASAP!!!! I was told to explain why these are rational numbers!!!

Mathematics

1 answer:

Svetlanka [38]3 years ago

5 0

In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number. Wikipedia

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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

What is the value of $12000 of principal earning 4.8% compounded annually for seven years?

ivanzaharov [21]

Okay. The formula for compound interest is P(1 + r)^t, with P = principal, r = percentage rate, and t = time in years. 4.8% is 0.048 in decimal form. We add 1 to that number to get 1.048. Because the amount of time compounded is 7 years, we raise 1.048 to the 7th power. 1.048^7 is 1.388445952. Do not delete this number from your calculator. Now, multiply that number by 12,000 to get 16,661.35142 or 16,661.35 when rounded to the nearest hundredth. There. The value after seven years is $16,661.35.

4 0

4 years ago

Work out the area of this circle. Give you answer in terms of pi and state it’s units

tino4ka555 [31]

Answer:

49π

Step-by-step explanation:

area of circle = πr^2

Handy Tip: cherry pies delicious; apple pies are(R) too(2)! so C = πd and A = πr^2

diameter = 14 cm

radius = 14/2 = 7cm

area of circle = π(7)^2

area of circle = 49π

Hope that helps!

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3 years ago

Brent's pick-up truck can carry 1/5 ton.Nina's pick-up truck can carry 500 pounds.Whose pick-up truck can carry more weight? Exp

frutty [35]

Nina's truck holds more, because Brent's pick-up holds 1/5 a ton, and a ton is 2000 pounds, so 2000 x 1/5 is 400, and is less than Nina's truck.

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4 years ago

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Which point is on the interior of ∠DEF?

LenKa [72]

G; Whatever point is in a 180 degree reach of the direction the angle is in is the interior. Think about it like a clock that can only reach for one side, up or down, of the 3 and 9. Whichever direction it is angled towards is the one you look in.

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4 years ago

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