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3 years ago

14)

Mathematics

1 answer:

DerKrebs [107]3 years ago

3 0

Volume= length x width x height

5 x 5 = 25

25 x 10 = 250

Volume= 250 inches ^3

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Find the solution to the systems. x+y=1 and 3y=-3x+3

jenyasd209 [6]

Answer:

infinite number of solutions

Step-by-step explanation:

x+y=1

3y=-3x+3 ⇒ y=-x+1 ⇒ y+x=1

both equations are the same, so they have infinite number of solutions

3 0

4 years ago

Factor the expression. 16j2 + 24j + 9

ohaa [14]

A² + 2ab + b² = (a+b)²

So we get
16j² + 24j + 9 = (4j+3)²

5 0

4 years ago

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Preview Activity 3.5.1. A spherical balloon is being inflated at a constant rate of 20 cubic inches per second. How fast is the

ArbitrLikvidat [17]

Answer:

The radius is increasing at a rate of approximately 0.044 in/s when the diameter is 12 inches.

Because $\frac{dr}{dt}=\frac{5}{36\pi }>\frac{dr}{dt}=\frac{5}{64\pi }$ the radius is changing more rapidly when the diameter is 12 inches.

Step-by-step explanation:

Let $r$ be the radius, $d$ the diameter, and $V$ the volume of the spherical balloon.

We know $\frac{dV}{dt}=20 \:{in^3/s}$ and we want to find $\frac{dr}{dt}$

The volume of a spherical balloon is given by

$V=\frac{4}{3} \pi r^3$

Taking the derivative with respect of time of both sides gives

$\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$

We now substitute the values we know and we solve for $\frac{dr}{dt}$ :

$d=2r\\\\r=\frac{d}{2}$

$r=\frac{12}{2}=6$

$\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}\\\\\frac{dr}{dt}=\frac{\frac{dV}{dt}}{4\pi r^2} \\\\\frac{dr}{dt}=\frac{20}{4\pi(6)^2 } =\frac{5}{36\pi }\approx 0.044$

The radius is increasing at a rate of approximately 0.044 in/s when the diameter is 12 inches.

When d = 16, r = 8 and $\frac{dr}{dt}$ is:

$\frac{dr}{dt}=\frac{20}{4\pi(8)^2}=\frac{5}{64\pi }\approx 0.025$

The radius is increasing at a rate of approximately 0.025 in/s when the diameter is 16 inches.

Because $\frac{dr}{dt}=\frac{5}{36\pi }>\frac{dr}{dt}=\frac{5}{64\pi }$ the radius is changing more rapidly when the diameter is 12 inches.

8 0

3 years ago

Whats 8 divided by 2 (2+2)

Blababa [14]

8 / 4+4
8/8
=1

Pls give brainliest

8 0

3 years ago

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1.) -4(n-7)+4n=-8-3(n-5) 2.) 4(-8n+10)+4(4n-4)=-6n+2n

Assoli18 [71]

Answer:

$\huge\boxed{1)\ n=-7}\\\boxed{2)\ n=2}$

Step-by-step explanation:

$1)\\-4(n-7)+4n=-8-3(n-5)\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\(-4)(n)+(-4)(-7)+4n=-8+(-3)(n)+(-3)(-5)\\\\-4n+28+4n=-8-3n+15\\\\\text{combine like terms}\\\\(-4n+4n)+28=-3n+(-8+15)\\\\28=-3n+7\\\\\text{subtract 7 from both sides}\\\\28-7=-3n+7-7\\\\21=-3n\\\\\text{divide both sides by (-3)}\\\\\dfrac{21}{-3}=\dfrac{-3n}{-3}\\\\-7=n\to\boxed{n=-7}$

$2)\\4(-8n+10)+4(4n-4)=-6n+2n\\\\\text{use the distributive property}\\\\(4)(-8n)+(4)(10)+(4)(4n)+(4)(-4)=-6n+2n\\\\-32n+40+16n-16=-6n+2n\\\\\text{combine like terms}\\\\(-32n+16n)+(40-16)=(-6n+2n)\\\\-16n+24=-4n\\\\\text{add}\ 16n\ \text{to both sides}\\\\-16n+16n+24=-4n+16n\\\\24=12n\\\\\text{divide both sides by 12}\\\\\dfrac{24}{12}=\dfrac{12n}{12}\\\\2=n\to\boxed{n=2}$

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4 years ago

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