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3 years ago

What is the completely factored form of x3 – 64x?

2 answers:

7 0

The answer is x(x-8)(x+8)
Here is the process;
x^3-64x
x(x^2-64)
You know that it will be a x- and a x+ becuase there is no middle x value
x(x-)(x+)
x(x-8)(x+8)

IrinaK [193]3 years ago

3 0

Remember difference of 2 perfect squares
a²-b²=(a-b)(a+b)

first factor out x

x(x²-64)
x(x²-8²)
x(x-8)(x+8)

answer is 3rd option

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3 years ago

The base of a triangle is 10 inches more than 3 times the height. If the area of the triangle is 16 square inches, find the base

USPshnik [31]

Let h represent the height of the triangle.

... b = 10 + 3h . . . . . . the base is 10 inches more than 3 times the height

... A = (1/2)bh . . . . . . formula for the area of a triangle in terms of base and height

... 16 = (1/2)(10 +3h)h . . . . substitute the known values

... 3h² + 10h - 32 = 0 . . . . rearrange to standard form

... (h -2)(3h +16) = 0

... h = 2 or -16/3 . . . . . . . . the negative solution is extraneous

... b = 10 + 3·2 = 16 . . . . . use the relation between b and h

The base and height of the triangle are 2 inches and 16 inches, respectively.

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3 years ago

After heating up in a teapot, a cup of hot water is poured at a temperature of 210°F. The cup sits to cool in a room at a temper

Fiesta28 [93]

Newton's Law of Cooling:

$T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}$

$T(t) =$ Temperature given at a time

$t =$ Time

$T_{s} =$ Surrounding temperature

$T_{o}=$ Initial temperature

$e =$ Constant (Euler's number) ≈ 2.72

$k =$ Constant

Using this information, find the value of $k$ , to the nearest thousandth, then use the resulting equation to determine the temperature of the water cup after 4 minutes.

First, plug in the given values in the equation and solve for $k$ :

$T(t) =$ 197°, $t =$ 1.5 minutes, $T_{s} =$ 70° and $T_{o}=$ 210°

$T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\197=70+(210-70)e^{-1.5k} \\197 -70 = (140)e^{-1.5k} \\127 =(140)e^{-1.5k}\\\frac{127}{140}=e^{-1.5k} \\ln(\frac{127}{140})=-1.5k\\-0.097=-1.5k\\0.0649 = k$