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What are the steps to (3w^3+7^2-4w+3) and (w+3)

Crazy boy [7]

Equation at the end of step 1 : Step 2 :Equation at the end of step 2 : Step 3 : 3w3 + 7w2 - 4w + 3 Simplify / w + 3 Checking for a perfect cube :

3.1 3w3 + 7w2 - 4w + 3 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: 3w3 + 7w2 - 4w + 3

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -4w + 3
Group 2: 3w3 + 7w2

Pull out from each group separately :

Group 1: (-4w + 3) • (1) = (4w - 3) • (-1)
Group 2: (3w + 7) • (w2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

3.3 Find roots (zeroes) of : F(w) = 3w3 + 7w2 - 4w + 3
Polynomial Roots Calculator is a set of methods aimed at finding values of w for which F(w)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers w which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 3 and the Trailing Constant is 3.

The factor(s) are:

of the Leading Coefficient : 1,3
of the Trailing Constant : 1 ,3

Let us test ....

P Q P/Q F(P/Q) Divisor -1 1 -1.00 11.00 -1 3 -0.33 5.00 -3 1 -3.00 -3.00 1 1 1.00 9.00 1 3 0.33 2.56 3 1 3.00 135.00

Polynomial Roots Calculator found no rational roots

Polynomial Long Division :

3.4 Polynomial Long Division
Dividing : 3w3 + 7w2 - 4w + 3
 ("Dividend")
 By : w + 3 ("Divisor")

dividend 3w3 + 7w2 - 4w + 3 - divisor * 3w2 3w3 + 9w2 remainder - 2w2 - 4w + 3 - divisor * -2w1 - 2w2 - 6w remainder 2w + 3 - divisor * 2w0 2w + 6 remainder - 3

Quotient : 3w2 - 2w + 2
 Remainder : -3

Final result : 3w3 + 7w2 - 4w + 3 over w + 3

5 0

3 years ago

A child's tent can be modeled as a pyramid with a square base whose sides measure 60 inches and whose height measures 84 inches.

IgorC [24]

Answer:

The volume of the tent is $100,800\ in^{3}$

Step-by-step explanation:

we know that

The volume of the square pyramid (child's tent) is equal to

$V=\frac{1}{3}b^{2}h$

we have

$b=60\ in$

$h=84\ in$

substitute

$V=\frac{1}{3}(60^{2})(84)=100,800\ in^{3}$

5 0

3 years ago

Read 2 more answers

Find the value of k so that 48x-ky=11 and (k+2)x+16y=-19 are perpendicular lines.

Rufina [12.5K]

Answer: k = -1 +/- √769

Step-by-step explanation:

48x - ky = 11

-48x -48x

-ky = -48x + 11

$\frac{-ky}{-k} = \frac{-48x}{-k} + \frac{11}{-k}$

$y =\frac{48x}{k} - \frac{11}{k}$

Slope: $\frac{48}{k}$

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(k + 2)x + 16y = -19

- (k + 2)x -(k + 2)x

16y = -(k + 2)x - 19

$\frac{16y}{16} = -\frac{(k + 2)x}{16} - \frac{19}{16}$

$y = -\frac{(k + 2)x}{16} - \frac{19}{16}$

Slope: $-\frac{(k + 2)}{16}$

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$\frac{48}{k}$ and $-\frac{(k + 2)}{16}$ are perpendicular so they have opposite signs and are reciprocals of each other. When multiplied by its reciprocal, their product equals -1.

$-\frac{(k + 2)}{16}$ * $\frac{k}{48}$ = -1