What is the factor of z^3+64

List all rational roots that are possible according to the rational zero theorem. x^3-5x^2-9x+45=0

Lina20 [59]

-3, 3, 5.

https://www.wolframalpha.com/input/?i=%28x%5E3%29-%285x%5E2%29-9x%2B45%3D0

8 0

3 years ago

Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t

makkiz [27]

Answer:

Step-by-step explanation:

$x + 2y + 3z = 12$

$z=\frac{12-x-2y}{3}$

Volume = $V=f(x,y) = xy(\frac{12-x-2y}{3} )$

find partial derivatives using product rule

$f_x =\frac{y}{3} (12-2x-2y)\\f_y = \frac{x}{3} (12-x-4y)$

i.e.

Using maximum for partial derivatives, we equate first partial derivative to 0.

y=0 or x+y =6

x=0 or x+4y =12

Simplify to get y =2, x = 4

thus critical points are (4,2) (6,0) (0,3)

Of these D the II derivative test gives

D<0 only for (4,2)

Hence maximum volume is when x=4, y=2, z= 4/3

Max volume is = 4(2)(4/3) = 32/3

6 0

3 years ago

What is a-2÷5a+a+2÷5a

Andrej [43]

Answer:

=2a

Step-by-step explanation:

a-2/5a and a+2/5a cancel each other out and your left with a+a aka 2a

4 0

3 years ago

Debbie found a suitcase that was originally 129 but now is on sale for 30% off. If sales tax is 8.75%, what is her final cost?

Marizza181 [45]

Step-by-step explanation:

To find the answer we first multiply 129 by 0.7 since the price descresed 30 percent. each percent is equal to 0.01.

129 * 0.7 = 90.3

Then we multiply 90.3 by 1.0875 since that is the sales tax

90.3 * 1.0875 = 98.2

so the cost is 98.2

6 0

2 years ago

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In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equat

NeTakaya

Answer:

The solution x = 229.89 ≅ 230 (since we cannot have a decimal number of sweatshirts)implies that, the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

Step-by-step explanation:

Here is the complete question

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. in the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league.

y=35x; y=-0.05(x-400)²+9,492

what does the solution of the system represent in this context?

Solution

The solution of the system is obtained when both equations are equal. That is y=35x = y=-0.05(x-400)²+9,492 .

So, 35x = -0.05(x-400)² + 9,492.

Expanding the right side, we have

35x = -0.05(x² - 800x + 160000) + 9492

35x = -0.05x² -800x × -0.05 + (-0.05) × 160000 + 9492

35x = -0.05x² +40x - 8000 + 9492

35x = -0.05x² +40x + 1492

Collecting all the terms to the left side, we have

0.05x² - 40x - 1492 + 35x = 0

0.05x² - 5x -1492 = 0

Using the quadratic formula,

$x = \frac{-(-5) +/- \sqrt{(-5)^{2} - 4 X 0.05 X - 1492} }{2X0.05} = \frac{5 +/- \sqrt{25 + 298.4} }{0.1} = \frac{5 +/- \sqrt{323.4} }{0.1}\\= \frac{5 +/- 17.983 }{0.1}\\= \frac{5 - 17.983 }{0.1} or \frac{5 + 17.983 }{0.1}\\= \frac{-12.983 }{0.1} or \frac{22.983 }{0.1}\\= -129.83 or 229.83$

We choose the positive answer x = 229.83. Since we cannot have a decimal number of sweatshirts, we approximate to the nearest whole number. So, x = 229.83 ≅ 230 sweatshirts.

The solution implies that the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

We confirm that by plugging in x = 229.83 in both equations.

y = 35x = 35(229.83) = 8044.05 ≅ 8044.1

y=-0.05(x-400)²+9,492 = y=-0.05(229.83-400)²+9,492 = y=-0.05(-170.17)²+9,492 = y=-0.05(28,957.8289)+9,492 = -1447.8914 + 9492 = 8044.11 ≅ 8044.1

3 0

3 years ago

Read 2 more answers