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3 years ago

The coefficient of xy in the product of (4x^2+2y) and (3x+y^2) is ...

Mathematics

1 answer:

LUCKY_DIMON [66]3 years ago

3 0

Here is your answer! The coefficient of xy is 6. To solve this problem, you need to multiply your two polynomials together. I used the FOIL Method- multiply the First two, the Outside two, the Inside two, and the Last two. You can see how I did it on the picture attached. Next, the answer that you get as a result from FOILing is your polynomial. If you look at the number before xy, that is the coefficient. A coefficient is a number that is right before and attached to a variable. I hope this helps you! :))

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I'm have some issues with the problem shown in the screenshot and would love some help.

KiRa [710]

The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;

Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.

Maximum volume of the box is approximately 1048.6 in.³

<h3>How can the dimensions and volume of the box be calculated?</h3>

The given dimensions of the cardboard are;

Width = 18 inches

Length = 35 inches

Let x represent the side lengths of the cut squares, we have;

Width of the box formed = 18 - 2•x

Length of the box = 35 - 2•x

Height of the box = x

Volume, V, of the box is therefore;

V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x

By differentiation, at the extreme locations, we have;

$\frac{d V }{dx} = \frac{d( 4 \cdot \: {x}^{3} - 106 \cdot \: {x}^{2} + 630\cdot \: {x} ) }{dx} = 0$

Which gives;

$\frac{d V }{dx} =12\cdot \: {x}^{2} - 212\cdot \: {x} + 630 = 0$

6•x² - 106•x + 315 = 0

$x = \frac{ - 6 \pm \sqrt{106 ^2 - 4 \times 6 \times 315} }{2 \times 6}$

Therefore;

x ≈ 4.55, or x ≈ -5.55

When x ≈ 4.55, we have;

V = 4•x³ - 106•x² + 630•x

Which gives;

V ≈ 1048.6

When x ≈ -5.55, we have;

V ≈ -7450.8

The dimensions of the box that gives the maximum volume are therefore;

Width ≈ 18 - 2×4.55 in. = 8.89 in.

Length of the box ≈ 35 - 2×4.55 in. = 24.89 in.

Height = x ≈ 4.55 in.

The maximum volume of the box, V ≈ 1048.6 in.³

Learn more about differentiation and integration here:

brainly.com/question/13058734

#SPJ1

7 0

1 year ago

ASAP 7x+42=0 Options x= 6 X= -6

lutik1710 [3]

The answer is 6x. You divide 42 by 7. Take out the x. 42 divided by 7 will equal 6.

6 0

2 years ago

A circle is defined by the equation x2 + y2 + 8x + 22y + 37 = 0. What are the coordinates for the center of the circle and the l

inn [45]

We can say that:
8x = -2ax
8 = -2a
a = -4

22y = - 2by
22 = -2b
b = -11

37 = a² + b² - r²
37 = (-4)² + (-11)² - r²
r² = 16 + 121 - 37
r² = 100
r = 10

With all this information, we can say that:
The center of the circle is: (-4 ; -11)
and the radius of the circle is r = 10

P.S:
(a - x)² + (b-y)² = r²
a² - 2ax + x² + b² -2by + y² - r² = 0
x² + y² -2ax - 2by + a² + b² - r² = 0

6 0

3 years ago

There are 4 students on a team for relay race. How many teams can be made from 27 students.

german

There will be 7 teams made.

8 0

2 years ago

Trisha and Byron are washing and vacuuming cars to raise money for a class trip. Trisha raised $38 washington 5 cars and vacuumi

ANEK [815]

Answer:

They charged $6 for washing and $2 for vacuuming the car.

Step-by-step explanation: