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2 years ago

Select all the expressions that could represent the volume of a box, which is a fourth degree polynomial in variables x and y.

Mathematics

1 answer:

guajiro [1.7K]2 years ago

7 0

Answer:

$(E) 3x^4y^4 - 3x^2y + 17xy^2 -10y$

Step-by-step explanation:

A fourth degree polynomial in variables x and y is a polynomial in which the highest power/index of x and y is 4.

We observe the options below for that which satisfies this condition.

Out of the given options,

$A. 3x^2y^2 + 6x^2 -7xy - 14x\\B. 10xy + 12x + 2xy^2 -y^2 - 5y - 6\\C. -6 + 7xy + 9x^2 + 2x^3y\\D. 2x^3y + 5x^2y - xy -6y\\E. 3x^4y^4 - 3x^2y + 17xy^2 -10y$

The expression that could represent the volume of a box is

$3x^4y^4 - 3x^2y + 17xy^2 -10y$

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mars1129 [50]

Answer:

Follows are the solution to this question:

Step-by-step explanation:

Following are the step which is used in the question:

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2 years ago

Read the passage.

alexandr1967 [171]

Answer:

D sentence 5

Step-by-step explanation:

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2 years ago

A box is in the shape of a rectangular prism. Nicole is trying to ship boxes of her homemade peanut butter cookies. The box she

Katyanochek1 [597]

So L = x-4, W = x-4, H = x

Volume = length * width * height

V = L * W * H

V = (x-4)*(x-4)*x

V = ???

x is the height, so x-4 is the length and also the width since length and a width of 4in. less than the height

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2 years ago

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Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to

nikklg [1K]

Answer:

Part 1)

See Below.

Part 2)

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

Step-by-step explanation:

Part 1)

The linear approximation L for a function f at the point x = a is given by:

$\displaystyle L \approx f'(a)(x-a) + f(a)$

We want to verify that the expression:

$1-36x$

Is the linear approximation for the function:

$\displaystyle f(x) = \frac{1}{(1+9x)^4}$

At x = 0.

So, find f'(x). We can use the chain rule:

$\displaystyle f'(x) = -4(1+9x)^{-4-1}\cdot (9)$

Simplify. Hence:

$\displaystyle f'(x) = -\frac{36}{(1+9x)^{5}}$

Then the slope of the linear approximation at x = 0 will be:

$\displaystyle f'(1) = -\frac{36}{(1+9(0))^5} = -36$

And the value of the function at x = 0 is:

$\displaystyle f(0) = \frac{1}{(1+9(0))^4} = 1$

Thus, the linear approximation will be:

$\displaystyle L = (-36)(x-(0)) + 1 = 1 - 36x$

Hence verified.

Part B)

We want to determine the values of x for which the linear approximation L is accurate to within 0.1.

In other words:

$\displaystyle \left| f(x) - L(x) \right | \leq 0.1$

By definition:

$\displaystyle -0.1\leq f(x) - L(x) \leq 0.1$

Therefore:

$\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1$

We can solve this by using a graphing calculator. Please refer to the graph shown below.

We can see that the inequality is true (i.e. the graph is between y = 0.1 and y = -0.1) for x values between -0.179 and -0.178 as well as -0.010 and 0.012.

In interval notation:

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

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2 years ago

Billy buys light bulbs in packs of 8 for $20. The shipping cost is $10 regardless of the number of packs bought. Billy has only

kirill115 [55]

Answer:

Step-by-step explanation:

He can buy 5 boxes of light bulbs..

20 x 5= 100

He only has 120 to spend - the shipping = 110

He can't get another box of lightbulbs. Therefor he can only buy 5!

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2 years ago

Read 2 more answers