What is the quotient when 2x^3-1 is divided by x - 1?

Mathematics

1 answer:

andrey2020 [161]2 years ago

4 0

Answer:

Step-by-step explanation:

Use synthetic division:

The coefficients of 2x^3 - 1 are {2, 0, 0, -1}. Setting up synthetic division, we get:

1 / 2 0 0 -1

2 2 2

---------------------------

2 2 2 1

Note that the remainder is 1. The same result would be obtained through long division.

The quotient is 2x^2 + 2x + 2 with a remainder of 1.

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The length of a rectangle is 7 ft longer than twice the width. If the perimeter is 92 ft find the length and width of the rectan

user100 [1]

Width of the rectangle is 13 ft and length of the rectangle is 33 ft

<u>Step-by-step explanation:</u>

Step 1:

Given perimeter of the rectangle = 92 ft. Let the width be x, then the length of the rectangle = 2x + 7. Use the formula for perimeter of a rectangle = 2(length + width) to find the dimensions.

92 = 2(2x + 7 + x) = 2(3x + 7) = 6x + 14

⇒ 92 = 6x + 14

⇒ 78 = 6x

⇒ x = 78/6

∴ x = 13 ft

⇒ Width of the rectangle = 13 ft

∴ Length of the rectangle = 2x + 7 = 26 + 7 = 33 ft

4 0

3 years ago

Suppose a tub has the shape of an elliptical paraboloid given by z = ax2+by2 (where a, b are some positive constants). If a marb

Umnica [9.8K]

Answer:

It would roll in this direction.

$\nu = (-a/\sqrt{a^2+b^2},-b/\sqrt{a^2+b^2})$

Step-by-step explanation:

It would roll to the direction of maximum decrease, which is the -1 times the direction of maximum increase, which is given by the gradient of the function.

Since

$z = ax^2 + by^2$