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3 years ago

What is a polynomial function in standard form with the zeros 1,2,-2 and -3

Mathematics

1 answer:

sweet [91]3 years ago

6 0

Answer:

x^4 + 2x^3 - 7x^2 - 8x + 12.

Step-by-step explanation:

In factor form this is (x - 1)(x - 2)(x + 2)(x+ 3)

= (x^2 - 3x + 2)(x^2 + 5x + 6)

= x^4 + 5x^3 + 6x^2 - 3x^3 - 15x^2 - 18x + 2x^2 + 10x + 12

= x^4 + 2x^3 - 7x^2 - 8x + 12.

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The volume of a rectangular box with a square base remains constant at 500 cm3 as the area of the base increases at a rate of 10

serious [3.7K]

Answer:

The rate of change of the height of the box at which is decreasing is $\frac{5000}{130321}$ centimeters per second.

Step-by-step explanation:

From Geometry the volume of a rectangular box ( $V$ ), measured in cubic centimeters, with a square base is modelled by the following formula:

$V = A_{b}\cdot h$ (Eq. 1)

Where:

$A_{b}$ - Area of the base, measured in square centimeters.

$h$ - Height of the box, measured in centimeters.

The height of the box is cleared within the formula:

$h = \frac{V}{A_{b}}$

If we know that $V = 500\,cm^{3}$ and $A_{b} = 361\,cm^{2}$ , then the current height of the box is:

$h = \frac{500\,cm^{3}}{361\,cm^{2}}$

$h = \frac{500}{361}\,cm$

The rate of change of volume in time ( $\frac{dV}{dt}$ ), measured in cubic centimeters per second, is derived from (Eq. 1):

$\frac{dV}{dt} = \frac{dA_{b}}{dt}\cdot h + A_{b}\cdot \frac{dh}{dt}$ (Eq. 2)

Where:

$\frac{dA_{b}}{dt}$ - Rate of change of the area of the base in time, measured in square centimeters per second.

$\frac{dh}{dt}$ - Rate of change of height in time, measured in centimeters per second.

If we get that $\frac{dV}{dt} = 0\,\frac{cm^{3}}{s}$ , $\frac{dA_{s}}{dt} = 10\,\frac{cm^{2}}{s}$ , $h = \frac{500}{361}\,cm$ and $A_{b} = 361\,cm^{2}$ , then the equation above is reduced into this form:

$0\,\frac{cm^{3}}{s} = \left(10\,\frac{cm^{2}}{s} \right)\cdot \left(\frac{500}{361}\,cm \right)+(361\,cm^{2})\cdot \frac{dh}{dt}$

Then, the rate of change of the height of the box at which is decreasing is:

$\frac{dh}{dt} = -\frac{5000}{130321}\,\frac{cm}{s}$

The rate of change of the height of the box at which is decreasing is $\frac{5000}{130321}$ centimeters per second.

5 0

3 years ago

Convert 48 °F to degrees Celsius. Round to nearest tenth.

KIM [24]

8.889 degrees celsius

5 0

4 years ago

Read 2 more answers

At the end of the summer a store marks down the outdoor furniture 8% a family bought 4 chairs in June at 35$ each then 2 more ch

frosja888 [35]

Answer:

$204.4

Step-by-step explanation:

The four chairs bought in June cost $35 each, all together $140. Then they bought 2 more chairs on sale for 8% off of $35 each or 92% of $35 which is $32.2 each, all together $64.4. Both buy's together would then equal $204.4

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3 years ago

Your parents are redecorating the dining room and want to place two rectangular pictures, each measuring 25 inches

Nostrana [21]

Answer:

There isnt a question in that

Step-by-step explanation:

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3 years ago

Complete the square of x^2+16x=1

Rus_ich [418]

The answer is approximately .062 and -16.06