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3 years ago

Pls check the attachment :) f(x)=x^5-9x^3

Mathematics

1 answer:

Galina-37 [17]3 years ago

5 0

Answer:

As x —> negative infinity, f(x) —> negative infinity

As x —> positive infinity, f(x) —> positive infinity.

Step-by-step explanation:

$y = {x}^{5} - 9 {x}^{3}$

An odd-degree function, meaning that the graph starts from negative infinity at x —> negative infinity and positive infinity at x —> positive infinity.

As x —> negative infinity, f(x) —> negative infinity

As x —> positive infinity, f(x) —> positive infinity.

An odd-degree function is an one-to-one function so whenever x approaches positive, f(x) will also approach positive.

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A parabola can be drawn given a focus of

Volgvan

Answer:

$y=-\frac{1}{4}(x-2)^{2}+9$

Step-by-step explanation:

Any point on a given parabola is equidistant from focus and directrix.

Given:

Focus of the parabola is at $(2,8)$ .

Directrix of the parabola is $y=10$ .

Let $(x,y)$ be any point on the parabola. Then, from the definition of a parabola,

Distance of $(x,y)$ from focus = Distance of $(x,y)$ from directrix.

Therefore,

$\sqrt{(x-2)^{2}+(y-8)^{2}}=|y-10|$

Squaring both sides, we get

$(x-2)^{2}+(y-8)^{2}=(y-10)^{2}\\(x-2)^{2}=(y-10)^{2}-(y-8)^{2}\\(x-2)^{2}=(y-10+y-8)(y-10-(y-8))...............[\because a^{2}-b^{2}=(a+b)(a-b)]\\(x-2)^{2}=(2y-18)(y-10-y+8)\\(x-2)^{2}=2(y-9)(-2)\\(x-2)^{2}=-4(y-9)\\y-9=-\frac{1}{4}(x-2)^{2}\\y=-\frac{1}{4}(x-2)^{2}+9$

Hence, the equation of the parabola is $y=-\frac{1}{4}(x-2)^{2}+9$ .

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3 years ago

A desk drawer is shaped like a rectangular prism. The height of the drawer is 7 inches. The bottom of the drawer has an area of

Bas_tet [7]

Answer:

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Step-by-step explanation:

Vol=length × width × height

But ALSO,

length × width = Area,

So we find another Volume equation,

Vol = BaseArea × height

This is the information you are given in the question.

Vol = 210 × 7

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A home-made baseball diamond is in the shape of a square. The distance from base to base is 80 feet because of space constraints

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3 years ago

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murzikaleks [220]

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3 years ago

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Answer:

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Step-by-step explanation:

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Pls check the attachment :) f(x)=x^5-9x^3​

Pls check the attachment :) f(x)=x^5-9x^3