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3 years ago

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Mathematics

1 answer:

sweet-ann [11.9K]3 years ago

6 0

Answer:

A = 81π cm²

Step-by-step explanation:

The area (A) of the cross section is calculated as

A = πr² ( r is the radius )

Find r by using the given circumference.

Given the circumference is 18π and circumference (C) is

C = 2πr = 18π ( divide both sides by 2π )

r = 9, thus

A = π × 9² = 81π cm²

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Let v1=(3,5) and v2=(-4,7) Compute the unit vectors in the direction of |v1| and |v2|?

AleksandrR [38]

By definition, the unit vector of v = (a,b) is
$\hat{v} = \frac{\vec{v}}{|v|}$

Therefore,
The unit vector of v₁ = (3,5) in the direction of |v₁| s
(3,5)/√[3² + 5²]
= (3,5)/√34

The unit vector of v₂ in the direction of |v₂| is
(-4,7)/√[(-4)² + 7²]
= (-4,7)/√65

Answer:
The unit vector of v₁ in the direction of |v₁} is $( \frac{3}{\sqrt{34}} , \frac{5}{\sqrt{34}} )$
The unit vector of v₂ in the directin of |v₂| is
$( \frac{-4}{\sqrt{65}} , \frac{7}{\sqrt{65}} )$

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3 years ago

Use inductive reasoning to describe the pattern. then find the next two numbers in the pattern. –3, 9, –27, 81, . . .

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Tmes -3 each times so next 2 numbers are -243 then 729

6 0

3 years ago

Read 2 more answers

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g100num [7]

Rudy answered 2 more questions correctly
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7 0

3 years ago

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

What is the perimeter of a rectangle with length x+4 and a width of 5x-7

AlladinOne [14]

Answer:

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Step-by-step explanation:

perimeter= 2l+2w

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8 0

3 years ago