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2 years ago

Find the area of an octagon with a radius of 11 units. Round your answer to the nearest hundredth. NO LINKS

Mathematics

1 answer:

xeze [42]2 years ago

8 0

Answer:

342.24 units²

Step-by-step explanation:

The area of one of the 8 triangular sections of the octagon is ...

A = (1/2)r²·sin(θ) . . . . . where θ is the central angle of the section

The area of the octagon is 8 times that, so is ...

A = 8·(1/2)·11²·sin(360°/8) = 242√2

A ≈ 342.24 units²

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Jake tutors students. He charges $10 for the first session and $5 for each additional session. Let x

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Answer: y = 5x + 10

Step-by-step explanation:

y= 5x + 10

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Find all real zeros of t<br>f(x)=x-14x² + 47x-18

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Answer:

x=3/7 and x= 3

Step-by-step explanation:

First simplify:

-14 x^2 +48x -18

divide everything by -2

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-2 (x^2 -24x +63)

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-2 [(x-3/7)(x-21/7)]

-2 [(7x-3)(x-3)]

Hence, the zeroes are 3/7 and 3

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2 years ago

Can anyone help me I was self isolating when my class was taught this and I can't get in contact with my teacher

Aleonysh [2.5K]

Answer:

Step-by-step explanation:

3x +2y = 13 -----------------(i)

x + 2y = 7 ----------------(ii)

Multiply the equation (ii) by (-1) and then add.

(i) 3x + 2y = 13

(ii)*(-1) <u>-x - 2y = -7 </u> {Now, add and y will be eliminated}

2x = 6

x = 6/2

x = 3

Plug in x = 3 in equation (i)

3*3 + 2y = 13

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3 years ago

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You have been asked to design a can shaped like right circular cylinder that can hold a volume of 432π-cm3. What dimensions of t

rosijanka [135]

Answer:

$Height = 12cm$

$Radius = 6cm$

Step-by-step explanation:

Given

Represent volume with v, height with h and radius with r

$V = 432\pi$

Required

Determine the values of h and r that uses the least amount of material

Volume is calculated as:

$V = \pi r^2h\\$

Substitute 432π for V

$432\pi = \pi r^2h$

Divide through by π

$432 = r^2h$

Make h the subject:

$h = \frac{432}{r^2}$

Surface Area (A) of a cylinder is calculated as thus:

$A=2\pi rh+2\pi r^2$

Substitute $\frac{432}{r^2}$ for h in $A=2\pi rh+2\pi r^2$

$A=2\pi r(\frac{432}{r^2})+2\pi r^2$

$A=2\pi (\frac{432}{r})+2\pi r^2$

Factorize:

$A=2\pi (\frac{432}{r} + r^2)$

To minimize, we have to differentiate both sides and set $A' = 0$

$A'=2\pi (-\frac{432}{r^2} + 2r)$

Set $A' = 0$

$0=2\pi (-\frac{432}{r^2} + 2r)$

Divide through by $2\pi$

$0= -\frac{432}{r^2} + 2r$

$\frac{432}{r^2} = 2r$

Cross Multiply

$2r * r^2 = 432$

$2r^3 = 432$

Divide through by 2

$r^3 = 216$

Take cube roots of both sides

$r = \sqrt[3]{216}$

$r = 6$

Recall that:

$h = \frac{432}{r^2}$

$h = \frac{432}{6^2}$

$h = \frac{432}{36}$

$h = 12$

Hence, the dimension that requires the least amount of material is when

$Height = 12cm$

$Radius = 6cm$

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2 years ago