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3 years ago

The total surface area of a cylinder is 690.8. Its diameter is 10 inches. What is it’s height?

Mathematics

1 answer:

AysviL [449]3 years ago

7 0

Answer:

$h=17\ in$

Step-by-step explanation:

we know that

The total surface area of a cylinder is equal to

$SA=2\pi r^{2}+2\pi rh$

where

r is the radius of the base of cylinder

h is the height of cylinder

we have

$SA=690.8\ in^2$

$r=10/2=5\ in$ ----> the radius is half the diameter

assume

$\pi=3.14$

substitute the given values and solve for h

$690.8=2(3.14)(5^{2})+2(3.14)(5)h$

$690.8=157+31.4h$

Solve for h

$31.4h=690.8-157$

$31.4h=533.8$

$h=17\ in$

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Find the vertex of the graph of the function.

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Explanation:

Te standard form of the parabola is,

$f(x)=a(x-h)^2+k$ .....(1)

Where, (h,k) is the vertex of the parabola.

(1)

The given equation is,

$f(x)=(x-5)^2+10$

Comparing this equation with equation (1),we get,

$h=5$ and $k=10$

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

$f(x)=3x^2-18x+24$

$f(x)=3(x^2-6x)+24$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $9$ . Since there is factor 3 outside the parentheses, so subtract three times of 9.

$f(x)=3(x^2-6x+9)+24-3\times 9$

$f(x)=3(x-3)^2-3$

Comparing this equation with equation (1),we get,

$h=3$ and $k=-3$

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

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The given equation is

$f(x)=4x^2+8x+7$

$f(x)=4(x^2+2x)+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $1$ . Since there is factor 4 outside the parentheses, so subtract three times of 1.

$f(x)=4(x^2+2x+1)+7-4$

$f(x)=4(x+1)^2+3$

Comparing this equation with equation (1),we get,

$h=-1$ and $k=3$

The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.

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The given equation is,

$y=x^2+4x+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $2^2$ .

$f(x)=x^2+4x+4+7-4$

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The given equation is,

$h=-16t^2+672t$

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$h=-16(t^2-42t)$

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3 years ago

7. a hockey arena has 10 920 seats. the first row of seats around the rink has 220 seats. the number of seats in each subsequent

Mazyrski [523]

The number of rows in the arena is 26

<h3>How to determine the number of rows?</h3>

The hockey arena illustrates an arithmetic sequence, and it has the following parameters:

First term, a = 220
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Common difference, d = 16

The number of rows (i.e. the number of terms) is calculated using:

$S_n = \frac{n}{2}(2a + (n -1) * d)$

So,we have:

$10920 = \frac{n}{2}(2 * 220 + (n -1) * 16)$

Evaluate the terms and factors

$21840 = n(440 + 16n -16)$

Evaluate the like terms

21840 = n(424+ 16n)

Expand

21840 = 424n + 16n^2

Rewrite as:

16n^2 + 424n - 21840 = 0

Using a graphical tool, we have:

n = 26

Hence, the number of rows in the arena is 26

Read more about arithmetic sequence at:

brainly.com/question/6561461

#SPJ1

4 0

2 years ago