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Angelina_Jolie [31]

2 years ago

11

Let abcd be a square piece of paper. A is folded into c and the b is folded into d. the area of the resulting figure is 9 square

inches. Find the perimeter of square ABCD
A.9
B.16
C.18
D.24
E.36

1 answer:

neonofarm [45]2 years ago

4 0

9 is the correct answer

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Luden [163]

Cone details:

height: h cm

radius: r cm

Sphere details:

radius: 10 cm

================

From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.

<u>Using Pythagoras Theorem</u>

(a)

TO² + TU² = OU²

(h-10)² + r² = 10² [insert values]

r² = 10² - (h-10)² [change sides]

r² = 100 - (h² -20h + 100) [expand]

r² = 100 - h² + 20h -100 [simplify]

r² = 20h - h² [shown]

r = √20h - h² ["r" in terms of "h"]

(b)

volume of cone = 1/3 * π * r² * h

===========================

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (\sqrt{20h - h^2})^2 \ ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20h - h^2) (h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20 - h) (h) ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} \pi h^2(20-h)$

To find maximum/minimum, we have to find first derivative.

(c)

<u>First derivative</u>

$\Longrightarrow \sf V' =\dfrac{d}{dx} ( \dfrac{1}{3} \pi h^2(20-h) )$

<u>apply chain rule</u>

$\sf \Longrightarrow V'=\dfrac{\pi \left(40h-3h^2\right)}{3}$

<u>Equate the first derivative to zero, that is V'(x) = 0</u>

$\Longrightarrow \sf \dfrac{\pi \left(40h-3h^2\right)}{3}=0$

$\Longrightarrow \sf 40h-3h^2=0$

$\Longrightarrow \sf h(40-3h)=0$

$\Longrightarrow \sf h=0, \ 40-3h=0$

$\Longrightarrow \sf h=0,\:h=\dfrac{40}{3}$ <u />

<u>maximum volume:</u> <u>when h = 40/3</u>

$\sf \Longrightarrow max= \dfrac{1}{3} \pi (\dfrac{40}{3} )^2(20-\dfrac{40}{3} )$

$\sf \Longrightarrow maximum= 1241.123 \ cm^3$

<u>minimum volume:</u> <u>when h = 0</u>

$\sf \Longrightarrow min= \dfrac{1}{3} \pi (0)^2(20-0)$

$\sf \Longrightarrow minimum=0 \ cm^3$

6 0

1 year ago

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A limited-edition soccer ball costs $30, and the sales tax is 6%. What is the total cost?

frez [133]

Answer:

$31.80

Step-by-step explanation:

The ball will cost 100% of its price plus 6% of its price for a total of 106%.

To use percentages as a factor and multiply, they must be divide by 100, making the multiplication factor version of 106% 1.06.

Multiply the cost of the ball by your multiplication factor:

30 x 1.06 = 31.8

Money is written to two decimal places, making your answer $31.80

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2 years ago

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Which degree of rotation is equivalent to a 90 degree clockwise rotation?

vodomira [7]

The answer will be A....

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2 years ago

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vredina [299]

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2 years ago

13 is the square root of what number

Firlakuza [10]

Answer:

169

Step-by-step explanation:

Square root means what number times its self is a different number. In this case, 13 times 13 = 169 so 13 times itself is 169.

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2 years ago