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2 years ago

5

What is the sum of ¾ + ⅔ in simplist form

2 answers:

natali 33 [55]2 years ago

7 0

Answer:

The answer is 17/12

Step-by-step explanation:

3/4 + 2/3

= 9/12 + 8/12

= 9 + 8/12

= 17/12

r-ruslan [8.4K]2 years ago

7 0

We must find the common denominator.

The list of multiples of 4: 0, 4, 8, 12, 16, 20, ...

The list of multiples of 3: 0, 3, 6, 9, 12, 15, 18, ...

The common denominator is 12.

$\dfrac{3}{4}=\dfrac{3\cdot3}{4\cdot3}=\dfrac{9}{12}\\\\\dfrac{2}{3}=\dfrac{2\cdot4}{3\cdot4}=\dfrac{8}{12}$

Therefore:

$\dfrac{3}{4}+\dfrac{2}{3}=\dfrac{9}{12}+\dfrac{8}{12}=\dfrac{9+8}{12}=\dfrac{17}{12}=\dfrac{12+5}{12}=1\dfrac{5}{12}$

<h3>Answer: 17/12 = 1 5/12</h3>

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Identify the question that is NOT statistical.

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2 years ago

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>

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

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

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1 year ago

Read 2 more answers

15 arches decreased by 80%

morpeh [17]

If it decreases by 80٪, then only 20٪ remains.

15×20٪=15×20/100=15×0.2=3

Answer: 3

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3 years ago

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