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4 years ago

32. Factor the following Quadratic: x2 + 4x - 12

Mathematics

1 answer:

Juliette [100K]4 years ago

3 0

Answer:

(x-2)(x+6)

Step-by-step explanation:

Use the method ac sum of b

Ac is -12

b is 4

find factors that multiply to -12 and add to -4

put x in front of the two factors so that you get the answer specified

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Hello people ~

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.

Using Pythagoras Theorem

(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)

First derivative

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

apply chain rule

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

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

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

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

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

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

$\Longrightarrow \sf h=0,\:h=\dfrac{40}{3}$

maximum volume: when h = 40/3

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

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

minimum volume: when h = 0

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

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

6 0

2 years ago

Read 2 more answers

If you raise 4 to the 214th power, what is the units digit of the result

Len [333]

$\begin{array}{lrlll}
4^1&\boxed{4}\\
4^2&1\boxed{6}\\
4^3&6\boxed{4}\\
4^4&25\boxed{6}\\
4^5&102\boxed{4}\\
4^6&409\boxed{6}
\end{array}\impliedby \textit{see the pattern for 4?}$

notice, it goes 4,6 then 4, 6 again, and so on and so on
based on whatever exponent it may have

now, you're being asked, what 214 will give? 4 or 6?

4 0

3 years ago

What is the value of x

9966 [12]

ANSWER

x=27

EXPLANATION

The two triangles are similar so the corresponding sides are equal.

$\frac{x}{x +1 8} = \frac{39}{39 + 26}$

$\frac{x}{x +1 8} = \frac{39}{65}$

Cross multiply to get;

$65x = 39(x + 18)$

Expand:

65x=39x+702

Group similar terms:

65x-39x=702

Simplify

26x=102

Divide both sides by 26,

x=702/26

x=27

3 0

3 years ago

I need this ctugkvhjkibnlbk;vhiglcufxoryifcuglvihk;b j;hviglucforxiy6eryfcuglvhk

Orlov [11]

Answer:

11(7 + 4) = 11 × 7 + 11 × 4

Step-by-step explanation:

11(7 + 4) = _ x 7 + 11 x _

use distributive property:

11(7 + 4) = 7 x 11 + 7 x 11

3 0

3 years ago

Read 2 more answers

What is a good way find the answer to this?

Natali5045456 [20]

What were you watching there on the tv? My little pony? Adventure time?

7 0

3 years ago