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2 years ago

If A is the midpoint of line segment LH and B is the midpoint of line segment LJ, then what is AH? 20,9,11,33?

Mathematics

1 answer:

Effectus [21]2 years ago

5 0

Answer:

Answer is 33. Got it right in my quiz

Step-by-step explanation:

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A cube made a silver has a density of 10,490 kg/m^3. If one of the sides were doubled without changing the mass of silver, how w

Sindrei [870]

Answer:

D- It would quadruple

Step-by-step explanation:

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3 years ago

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

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Alicia estimates that the surface area of a rectangular prism with a length of 11 meters,a width of 5.6 meters,and a height of 7

Veseljchak [2.6K]

Let's calculate the actual area: it is 11*5.6*7.2 or 443.52 cubic meters. Is the 100+ cubic meters error reasonable? :)

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2 years ago

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Question 6: please help me out here :(((

Murljashka [212]

Answer:

m∠1 = 106

Step-by-step explanation:

Given: m∠5 = 106

Vertical angles are congruent

The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent.

Therefore: m∠1 = 106

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2 years ago

Marina correctly simplified the expression (-4a^-2 b^4)/(8a^-6b^-3) assuming that a does not equal 0 and b does not equal 0. Her

Elza [17]

For this case we have the following expression:
(-4a ^ -2 b ^ 4) / (8a ^ -6b ^ -3)
We can rewrite the expression using properties of exponents.
We have then:
(-4/8) * ((a ^ (- 2 - (- 6))) (b ^ (4 - (- 3))))
Rewriting we have:
(-2/4) * ((a ^ (- 2 + 6)) (b ^ (4 + 3)))
(-1/2) * ((a ^ 4) (b ^ 7))
-1 / 2a ^ 4b ^ 7
Answer:
The exponent of the variable b in Marina's solution should be 7

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3 years ago

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