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3 years ago

Which is the equation of the axis of symmetry of the graph of y=-3(x-6)^2+5

Mathematics

2 answers:

SVEN [57.7K]3 years ago

8 0

Answer:

axis of symmetry at x=6

Step-by-step explanation:

$y=-3(x-6)^2+5$

The given equation is in vertex form $y=a(x-h)^2+k$

(h,k) is the vertex

Compare the vertex form of the equation with the given equation.

$y=-3(x-6)^2+5$

The value of h = 6 and the value of k = 5

So vertex is (6,5)

Axis of symmetry lies at the x coordinate of the vertex

x coordinate of the vertex is 6

So axis of symmetry at x=6

enot [183]3 years ago

3 0

X=6 is the answer. good luck

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Which answer choice identifies the relevant information in the problem? Sarah left the house at 12:15 p.M. To go to the store. S

77julia77 [94]

Answer:

Answer choices A, B and C identifies the relevant information in the problem

Step-by-step explanation:

Sarah left the house at 12:15 pm

She spent $42.20 on two books for her children

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Sarah arrived home at 1:00 pm

How much did Sarah spent on each book?

If she spent $42.20 on two books for her children,

Then, it means she has two children and the book cost $21.10 each

Answer choices A, B and C identifies the relevant information in the problem

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3 years ago

A rectangular prism has a length of 6 meters, a height of 8 meters, and a width of 5

kati45 [8]

Heyo just a freshman answering your question. To find the volume of a rectangular prism is by using its volume formula, vol=length*width*height. Your answer is 240 meter^3

6 0

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

Read 2 more answers

Mary has walked 8 km, which is 55% of the total distance she will walk. How much farther

Viefleur [7K]

To find the total distance, Divide distance already walked by percentage:

8 / 0.55 = 14.55 km

She already walked 8 so now subtract:

14.55 - 8 = 6.55 km left to walk

3 0

3 years ago

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Arisa [49]

Answer:

8√21

Step-by-step explanation:

A rectangle has 2 congruent pairs. Those 2 pairs are ST/RU and SR/UT. If that is the case, then that means UV is 5 and SV is also 5. Now we have triangle SRU with a hypotenuse of 10 and a side of 4. Pythagorean Theorem:

4² + b² = 10²

b² = 84

b = 2√21

Segment SR is then equal to b. Now we move on to the area formula:

(2√21)(4) = 8√21

And that is your final answer.

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3 years ago

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