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3 years ago

Explain how to find the coordinates of the focus of a parabola with vertex (0,0) and the directrix y=5

Mathematics

1 answer:

Ghella [55]3 years ago

7 0

Keep in mind that, the directrix is "p" distance units away from the vertex, and the focus point is also "p" distance units from the vertex but in the opposite direction, so in short the vertex is half-way between both of them.

in this case the vertex is at the origin, and the directrix 5 units above it, so that means the parabola is vertical and opening downwards, like the one in the picture below, and the focus point is 5 units the other way.

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In 2018, the population will grow over 700,000.The population of a city in 2010 was 450,000 and was growing at a rate of 5% per

Firlakuza [10]

Answer:

The year is 2020.

Step-by-step explanation:

Let the number of years passed since 2010 to reach population more than 7000000 be 'x'.

Given:

Initial population is, $P_0=450,000$

Growth rate is, $r=5\%=0.05$

Final population is, $P=700,000$

A population growth is an exponential growth and is modeled by the following function:

$P=P_0(1+r)^x$

Taking log on both sides, we get:

$\log(P)=\log(P_0(1+r)^x)\\\log P=\log P_0+x\log (1+r)\\x\log (1+r)=\log P-\log P_0\\x\log(1+r)=\log(\frac{P}{P_0})\\x=\frac{\log(\frac{P}{P_0})}{\log(1+r)}$

Plug in all the given values and solve for 'x'.

$x=\frac{\log(\frac{700,000}{450,000})}{\log(1+0.05)}\\x=\frac{0.192}{0.021}=9.13\approx 10$

So, for $x > 9.13$ , the population is over 700,000. Therefore, from the tenth year after 2010, the population will be over 700,000.

Therefore, the tenth year after 2010 is 2020.

8 0

3 years ago

How is a topic different from a theme?

jek_recluse [69]

Hi!

A topic is just a general thing you discuss, with no true moral ending you take away from it. A theme, on the other hand, wants to communicate a life lesson.

Hopefully, this helps! =)

8 0

3 years ago

Read 2 more answers

The product of w and 2 is greater than or equal to 19.

madam [21]

Equation Form:

w x 2 $\geq$ 19

Divide both sides by 2:

w $\geq$ 9.5

So, w must be equal to or greater than 9.5 for this equation to work.

5 0

2 years ago

Pleaseeeeee help me pleasee

Nikitich [7]

Lol I just needed help with this kinda stuff...

I’m not very caught up with this stuff I feel your pain I’m very sorry if I’m wrong =/

10?

6 0

3 years ago

Who knows this, Find m∠UTS, if m∠UTV=x+15, m∠VTS=140∘, and m∠UTS=15x+15

kakasveta [241]

Answer:

165

Step-by-step explanation:

First, m<UTS=m<UTV+m<VTS by Angle Addition Postulate. Then, you substitute all the values that you provided for the angles. 15x+15=x+15+140. You then solve for x.

15x+15=x+155

14x=140

x=10

You then plug back in 10 for X in the value of m<UTS. 15(10)+15=165

5 0

4 years ago