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2 years ago

Write an equation of a parabola with a vertex at the origin and the given focus 10. Focus at (-1,0)

Mathematics

1 answer:

Nostrana [21]2 years ago

3 0

Step-by-step explanation:

focus(p) is on the x axis= -1

vertex=(0,0)

parabola equation----- (y-h)^2 =4p(x-k)

(h, k)=(0,0)

(y-0)^2 =4(-1)(x-0)

y^2 = -4x

that is the answer

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Please help, due tonight.

VashaNatasha [74]

A. slope intercept form is y=mx+b where m is your slope and b is your y-intercept. Since it gives you the slope (4) and the y-intercept (-9) all you have to do is plug it into the equation to get y=4x-9

b. This one is a little bit trickier but by no means impossible. the first thing we want to do is find the slope, and in order to do this we take the second y minus the first and divide it by the difference of the second x and the first x. the way that would look in this case is (10-6)/(4-0) and when we simplify this we get 4/4=1
Since our slope is 1, we just need to find the value of y when x=0, In this problem it is given to us with the point (0,6) if we plug both of this into our equation we get y=x+6 (the 1 in front of the x is optional

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3 years ago

Let f(x) = x2 − 81. Find f−1(x).

Umnica [9.8K]

F(x) = x² - 81

Finding f⁻¹(x) the inverse function

Let y = f(x) and solve for x.

y = x² - 81

y + 81 = x²

x² = y + 81

x = √(y + 81)

Recall f(x) = y, that means x = f⁻¹(y)

x = √(y + 81)

f⁻¹(y) = √(y + 81)

Therefore f⁻¹(x) = √(x + 81)

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3 years ago

A county is considering rasing the speed limit on a road because they claim that the mean speed of vehicles is greater than 30 m

DochEvi [55]

Answer:

No, at alpha equals 0.10, we do not have enough evidence to support the county's claim.

Step-by-step explanation:

We are given that a county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 30 miles per hour.

A random sample of 15 vehicles has a mean speed of 31 miles per hour and a standard deviation of 4.7 miles per hour.

Let $\mu$ = true mean speed of the vehicles.

SO, Null Hypothesis, $H_0$ : $\mu \leq$ 30 miles per hour {means that the mean speed of vehicles is lesser than or equal to 30 miles per hour}

Alternate Hypothesis, $H_A$ : $\mu$ > 30 miles per hour {means that the mean speed of vehicles is greater than 30 miles per hour}

The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;

T.S. = $\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean speed of 15 vehicles = 31 mph

s = sample standard deviation = 4.7 mph

n = sample of vehicles = 15

So, test statistics = $\frac{31-30}{\frac{4.7}{\sqrt{15} } }$ ~ $t_1_4$

= 0.824

Hence, the value of test statistics is 0.824.

Now at 0.10 significance level, the t table gives critical value of 1.345 at 14 degree of freedom for right-tailed test. Since our test statistics is less than the critical value of t as 0.824 < 1.345, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the mean speed of vehicles is lesser than or equal to 30 miles per hour which means that the county's claim is not supported.

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3 years ago

Am I overweight? Should I go to the gym and get the meat off my bones?

il63 [147K]

Get running mate I believe you may have heart disease in the near future but good luck and try not to eat any more people

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3 years ago

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The Crayola crayon company can make 2400 crayons in 4 minutes. How many crayons can they make in 15 minutes? Solve this problem

algol [13]

The Crayola crayon company can make 9000 crayons in 15 minutes.

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3 years ago