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3 years ago

Find a parabola with equation y=ax^2+bx+c that has a slope 10 at x=1, slope -26 at x=-1, and passes through the point (2,29)

Mathematics

1 answer:

Hatshy [7]3 years ago

6 0

9514 1404 393

Answer:

y = 9x^2 -8x +9

Step-by-step explanation:

The given equation has derivative ...

y' = 2ax +b

The requirements on slope give rise to two equations:

2a(1) +b = 10

2a(-1) +b = -26

Adding these equations together gives ...

2b = -16 ⇒ b = -8

Then we have ...

2a -8 = 10

a = (10 +8)/2 = 9

The given point lets us find the constant term c.

y = 9x^2 -8x +c

c = y -(9x -8)x = 29 -(9(2) -8)(2) = 29 -20 = 9

The equation of the parabola is ...

y = 9x^2 -8x +9

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Find the measure of each side of this triangles. Answer in exact form. Find x and y

Firdavs [7]

Answer:

x = 24/√3

4√3 = y

Step-by-step explanation:

We are given that this is a right triangle as well as two angles and a side.

Given that the angles in a triangle add up to 180 degrees, and a right angle is 90 degrees, we can say that the missing angle is equal to

(180-90-30) = 60 degrees

Next, given sohcahtoa, we can say that

sin(30) = opposite/hypotenuse = y/x

cos(30) = adjacent/hypotenuse = 12/x

tan(30) = opposite/adjacent = y/12

We want to only have one variable per equation so we can solve for the variable, so we can use

cos(30) = 12/x and tan(30) = y/12

Starting with cos(30) = 12/x, we can multiply both sides by x to remove the denominator to get

cos(30) * x = 12, and divide both sides by cos(30) to isolate the x and get

x = 12/cos(30). Next, cos(30) = √3/2, so we have

x = 12/(√3/2)

x = (12/1) / (√3/2)

x = (12/1) * (2/√3)

x = 24/√3

For y, we have

tan(30) = y/12

multiply both sides by 12 to isolate the y and remove the denominator

tan(30) * 12 = y

√3/3 * 12 = y

√3 * 4 = y

4√3 = y

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3 years ago

Rewrite the following equation in exponential form log3 3=1

yawa3891 [41]

Answer: (X) = y => b^y = x

use that equation to get the exponential form

Step-by-step explanation:

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Step-by-step explanation:

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Adiba bought 3 pizzas for her sleepover. 13 slices were eaten. How much pizza is remaining if each pizza was cut into 8 slices?

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Answer:

Step-by-step explanation:

3*8=24

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5 0

2 years ago

jar contains 51 coins which are either quarters or nickels. total value of jar is 5.15. how many of each type of coin do they ha

docker41 [41]

I believe there are 20 quarters and 3 nickels.....

Total value of the jar is $5.15.....

Quarters are worth 25 cents
And nickels are worth 5 cents.

First you know that there are 4 quarters in a dollar.
You have 5 dollars so you do 4 x 5 = 20

So five dollars ($5.00) is 20 quarters.
And you still have 15 cents left.

Because quarters are 25 cents the rest are nickels.

Nickels are worth 5 cents so you'd do 5 x 3 = 15.

15 cents!

Add all this together and get $5.15.

So your answer is

There are 20 quarters and 3 nickels in the jar.

8 0

3 years ago