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3 years ago

What is the equation of a parabola with (-1,-3) as its focus and y=1 as its directrix?

1 answer:

3 0

Hmm, y=1 is directix
means it opens up or down
we will be using
(x-h)²=4p(y-k) where (h,k) is vertex and p is the distnace from focus to vertex and from vertex to direcitx
focus is (-1,-3)
find distance between y values because directix is a y value
midpoint is the vertex
from -3 to 1 is 2 units
since focus is below directix, it opens down, and p is negative
it is 2 units above focus
so at (-1,-1)
and p=-2

(x-(-1))²=4(-2)(y-(-1))
(x+1)²=-8(y+1) is da equation

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Write 32 as a number with an exponent by using 2 as the base

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3 years ago

Joel can run around a 14– mi track in 81 sec, and Jason can run around the track in 69 sec. If the runners start at the same poi

Alenkasestr [34]

Answer:37.2 sec

Step-by-step explanation:

Given

Joel takes 81 sec for 14 mile long track

speed of joel $\frac{14}{1.35}$ mi/min=10.37 mi/min

Jason takes 69 sec for 14 mi track

so jason speed is $\frac{14}{1.15} mi/min=12.17 mi/min$

if both starts from same spot in opposite direction then

$\frac{x}{10.37}=\frac{14-x}{12.17}$

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then x=6.44 miles

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4 years ago

A quarterback throws a football to a teammate. The football is 6.5ft above the ground when it leaves the quarterback's hand. His

sergejj [24]

Answer:

y = - 16t² + 55.6t + 6

Step-by-step explanation:

Using y - y₀ = vt - 1/2gt² where g = 32 ft/s², and v the velocity of the football

So y = y₀ + vt - 1/2 × (32 ft/s²)t²

y = y₀ + vt - 16t² where y₀ = 6.5 ft

y = 6 + vt - 16t²

Now, when t = 3.5 s, that is the time the teammate catches the ball after the quarterback throws it, y = 5 ft. Substituting these into the equation, we have

5 = 6.5 + v(3.5 s) - 16(3.5 s)²

5 = 6.5 + 3.5v - 196

collecting like terms, we have

5 - 6.5 + 196 = 3.5v

194.5 = 3.5v

v = 194.5/3.5 = 55.57 ft/s ≅ 55.6 ft/s

So, substituting v into y, our quadratic model is

y = 6 + 55.6t - 16t²

re-arranging, we have

y = - 16t² + 55.6t + 6

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3 years ago

Harlee uses a device to convert her electronic textbook into braille. Unfortunately, the textbook did not include text descripti

Ainat [17]

Answer:

Mean: 1.5

Standard Deviation: 0.9

Step-by-step explanation:

2/3 of the pages have diagrams, and N is the number of pages Harlee reads to reach a page with a diagram. In order to find the mean, divide 1/(2/3) to get 1.5 as your mean, and then divide sqrt(1-(2/3))/2/3 to get .8660, which rounds to .9.

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3 years ago

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telo118 [61]

Answer: slope is 1

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Read 2 more answers