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3 years ago

Write an equation for the parabola whose vertex is at (4, 12) and which passes through (5, 21)

Mathematics

1 answer:

laiz [17]3 years ago

8 0

Answer:

y - 12 = 9(x - 4)

Step-by-step explanation:

The vertex (h, k) is (4, 12) and the point (5, 21) is on the graph. Assuming that this is a vertical parabola, opening up (because the coordinate 21 is greater than the coordinate 12), we insert the knowns into y - k = a(x - h)^2, obtaining

21 - 12 = a(5 - 4), or 9 = a. With a known, we can write the desired equation:

y - 12 = 9(x - 4)

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3 years ago

Find the additive inverse of 7/10

11111nata11111 [884]

$\huge\fbox{Hi~there!}$

Remember, a number's additive inverse is simply its opposite.

Let's say we have a number a.

The opposite of a is -a, and the opposite of -a is a.

Thus, the additive inverse of

$\displaystyle\frac{7}{10}$ is

$\displaystyle-\frac{7}{10}$

Hope it helps.

~Just a felicitous girl

#HaveAnAmazingDay

Feel free to ask if you have any doubts.

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3 years ago

Hi, does anyone know the answer to this question? I’m bad at geometry and I’m struggling to answer it.

arsen [322]

Answer:

QT = 16

Step-by-step explanation:

ΔQRS ~ ΔQRT

In similar triangles, corresponding angles are in same ratio.

$\frac{QS}{QR}=\frac{QR}{QT}\\\\\frac{25}{20}=\frac{20}{QT}$

Cross multiply,

QT * 25 = 20 * 20

$QT =\frac{20*20}{25}\\\\QT = 4*4\\\\QT = 16$

3 0

3 years ago

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1

charle [14.2K]

<u>Answer-</u> Length of the curve of intersection is 13.5191 sq.units

<u>Solution-</u>

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ $\frac{dx}{dt} = -\sin t$

$\frac{dy}{dt} = 2 \cos t$

$\frac{dz}{dt} = \sin t-2cos t$

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

∴ Arc length

$= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}$

$=\int_{0}^{2\pi}\sqrt{(-\sin t)^{2}+(2\cos t)^{2}+(\sin t-2\cos t)^{2}$

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$

Now evaluating the integral using calculator,

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$ $= 13.5191$

8 0

3 years ago