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3 years ago

Find the vertex and the length of the latus rectum. x= 1/2 (y - 5)² + 7

Mathematics

1 answer:

GalinKa [24]3 years ago

3 0

Answer:

Vertex = (7,5)

Length of latus rectum = 2 units

Step-by-step explanation:

The vertex form of a parabola is

$x=a(y-k)^2+h$ ...(1)

where, (h,k) is vertex and length of latus rectum is $\left|\dfrac{1}{a}\right|$ .

The given equation is

$x=\dfrac{1}{2}(y-5)^2+7$ ...(2)

On comparing (1) and (2), we get

$h=7,k=5,a=\dfrac{1}{2}$

So, vertex of parabola is (7,5).

Length of latus rectum is

$L.R.=\left|\dfrac{1}{a}\right|=\left|\dfrac{1}{\frac{1}{2}}\right|=2$

Therefore, the length of the latus rectum is 2 units.

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2 years ago

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oksian1 [2.3K]

Answer:

3.2

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3 years ago

Read 2 more answers

10 normal six sided dice are thrown.Find the probability of obtaining at least 8 failuresif a success is 5 or 6.

erastova [34]

Answer:

0.2992 = 29.92% probability of obtaining at least 8 failures.

Step-by-step explanation:

For each dice, there are only two possible outcomes. Either a failure is obtained, or a success is obtained. Trials are independent, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$