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2 years ago

A parabola is given by the equation y2 = -24x. The equation of the directrix of the parabola is . The focus of the parabola is .

Mathematics

1 answer:

Firdavs [7]2 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

The standard form of the equation of a parabola with it's principal axis along the x-axis and the vertex at the origin is

y² = 4ax ( a is the distance of the directrix/ focus from the vertex )

If 4a is positive the curve opens to the right. If 4a is negative the curve opens to the left.

y² = - 24x is in this form

Hence the vertex is at the origin and the curve opens to the left.

equating 4a = - 24 ⇒ a = - 6

Hence the focus is on the x-axis with coordinates (- 6, 0 )

The directrix is a vertical line 6 units to the right of the vertex with equation x = 6

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Which exponential function has an initial value of 3?

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Answer:

1,3.5

Step-by-step explanation:

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2 years ago

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Calculating conditional probabilities - random permutations. About The letters (a, b, c, d, e, f, g) are put in a random order.

Evgesh-ka [11]

A="b is in the middle"

B="c is to the right of b"

C="The letter def occur together in that order"

a) b can be in 7 places, but only one is the middle. So, P(A)=1/7

b) X=i, "b is in the i-th position"

Y=j, "c is in the j-th position"

$P(B)=\displaystyle\sum_{i=1}^{6}(P(X=i)\displaystyle\sum_{j=i+1}^{7}P(Y=j))=\displaystyle\sum_{i=1}^{6}\frac{1}{7}(\displaystyle\sum_{j=i+1}^{7}\frac{1}{6})=\frac{1}{42}\displaystyle\sum_{i=1}^{6}(\displaystyle\sum_{j=i+1}^{7}1)=\frac{6+5+4+3+2+1}{42}=\frac{1}{2}$

P(B)=1/2

c) X=i, "d is in the i-th position"

Y=j, "e is in the j-th position"

Z=k, "f is in the i-th position"

$P(C)=\displaystyle\sum_{i=1}^{5}( P(X=i)P(Y=i+1)P(Z=i+2))=\displaystyle\sum_{i=1}^{5}(\frac{1}{7}\times\frac{1}{6}\times\frac{1}{5})=\frac{1}{210}\displaystyle\sum_{i=1}^{5}(1)=\frac{1}{42}$

P(C)=1/42

P(A∩C)=2*(1/7*1/6*1/5*1/4)=1/420

$P(B\cap C)=\displaystyle\sum_{i=1}^{3} P(X=i)P(Y=i+1)P(Z=i+2)\displaystyle\sum_{j=i+3}^{6}P(V=j)P(W=j+1)=\displaystyle\sum_{i=1}^{3}\frac{1}{6}\frac{1}{7}\frac{1}{5}(\displaystyle\sum_{j=1+3}^{6}\frac{1}{4}\frac{1}{3})=1/420$

P(B∩A)=3*(1/7*1/6)=1/14

P(A|C)=P(A∩C)/P(C)=(1/420)/(1/42)=1/10

P(B|C)=P(B∩C)/P(C)=(1/420)/(1/42)=1/10

P(A|B)=P(B∩A)/P(B)=(1/14)/(1/2)=1/7

P(A∩B)=1/14

P(A)P(B)=(1/7)*(1/2)=1/14

A and B are independent

P(A∩C)=1/420

P(A)P(C)=(1/7)*(1/42)=1/294

A and C aren't independent

P(B∩C)=1/420

P(B)P(C)=(1/2)*(1/42)=1/84

B and C aren't independent

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2 years ago

A toy store owner purchased 70 puppets for $1006. She sold them for $1412. How much profit did she make per puppet?

Marizza181 [45]

Answer:

5.80

Step-by-step explanation:

How much was the total profit

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The profit per puppet is the profit divided by the number of puppets

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2 years ago

If a fish experiences an acceleration of 9.8 m/s^2 over a period of 1.4s (It must be falling), then what is its change in veloci

JulsSmile [24]

Answer:

Change In velocity= 13.72 ms^-1

Step-by-step explanation:

fish experiences an acceleration of

9.8 m/s^2 over a period of 1.4s

Change in velocity/time= acceleration

Time in seconds= 1.4 s

Acceleration in meter per second square= 9.8 m/s^2

Change in velocity/time= acceleration

Change In velocity= acceleration*time

Change In velocity= 9.8*1.4(m/s^2 *s)

Change In velocity= 13.72 ms^-1

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2 years ago

What are the domain and range of f (x) = (one-fifth) Superscript x?

natka813 [3]

Answer:

The domain of the function is all real numbers $(-\infty,\infty)$ and the range is all positive real numbers $(0,\infty)$

Step-by-step explanation:

We have the following function $f(x)=(\frac{1}{5} )^x$ and we want to find the domain and the range.

The function we have is an example of an exponential function $f(x)=b^x$ with b > 0 and b ≠ 1. This types of functions in general have the following properties:

It is always greater than 0, and never crosses the x-axis
Its domain is the set of real numbers
Its Range is the Positive Real Numbers $(0,\infty)$

The domain of a function is the specific set of values that the independent variable in a function can take on.

When determining domain it is more convenient to determine where the function would not exist.

This function has no undefined points nor domain constraints. Therefore the domain is $(-\infty,\infty)$ .

The range is the resulting values that the dependent variable can have as x varies throughout the domain. Therefore the range is $(0,\infty)$ .

We can check our results with the graph of the function.

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2 years ago

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