Find 7/8 (-2 • 2/5) Write your answer in simplest form.

Find the vertex, focus, directrix, and focal width of the parabola. x2 = 12y

Molodets [167]

$\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
4p(x- h)=(y- k)^2
\\\\
\boxed{4p(y- k)=(x- h)^2}
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ( h, k)\\\\
 p=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\
-------------------------------\\\\
x^2=12y\implies (x-0)^2=12(y-0)\implies (x-\stackrel{h}{0})^2=4(\stackrel{p}{3})(y-\stackrel{k}{0})$

so, the vertex of h,k is at the origin, as you can see 0,0.

4p is the focal width, which is well, 4*3.

now, the parabola has a positive leading term's coefficient, namely 1x², the 1 is positive, well, that simply means that, since the squared variable is the "x", is a vertical parabola, and since its coefficient is positive, is opening upwards, like a bowl.

the focus point will be "p" distance from the vertex, and the directrix is also "p" distance from the vertex as well, but in the opposite direction.

since the parabola is opening upwards, that's where the focus point is at, 3 units UP from 0,0, namely at (0,3).

and due to the same reason as above, the directrix is 3 units DOWN from the vertex, namely a horizontal line running over y = -3.

5 0

3 years ago

7y ^3 −7x^3 +4−5+6−3x^3 +6x^3<br>Combine Like Terms

snow_lady [41]

Answer:

-4x^3 + 7y^3 + 5

Step-by-step explanation:

7y^3 - 7x^3 + 4 - 5 + 6 - 3x^3 + 6x^3 Given

7y^3 - 7x^3 - 3x^3 + 6x^3 + 4 - 5 + 6 Rearrange

7y^3 - 4x^3 + 5 Combine the like terms

or

-4x^3 + 7y^3 + 5 Answer

8 0

4 years ago

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to d

k0ka [10]

Part A:

From the central limit theorem, since the number of samples is large enough (up to 30), the mean of the the mean of the average number of moths in 30 traps is 0.6.

Part B:

The standard deviation is given by the population deviation divided by the square root of the sample size.

$standard \ deviation= \frac{\sigma}{\sqrt{n}} = \frac{0.4}{\sqrt{30}} = \frac{0.4}{5.477} =0.073$

Part C:

The probability that an approximately normally distributed data with a mean, μ, and the standard deviation, σ, with a sample size of n is greater than a number, x, given by

$P(X\ \textgreater \ x)=1-P(X\ \textless \ x) \\ \\ =1-P\left(z\ \textless \ \frac{x-\mu}{\sigma/\sqrt{n}} \right)$

Thus, given that the mean is 0.6 and the standard deviation is 0.4, the probability that <span>the average number of moths in 30 traps is greater than 0.7</span> given by:

$P(X\ \textgreater \ 0.7)=1-P(X\ \textless \ 0.7) \\ \\ =1-P\left(z\ \textless \ \frac{0.7-0.6}{0.073} \right)=1-P(z\ \textless \ 1.369) \\ \\ =1-0.91455=\bold{0.0855}$

7 0

4 years ago

Is there

Basile [38]

Answer:

no

Step-by-step explanation:

no because 29 is a prime number, meaning its only factors are 1 and 29. if you were to have more than 1 book on each shelf then you would go into half and quarters of books.

8 0

3 years ago

Read 2 more answers

Define an operation ‘&’ on the set of positive integers such that: 2 & 1 = 5 3 & 2 = 13 5 & 3 = 34

Scilla [17]

Answer:What are the equivalence classes of the equivalence relations in Exercise 3? A binary relation defined on a set S is said to be equivalence relation if it is reflexive, symmetric and transitive. An equivalence relation defined on a set S, partition the set into disjoint equivalence classes

7 0

4 years ago