PLEASE HELP QUICK 10 POINTS AND I GIVE BRAINLEIST!!! what is the <br> GCF of 110 and 132

Which is the equation of a hyperbola with directrices at y = ±2 and foci at (0, 4) and (0, −4)?

Advocard [28]

Answer:

Step-by-step explanation:

First off, I'm assuming that when you said "directrices" you mean the oblique asymptotes, since hyperbolas do not have directrices they have oblique asymptotes.

If we plot the asymptotes and the foci, we see that where the asymptotes cross is at the origin. This means that the center of the hyperbola is (0, 0), which is important to know.

After we plot the foci, we see that they are one the y-axis, which is a vertical axis, which means that the hyperbola opens up and down instead of sideways. Knowing those 2 characteristics, we can determine that the equation we are trying to fill in has the standard form

$\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1$

We know h and k from the center, now we need to find a and b. Those values can be found from the asymptotes. The asymptotes have the standard form

y = ± $\frac{a}{b}(x-h)+k$

Filling in our asymptotes as they were given to us:

y = ± $\frac{2}{1}(x-0)+0$ where a is 2 and b is 1. Now we can write the formula for the hyperbola!:

$\frac{(y-0)^2}{4}-\frac{(x-0)^2}{1}=1$ which of course simplifies to

$\frac{y^2}{4}-\frac{x^2}{1}=1$

4 0

4 years ago

A closed-top cylindrical container is to have a volume of 250 in2. 250 , in squared , . What dimensions (radius and height) will

miv72 [106K]

Answer:

radius r = 3.414 in

height h = 6.8275 in

Step-by-step explanation:

From the information given:

The volume V of a closed cylindrical container with its surface area can be expressed as follows:

$V = \pi r^2 h$

$S = 2 \pi rh + 2 \pi r^2$

Given that Volume V = 250 in²

Then;

$\pi r^2h = 250 \\ \\ h = \dfrac{250}{\pi r^2}$

We also know that the cylinder contains top and bottom circle and the area is equal to πr²,

Hence, if we incorporate these areas in the total area of the cylinder.

Then;

$S = 2\pi r h + 2 \pi r ^2$

$S = 2\pi r (\dfrac{250}{\pi r^2}) + 2 \pi r ^2$

$S = \dfrac{500}{r} + 2 \pi r ^2$

To find the minimum by determining the radius at which the surface by using the first-order derivative.

$S' = 0$

$- \dfrac{500}{r^2} + 4 \pi r = 0$

$r^3 = \dfrac{500 }{4 \pi}$

$r^3 = 39.789$

$r =\sqrt[3]{39.789}$

r = 3.414 in

Using the second-order derivative of S to determine the area is maximum or minimum at the radius, we have:

$S'' = - \dfrac{500(-2)}{r^3}+ 4 \pi$

$S'' = \dfrac{1000}{r^3}+ 4 \pi$

Thus, the minimum surface area will be used because the second-derivative shows that the area function is higher than zero.

Thus, from $h = \dfrac{250}{\pi r^2}$

$h = \dfrac{250}{\pi (3.414) ^2}$

h = 6.8275 in

7 0

3 years ago

Which transformations have been applied to the graph of f(x) = x2 to produce the graph of g(x) = –5x2 + 100x – 450? Select three

RSB [31]

Answer:

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

Step-by-step explanation:

we have

$f(x)=x^{2}$

This is a vertical parabola open upward

The vertex is a minimum

The vertex is the origin (0,0)

$g(x)=-5x^{2}+100x-450$

This is a vertical parabola open downward

The vertex is a maximum

The first thing to note is that fx) is a parabola that opens up and g(x) opens down, so a reflection across the x-axis must have been applied.

Find the vertex of g(x)

Convert to vertex form

$g(x)=-5x^{2}+100x-450$

Complete the square

$g(x)=-5(x^{2}-20x)-450$

$g(x)=-5(x^{2}-20x+100)-450+500$

$g(x)=-5(x^{2}-20x+100)+50$

$g(x)=-5(x-10)^{2}+50$

The vertex is the point (10,50)

so

To translate the vertex of (0,0) to (10,50)

The rule of the translation is

(x,y) ------> (x+10,y+50)

That means ----> The translation is 10 units at right and 50 units up

therefore

The transformations are

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

5 0

3 years ago

Read 2 more answers

If angle X has a measure of 40 degrees and angle Y is vertical to angle X, what is the measure of angle Y? Show your work and ex

elena-14-01-66 [18.8K]

Answer:

Angle y is also 40 degrees. Angle x and y are vertical angles, thus they have the same angle measure.

8 0

4 years ago

Read 2 more answers

Find a point-slope form for the line with slope 1/5 and passing through the point (-6,-9).

Elenna [48]

Answer:

y=1/5x-39/5

Step-by-step explanation:

y=mx+b (slope y intercept formula)

y=1/5x+b

take (-6,-9) and put in appropiate places

-9= -6/5+b

*multiply lhs and rhs by 5

-45= -6+5b

-45+6=5b

-39=5b

-5b=39

b=39/-5

y=1/5x-39/5

5 0

3 years ago

PLEASE HELP QUICK 10 POINTS AND I GIVE BRAINLEIST!!! what is the GCF of 110 and 132