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3 years ago

Find an equation in standard form for the hyperbola with vertices at (0, ±6) and foci at (0, ±9).

1 answer:

4 0

For given hyperbola:
center: (0,0)
a=7 (distance from center to vertices)
a^2=49
c=9 (distance from center to vertices)
c^2=81
c^2=a^2+b^2
b^2=c^2-a^2=81-49=32
Equation of given hyperbola:

..
2: vertices (0,+/-3) foci (0,+/-6)
hyperbola has a vertical transverse axis
Its standard form of equation: , (h,k)=(x,y) coordinates of center
For given hyperbola:
center: (0,0)
a=3 (distance from center to vertices)
a^2=9
c=6 (distance from center to vertices)
c^2=36 a^2+b^2
b^2=c^2-a^2=36-9=25
Equation of given hyperbola:

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Step-by-step explanation:

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Find the total surface area of this triangular prism. 21 cm 29 cm 22 cm 20 cm

mixer [17]

Answer:

313

Step-by-step explanation:

First of all you need to find out the surface of the front.

So you need to do 29cm + 29cm = 58cm.

You then have to do 22cm + 22cm = 44cm

So if you add those two numbers up you will get the front surface which is 102cm.

Next, you need to find the surface of the side.

So you need to do 20cm + 21cm = 41cm

After that, you need to find the back surface.

So you need to add 22cm +22cm = 44cm

Then you have to do 21cm + 21cm = 42cm

Add those two together to get 86cm

Then, you need to do the bottom of the shape.

So you need to add 22cm + 22cm (again) = 44cm

You then need to do 20cm + 20cm = 40cm

Add those together to get 84cm

Finally, you need to add 84cm + 86cm + 102cm + 41cm = 313cm

So your answer is:

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2 years ago

Recursive & Explicit Definitions

natali 33 [55]

Answer:

$T_{15} = 9565938$

Step-by-step explanation:

Given

Sequence: 2, 6, 18, 54, 162,

Required

Determine the 15th term

The above sequence is a geometric sequence. So, first, we calculate the common ratio (r)

$r = \frac{T_2}{T_1}$

$r = \frac{6}{2}$

$r = 3$

The 15th term is calculated as thus:

$T_n = ar^{n-1}$

Where

$a = 2$ and $n = 15$

$T_n = 2 * 3^{15-1}$

$T_n = 2 * 3^{14}$

$T_{15} = 2 * 4782969$

$T_{15} = 9565938$

The 15th term is 9,565,938

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3 years ago

Classify the following polynomial function, −3x(x2−4)(2x2+5)based on degree and number of terms.

Free_Kalibri [48]

Answer:

Quintic Trinomial (2nd option)

Step-by-step explanation:

We know that this is a quintic polynomial because the degrees add up to 5. If we expand the polynomial, we have $-3x(x^2-4)(2x^2+5)=(-3x^3-12x)(2x^2+5)=-6x^5-45x^3-24x^3-60x=-6x^5-69x^3-60x$

So, there are 3 terms, which is a trinomial.

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2 years ago