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chubhunter [2.5K]
3 years ago
15

Find the coefficient of the t4 term in the expansion of (4t– 3)^5

Mathematics
1 answer:
Sauron [17]3 years ago
5 0

Answer:

-4320t^2

Step-by-step explanation:

Use Pascal's triangle to figure out the variables.

In the 5th expansion, we see that the 4th term is:

10x^2 y^3

Plug in the values,

10*(4)^2 * (-3)^3 = -4230.

However, since the -3 in the original expression does not have a variable next to it, we do not include it in our answer.

Therefore, the 4th term is -4230t^2

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Answer:

(a) Circle Q is 9.4 units to the center of circle P

(b) Circle Q has a smaller radius

Step-by-step explanation:

Given

P:(x - 1)^2 + (y + 6)^2 = 9

Q:(x + 4)^2 + (y + 14)^2 = 4

Solving (a): The distance between both

The equation of a circle is:

(x - h)^2 + (y - k)^2 = r^2

Where

Center: (h,k)

Radius:r

P and Q can be rewritten as:

P:(x - 1)^2 + (y + 6)^2 = 3^2

Q:(x + 4)^2 + (y + 14)^2 = 2^2

So, for P:

Center = (1,-6)

r = 3

For Q:

Center = (-4,-14)

r = 2

The distance between them is:

d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2

Where:

Center = (1,-6) --- (x_1,y_1)

Center = (-4,-14) --- (x_2,y_2)

So:

d = \sqrt{(1 - -4)^2 + (-6 - -14)^2

d = \sqrt{(5)^2 + (8)^2

d = \sqrt{25 + 64

d = \sqrt{89

d = 9.4

Solving (b): The radius;

In (a), we have:

r = 3 --- circle P

r = 2 --- circle Q

By comparison

2 < 3

<em>Hence, circle Q has a smaller radius</em>

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3 years ago
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Answer:

b

Step-by-step explanation:

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The area of a piece of pie in the shape of a sector is 7.1 in^2. The angle of the sector is 40°. Round your answers to the neare
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Step-by-step explanation:

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There are 3600 students at Canyon High School and 3/8 of these students are sophomores. If 3/5 of the sophomores are opposed to
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Answer:

765

Step-by-step explanation:

First, find the number of sophomores

3600 * 3/8 =1350

Use the number of sophomores and multiply by 3/5 to find the amount of sophomores opposed to rock climbing

1350 * 3/5 =810

Then subtract the amount of sophomores from the total amount of students

3600 - 1350 =2250

And multiply the remaining students by 9/10 to find the amount of non-sophomores opposed to rock climbing

2250 * 9/10 =2025

Add the amount of sophomores and non-sophomores opposed to rock climbing

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The amount of students in favor of rock climbing would be

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Factorise<br> (2x-2)³+ (2-3y)³+ (3y-2x)³
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