All categories

3 years ago

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

You might be interested in

Circle P is described by the equation (x−1)2+(y+6)2=9 and circle Q is described by the equation (x+4)2+(y+14)2=4. Select from th

xeze [42]

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>

4 0

3 years ago

HELPPP FOR EXTRA POINTSSSSSSS!

larisa86 [58]

Answer:

Step-by-step explanation:

8 0

3 years ago

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

irinina [24]

Answer:

Step-by-step explanation:

8 0

3 years ago

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

posledela

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

810 + 2025 =2835

The amount of students in favor of rock climbing would be

3600 - 2835 =765

3 0

3 years ago

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

madam [21]

Answer:

6 ( − 4 x^ 2+ 4 x − 6 y + 9 y^ 2 − 9 y ^2 x + 6 y x ^2 )

Step-by-step explanation:

5 0

3 years ago