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3 years ago

Please answer the above question correctly while showing detailed working.

Mathematics

2 answers:

Alika [10]3 years ago

5 0

this is the answer I wish it will help u

Brilliant_brown [7]3 years ago

3 0

Answer:

we have:

8x³ + 8x² + 6x + 2

= 8x³ + 4x² + 4x² + 2x + 4x + 2

= 2x²(4x + 2) + x(4x + 2) + (4x +2)

= (2x² + x + 1)(4x + 2)

=> if we divide 8x³ + 8x² + 6x + 2 by 4x + 2 => the result is 2x² + x + 1

Step-by-step explanation:

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"(b) use part (a) to find a power series for f(x) = 1 (4 + x)3 ."

Firdavs [7]

Assuming

$f(x)=\dfrac1{(4+x)^3}$

Recall that for $|x|$ ,

$\displaystyle\sum_{n\ge0}x^n=\frac1{1-x}$

Denote the above by $s(x)$ . Then

$s'(x)=\displaystyle\sum_{n\ge1}nx^{n-1}=\frac1{(1-x)^2}$
$s''(x)=\displaystyle\sum_{n\ge2}n(n-1)x^{n-2}=\frac2{(1-x)^3}$

Now,

$\dfrac1{(4+x)^3}=\dfrac1{4^3}\dfrac1{\left(1-\left(-\frac x4\right)\right)^3}=\dfrac1{2^7}\dfrac2{\left(1-\left(-\frac x4\right)\right)^3}$

which means we have

$f(x)=\dfrac1{2^7}s''(x)=\dfrac1{128}\displaystyle\sum_{n\ge2}n(n-1)\left(-\frac x4\right)^{n-2}$

which is valid for $\left|-\dfrac x4\right|$ , or $|x|$ .

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3 years ago

What is the final transformation in the composition of transformations that maps pre-image ABCD to image A"B'C"D"?

tatyana61 [14]

Answer: c. a 270° rotation about point B'

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3 years ago

Read 2 more answers

A rectangle has a length that is 3 more than twice the width. Its perimeter is 96 inches.

valina [46]

Answer:

8x=96 inch

Step-by-step explanation:

How its in the draw you have this situation then the equation that model is the next one:

2*(3X) + 2*X = 96 inch

6X + 2X = 96 inch

8X=96 inch

We must multiply due that there is two sides that measure the same.

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7 0

4 years ago

Each month, Terrance spends $128.00 on his car payment, $63.00 for car insurance, and $45.00 on gas. Round each amount to the ne

max2010maxim [7]

The answer is $240.

If you round each amount to the nearest ten you get $130.00, $60.00, and 50.00. When you add all of those together you get an estimated amount of $240.

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3 years ago

In a 30-60-90 triangle, the length of the hypotenuse i 6. What is the length of the shortest side?

True [87]

Answer:

3 units

Step-by-step explanation:

In a 30-60-90 triangle, the length are given by:

$x \\ \\ \frac{x}{2} \\ \\ \frac{x}{2} \sqrt{3}$

Where the longest side x, is the hypotenuse.

The shortest side is

$\frac{x}{2}$

Since x=6 is the hypotenuse, the shortest side length is:

$\frac{6}{2} = 3$

8 0

3 years ago

Please answer the above question correctly while showing detailed working. ​

Please answer the above question correctly while showing detailed working.