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3 years ago

What is the remainder when x3 + x2 − 5x − 6 is divided by x − 2 ?

Mathematics

1 answer:

pishuonlain [190]3 years ago

4 0

I believe the answer is C) 0

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Please help i beg i never get these right

Anuta_ua [19.1K]

Answer:

$\sin(105) = \frac{\sqrt 2 + \sqrt 6}{4}$

Step-by-step explanation:

Given

$\sin(105^o)$

Required

Solve

Using sine rule, we have:

$\sin(A + B) = \sin(A)\cos(B) + \sin(B)\cos(A)$

This gives:

$\sin(105^o) = \sin(60 + 45)$

So, we have:

$\sin(60 + 45) = \sin(60)\cos(45) + \sin(45)\cos(60)$

In radical forms, we have:

$\sin(60 + 45) = \frac{\sqrt 3}{2} * \frac{\sqrt 2}{2} + \frac{\sqrt 2}{2} * \frac{1}{2}$

$\sin(60 + 45) = \frac{\sqrt 6}{4} + \frac{\sqrt 2}{4}$

Take LCM

$\sin(60 + 45) = \frac{\sqrt 6 + \sqrt 2}{4}$

Rewrite as:

$\sin(60 + 45) = \frac{\sqrt 2 + \sqrt 6}{4}$

Hence:

$\sin(105) = \frac{\sqrt 2 + \sqrt 6}{4}$

3 0

2 years ago

For what values of θ on the polar curve r=θ, with 0≤θ≤2π , are the tangent lines horizontal? Vertical?

Bond [772]

Given that $r=\theta$ , then $r'=1$

The slope of a tangent line in the polar coordinate is given by:

$m= \frac{r'\sin\theta+r\cos\theta}{r'\cos\theta-r\sin\theta}$

Thus, we have:

$m= \frac{\sin\theta+\theta\cos\theta}{\cos\theta-\theta\sin\theta}$

Part A:

For horizontal tangent lines, m = 0.

Thus, we have:

$\sin\theta+\theta\cos\theta=0 \\ \\ \theta\cos\theta=-\sin\theta \\ \\ \theta=- \frac{\sin\theta}{\cos\theta} =-\tan\theta$

Therefore, the values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:

θ = 0

θ = 2.02875783811043

θ = 4.91318043943488

Part B:

For vertical tangent lines, $\frac{1}{m} =0$

Thus, we have:

$\cos\theta-\theta\sin\theta=0 \\ \\ \Rightarrow\theta\sin\theta=\cos\theta \\ \\ \Rightarrow\theta= \frac{\cos\theta}{\sin\theta} =\sec\theta$

Therefore, the values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:

θ = 4.91718592528713

3 0

3 years ago

Find the area of an equilateral triangle (regular 3-gon) with the given measurement.

Dmitriy789 [7]

Whats the given measurements

6 0

3 years ago

which values of x and y are solutions to the open sentence? 4y ≥ 3x 2 a. x = 3, y = 0 b. x = 4, y = 3 c. x = 6, y = 5 d. x = 7,

boyakko [2]

4y ≥ 3x + 2

Plugging in the values in the options, then the required values are when x = 6 and y = 5, then
4(5) ≥ 3(6) + 2
20 ≥ 18 + 2
20 ≥ 20

8 0

3 years ago

James went out for. a long walk . he walked 3/4 mile and then sat down to take rest. then walked 1/8 of a mile how far did he wa

Karo-lina-s [1.5K]

change 3/4 to 6/8 and add 6/8 and 1/8 to get 7/8

he walked 7/8 miles in total :)

6 0

3 years ago