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Nookie1986 [14]
3 years ago
10

What is the product?

Mathematics
2 answers:
ad-work [718]3 years ago
7 0

Answer is C, just multiply and expand.

LekaFEV [45]3 years ago
4 0

Answer:C

Step-by-step explanation:

I just took the test.

Multiply the equation and expand it

You might be interested in
Question (c)! How do I know that t^5-10t^3+5t=0?<br> Thanks!
astra-53 [7]
(a) By DeMoivre's theorem, we have

(\cos\theta+i\sin\theta)^5=\cos5\theta+i\sin5\theta

On the LHS, expanding yields

\cos^5\theta+5i\cos^4\theta\sin\theta-10\cos^3\theta\sin^2\theta-10i\cos^2\theta\sin^3\theta+5\cos\theta\sin^4\theta+i\sin^4\theta

Matching up real and imaginary parts, we have for (i) and (ii),


\cos5\theta=\cos^5\theta-10\cos^3\theta\sin^2\theta+5\cos\theta\sin^4\theta
\sin5\theta=5\cos^4\theta\sin\theta-10\cos^2\theta\sin^3\theta+\sin^5\theta

(b) By the definition of the tangent function,

\tan5\theta=\dfrac{\sin5\theta}{\cos5\theta}
=\dfrac{5\cos^4\theta\sin\theta-10\cos^2\theta\sin^3\theta+\sin^5\theta}{\cos^5\theta-10\cos^3\theta\sin^2\theta+5\cos\theta\sin^4\theta}

=\dfrac{5\tan\theta-10\tan^3\theta+\tan^5\theta}{1-10\tan^2\theta+5\tan^4\theta}
=\dfrac{t^5-10t^3+5t}{5t^4-10t^2+1}


(c) Setting \theta=\dfrac\pi5, we have t=\tan\dfrac\pi5 and \tan5\left(\dfrac\pi5\right)=\tan\pi=0. So

0=\dfrac{t^5-10t^3+5t}{5t^4-10t^2+1}

At the given value of t, the denominator is a non-zero number, so only the numerator can contribute to this reducing to 0.


0=t^5-10t^3+5t\implies0=t^4-10t^2+5

Remember, this is saying that

0=\tan^4\dfrac\pi5-10\tan^2\dfrac\pi5+5

If we replace \tan^2\dfrac\pi5 with a variable x, then the above means \tan^2\dfrac\pi5 is a root to the quadratic equation,

x^2-10x+5=0

Also, if \theta=\dfrac{2\pi}5, then t=\tan\dfrac{2\pi}5 and \tan5\left(\dfrac{2\pi}5\right)=\tan2\pi=0. So by a similar argument as above, we deduce that \tan^2\dfrac{2\pi}5 is also a root to the quadratic equation above.

(d) We know both roots to the quadratic above. The fundamental theorem of algebra lets us write

x^2-10x+5=\left(x-\tan^2\dfrac\pi5\right)\left(x-\tan^2\dfrac{2\pi}5\right)

Expand the RHS and match up terms of the same power. In particular, the constant terms satisfy

5=\tan^2\dfrac\pi5\tan^2\dfrac{2\pi}5\implies\tan\dfrac\pi5\tan\dfrac{2\pi}5=\pm\sqrt5

But \tanx>0 for all 0, as is the case for x=\dfrac\pi5 and x=\dfrac{2\pi}5, so we choose the positive root.
3 0
3 years ago
What is the y-value of the vertex of 4x^+ 8x - 8?
deff fn [24]

Answer: The y-value of the vertex is

Step-by-step explanation: we know that

The equation of a vertical parabola into vertex form is equal to

where

(h,k) is the vertex of the parabola

In this problem we have

-----> this a vertical parabola open upward

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Factor the leading coefficient

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

The vertex is the point

The y-value of the vertex is

5 0
1 year ago
Please I need help!
Monica [59]

Answer:

1)

\text{ Slope = -3}

2)

y+4=-\frac{7}{8}(x-7)

3)

y=-\frac{7}{8}x+\frac{17}{8}

Step-by-step explanation:

We want to write the equation of the line that passes through the points (7, -4) and (-1, 3) first in point-slope form and then in slope-intercept form.

1)

First and foremost, we will need to find the slope of the line. So, we can use the slope-formula:

m=\frac{y_2-y_1}{x_2-x_1}

Let (7, -4) be (x₁, y₁) and let (-1, 3) be (x₂, y₂). Substitute them into our slope formula. This yields:

m=\frac{3-(-4)}{-1-7}

Subtract. So, our slope is:

m=\frac{7}{-8}=-7/8

2)

Now, let's use the point-slope form:

y-y_1=m(x-x_1)

We will substitute -7/8 for our slope m. We will also use the point (7, -4) and this will be our (x₁, y₁). So, substituting these values yield:

y-(-4)=-\frac{7}{8}(x-7)

Simplify. So, our point-slope equation is:

y+4=-\frac{7}{8}(x-7)

3)

Finally, we want to convert this into slope-intercept form. So, let's solve for our y.

On the right, distribute:

y+4=-\frac{7}{8}x+\frac{49}{8}

Subtract 4 from both sides. Note that we can write 4 using a common denominator of 8, so 4 is 32/8. This yields:

y=-\frac{7}{8}x+\frac{49}{8}-\frac{32}{8}

Subtract. So, our slope-intercept equation is:

y=-\frac{7}{8}x+\frac{17}{8}

And we're done!

7 0
3 years ago
Read 2 more answers
Under his cell phone plan, Nathaniel pays a flat cost of $41 per month and $4 per gigabyte. He wants to keep his bill at $45.80
ladessa [460]

Answer:

equation: 41+4x=45.80

answer: x=1.20

Step-by-step explanation:

7 0
2 years ago
Mathematics Financial literacy
hichkok12 [17]

Answer:

$10,500

Step-by-step explanation:

since his income is b/n $50,000 and $100,000, he pays 15%, (15/100)70,000=$10,500

7 0
3 years ago
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