All categories

3 years ago

Which of the following is the correct factorization of the polynomial below? 2p^2 - 10pq+ 25q^2

Mathematics

1 answer:

diamong [38]3 years ago

3 0

Answer:

answer is in the photo

Step-by-step explanation:

You might be interested in

Help me with trigonometry

poizon [28]

Answer:

See below

Step-by-step explanation:

It has something to do with the Weierstrass substitution, where we have

$\int\, f(\sin(x), \cos(x))dx = \int\, \dfrac{2}{1+t^2}f\left(\dfrac{2t}{1+t^2}, \dfrac{1-t^2}{1+t^2} \right)dt$

First, consider the double angle formula for tangent:

$\tan(2x)= \dfrac{2\tan(x)}{1-\tan^2(x)}$

Therefore,

$\tan\left(2 \cdot\dfrac{x}{2}\right)= \dfrac{2\tan(x/2)}{1-\tan^2(x/2)} = \tan(x)=\dfrac{2t}{1-t^2}$

Once the double angle identity for sine is

$\sin(2x)= \dfrac{2\tan(x)}{1+\tan^2(x)}$

we know $\sin(x)=\dfrac{2t}{1+t^2}$ , but sure, we can derive this formula considering the double angle identity

$\sin(x)= 2\sin\left(\dfrac{x}{2}\right)\cos\left(\dfrac{x}{2}\right)$

Recall

$\sin \arctan t = \dfrac{t}{\sqrt{1 + t^2}} \text{ and } \cos \arctan t = \dfrac{1}{\sqrt{1 + t^2}}$

Thus,

$\sin(x)= 2 \left(\dfrac{t}{\sqrt{1 + t^2}}\right) \left(\dfrac{1}{\sqrt{1 + t^2}}\right) = \dfrac{2t}{1 + t^2}$

Similarly for cosine, consider the double angle identity

Thus,

$\cos(x)= \left(\dfrac{1}{\sqrt{1 + t^2}}\right)^2- \left(\dfrac{t}{\sqrt{1 + t^2}}\right)^2 = \dfrac{1}{t^2+1}-\dfrac{t^2}{t^2+1} =\dfrac{1-t^2}{1+t^2}$

Hence, we showed $\sin(x) \text { and } \cos(x)$

======================================================

$5\cos(x) =12\sin(x) +3, x \in [0, 2\pi ]$

Solving

$5\,\overbrace{\frac{1-t^2}{1+t^2}}^{\cos(x)} = 12\,\overbrace{\frac{2t}{1+t^2}}^{\sin(x)}+3$

$\implies \dfrac{5-5t^2}{1+t^2}= \dfrac{24t}{1+t^2}+3 \implies \dfrac{5-5t^2 -24t}{1+t^2}= 3$

$\implies 5-5t^2-24t=3\left(1+t^2\right) \implies -8t^2-24t+2=0$

$t = \dfrac{-(-24)\pm \sqrt{(-24)^2-4(-8)\cdot 2}}{2(-8)} = \dfrac{24\pm 8\sqrt{10}}{-16} = \dfrac{3\pm \sqrt{10}}{-2}$

$t=-\dfrac{3+\sqrt{10}}{2}\\t=\dfrac{\sqrt{10}-3}{2}$

Just note that

$\tan\left(\dfrac{x}{2}\right) = \dfrac{3\pm 8\sqrt{10}}{-2}$

and $\tan\left(\dfrac{x}{2}\right)$ is not defined for $x=k\pi , k\in\mathbb{Z}$

6 0

3 years ago

A family buys 4 airline tickets online. The family buys travel insurance that costs $19 per ticket. The total cost is $752. Let

Ede4ka [16]

A. x = 752 / 4 - 19

B. 169

7 0

3 years ago

Read 2 more answers

If the nth term of a sequence is 3n+2 them T³= T⁵=T¹⁵=

Katena32 [7]

Answer:

T^75

Step-by-step explanation:

3 times 5 = 15

5 times 15 = 75

7 0

3 years ago

F(x) = 9x^3 + 2x^2 - 5x + 4 and g(x) = 5x^3 - 7x + 4. What is f(x) - g(x)?

sasho [114]

F(x)= 9x^3 + 2x^2 - 5x + 4
g(x)= 5x^3 - 7x + 4

f(x) - g(x)
9x³ + 2x² - 5x + 4 - (5x³ - 7x + 4)
9x³ + 2x² - 5x + 4 - 5x³ +7x - 4
9x³ - 5x³ + 2x² -5x + 7x + 4 - 4
4x³ + 2x² + 2x

5 0

3 years ago

Which is the sixth sequence: an=1/125 (5n-1)

Volgvan

1. Distribute
1/125 x 5n - 1/125
2. Simplify 1/125 x 5n to n/25
n/25 - 1/125

5 0

3 years ago