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3 years ago

20. Please help I really need it

Mathematics

1 answer:

sertanlavr [38]3 years ago

5 0

Step-by-step explanation:

d if not d a.................

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Rewrite with only sin x and cos x.

Annette [7]

Option A

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Solution:

Given that we have to rewrite with only sin x and cos x

Given is cos 3x

$cos 3x = cos(x + 2x)$

We know that,

$\cos (a+b)=\cos a \cos b-\sin a \sin b$

Therefore,

$\cos (x+2 x)=\cos x \cos 2 x-\sin x \sin 2 x$ ---- eqn 1

We know that,

$\sin 2 x=2 \sin x \cos x$

$\cos 2 x=\cos ^{2} x-\sin ^{2} x$

Substituting these values in eqn 1

$\cos (x+2 x)=\cos x\left(\cos ^{2} x-\sin ^{2} x\right)-\sin x(2 \sin x \cos x)$ -------- eqn 2

We know that,

$\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x$

Applying this in above eqn 2, we get

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

$\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}$

$\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x$

Therefore,

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Option A is correct

7 0

2 years ago

The Natchez Trace Bridge in Franklin, Tennessee, is 1,500 feet long. Suppose you build a model of the bridge using a scale of 1

noname [10]

Set this up as a ratio putting inches on top and feet on bottom. Then your first ratio would be 1/25 since 1 inch is the same as 25 feet. In between them goes an equals sign and the the other ratio has an x on top (because inches is what we are looking for) and the 1500 on the bottom. Cross multiply to solve for x:
1(1500) = x(25). Divide both sides by 25 to get 60

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3 years ago

What value of x satisfies this equation, 4/5 x - 6 = -2 ? Group of answer choices

andrew11 [14]

Answer:

Step-by-step explanation:

4/5 x -6 = -2

4 x -30 = -10

-120 = -10

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2 years ago

What is an equation in point-slope form for the line that passes through the points (−3,5) and (2,−3)?

fredd [130]

(-3,5). (2,-3)
x1,y1. x2,y2

y2-y1. -3-5. -8
--------- = ------- = ----- =8 =m
x2-x1. 2-3. -1

plug the rest in

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2 years ago

Explain why the graph of quadratic function could not contain both a minimum vertex and a maximum vertex at the same time.

KonstantinChe [14]

A quadratic function is a function of the form $f(x)=ax^2+bx+c$ . The vertex, $(h,k)$ of a quadratic function is determined by the formula: $h= \frac{-b}{2a}$ and $k=f(h)$ ; where $h$ is the x-coordinate of the vertex and $k$ is the y-coordinate of the vertex. The value of $a$ determines if the parabola opens upward or downward; if $a$ is positive, the parabola opens upward and the vertex is the minimum value, but if $a$ is negative the graph opens downward and the vertex is the maximum value. Since the quadratic function only has one vertex, it could not contain both a minimum vertex and a maximum vertex at the same time.

3 0

3 years ago

20. Please help I really need it​

20. Please help I really need it