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4 years ago

Find exact solutions of

Mathematics

1 answer:

MrRa [10]4 years ago

5 0

Answer:

Step-by-step explanation:

cos(2x+√3)+cos 2x=0

2 cos (2x+√3+2x)/2 cos (2x+√3-2x)/2=0

or cos(2x+√3/2) cos √3/2=0

or cos (2x+√3/2)=0=cos (2n+1)π/2

or 2x+√3/2=(2n+1)π/2

or x=(2n+1)π/4+√3/4

x=π/4+√3/4=(π+√3)/4,(3π+√3)/4,(5π+√3)4,(7π+√3)/4,(9π+√3)/4,(11π+√3)/4,(13π+√3)/4,(15π+√3)/4

(4π=4×3.14=12.56 nearly)

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I'm super confused on parts g and h because no formula is given, just the limit values. These are the values:

Mrrafil [7]

Answer:

See below.

Step-by-step explanation:

So we have the limit:

$\lim_{x\to 4} (f\circ g)(x)$

This is equivalent to:

$\lim_{x\to 4} f(g(x))$

To solve, we can use the following property:

$\lim_{x \to c} f(g(x))=f( \lim_{x \to c} g(x))$

Therefore, our limit is the same as:

$\lim_{x\to 4} f(g(x))\\=f(\lim_{x\to 4} g(x))$

We are already given that the limit as x approaches 4 of g(x) is -2. Therefore:

$=f(-2)$

You simply need to evaluate this to solve the limit. I don't have enough information to solve this, so maybe you have something more.

Similarly, for the second one:

We have:

$\lim_{x\to 4} (g\circ f)(x)\\=\lim_{x\to 4}g(f(x))$

Using the same property:

$=g(\lim_{x\to 4} f(x))$

And we are told that this is 16, so:

$=g(16)$

And we just need to evaluate this to find the limit.

I hope you find this helpful!

8 0

3 years ago

What is the answer to 2 X 2/3<br> Need help ASAP

Alona [7]

Answer:

1.33333333333 , simplified to 1.3

Step-by-step explanation:

Our equation is 2 multiplied by 2 over 3.

Fractions mean division.

So, let's multiply 2 by 2/3.

We get 1.33333333333

That's too long! What can we simplify it to?

1.3

Hope this helped!

- Melanie

8 0

3 years ago

Read 2 more answers

Kirk has 42 pieces of candy to divide evenly between his three children if he puts the pieces into three boxes how many pieces o

noname [10]

So what you would do is, 42 divided by 3, which would equal 14, so Kirk would put 14 pieces of candy in a box. I hope this could help.

3 0

4 years ago

PLS HELP ME WITH MY COUSIN HOMEWORK

wariber [46]

Answer:

Decrease

Increase

Decrease

Increase

Step-by-step explanation:

(I am slightly guessing because I am still slightly confused, buttt)

Just looking at the distance, it would depend on what the orginal was though so I am not 100% confident!

5 0

3 years ago

Find two consecutive even integers such that the square of the second, decreased by twice the first is 52

Fiesta28 [93]

Let the first integer be $x$ . So, the next even number is $x+2$

Let's translate the formula: the square of the second is $(x+2)^2$ , twice the first is $2x$ . So, the equation is

$(x+2)^2 - 2x = 52$

Expand the square to get

$x^2+4x+4-2x = 52 \iff x^2+2x+4 = 52 \iff x^2+2x - 48 = 0$

The solutions to this equations are

$x = -8,\quad x = 6$

So, the possible consecutive even numbers are

$-8\text{ and } -6\quad\text{or}\quad 6\text{ and } 8$

8 0

3 years ago