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3 years ago

F(x) = 2^x what is the domain ? range ? asymptote ? and transformation

Mathematics

1 answer:

erica [24]3 years ago

7 0

y=2x

Step-by-step explanation:

I dont know what else there is sry

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A circle with center c(4,-2) contains the point D( 8,1). What is the equation of the line perpendicular to the radius of the cir

Nady [450]

Answer:

4x +3y = 10

Step-by-step explanation:

The radius CD has slope Δy/Δx = (1-(-2))/(8-4) = 3/4.

The equation for the perpendicular line through point C(4, -2) can be written as ...

Δx(x -4) +Δy(y -(-2)) = 0

4(x -4) +3(y +2) = 0

4x +3y -10 = 0 . . . . . . general form equation for the line

4x +3y = 10 . . . . . . . . .standard form equation for the line

8 0

3 years ago

Solve the equation for all real values of x.<br> cosxtanx - 2 cos x=-1

IceJOKER [234]

Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

<u>Step-by-step explanation:</u>

Here we have , $cosxtanx - 2 cos^2 x=-1$ . Let's solve :

⇒ $cosxtanx - 2 cos^2 x=-1$

⇒ $cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1$

⇒ $sinx = 2 cos^2 x-1$

⇒ $sinx = 2 (1-sin^2x)-1$

⇒ $sinx = 1-2sin^2x$

⇒ $2sin^2x+sinx-1=0$

By quadratic formula :

⇒ $sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}$

⇒ $sinx = \frac{-1 \pm3}{4}$

⇒ $sinx = \frac{1}{2} , sinx =-1$

⇒ $sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}$

⇒ $x=\frac{\pi}{6} , x=\frac{3\pi}{2}$

But at $x=\frac{3\pi}{2}$ we have equation undefined as $cos\frac{3\pi}{2}=0$ . Hence only solution is :

⇒ $x=\frac{\pi}{6}$

Since , $sin(\pi -x)=sinx$

⇒ $x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}$

Now , General Solution is given by :

⇒ $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$

Therefore , Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

3 0

3 years ago

I WILL GIVE BRAINIEST TO THE BEST ANSWER

Natalka [10]

Domain is the values of x. x is from -5 to 7, it includes -5 ([ ] is the include symbol, but doesn't include 7, so C is the answer

6 0

3 years ago

Read 2 more answers

6) The sum of three consecutive numbers is 120.<br> What is the smallest of the three numbers ?

bekas [8.4K]

Answer:

Step-by-step explanation:

Let the smallest number be n,

then the three numbers are n, n+1 and n+2

Therefore, n+(n+1)+(n+2)=120

Collecting like terms,

n+n+n=120-1-2

3n=117

n=117/3

n=39

Therefore the numbers are 39,40 and 41.

And the smallest number is 39.

8 0

3 years ago

Please help ASAP Use the screenshot answer the question

Hoochie [10]

Answer:

0.35, 0.40

Step-by-step explanation:

4 0

2 years ago