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Paradoxically, when you multiply x by 2   in the trig functions    cos 2x     the period is HALVED    so    pi

sooooooo......you should be able to figure out what the second one is.....    cos 2x

For the third one, continuing.....the period is still  2pi   but the amplitude is reduced to 1/2  ....and it is FLIPPED ...so    -1/2 cos x

Frequency = 1/period = 1/pi     (1 cycle in pi time    1/pi)

For the last one....just make the cosine  wave 4 times taller      at    pi/2    and   3pi/2  the value is still 0  

thank you for the help!!

The maximum value of the waveform is -2

Amplitude is 1/2 of the total wave height    1/2 * 10 = 5

Sine wave shifted upby 4     Midline is between the min and max of the wave

                                                 min 2   max 6      midway would be y = 4

You want to solve the given equation for y = 1

1=-16t^2+8t    re-arrange

-16t^2+8t-1 = 0    solve for t using quadratic formula    a = -16   b = 8  c = -1

t= 1/4 sec

When y = 0 the paintbrush hits the ground.

0=25-16t^2       solve for t

25=16t^2

25/16 = t^2

t = 5/4 sec      (the other solution for t^2)   -5/4 sec is invalid for a time

The secant will only be positive where the cosine is positive

From   - 180  to -90   the cosine is negative

From  (-90 to 90 )   the cosine is positive

Note    sec  θ =  2      means that   cos  θ   =  1/2

And this happens at    -60°     and   60°     on the requested interval

Sec = 1/cos

1/cos =2

1 = 2 cos

1/2 = cos        60 degrees  and -60 degrees         Cos of -120 = -1/2   cos of -180 = -1  

25%  =  .25

"Of" means " multiply"   ...  so...

.25 * 40  =

10

We have infinite values of a  and b that work

a = 4    b  = 1

a = 6   b = 2/3

a = 8   b  = 1/2

etc.....

#/# like 1/2

4.

Which statement is true about this argument?

Argument

if a number is divisible by 2, then it is even.

The number 4 is even.

Therefore, the number 4 is divisible by 2.

Let  P  =   a number is divisible by 2

Let Q =  the number is even

Then we have the form....

Statement 1 : If P, then Q

Statement 2  :   Q

Conclusion :  P

This follows the Law of Detachment

Thanks so much!

See my answer, here, JGA....it's the second one...

https://web2.0calc.com/questions/help-plz-plz

2.For the conditional statement, "if you fly from new york to californi, then you travel from east to west," which other form of the conditional must be true?

The one that is true is :

if you do not travel from east to west, then you do not fly from new york to california

This is the contrapositive to the original conditional

We have that

F = (9/5)C + 32

We are trying to convert 34C   to  Fahrenheit

So.....the first step is to sub in 34 for C

Yay! Thank you

Let's list the first few terms....

5 , 8, 11, 14....

So....the rule is

a_n = 3n + 2

Let's list the first few terms

- 2, - 6, - 18, -54

Note that each succesive term is just 3 times the previous.....so....

The recursive rule is

a_n =  3* a_n-1, a1 = -2

Degree =   5 + 3   =  8

Number of Terms = 3

Leading coefficient  = 5

Descending   x⁵ ⇒ x³ ⇒ x

1. Which statement about the following argument is true?

If an animal is a koala, then it must be a marsupial. That animal is a marsupial. Therefore, it is a koala.

This is not a valid argument

An animal may be a marsupial.....but not necessarily be a koala...

The third one......test it by putting in values for the n

n=1    she saves 1 dime    2^(1-1) = 2^0 =1       Check!

day2 n=2     she saves 2 dimes    2^(2-1) = 2^1 = 2    check !

day3 n=3 she saves 4 dimes       2^(3-1) = 2^2 = 4     check!

etc

etc.

Looks about right.

In general

m angle 3  +  angle 4 = 180 degrees