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I'm not great at Physics, but I think we can use these equations

(vf )^2  =( vi )^2 + 2ad     (1)    and

vf  = vi + a*t      →  (vf)^2  =  (vi)^2 + 2vi *a*t + (a*t)^2   (2)

Equate  (1)  and (2)

( vi )^2 + 2ad  =  (vi)^2 + 2vi *a*t + (a*t)^2      simplify

2ad  =  2vi *a*t + (a*t)^2      fill in what we know

2(35)60  = 2( vi) (35)(1.6)+ (35 * 1.6)^2

4200 = 112* vi  + 3136      subtract   3136 from both sides

1064  =  112*vi      divide both sides by 112

9.5 m/s =  vi  = initial velocity

And

vf  = vi + a*t

vf  = 9.5 + 35*1.6  =  65.5 m/s  = final velocity

Use a calculator to add this all up and you will get:

SOLUTION: Profit = $555.20

Hope that helps!

 <---- You 

Well, I have two answers for you.

1. What is 9 + 10 = 19

2. What is 9 + tan = 9tan or 9t

3. What is 9 please tan = 9 and tan

4. What is 9 please 10:  9 cannot be 10 so 9 please 10 = 9

Hope that helps!

 <---- You

Sir CPill’s answer is right. Normally, in selecting combinations the order of selection is irrelevant.  (XY is the same as YX).

However

P(35000, 2) = 1,224,965,000

This implies the enumeration counts the order of selections in addition to the combinations. In other words, order matters.   The question should state that, if that is the case. If it does not, then none of the answer choices is correct. You should let your teacher know. 

We don't know what the periods are, but the graphs appear to be normally situated....thus they are not "flipped over"  which result in both a₁ and a₂ being negative...so both are positive 

However, the amplitude of the sine graph is greater than that of the cosine graph...so...

B is the correct answer  →  0 < a₂ < a₁

A train is scheduled to make a 616 mile trip in 9 hours. The train averages 60 mph during the first 240 miles and 80 mph during the next 160 miles. What must be the average speed of the train for the remainder of the trip in order for the train to arrive on schedule?

Time traveled in the first part  =  240 / 60  =  4 hrs

Time traveled  in the second part = 180 / 80  =  2 hrs

So......240 + 160  =  400 miles have been traveled

And  616 - 400  =  216  miles are left to travel

And  there are 3 hours left to travel

So

Distance left to travel / Time left to travel  = Rate  =  216 / 3  = 72 mph

So.....the train must average 72 mph to finsih the trip on time

We want to choose any 2 of the 35,000

So  

C(35000, 2)  =  612,482,500  ways (pairs)

Sorry....footballgirl....it doesn't appear that any of the choices you have been given are correct....

Thanks!

OK.....!!!

Here's the equation we need

I  =  k / D^2   .....  and we need to find the proportionality constant, "k"....

So we have....

2  = k / 5^2

2 = k / 25       multiply both sides by 25

50  = k

And we need to solve this

I  =  50 / 15^2

I  = 50 / 225

I = 10 / 45   =   2 / 9  foot-candles

Find k if 2 is a root of x^3-(k+1)x+k=0

If 2 is a root, we have

(2)^3 - (k + 1)(2) + k  = 0      simplify

8 - 2k - 2 + k  = 0

6 - k  =  0         add k to both sides

6  =  k

Oh! The second 5 feet is supposed to be 15 feet.

Did you ask the correct queston???...we aleady know the intensity 5 feet from the light....

Thank you very much for your help! (☞ﾟヮﾟ)☞ ☜(ﾟヮﾟ☜)

I don't see a way to simplify it other the fact that the negatives cancel.

\(\frac{-3}{-5c}=\frac{3}{5c}\)

Here's the second one

25^4x  = (1/5)^{x^2}

Note that 1/5  =  5^-1    and 25  = 5^2 ....so we have....

(5^2)^4x =  (5^-1)^{x^2}

5^8x =  5^{-x^2}    the bases are the same....solve for the exponents

8x  = -x^2     add x^2 to both sides

x^2 + 8x  = 0      factor

x ( x + 8)  = 0       set both factors to 0  and solve for x and we get that

x = 0    or   x  = -8

Yes, it is like that  I still need to get the hang of writing these on a computer! Thanks!

Hard to read the frst one but I assume this is :

1. 5^{16 -(x^2 - x)}  =  25^{-(x^2 - 8)}   simplify as

   5 ^{-x^2 + x + 16}  =  (5²) ^{8 - x^2} 

    5 ^{-x^2 + x + 16}  =  5^{16 -x^2}      

Since the bases are the same.....solve for the exponents

-x^2 + x + 16   =   16  - x^2    subtract x^2 from both sides

x + 16  =  16       subtract 16 from both sides

x  = 0

[Shift] + [Mode] + [7] + [The amount of digits you want your answer to have 0~9]

What's the number ???

Let x be the smaller number and y be the larger.....so....

x + y  = 2    →   y  =  2 - x      (1)

" The difference between eight and twice the smaller number is two less than four times the larger"

translates as         [ 8 - 2x ]  + 2  =  4y   (2)

Put  (1)  into (2)   and we have that

[8 - 2x ] + 2  = 4 [ 2 - x ]      simplify

10 - 2x   =  8 - 4x           add 4x to both sides, subract 10 from both sides

2x  = -2                  divide both sides by 2

x  = -1

Sub this into (1)  to find y

y  =  2  - (-1)   =  2 + 1  =  3

Infinite solutions.....

Here's the graph :  https://www.desmos.com/calculator/dnu9y5axxn

The shaded area is the solution set.....it consists of infinite points

Thank you!!

Let's take this in parts

"The difference between four times a number and 5"  = 4N - 5

And twice this  =  2(4N - 5)   = 6

So

2(4N - 5)  = 6     divide both sides by 2

4N - 5   =  3        add 5 to both sides

4N  =  8           divide both sides by 4

N  = 2

The interest rate of 6% is not specific enough. Is it APR (Annual Percentage Rate), or is it just for the 3 months stated. Also, how often is it compounded? Is it daily, weekly monthly, quarterly,  semi-annually, annually.....etc. It is very important that the interest rate be quoted very accurately, otherwise, you will get the wrong result.

As a result, I'm going to assume that your 6% interest is annual and compounded monthly. Also, I don't quite understand your formula for a monthly payment. Therefore, I'm going to use a familiar formula that is "universal" !!.

PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}, Where R=Interest rate per period, N=number of periods, PMT=periodic payment, PV=Present value.

Under my assumption, your monthly interest rate would be =6% / 12 = 1/2%.

PMT =4,000 x 0.06/12{[1 + 0.06/12]^3 / [1 + 0.06/12]^3 - 1}

PMT =20 x {[1.005]^3 / [1.005]^3 - 1}

PMT = 20 x {1.015075125 / (1.015075125 - 1)}

PMT = 20 x {1.015075125 / 0.015075125}

PMT = 20 x                67.33444167........

PMT =$1,346.69 - This is the payment for 3 months on $4,000 loan @ 6% compounded monthly.

The product of 4 and a number  = 4N....so......we have

4N  -  12