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1150 + 150n     n from 1 to 12

n = 12    an = 1150+1800=2950

s= n (a1+ an)/2

12(1150+2950)/2=24600

Explains why CPhills is so high...

To solve the first one, let's try to first find the 26th number. Notice there is a pattern:

To get to the second number from the first, we take one step and go forward 4.

To get to the third number from the first, we take 2 steps and go forward 8.

To get to the fourth pattern from the first, we take 3 steps and go forward 12.

See the pattern? To get to the nth term from the first, we take n - 1 steps and go forward 4(n - 1). (It is multiplied by 4 because the difference between two neighbouring numbers is 4.) We want to get to the 26th term, so we take 25 steps and go forward 4 * 25 = 100. So, the 26th term is 100 + 7 = 107.

To find the sum of 7 + 11 + 13 + 17 + 21 + ...... + 99 + 103 + 107, imagine pairing the 1st with the 26th, the 2nd with the 25th, the 3rd with the 24th, and so on. There will be 26 / 2 = 13 pairs with each one summing to 7 + 107 = 114. So, the sum is 13 * 114 = 1482.

To solve the second one, first note that the weird looking symbol just means summation. The n = 1 on the bottom tells us what number to plug into the expression on the side, 4n + 1. Then, we repeat with 2, 3, 4, 5, all the way up to the number on the top, 32. Then, we sum all of these values. So, what we want is 5 + 9 + 13 + 17 + ..... + 121 + 125 + 129. Pair them up again to get 32 / 2 = 16 pairs with each one having a sum of 5 + 129 = 134. Multiply to get 16 * 134 = 1600 + 480 + 64 = 2080 + 64 = 2114.

To solve the third one, we already know what we want: 1 + 2 + 3 + 4 + 5 + ..... + 199 + 200. Pair these up to get 200 / 2 = 100 pairs, with each one summing to 1 + 200 = 201. So, the sum is 20100.

The answers are:

1. 1482

2. 2114

3. 20100

Hope this helped, 

asdf334

Sn=n(a1 + an)/2

First one:  n=26   a₁=7   an= 7+25(4)      Can you do it now?

Second one    n=32    a1=5    a32= 1+4*32

third one    a1 = 1    an=200   n= 200

The period has pi in it, so the answer can't be A or D. We know that (0, 10) is on the graph because the y-intercept is 10. Plug this into both of them to get 3 = 10 and 10 = 10. The one that is true is 10 = 10, which corresponds to \(\boxed{C}\).

For each one, we check to see if any part of the interval is below the x-axis. If so, we do not check that one. For (-2, 0), we can tell that the whole function is negative, not positive. (An example is (-1, -1.475), where the y-coordinate is negative.) For (0, 4), by inspection, there is no part of the graph below the x-axis. For (4, ∞), we see that something like (5, y) is already way under the x axis, so this is not a choice. 

For (-∞, -2), we can see that all of it is above the x-axis. So, this is an option. For (2, 2.5), this includes the interval at the topmost part of the second curve. This is above the x-axis, so this is a choice. Finally, for (-1.5, -1), this is the bottommost part of the first curve, which is below the x-axis. So, this does not work.

So, our final answers are (0, 4), (-∞, -2), and (2, 2.5). (2nd, 4th, and 5th choices.)

~ asdf334

I think that shows their activity.....as a bar graph

it is a right isosceles triangle.  Notice the formula is the same as the double angle formula sin(2x) = 2sin(x)cos(x).  Here 2x = A and x = B = C.  Without proof I show that sin(90) - 2sin(45)cos(45) = 0 since 1 -2(1/sqrt2)(1/sqrt2) = 0.

But a proof shows that it does not have to be a right triangle -- just any isosceles triangle

sinA = 2sinBcosC

sinA = sin(180 -(B + C)) = sin(B + C)

sinA = sinBcosC + cosBsinC

2sinBcosC = sinBcosC + cosBsinC

simplifying

sinBcosC = cosBsinC

sinB/cosB = sinC/cosC

tanB = tanC

B = C

the triangle is isosceles

Not sure I agree with this Chris......as I stated...it IS true that it is positive for this interval too  (2,2,5)

Yeppers!  

Ohhh I see and it is a decrease, so the first option should be the correct answer I believe

No, you did it correctly    -10.6  is in thousands as the question stated....

I did (217.2 - 238.4) / 2 on my calc and got -10.6.

Did i do something wrong?

Yes.....................5.3 years

(Year 4 profit - year 2 profit )  / 2  = average      DOes that help?    (if it is negative...it is a decrease)

Sorry...I misread the question and edited my answer...... third choice

Ok thx, & you said the answer for the second question is 5.3?

 I dunno.....I think he may have gone for a beer !

Thanks, ElectricPavlov! Is CPhill still typing an answer?

When debt = 0   f(x) = 0

0 = -4x^2+10x+60       Solve for x

I used quadratic formula

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)      with a = -4  b = 10  c = 60   to find x = -2.82   and  5.32    (throw out the negative)   5.3 years

First equation gives the input  RATE.....second equation gives the output RATE

first equation - second equation = net input rate    (like how much is filling the tub)

(3)    will tell you the NET RATE of tank filling at 3 hr

3(3^2)+2     -   (4(3)-1 )=

29 - 11 = 18     After 3 hours THE FILLING RATE is 18 gallons/hr

5/7   x  49 =  35 sold

It is positive  on the  interval(s)  on x where the function is above the x axis.....note that these are

(-inf, -2)  and (0, 4)