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@Guest 

I'm not sure if you're the same human who keeps helping me, but you have helped me sooo much! Thank you :)

This is the graph of a cubic equation that has zeros at 0, 1, and 2.

Its function is:  y  =  a(x - 0)(x - 1)(x - 2)

[There is no constant term since the graph passes through the origin.]

Since this function passes through the point (4, 3), we can substitute 4 for x and 3 for y:

     y  =  a(x - 0)(x - 1)(x - 2)     --->     3  =  a(4 - 0)(4 - 1)(4 - 2)     --->     3  =  a(4)(3)(2)     --->     3  =  24a

              --->  a = 1/8

Therefore, the function is:  y  =  (1/8)(x)(x - 1)(x - 2)     --->     y  =  (1/8)(x³ - 3x² + 2x)

               --->      y  =  (1/8)x³ - (3/8)x² + (1/4)x

--->     a = (1/8)     b = -3/8     c = 1/4     d = 0

--->     8a - 4b + 2c - d  =  8(1/8) -4(-3/8) + 2(1/4) - 0     =     1 + 3/2 + 1/2 - 0     =     3

ALL the denominators of your sequence follow this pattern:

a(n) = n^3 + 3 n^2 + 2 n (for all terms given) . Therefore, your sequence sums up to:

sum_(n=1)^1000000 2/(n^3 + 3 n^2 + 2 n)≈1/2

FV = PV x [1 + R]^N

FV = $0.93 x 1.0225^1,000

FV =$0.93 x 4,605,923,064.21

FV = 4,283,508,449.71 - This is how much you will have after 1,000 years @ 2.25%.

Translate it into "Plaintext", so that we can see what you have.

OK. I just saw it online. That is a lousy calculator. Here is an excellent financial calculator that will solve ALL your financial questions. Learn to use it. It will help you a lot.

https://arachnoid.com/finance/index.html

If you tell me what type of calculator you have, I will guide you through step by step to solve this problem on your calculator.

May I ask, what type of calculator do you have? It should have these keys:

N     I%YR     PV     PMT       FV

Make sure N is in MONTHS for this problem. Enter 36 under N.

Enter $4,300 under PV

Enter zero(0) under FV

Enter $156.54 under PMT. You may have to make it negative or -$156.54.

Solve for I%YR. It should give you the interest rate per month. Just multiply by 12 to give you annual interest rate compounded monthly. Depending on the calculator, it may give you annual interest rate.

Just try it and see if you get the same rate that I got above. Good luck.

There is no question here !

@Melody I have this calculator that calculates the interest for me, but I'm not good at plugging in. http://www.zenwealth.com/businessfinanceonline/TVM/TVMCalculator.html

If you hve tables Julius you may be able to use them backwards to find the approximate interest rate.

VERY NICE    

I see it is a BYO     (Bring your own)     People that is   LOL   :))

Looks a little lonely at present :)

Sachi buys a couch and a love seat for $4800. She pays $500 and finances the rest at $156.54 per month for 3 years. What annual interest rate, compounded monthly, is Sachi being charged? Round your answer to two decimal places.

$4,800 - $500 = $4,300 Amount Financed.

PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}

$156.54 =$4,300.R{[1 + R]^36 / [1 + R]^36 - 1}

P.S. There is no DIRECT or algebraic way of solving for interest rate. However, iteration and interpolation are used to get closer and closer to the actual rate. After doing that half a dozen times, I got: 1.5416667 per month or: 1.5416667 x 12 =18.5% compounded monthly.

If he spent  a    1/4   then he must have 3/4   left

So   $90   is   3/4     of the original amount

If you divide that by 3 you will have 1/4 of the original amount so

90 / 3   =  $30

$30 is   1/4   of the original amount.  

If you multiply that by 4 you will have the orriginal amount.

$30 * 4 =   $120

Take the integral:
 integral1/(3 sin(x) - 4 cos(x)) dx
For the integrand 1/(3 sin(x) - 4 cos(x)), substitute u = tan(x/2) and du = 1/2 dx sec^2(x/2). Then transform the integrand using the substitutions sin(x) = (2 u)/(u^2 + 1), cos(x) = (1 - u^2)/(u^2 + 1) and dx = (2 du)/(u^2 + 1):
 = integral2/((u^2 + 1) ((6 u)/(u^2 + 1) - (4 (1 - u^2))/(u^2 + 1))) du
Simplify the integrand 2/((u^2 + 1) ((6 u)/(u^2 + 1) - (4 (1 - u^2))/(u^2 + 1))) to get 1/(2 u^2 + 3 u - 2):
 = integral1/(2 u^2 + 3 u - 2) du
For the integrand 1/(2 u^2 + 3 u - 2), complete the square:
 = integral1/((sqrt(2) u + 3/(2 sqrt(2)))^2 - 25/8) du
For the integrand 1/((sqrt(2) u + 3/(2 sqrt(2)))^2 - 25/8), substitute s = sqrt(2) u + 3/(2 sqrt(2)) and ds = sqrt(2) du:
 = 1/sqrt(2) integral1/(s^2 - 25/8) ds
Factor -25/8 from the denominator:
 = 1/sqrt(2) integral-8/(25 (1 - (8 s^2)/25)) ds
Factor out constants:
 = -(4 sqrt(2))/25 integral1/(1 - (8 s^2)/25) ds
For the integrand 1/(1 - (8 s^2)/25), substitute p = (2 sqrt(2) s)/5 and dp = (2 sqrt(2))/5 ds:
 = -2/5 integral1/(1 - p^2) dp
The integral of 1/(1 - p^2) is tanh^(-1)(p):
 = -2/5 tanh^(-1)(p) + constant
Substitute back for p = (2 sqrt(2) s)/5:
 = -2/5 tanh^(-1)((2 sqrt(2) s)/5) + constant
Substitute back for s = sqrt(2) u + 3/(2 sqrt(2)):
 = -2/5 tanh^(-1)((4 u)/5 + 3/5) + constant
Substitute back for u = tan(x/2):
 = -2/5 tanh^(-1)(1/5 (4 tan(x/2) + 3)) + constant
Which is equivalent for restricted x values to:
Answer: | = 1/5 (log(cos(x/2) - 2 sin(x/2)) - log(sin(x/2) + 2 cos(x/2))) + constant

C(14) = 400 x 2^-(22,920/5,730)

C(14) = 400 x 2^-4

C(14) = 400 x  0.0625

C(14) = 25 grams of Carbon 14 remains after 22,920 years.

1.

(a)

Since   ∠C = ∠S  , these triangles are similar IF

\(\frac{30}{45}=\frac{16}{24} \\~\\ \frac{30\,\div\,15}{45\,\div\,15}=\frac{16\,\div\,8}{24\,\div\,8} \\~\\ \frac23=\frac23\qquad\text{true}\)

So, these triangles are similar.

(b)

Since these triangles are similar...

\(\frac{y}{14}=\frac{30}{16} \\~\\ y=\frac{30}{16}\,*\,14 \\~\\ y=26.25\)

2.

volume of cone  =  (1/3) * (pi * radius²) * (height)

                          =  (1/3) * (pi * 2²) * (8)

                          =  (1/3) * pi * 4 * 8

                          =  32pi / 3                 cubic inches

volume of block  =  length * width * height

                           =  1 * 1 * 2

                           =  2                          cubic inches

How many blocks fit into the cone?

How many   2 cubic inches   fit into    32pi / 3 cubic inches ?

\(\frac{32\pi}{3}\,\div\,2 \,=\,\frac{32\pi}{3}\,*\,\frac12\,=\,\frac{32\pi}{6}\,\approx\,16.755\)

Let's call the amount of money he withdrawed   " m " .

m - ( \(\frac14\) )m  =  90            Factor out an  m  on the left side.

m( 1 - \(\frac14\) )   =  90

m(\(\frac44-\frac14\))  =  90

m(\(\frac34\))  =  90                     Multiply both sides of the equation by \(\frac43\)

m  =  90 * \(\frac43\)

m  =  120

do 71*6

71*6=426

They will have 426 white shirts.

i am good

yoy that is cool