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Basicall the logarithm of a number is the EXPONENT to which TEN needs to be raised to get that number   (this is called a BASE 10 logarithm)

100 = 10^2    so the LOG of 100 is '2'  (the exponent)

45 = 10^(1.653)   so the LOG (45) = 1.653

A pascal is a  N/m^2   or kg/  m/sec^2

100, 000 kg /  (m/sec^2)  = x m x 9.81 m/sec^2 x 1000 kg/m^3

x =10.19 m    Which is a long tube to deal with  so : Often MERCURY is used instead (it is 13.56 times denser than water)

10.19 m / 13.56 = .751 m = 751 mm      so a tube of less than 1 meter could be used if you use mercury instead of H2o

1. Amy has deposited $661 in a savings account that earns interest at a rate of 3.1% compounded monthly. What will the account balance be in 15 years?

Compound interest= p*(1+r)^t

661*(1+​3.1/100)^15

I=1044.916143

Why aren't you satisfied with the answers given to you by Max Wong in your first post??? He is as good at CALCULUS as anybody else!.

7,726.99 - 5,278 =$2,448.99 simple interest earned over 16 years.

$2,448.99 / 16 =$153.06 simple interest earned per year.

$153.06 / $5,278 =0.029 x 100 =2.9% simple annual interest rate.

40 / (5/12) =96 total marbles needed

96 - (20+40) =36 new purple marbles needed.

x = number of marbles to add

the total number of marbles will be   20 + 40 + x    of which 40 will be green for a fraction of green:

40 / (20+40+x)  = 5/12      solve for x

40/(60+x) = 5/12

40 /  (5/12) = 60 + x

96    = 60 + x

x = 36 purple marbles need to be added

Thanks :)

For SIMPLE interest (no compounding)

FV = PV(1 + nr)        FV = Future value (7726.99)  PV= 5278    n = number of periods(16 years)  r= decimal interest(?)

7726.99 = 5278(1+16r)

7726.99/5278  - 1  = 16r

.463999 = 16 r

r=.028999 ~ ..029   = 2.9% interest rate

I may be wrong, but when I graph this I see no place where this equation would have a solution....   Anyone else?

Hope I am wrong and can learn something (like you!)  .....

The INTEREST Malcom receives EACH year is   567.21 x .026   and he will get EIGHT times that, PLUS his original deposit.

567.21 (1 + 8(.026) )  = $685.19 after 8 years

Make the MIDDLE number 'x'

then the number BEFORE it is 'x-1'

and the number AFTER it is 'x+1'

add them together to see if they equal   3 * x      (three times the middle number)

(x-1) + x + (x+1)  = ?   3x ?

x-1+x+x-1 =?   3x

x+x+x  = ?   3x

3x = 3x                   Proof!

HELP ME PLEASE

anyone can help me

How much VOLUME (ft^3) is in a 40kg bag of cement.....   1?   1.5?    You will need that info....PLUS are we to assume the blocks are a HOLLOW volume with no 'web' and no wall thickness?

 It would be best to know the inside dimensions of the block wall volumes.....with a wall that big, I would get a cement truck to fill it !    Bags?...ugh!   As a GUESS, this is 600+   bags of cement

These questions correct

These questions correct

Can someone answer this please...... My curiousity is telling me to take this knowledge ASAP......

We cannot show true for this for n = 0.....

If we substitute n = 0 in the LHS the last term of LHS will become \(\dfrac{1}{r}\).

So we show that this is true for n = 1......

Proof: (Induction) Basis: Show true for n = 0. LHS = 1. RHS = [r (0+1) - 1]/(r - 1) = (r-1)/(r-1) = 1. Therefore LHS = RHS. Induction: Assume 1+r+r 2+...+r k = r (k+1)-1/r-1. Show 1+r+r 2+...+r k+r (k+1) = [r (k+2) - 1]/(r - 1). Now, 1+r+r 2+...+r k+r (k+1) = r (k+1)-1/r-1 + r (k+1) = [r (k+1) - 1 + (r - 1)r (k+1) ]/(r - 1) = [r (k+1) - 1 + r×r (k+1) - r (k+1) ]/(r - 1) = [r (k+2) - 1]/(r - 1). QED

Maybe but I love puns more.

~ The smartest cookie in puns LOL

LHS stands for Left Hand Side and RHS stands for RHS. Use whatever notation your teacher tell you to use.

When n = 1,

LHS = 1

RHS = 1

LHS = RHS.

Assume that when n = k, LHS = RHS.

When n = k + 1,

\(LHS\\ = 1 + r + r^2 +... + r^k \\ =\dfrac{1-r^k}{1-r} + r^k\\ =\dfrac{1-r^k}{1-r} + \dfrac{r^k-r^{k+1}}{1-r}\\ =\dfrac{1-r^{k+1}}{1-r}\\ =RHS\)

\(\therefore\)1+r+r^2+r^3+...+r^n-1=1-r^n/1-r is true for all positive integer n.

~The smartest cookie in the world

Max: You have to qualify your statement as "The smartest cookie IN CALCULUS!"

Only 11 and a half minutes of sleep...... How did the one do it XDDDDD

1. \(f(x) = 5\pi^2\\ f'(x) = 0\text{ as it is a constant}\)

2. \(f(x) = 5\sqrt x = 5x^{1/2}\\ f'(x) = \dfrac{5}{2}\cdot x^{-1/2}=\dfrac{5}{2\sqrt x}\)

3.\(f(x) = 1x^4 = x^4\\ f'(x) = 4 x^3\)

4.\(f(x) = 2x^7 - 5x - 7\\ f'(x) = 14x^6- 5\)

5.\(f(x) = 2x - 1x^3\\ f'(x) = 2 - 3x^2\\ f'(1) = 2- 3(1)^2 = -1\)

6. \(f(x) = 3x^4\ln x\\ f'(x) = 12x^3\ln x + 3x^3\\ f'(1) = 12(1)^3 \cdot \ln 1 + 3(1)^3 = 3\)

7.\(f(x) = 8\sqrt{x + 6x^{34}}\\ f'(x) = 8\left(\left(204x^{33}+1\right)\left(\dfrac{1}{2\sqrt{x+6x^{34}}}\right)\right)\\\quad\quad\;=4\left(\dfrac{204x^{33}+1}{\sqrt{x+6x^{34}}}\right)\)

8.\(y = 5x^2 - 3\sqrt x + 5x^4\\ \dfrac{\mathtt{dy}}{\mathtt{dx}}=10x - \dfrac{3}{2\sqrt x} + 20x^3\)

9.\(y = (6x^3 + 2)(5x - 3)\\ \dfrac{\mathtt{dy}}{\mathtt{dx}}=(18x^2)(5x - 3)+(6x^3 + 2)(5) = 120x^3 -54x^2+10\)

10. \(f(t) = (8t-3)(2t+5)t - 7\\ f'(t) = (8t-3)(2t+5)+2t(8t-3)+8t(2t+5)=48t^2 +68t - 15\\ f'(1) = 48(1)^2 + 68(1) - 15 = 101\)

Finally some fun calculus questions. I was so bored in those algebra 1 in school. LOL

PS: I am 14!! :D

~The smartest cookie in the world