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6 i tink. pretty shure.

Solve ln (2x + 3) = 7   in exponential form, we have

e^7 = 2x + 3       subtract 3 from both sides

e^7 - 3  = 2x       divide by 2 on both sides

[e^7 - 3] / 2  = x   = about 546.817

Just set the onsite calculator to radian mode at the bottom left...... key in tan(4) and hit "="

Well....I don't know what we did......but we're always glad to hear success stories !!!!

I assume you have  (1/4)x^3...if so......forget the 1/4 part for a second

And the derivative of x^3, by the Power Rule, is just 3x^2....so...multiplying this by the 1/4, we have

(1/4)*3x^2  =   (3/4)x^2       and that's it.....

This equals 5/12

none bc ur stupid

Here's the last one

lim x→ 0   [3x - tan^2(7x)] / (2x)      you have the first part correct........let's look at this part

lim x→ 0   [ - tan^2(7x)] / (2x)     note we can write this as.....

lim x→ 0    -[ tan(7x)] * [tan(7x)] / (2x)...note, we can use a "trick" here for the second expression.....multiply the top and bottom by 7....this gives

lim x→ 0    -[ tan(7x)] * [7tan(7x)] / (7*2x)  =  lim x→ 0   -[ tan(7x)] * [7tan(7x)] / (2 * 7x) =

lim x→ 0   (-7/2)[ tan(7x)] * [tan(7x)] / ( 7x)      and concentrating on  [tan(7x)] / ( 7x), we can write

sin(7x)/[cos(7x)*7x] = sin(7x)/7x *1/ cos(7x)]   and using an identity,  lim x → 0   sin(7x)/7x) = 1, and

lim x→ 0   1/ cos(7x)  = 1...so we're left with

lim x→ 0   (-7/2)[ tan(7x)]   and as x → 0, tan(7x) → 0    so.... (-7/2)* 0 = 0

And your final answer of 3/2 is correct.....!!!!

so my answer is correct ! 

Oops....I'll do an edit to the original post.....sorry!!!!

the equation is:  y  =  5500ln(9t + 4)   and  t = 6

--->   y  =  5500ln(9(6) + 4)

--->   y  =  5500ln(58)

--->   y  =  22332

1 - e^1.2  =  -2.320  (approximately)

The surface area of a cone, not including the base, is:  SA  =  π·r·√(h² + r²)

Since the diameter is 12', the radius is 6'.

SA  =  π(6)√(8² + 6²)  =  6π√100  =  60π

Yeah, thanks guys that really does help! I forgot that i could just (trick or) treat it as any other equation: either 6-b=0 or a=0! 

The equation of the line is:  2x - 7y  =  35.

chris .. 

the question is  lim when x approaches to 3   not zero 

Assuming that all machines are functioning independently:

a) If the probability of failing is p, then the probability of working is (1 - p).

    The probability that all will keep working is (1 - p)^n; thus, the probability that at least one will fail is 

             1 - (1 - p)^n

b) The probability that exactly k machines will fail is n nCr k ·p^k·(1 - p)^(n- k)

c) Part b gives the individual probabilities, their sum will be the sum found in part a.

Oops! Thanks. I'm still a little confused as to what the answer turned out to be. Is it 2x - 7=35 ?

tan^2(7x)  ... 

The clarification that I would make is that the slope of a line is not found by using exponents:  rather,

m  = (y2 - y1) / (x2 - x1)  =  (-7 - -1) / (-7 - 14) =  -6 / -21  =  2/7.

So, I agree with your calculations, just not how the formula was stated.

To find the equation of the line, use the point-slope form:  y - y1  =  m(x - x1)

--->   y - -1  =  (2/7)(x - 14)   --->   y + 1  +  (2/7)(x - 14)

--->   7y + 7  =  2(x - 14)   --->  7y + 7  =  2x - 28   --->   -2x + 7y  =  -35  --->  2x - 7y  =  35

A line going through (a, b) with a slope of 0 has the equation y = b

So  a line going through (-5, -2) with a slope of 0 has the equation  y = -2

What is the number on "x" in the "tan^2"  term??

Here's (b) again

lim x → 3     (x - 3) / (1/x - 1/3)^2

Note that, getting a common denominator,   (1/x - 1/3)   becomes (3 - x) / 3x......so we have

lim x → 3     (x - 3) / [(3 - x) / 3x]^2        and notice that we can write the numerator as -(3 - x)......and this "cancels"  with one of the linear factors of (x - 3)^2 in the denominator leaving just -1 in the numerator....so we have...

lim x → 3     -1 ÷ [(3 - x) / [3x]^2].......so, if we had   -1 ÷ (5/6)    we would just invert the second fraction and change to multiplication.....doing the same thing here, we have.....

lim x → 3    -1 x   [3x]^2 / (3 - x)  =

lim x → 3    - [3x]^2 /(3 - x)

Note, that when x → 3^-, this function is negative. And when x  → 3⁺ , it's positive. Thus, the limit does not exist.