6) Evaluate using U-Substitution

a) x2x3+5 dx           ;       Let U = x³ + 5

b) e5x dx            ;        Let U = 5x

c) dx25- x2            ;         Let x = 5 sin U  

d) (sec²(1 - 4x) dx

5. 01(3t-1)50 dt

Solve for​ Y(s), the Laplace transform of the solution​ y(t) to the initial value problem below. y'''+7y''+4y'-12y= -24, y(0) = 11, y'(0)= 5, y''(0) = -43

Solve linear equations by Gaussian Elimination

2x-3y+z-w+u=0

4x-6y+2z-3w-u=-5

-2x+3y-2z+2w-u=3

Let f(t) be the weight (in grams) of a solid sitting in a beaker of water after t minutes have elapsed. Suppose that the solid dissolves in such a way that the rate of change (in grams/minute) of the weight of the solid at any time t can be determined from the weight using the forumula:

f′(t)=−4f(t)(6+f(t))

If there is 1 grams of solid at time t=2 estimate the amount of solid 1 second later.

(1 point) If C is the curve given by r(t)=(1+5sint)i+(1+3sin2t)j+(1+3sin3t)k, 0≤t≤π2 and F is the radial vector field F(x,y,z)=xi+yj+zk, compute the work done by F on a particle moving along C.

688^79 mod 3337 (i think it is about RSA and I want the detail step)Thanks

Consider the following vectors:

→a =

5

−1

3

3

→b =

5

0

1

0

→c =

−10

3

−3

−7

For each of the following vectors, determine whether it is in span{→a, →b, →c}. If so, express it as a linear combination using a, b, and c as the names of the vectors above.

→v₁ =

5

−3

2

7

< Select an answer >

→v₂ =

2

7

6

−7

< Select an answer >

→v₃ =

30

−7

10

17

< Select an answer >

Prove that the angle bisectors of a triangle are concurrent using the Pointwise Characterization of an Angle Bisector.

Suppose a system of linear equations has 2 equations and 3 variables.

(a) True or False: The system could have no solutions.

(b) Produce an example of a system with 2 equations and 3 variables that

has no solution, or explain why such a system is impossible.

Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of 30 dollars and a standard deviation of 9 dollars.

A. What proportion of the bank's Visa cardholders pay more than 34 dollars in interest?

B. What proportion of the bank's Visa cardholders pay more than 39 dollars in interest?

C. What proportion of the bank's Visa cardholders pay less than 21 dollars in interest?

D. What interest payment is exceeded by only 19% of the bank's Visa cardholders?

Use the definition of Taylor series to find the first three nonzero terms of the Taylor series (centered at c) for the function f.

f(x) = 7 tan x,  c = 9π

A pair of fair dice are rolled once. Suppose that you lose $7 if the dice sum to 3 and win $12 if the dice sum to 4 or 12. How much should you win or lose if any other sum turns up in order for the game to be fair.

I got a negative answer and im not sure thats correct.

Using either logarithms or a graphing​ calculator, find the time required for ​$5000 to be at least equal to ​$9000 when deposited at 5 ​% compounded monthly.