1. If f'(x) = x² sin 2x, what is the first value of x where the graph of f(x) changes concavity on the interval (0,5).
A. 0
B. 1.144
C. 1.571
D. 3.412
E. 2.290

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

i wish i could you, i have no idea how to answer this

step-by-step explanation:

the exponential expression to find the value of the cd, in dollars, after t years will be:  

step-by-step explanation:

formula of compound interest:   , where final value after years,   initial value, rate of interest in decimal and number of compounding in a year.

oliver plans to purchase a $1,500 certificate of deposit (cd) at his bank. that means,  

the cd will earn 2.3% interest, compounded semi-annually.

so,   and  

now, plugging these values into the above formula, we will

(rounded to the nearest ten-thousandth)

so, the exponential expression to find the value of the cd, in dollars, after t years will be: