This is a differential equations problem. We are to work backwards and determine the function f(x) when given f "(x) and initial values.
<span>f ''(x) = 12x^2 + 6x − 4, when integrated with respect to x, yields:
x^3 x^2
f '(x) = 12------ + 6----- - 4x + C, or 4x^3 + 3x^2 - 4x + C, and
3 2
x^4 x^3 x^2
f(x) = 4------- + 3------- - 4------ + Cx + D, or f(x)=x^4 + x^3 - 2x^2 + Cx + D
4 3 2
Now, because f(0)=5, 5=0^4 + 0^3 -2(0)^2 + C(0) + D, so that D=5.
Determine D in the same manner: Let x=1 and find the value of C.
Then the solution, f(x), is x^4 + x^3 - 2x^2 + Cx + 5. Replace C with this value and then you'll have the desired function f(x).</span>
Answer:
To be greater than 20, we can either use values of 2 through 9 for the first digit, which is a total of 8 digits. For the second digit, in order to be even, we can use 1, 3, 5, 7, or 9. ( 5 options). Multiply together and we have the total number of possibilities.
Answer:
-3/19
Step-by-step explanation:
slope = rise/run = (y1 - y2) / (x1 - x2)
s = (19 - 16) / (-9 -10)
s = 3/-19 = -3/19
Answer:
x = 19/3
Step-by-step explanation:
30 - 11 = 3x
3x = 19
x = 19/3
hope it helps!
Remember
∛(xy)=(∛x)(∛y)
3rd power
factor inside and group
384=2*2*2*2*2*2*2*3=2^3*2^3*2*3=2^3*2^3*6
∛384=(∛2^3)(∛2^3)(∛6)=(2)(2)(∛6)=4∛6
C
