Answer:
2a²
Step-by-step explanation:
Pair 'like' terms with 'like' terms, ie numbers go with numbers, and 'a's go with 'a's.
Lets deal with the top of the fraction first:
4ax3a³
Rearrange it so you have numbers beside numbers and 'a's beside 'a's:
(4x3)x(axa³)
12x(a⁴) <em>(because nᵃxnᵇ=nᵃ⁺ᵇ)</em>
12a⁴
Now, instead of (4ax3a³)/6a², we have 12a⁴/6a²
First divide the numbers: 12/6 =2
Now divide the 'a' parts: a⁴/a²=a² <em>(because nᵃ/nᵇ=nᵃ⁻ᵇ)</em>
Now we have 2a²
Yay, implicit differnentiation
when you take the derivitive of y, you multiply it by dy/dx
example
dy/dx y^2=2y dy/dx
for x, the dy/dx dissapears
ok
so differnetiate and solve for dy/dx
3y² dy/dx-(y+x dy/dx)=0
expand
3y² dy/dx-y-x dy/dx=0
3y² dy/dx-x dy/dx=y
dy/dx (3y²-x)=y
dy/dx=y/(3y²-x)
so at (7,2)
x=7 and y=2
dy/dx=2/(3(2)²-7)
dy/dx=2/(3(4)-7)
dy/dx=2/(12-7)
dy/dx=2/5
answer is 2/5
The answer is <span>f(x) = 2x2 + 3x – 3
</span>
f(x) = ax² + bx + c
a - the leading coefficient
c - the constant term
<u>We are looking for a = 2, c = -3</u>
Through the process of elimination:
The first (f(x) = 2x3 – 3) and the third choice (f(x) = –3x3 + 2) have x³ so these are not quadratic function.
In the function: <span>f(x) = –3x2 – 3x + 2
</span>a = -3
c = 2
In the function: f(x) = 2x2 + 3x – 3
a = 2
c = -3
