Please use " ^ " to denote exponentiation:
<span>f(x) = –(x + 8)^2 – 1
Find the first derivative: f '(x) = -2(x+8)(1)
Set this = to 0: -2(x+8) = 0
solve for x: x = -8
Divide the number line into subintervals based upon x=-8:
(-inf, -8) and (-8, inf)
Choose a test value for x from each interval, e. g., -10 from the first interval and 20 from the second.
Subst. this test value into the derivative, shown above.
If the result is + the function is incr on that interval; if - the fn. is decr.
Questions welcome!</span>
We have that
y=x²----> equation 1<span>
y=x+2-----> equation 2
multiply equation 1 by -1
-y=-x</span>²
add equation 1 and equation 2
-y=-x²
y=x+2
------------
0=-x²+x+2-------------> -x²+x+2=0-----> x²-x-2=0
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
(x²-x)=2
<span>Complete
the square. Remember to balance the equation by adding the same constants
to each side
</span>(x²-x+0.5²)=2+0.5²
Rewrite as perfect squares
(x-0.5)²=2+0.5²
(x-0.5)²=2.25-----> (x-0.5)=(+/-)√2.25-----> (x-0.5)=(+/-)1.5
x1=1.5+0.5-----> x1=2
x2=-1.5+0.5---- > x2=-1
for x=2
y=x²----> y=2²----> y=4
the point is (2,4)
for x=-1
y=x²----> y=(-1)²---> y=1
the point is (-1,1)
the answer isthe solution of the system are the points(2,4) and (-1,1)
2x+4=3x+1 they've substituted y =2x+4 into the second eq.
The answer to this should be 1.51
Answer:
d
Step-by-step explanation:
598.60
You are given the equation
A(t) = P*e^(rt)
Where P = Principal
r = interest rate
t = time
e is a mathematical constant equivalent to approx 2.71828
You're told the initial Principal is $500, the interest rate is 3%, over 6 years. So you have everything that you need to solve the problem, just plug in the values and solve for A(6)
A(t) = P*e^(rt)
A(6) = 500 * e^(0.03 * 6)
A(6) = 500 * e^(0.18)
A(6) = 500 * 2.71828^(0.18)
A(6) = 500 * 1.19721
A(6) = 598.60861
So $500 invested 6 years ago at 3% would be worth $598.61 today.
