Answer:
2. a and b only.
Step-by-step explanation:
We can check all of the given conditions to see which is true and which false.
a. f(c)=0 for some c in (-2,2).
According to the intermediate value theorem this must be true, since the extreme values of the function are f(-2)=1 and f(2)=-1, so according to the theorem, there must be one x-value for which f(x)=0 (middle value between the extreme values) if the function is continuous.
b. the graph of f(-x)+x crosses the x-axis on (-2,2)
Let's test this condition, we will substitute x for the given values on the interval so we get:
f(-(-2))+(-2)
f(2)-2
-1-1=-3 lower limit
f(-2)+2
1+2=3 higher limit
according to these results, the graph must cross the x-axis at some point so the graph can move from f(x)=-3 to f(x)=3, so this must be true.
c. f(c)<1 for all c in (-2,2)
even though this might be true for some x-values of of the interval, there are some other points where this might not be the case. You can find one of those situations when finding f(-2)=1, which is a positive value of f(c), so this must be false.
The final answer is then 2. a and b only.
Answer:
x=−2 or x=4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
x2−2x−3=5
Step 2: Subtract 5 from both sides.
x2−2x−3−5=5−5
x2−2x−8=0
Step 3: Factor left side of equation.
(x+2)(x−4)=0
Step 4: Set factors equal to 0.
x+2=0 or x−4=0
x=−2 or x=4
To determine the length of the hypotenuse, apply Pythagorean theorem.
A^2 + B^2 = C^2
(10)^2 + (24)^2 = C^2
100 + 576 = C^2
676 = C^2
C = 26 cm.
The hypotenuse is 26 cm.
The following formula is used to find the answer.
D = 50 mg (0.6^n)
D is the dosage
n is at any hour
Using this formula and solving the equation for it, the answer is 18.
