The three angles of a triangle measure 2x – 6, 3x + 5, and 2x + 20. What is the measure of the smallest angle in degrees
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
you can find where the first derivative is 0 to find the critical points
g'(x) = ( x^4 -5x^2 +4)' = 4x³-10x
g'(x) =0, make y =0 to find find where g'(x) is 0
4x³-10x =0 , factor 2x
2x(2x²-5)= 0 , each factor must be 0
2x= 0, so x= 0
2x²-5 =0, so x = ±√5/2
we now have 3 critical points -√5/2, 0, and √5/2
make intervals (-∞, -√5/2), (-√5/2, 0) , (0, √5/2) and (√5/2, +∞)
pick a point to test on each interval: -2, -1, 1 and 2 for example, and
calculate g'(x) = 4x³-10x at those points
for x= -2 we have 4(-2)³-10(-2) = -12 , negative number, decrease
for x= -1 we have 4(-1)³-10(-1) =6, positive number, increase
for x= 1 we have 4(1)³-10(1) = -6, negative number, decrease
for x= 2 we have 4(2)³-10(2) = 12, positive number, increase
we went from a decrease to an increase on intervals (-∞, -√5/2), (-√5/2, 0) so x= - √5/2 ≈ -1.58 is a minimum
we went from a decrease to an increase on intervals (0, √5/2), (√5/2, +∞) so
x= √5/2 ≈ 1.58 is a minimum as well
We have been given that during one period extreme cold, the average daily temperature decreased degree F each day. We are asked to find number of days it will take for the temperature to decrease by 9 degree F.
First of all we will convert our mixed fraction into improper fraction.
Now we will divide total temperature change (9) by average daily temperature change () to find number of days.
Dividing a number by a fraction is same as multiplying the number by reciprocal of the fraction.
Therefore, it will take 6 days for the temperature to decrease by 9 degree F.