Minimum value is equal to x=8, y=-4First find the derivative of the original equation which equals= d/dx(x^2-16x+60) = 2x - 16at x=8, f'(x), the derivative of x equals zero, so therefore, at point x = 8, we have a minimum value.Just plug in 8 to the original equation to find the answer for the minimum value.
Answer:
Step-by-step explanation:
Find the slope, denoted m
This is done by using the formula m = (y2 - y1)/(x2 - x1)
The slope for this problem is
m = [-3 - (-1)]/[8 - (-2)]
m = -2/10 = -1/5
Answer:
Step-by-step explanation:
Given the expression cosec (x) = 4 and tan(x)< 0
since cosec x = 1/sinx
1/sinx = 4
sinx = 1/4
From SOH, CAH TOA
sinθ = opposite/hypotenuse
from sinx = 1/4
opposite = 1 and hypotenuse = 4
to get the adjacent, we will use the Pythagoras theorem
adj² = 4²-1²
adj² = 16-1
adj ²= 15
adj = √15
cosx = adj/hyp = √15/4
tanx = opposite/adjacent = 1/√15
since tan < 0, then tanx = -1/√15
From double angle formula;
sin2x = 2sinxcosx
sin2x = 2(1/4)(√15/4)
sin2x = 2√15/16
sin2x = √15/8
for cos2x;
cos2x = 1-2sin²x
cos2x = 1-2(1/4)²
cos2x = 1-2(1/16)
cos2x= 1-1/8
cos2x = 7/8
for tan2x;
tan2x = tanx + tanx/1-tan²x
tan2x = 2tanx/1-tan²x
tan2x = 2(-1/√15)/1-(-1/√15)²
tan2x = (-2/√15)/(1-1/15)
tan2x = (-2/√15)/(14/15)
tan2x = -2/√15 * 15/14
tan2x = -30/14√15
tan2x = -30/7√15
rationalize
tan2x = -30/7√15 * √15/√15
tan2x = -30√15/7*15
tan2x = -2√15/7
Answer:
2 and 3/4
11/4
Step-by-step explanation:
an improper fraction is any fraction with a numerator bigger then the denominator.
a mixed number is the "proper" version of an improper fraction.
the fraction 11/4 as a mixed number is 2 and 3/4.
to make an improper fraction a mixed number, find out how many times the denominator goes into the numerator. whatever you have left that didn't make 1 whole, turns into the fraction .
hope this helped
