I'm only going to alter the left hand side. The right side will stay the same the entire time
I'll use the identity tan(x) = sin(x)/cos(x) and cot(x) = cos(x)/sin(x)
I'll also use sin(x+y) = sin(x)cos(y)+cos(x)sin(y) and cos(x+y) = cos(x)cos(y)-sin(x)sin(y)
So with that in mind, this is how the steps would look:
tan(x+pi/2) = -cot x
sin(x+pi/2)/cos(x+pi/2) = -cot x
(sin(x)cos(pi/2)+cos(x)sin(pi/2))/(cos(x)cos(pi/2)-sin(x)sin(pi/2)) = -cot x
(sin(x)*0+cos(x)*1)/(cos(x)*0-sin(x)*1) = -cot x
(0+cos(x))/(-sin(x)-0) = -cot x
(cos(x))/(-sin(x)) = -cot x
-cot x = -cot x
Identity is confirmed
<h3>Given</h3>
Two positive numbers x and y such that xy = 192
<h3>Find</h3>
The values that minimize x + 3y
<h3>Solution</h3>
y = 192/x . . . . . solve for y
f(x) = x + 3y
f(x) = x + 3(192/x) . . . . . the function we want to minimize
We can find the x that minimizes of f(x) by setting the derivative of f(x) to zero.
... f'(x) = 1 - 576/x² = 0
... 576 = x² . . . . . . . . . . . . multiply by x², add 576
... √576 = x = 24 . . . . . . . take the square root
... y = 192/24 = 8 . . . . . . . find the value of y using the above equation for y
The first number is 24.
The second number is 8.
Answer:
$51.30
Step-by-step explanation:
76 decrease 25% =
76 × (1 - 25%) = 76 × (1 - 0.25) = 57
57 decrease 10% =
57 × (1 - 10%) = 57 × (1 - 0.1) = 51.3
Answer:
(1,64 °F − 32) × 5/9 = 73,333 °C
