<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.
We know that two complements add up to 90.
Let's call the smaller angle x and the larger y.
3x = y
x + y = 90
We can use simple substitution.
x + 3x = 90
4x = 90
x = 22.5
Then, since we know that 3x=y, we can find the larger angle.
3*22.5 = 67.5
It will automatically be over 1
Answer:
4.908
Step-by-step explanation:
Expanded Notation Form:
4
+ 0.9
+ 0.00
+ 0.008
Expanded Factors Form:
4 × 1
+ 9 × 0.1
+ 0 × 0.01
+ 8 × 0.001
Expanded Exponential Form:
4 × 100
+ 9 × 10-1
+ 0 × 10-2
+ 8 × 10-3
Word Form:
four and nine hundred eight thousandths
0.84 more pounds of fuji apples than golden delicious apples.
