24- sqrt(720/4) divide 720 by 4
24 - sqrt (180) now break down 180 to 9*4*5
24- sqrt(9) *sqrt(4) *sqrt (5) so 9becomes 3, 4 becomes 2
24- 3*2*sqrt(5) multiply 3 and 2
24-6sqrt(5)
Answer:
approx. 24.6 ft
Step-by-step explanation:
x=the distance of the fire from the base of the tower
200ft=the height of the tower
7 degrees=the angle of depression
Using these values you can draw a diagram that highlights that you need to use trig. to work out the answer.
Using Tan:
Tan 7=x/200 ft
multiply both sides by 200 ft
200*tan 7=24.55691218
approx. 24.6 ft
These equations do match up. All you have to do is find the solution to the first equation. After that, plug in that solution to the second equation. If it makes the equation true, then the equations match.
Hope this helps!
Answer:
m MN = 70°
Step-by-step explanation:
∠MLN is an angle formed by the chords ML and LN and is calculated as
∠MLN = 0.5( m arc MN ), that is
35° = 0.5 arc MN ( multiply both sides by 2 )
arc MN = 2 × 35° = 70°
Answer:
t-shirts: 2790
profit: $12209
Step-by-step explanation:
Given the function:
p(x) = -x³ + 4x² + x
we want to maximize it.
The following criteria must be satisfied at the maximum:
dp/dx = 0
d²p/dx² < 0
dp/dx = -3x² + 8x + 1 = 0
Using quadratic formula:
d²p/dx² = -6x + 8
d²p/dx² at x = -0.12: -6(-0.12) + 8 = 8.72 > 0
d²p/dx² at x = 2.79: -6(2.79) + 8 = -8.74 < 0
Then, he should prints 2.79 thousands, that is, 2790 t-shirts to make maximum profits.
Replacing into profit equation:
p(x) = -(2.79)³ + 4(2.79)² + 2.79 = 12.209
that is, $12209
