This creates a right triangle. One leg of the triangle is 25 feet and the other is 10 feet. To find the length of the ladder, we must use Pythagorean theorem.
a = 25
b = 10
c = ?
(25)^2 + (10)^2 = c^2. Square all the terms to the left of the equation and add them together.
725 = c^2. Take the square root of each side.
c = 26.93 feet.
The ladder needs to be 26.93 feet tall.
If the number is taken as x,
15x - 8
<span>A. 504 in2 B. 396 in2 C. 312 ... ... A. 155 in2 B. 270 in2 C. 300 in2 D. 310 in2 H=15 l=5 w=4 ... The formula for the rectangular prism surface area is 2(wl+hl+hw).</span><span>300 in2</span>
Answer:
y = (11x + 13)e^(-4x-4)
Step-by-step explanation:
Given y'' + 8y' + 16 = 0
The auxiliary equation to the differential equation is:
m² + 8m + 16 = 0
Factorizing this, we have
(m + 4)² = 0
m = -4 twice
The complimentary solution is
y_c = (C1 + C2x)e^(-4x)
Using the initial conditions
y(-1) = 2
2 = (C1 -C2) e^4
C1 - C2 = 2e^(-4).................................(1)
y'(-1) = 3
y'_c = -4(C1 + C2x)e^(-4x) + C2e^(-4x)
3 = -4(C1 - C2)e^4 + C2e^4
-4C1 + 5C2 = 3e^(-4)..............................(2)
Solving (1) and (2) simultaneously, we have
From (1)
C1 = 2e^(-4) + C2
Using this in (2)
-4[2e^(-4) + C2] + 5C2 = 3e^(-4)
C2 = 11e^(-4)
C1 = 2e^(-4) + 11e^(-4)
= 13e^(-4)
The general solution is now
y = [13e^(-4) + 11xe^(-4)]e^(-4x)
= (11x + 13)e^(-4x-4)
