And is C
Caitlin can eliminate $54 from Food/Clothes and $120 from Entertainment.
Answer:
1 dependent
234 independent
Step-by-step explanation:
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)
Let the number of bike be x and the number of skates be y, then
21x + 20y ≥ 362 . . . (1)
2y = x . . . (2)
Putting (2) into (1), then
21(2y) + 20y ≥ 362
42y + 20y ≥ 362
62y ≥ 362
y ≥ 5.84
The least number of pairs of skates they need to rent each day to make their minimum is 6.
Answer:
Step-by-step explanation:
<u>The two angles of the triangle ADB are:</u>
- m∠A/2 and m∠B/2 or
- α/2 and β/2
<u>The three interior angles add to 180°, so the missing angle is:</u>
- m∠ADB = 180° - 1/2(α + β)
