This is how you solve this problem:
.10d + .05n = 5.25
(plug in the number of dimes we have)
(21 x .1) + .05n = 5.25
(multiply number of dimes x value of the dime)
2.10 + .05n = 5.25
(subtract 2.10 from both sides)
.05n = 3.15
(divide both sides by .05 to get the number of nickels)
n = 63 nickels
Hope this helps!
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)
Answer:
Remove parentheses. xy³
z^4
4Step-by-step explanation:
Answer:
y = 6x² -13x -5
Step-by-step explanation:
(1,-12) (2,-7) (5,80)
y = ax² + bx + c
-12 = a*1² + b*1 + c = a+b+c (1)
-7 = 4a + 2b + c (2)
80 = 25a + 5b + c (3)
(2)-(1): 3a + b = 5 (4)
(3)-(2): 21a + 3b = 87 (5)
(4)*3: 9a + 3b = 15 (6)
(5)-(6): 12a = 72 a = 6
(4) b = -13
(2) c = -5
