Answer:
y=2e^(−x)cosx−e^(−x)sinx
Satisfies the equation
Step-by-step explanation:
Answer:
y=2e^(−x)cosx−e^(−x)sinx
y = e^(-x)[2cosx - sinx]
Find y' and y" using product law
y' = -e^(-x)[2cosx - sinx] + e^(-x)[-2sinx - cosx]
y' = -e^(-x)[2cosx - sinx + 2sinx + cosx]
y' = -e^(-x)[3cosx + sinx]
y" = e^(-x)[3cosx + sinx] - e^(-x)[-3sinx + cosx]
y" = e^(-x)[3cosx - cosx + sinx + 3sinx]
y" = e^(-x)[2cosx + 4sinx]
y" + 2y' + 2y
e^(-x)[2cosx + 4sinx] - 2e^(-x)[3cosx + sinx] +2e^(-x)[2cosx - sinx]
e^(-x)[4sinx - 2sinx - 2sinx + 2cosx - 6 cosx + 4cosx]
= e^(-x) × 0
= 0
Answer:
11 m and 14 m
Step-by-step explanation:
Legs: x and y
---
1/2xy= 77 ⇒ xy= 154
√x²+y²= √317 ⇒ x²+y²=317
x²+y²+2xy= (x+y)²= 2*154+317= 625 ⇒ x+y= √625= 25
x= 25-y
xy=154 ⇒ y(25-y)= 154 ⇒ 25y- y²=154 ⇒ y²- 25y +154=0 ⇒ y=11 and y=14
x= 25-y= 14 and 11
Answer:
x = -8/5
Step-by-step explanation:
-3(x+4) -> -3x-12
-3x-12=7x+4
-7x
-10x-12=4
+12
-10x=16
16/-10 = -8/5
-8/5 = x
Answer:
q = 8
x₁ = -2, x₂ = -4
Step-by-step explanation:
For a quadratic equation ax² + bx + c, the sum of the roots is -b/a, and the product of the roots is c/a.
If the roots are x₁ and x₂, then:
-6/1 = x₁ + x₂
q/1 = x₁ x₂
Since we know one root is double the other, we can say x₂ = 2x₁. Plugging into the first equation and solving:
-6 = x₁ + 2x₁
-6 = 3x₁
x₁ = -2
Which means x₂ = -4. So the value of q must be:
q/1 = (-2) (-4)
q = 8
Answer:
Step-by-step explanation:
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