Answer:
ABD = CDB
AB is parallel to DC
Step-by-step explanation:
angle a and c are right angles so they are equal and angle b and d are equal because they have a line that touch both letters
AB and DC are parellel because they are the same looking lines just on oppisite sides
Answer:
isometry
Step-by-step explanation:
Answer:
y(t) = 2.5 e⁶ᵗ + 2.5 e⁻⁶ᵗ
Or
y(t) = 5 e⁻⁶ᵗ
Step-by-step explanation:
y(t) = c₁ e⁶ᵗ + c₂ e⁻⁶ᵗ
Let us find our value for y(t) that satisfies the conditions
1) y" - 36y = 0
y" = (d²y/dt²)
y(t) = c₁ e⁶ᵗ + c₂ e⁻⁶ᵗ
y' = (dy/dt) = 6c₁ e⁶ᵗ - 6c₂ e⁻⁶ᵗ
y" = (d/dt)(dy/dt) = 36c₁ e⁶ᵗ + 36c₂ e⁻⁶ᵗ
y" - 36y = 36c₁ e⁶ᵗ + 36c₂ e⁻⁶ᵗ - 36(c₁ e⁶ᵗ + c₂ e⁻⁶ᵗ) = 36c₁ e⁶ᵗ + 36c₂ e⁻⁶ᵗ - 36c₁ e⁶ᵗ - 36c₂ e⁻⁶ᵗ = 0.
The function satisfies this condition.
2) y(0) = 5
y(t) = c₁ e⁶ᵗ + c₂ e⁻⁶ᵗ
At t = 0
y(0) = c₁ e⁰ + c₂ e⁰ = 5
c₁ + c₂ = 5 (e⁰ = 1)
3) lim t→+[infinity] y(t)=0
y(t) = c₁ e⁶ᵗ + c₂ e⁻⁶ᵗ
y(t) = c₁ e⁶ᵗ + c₂ e⁻⁶ᵗ = 0 as t→+[infinity]
c₁ e⁶ᵗ = - c₂ e⁻⁶ᵗ as t→+[infinity]
c₁ = - c₂ e⁻¹²ᵗ as t→+[infinity]
e⁻¹²ᵗ = 0 as t→+[infinity]
c₁ = c₂ or c₁ = 0
Recall c₁ + c₂ = 5
If c₁ = 0, c₂ = 5
If c₁ = c₂, c₁ = c₂ = 2.5
y(t) = c₁ e⁶ᵗ + c₂ e⁻⁶ᵗ = 2.5 e⁶ᵗ + 2.5 e⁻⁶ᵗ
Or
y(t) = 5 e⁻⁶ᵗ
Answer: 122
Explanation: 250 - 5 = 245
(The 5 comes from the president, Vice President, two volunteers, and guess speaker)
245/2 = 122.5
Half a couple cannot attend so the answer would be 122 couples can attend
Question #1 is x=-44
Question #2 is both points are a local minimum
Question #3 is g''=(x^2-4x+16)/(x-2)^2 since g'' is never negative, g is never concave down
Question #4 is y-4=-9(x-3)
Question #5 is since the graph is always concave up, any tangent lines muse lie below the graph.
I hope that helped