Answer:
Step-by-step explanation:
(d + 5) + (d + 5) + (d + 5).....combine like terms
3d + 15 <===
Answer:
dy/dx = e⁻²ᵗ (1 − t)
d²y/dx² = -e⁻³ᵗ (3 − 2t)
(1.5, ∞)
Step-by-step explanation:
x = eᵗ
y = te⁻ᵗ
dx/dt = eᵗ
dy/dt = -te⁻ᵗ + e⁻ᵗ
dy/dt = e⁻ᵗ (1 − t)
dy/dx = (dy/dt) / (dx/dt)
dy/dx = e⁻ᵗ (1 − t) / eᵗ
dy/dx = e⁻²ᵗ (1 − t)
d²y/dx² = d(dy/dx)/dt / (dx/dt)
d²y/dx² = (-e⁻²ᵗ − 2(1 − t) e⁻²ᵗ) / eᵗ
d²y/dx² = -e⁻²ᵗ (1 + 2(1 − t)) / eᵗ
d²y/dx² = -e⁻³ᵗ (3 − 2t)
The function is concave up when the second derivative is positive. -e⁻³ᵗ is always negative, so the second derivative is positive when 3 − 2t is negative.
3 − 2t < 0
3 < 2t
t > 3/2
Or, in interval notation, (1.5, ∞).
Answer:
Step-by-step explanation:
9x - 77 = 7x - 43
2x - 77 = -43
2x = 34
x = 17
9(17) - 77 = 153 - 77 = 76
7(17) - 43 = 119 - 43 = 76
z + 76 = 180
z= 104
The answer is c which is correct
