This problem can be solved with simple subtraction. 150.25 minus 78 will give you the answer you need. (72.25 yards of rope)
Answer:
Step-by-step explanation:
take 45 degree as reference angle
using sin rule
sin 45 =opposite /hypotenuse
1/
=24/k(do cross multiplication)
24=k
Answer:
Step-by-step explanation:
A) Using the foil method and distribution, you should get x²+10x+7x+70 from (X×X)+(X×10)+(X×7)+(7×10). When you combine these like terms, you get x²+17x+70.
B) Using the same ideology from part A, when you multiply x-3 into x-9. you should get x²-9x-3x+27. Simplifying this will give you x²-12x+27.
Answer:
perpendicular
Step-by-step explanation:
if you find the slope of the points, they are completely opposite 4/3 and -3/4
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, ∞).
