Answer:
d = 6
Step-by-step explanation:
The nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₄ = 23 and a₁₁ = 65 , then
a₁ + 3d = 23 → (1)
a₁ + 10d = 65 → (2)
Subtract (1) from (2) term by term to eliminate a₁
10d - 3d = 65 - 23
7d = 42 ( divide both sides by 7 )
d = 6
Answer:
666,000
Step-by-step explanation:
18000
×37= 666,000
Answer: 335ft
Step-by-step explanation:
The tangent of the angle of elevation is the ratio of the dam height h to the horizontal distance downriver of the observer. This gives us two equations for the height:
h= atan(1.1) = (155+a) tan(0.8)
⟹a= h/tan(1.3), 155+a= h/tan(0.8).
Subtracting the first equation from the second,
155=(155+a)−a =h/tan(0.8)−h/tan(1.1)
=h(1/tan(0.8)−1/tan(1.1)).
Solving for h,
h=155 ft (1tan(0.8)−1tan(1.1))−1
155(0.9713 - 0.5090)^-1
155(2.1631) ≈335 ft .
