Answer:
69.01 m
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
Tan = Opposite/Adjacent
The tangent function is useful for problems like this. Let the height of the spire be represented by h. The distance (d) across the plaza from the first surveyor satisfies the relation ...
tan(50°) = (h -1.65)/d
Rearranging to solve for d, we have ...
d = (h -1.65)/tan(50°)
The distance across the plaza from the second surveyor satisfies the relation ...
tan(30°) = (101.65 -h)/d
Rearranging this, we have ...
d = (101.65 -h)/tan(30°)
Equating these expressions for d, we can solve for h.
(h -1.65)/tan(50°) = (101.65 -h)/tan(30°)
h(1/tan(50°) +1/tan(30°)) = 101.65/tan(30°) +1.65/tan(50°)
We can divide by the coefficient of h and simplify to get ...
h = (101.65·tan(50°) +1.65·tan(30°))/(tan(30°) +tan(50°))
h ≈ 69.0148 ≈ 69.01 . . . . meters
The tip of the spire is 69.01 m above the plaza.
Answer:
x = 3
Step-by-step explanation:
Subtract 8x from both sides.
3x+4−8x=8x−11−8x
−5x+4=−11
Subtract 4 from both sides.
−5x+4−4=−11−4
−5x=−15
Divide both sides by -5.
−5x
−5
=
−15
−5
x=3
Answer:
102 1/3
Step-by-step explanation:
To find the 6th term, add the common difference to the 5th term:
103 + (-6 2/3) = 102 1/3
C(x) = 80000 + 100x is the total cost as function of number of cycles produced
C(90) = 89000 and it costs $ 89000 to produce 90 bicycles
<em><u>Solution:</u></em>
Given that, company that manufactures bicycles has a fixed cost of $80,000
Fixed cost = $ 80,000
Let x be the number of cycles produced
Let C(x) be the total cost as function of number of cycles produced
It costs $100 to produce each bicycle
Variable cost = 100 x number of cycles produced
variable cost = 100x
The total cost for the company is the sum of its fixed cost and variable costs
total cost = fixed cost + variable cost
C(x) = 80000 + 100x
Thus total cost as function of "x" is found
<em><u>Find and interpret C(90)</u></em>
Substitute x = 90 in C(x)
C(90) = 80000 + 100(90)
C(90) = 80000 + 9000
C(90) = 89000
Thus it costs $ 89000 to produce 90 bicycles
An equation that represents the minimum and maximum scores is; |x - 82| = 3.2.
<h3>How to write an absolute value equation?</h3>
The absolute value function is defined by:
f(x) = x, x ≥ 0.
f(x) = x, x < 0.
It measures the distance of a point x to the origin.
For this problem, the distance between the minimum and the maximum scores and the mean is of 3.2, that is, the difference between these scores x and the mean of 82 is of 3.2, hence the absolute value equation that represents this situation is given by:
|x - 82| = 3.2.
Read more absolute Value equation at; brainly.com/question/5012769
#SPJ1
