Question 1:
A boat and a lighthouse are 70 miles apart. The bearing of the
lighthouse from the boat is 051°.
Using the scale 1 cm : 10 miles, construct a diagram showing
the relative positions of the lighthouse and the boat.
8
step-by-step explanation:
just put √(2) * √(32) into a calculator. that will make the answer be 8.
step-by-step explanation:
part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.
part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.
g[h] = (3/4)·g[h-1]
g[1] = 384 . . . . initial value required for a recursive definition
part c. the general formula for a geometric sequence is
a[n] = a[1]·r^(n-1)
we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is
g[h] = 384·(3/4)^(h-1)
part d. filling in the value and doing the arithmetic, we have
g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons
part e. each gallon is 4 quarts, so
16.2183 gal × 4 qt/gal = 64.8732 qt
the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).
lighthouse from th...