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2 years ago

Part A: Solve −np − 70 < 40 for n.

1 answer:

5 0

Solve for n the first can be like:-NP<40+70. -NP<110 the second one can be like : 4w-7k =28. solve for k and then, -7k=28-4w divide both sides by -7 that equal to k =-4-4w

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A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, t

maksim [4K]

Answer:

Boat traveled 553.24 feet towards the lighthouse.

Step-by-step explanation:

In the figure attached AB is the light house of height 200 feet.

Angle of depression of the boat from the top of a lighthouse = angle of elevation of the lighthouse from the boat = 14°52'

so 1' = $\frac{1}{60}$ degree

so angle of elevation at point C = 14 + $\frac{52}{60}$

So angle of elevation from C = (14 + 0.87) = 14.87°

Similarly, when boat arrives at point D angle of elevation = 45°10' = 45 + $\frac{10}{60}$ = 45.17°

Now we have to calculate the distance CD, traveled by the boat.

In ΔABC

tan14.87 = $\frac{200}{BC}$

0.2655 = $\frac{200}{BC}$

BC = $\frac{200}{0.26552}$

BC = 753.239 feet

Similarly in ΔABD

tan45.17 = $\frac{200}{BD}$

1 = $\frac{200}{BD}$

BD = 200 feet

So distance CD = BC - BD

CD = 753.239 - 200

= 553.24 feet

Therefore, Boat traveled 553.24 feet towards the lighthouse.

7 0

2 years ago

Read 2 more answers

The function D(t) defines a traveler's distance from home, in miles, as a function of time, in hours. D(t) = StartLayout enlarge

nalin [4]

- At 2 hours, the traveler is 725 miles from home.

- At 3 hours, the distance is constant, at 880 miles. --> TRUE.

- The total distance from home after 6 hours is 1,062.5 miles --> TRUE.

Step-by-step explanation:

The function D(t) is defined as follows:

$D(t) = 300t+125$ for $t< 2.5$

$D(t) = 880$ for $2.5 \leq 3.5$

$D(t) = 75t+612.5$ for $t\leq 6$

Where

t is the time in hours

D(t) is the distance covered, in miles, after t hours

Now let's analyze the different statements:

- The starting distance, at 0 hours, is 300 miles. --> FALSE. In fact, if we substitute t = 0 into the 1st equation, we get

$D(0) = (300)(0)+125 = 125$

So, the distance at t = 0 is 125 miles.

- At 2 hours, the traveler is 725 miles from home. --> TRUE. In fact, if we substitute t = 2 into the 1st equation,

$D(2) = (300)(2)+125 = 725$

- At 2.5 hours, the traveler is 875 miles from home. --> FALSE. In fact, for t=2.5 we have to use the 2nd equation, which states that the distance is:

D(t) = 880

So, not 875 miles.

- At 3 hours, the distance is constant, at 880 miles. --> TRUE. This is clearly visible from the 2nd equation: for t between 2.5 and 3.5 (so, in this case), the distance is

D(t) = 880

- The total distance from home after 6 hours is 1,062.5 miles --> TRUE. In fact, if we replace t = 6 into the last equation,

$D(6)) = 75(6)+612.5=1062.5$