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3 years ago

PLEASE HELP ME PRE CAL/TRIG

Mathematics

1 answer:

miss Akunina [59]3 years ago

3 0

Answer:

A) 60 Degrees

B) 550 Feet

C) 2.5 minutes

Step-by-step explanation:

a) So the wheel has completed one revolution in 10 minutes so lets first divide 100 secs with 10 minutes to calculate the the fraction of revolution

1 min = 60 secs

10 min = 600 secs

100/600 = 1/6

One complete revolution is 360 degrees and 1/6 of 360 degrees will be 60 degrees .

360/6 = 60°

b) It takes 10 minutes to complete one revolution so if the person is on it for 7 minutes it would be 7/10 of a revolution . The ferris wheel has a diameter of 250 feet so the radius will be 125 feet because it is the half of the diameter and the circumference will be 250 π . To calculate the distance lets multiple the fraction of the revolution which is 7/10 into the circumference $\frac{7}{10} * (250 pi)$ = 550 Feet.

C)It took 10 minutes to travel 250 π now we will use this relation to calculate 200 feet . lets suppose t is for time .

$\frac{250pi}{10} =\frac{200}{t}$ .

After solving this equation as there is only one unknown which is "<em>t</em> "the answer will be 2.5 minutes.

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Two boats leave a dock at the same time. One boat travels south at 32 mi divided by hr32 mi/hr and the other travels east at 60

TEA [102]

Answer: the rate at which the distance between the boats is increasing is 68 mph

Step-by-step explanation:

The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.

Let x represent the length the shorter leg(south) of the right angle triangle.

Let y represent the length the longer leg(east) of the right angle triangle.

Let z represent the hypotenuse.

Applying Pythagoras theorem

Hypotenuse² = opposite side² + adjacent side²

Therefore

z² = x² + y²

To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes

2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1

One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that

dx/dt = 32

dy/dt = 60

Distance = speed × time

Since t = 0.5 hour, then

x = 32 × 0.5 = 16 miles

y = 60 × 0.5 = 30 miles

z² = 16² + 30² = 256 + 900

z = √1156

z = 34 miles

Substituting these values into equation 1, it becomes

2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60

68dz/dt = 1024 + 3600

68dz/dt = 4624

dz/dt = 4624/68

dz/dt = 68 mph

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3 years ago

Suppose r(140°, P)(A) = B and (RPD←→∘RPC←→)(A) = B, what is m∠CPD?

NISA [10]

An angle bisector divides an angle into two equal halves.

The measure of angle $\angle CPD$ is 70 degrees

The complete question is an illustrates the concept of angle bisector;

Where:

$\angle RPD = 140^o$ , and line PC bisects $\angle RPD$

Because line PC bisects $\angle RPD$ , then it means that the measure of RPD is twice the measure of CPD:

So, we have:

$\angle RDP = 2 \times \angle CPD$

Substitute $\angle RPD = 140^o$

$140^o = 2 \times \angle CPD$

Divide both sides by 2

$70^o = \angle CPD$

Apply symmetric property of equality:

$\angle CPD = 70^o$

Hence, the measure of angle $\angle CPD$ is 70 degrees