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3 years ago

A circular patio has a radius of 4 yards. The patio is expanded so that the

Mathematics

1 answer:

stepan [7]3 years ago

6 0

Answer:

20pi or 62.83

Step-by-step explanation:

when r=4

pi r^2

16pi

when r=6

pi r^2

36pi

36pi-16pi=20pi or 62.83

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For the amusement of the guests, some hotels have elevators on the outside of the building. One such hotel is 400 feet high. You

Mariana [72]

9514 1404 393

Answer:

a. h(t) = -20t +400

b. θ(t) = arctan(2 -2/15t); dθ/dt = -30/(1125 -120t +4t^2)

c. 15 seconds; 100 ft

Step-by-step explanation:

a. The initial height of the elevator is 400 ft. The rate of change of height is -20 ft/s, so the height equation can be ...

h(t) = -20t +400

b. The tangent of the angle above the line of sight is "opposite"/"adjacent":

tan(θ) = (h(t) -100)/(150) = -2/15t +2

θ(t) = arctan(2 -2/15t) . . . . radians

The derivative of the angle function is ...

dθ/dt = 1/(1+(2 -2/15t)^2)(-2/15)

dθ/dt = -30/(1125 -120t +4t^2)

c. The value of dθ/dt will have a peak where the denominator has a minimum, at t = -(-120)/2(4)) = 15. (The quadratic vertex coordinate is t=-b/(2a).)

The elevator appears to be moving fastest at t=15 seconds.

The height at that time is ...

h(15) = 400 -20(15) = 100

The elevator appears to be moving fastest when it is at eye level, 100 ft above the ground.

5 0

3 years ago

I need help with this question

bearhunter [10]

Answer:

7.28 miles

Step-by-step explanation:

Suppose the distance at closest approach is represented by x. Then the distance to the point of closest approach at the first sighting is ...

d1 = x·tan(62°)

At the second sighting, the distance to the point of closest approach is ...

d2 = x·tan(38°)

The difference of these distances is 8 miles, so we have ...

d1 -d2 = 8 = x(tan(62°) -tan(38°))

Dividing by the coefficient of x, we find ...

x = 8/(tan(62°) -tan(38°)) ≈ 7.2764 . . . . miles

The point of closest approach is about 7.28 miles from the landmark.

5 0

3 years ago

In the figure below, solve for the value of a. a = ______ in. (round to the nearest tenth and do NOT include units in your answe

GrogVix [38]

Answer:

6.9

Step-by-step explanation:

sinX=opposite/hypotenuse

sin35=a/12

a=12*0.57357643635

a=6.88291723621≈6.9

3 0

3 years ago

Angel is making bags of trail mix for hiking club. He will use 20 ounces of walnuts, 11.2 ounces of almonds, and 14.3 ounces of

zheka24 [161]

Answer:

1.82 oz.

Step-by-step explanation:

20 oz. walnuts/25 bags = 0.8

11.2 oz. almonds/25 bags = 0.448

14.3 oz. cashews/25 bags= 0.572

8 0

3 years ago

Evaluate the function at the given value:

vivado [14]

Answer:

Step-by-step explanation:

Substitute the value of a

3(2)³+10(2)²-3(2)-7

3(8)+10(4)-3(2)-7

24+40-6-7

64-13

7 0

3 years ago