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Marta_Voda [28]
3 years ago
10

the angle of elevation from a viewer to the top of a flagpole is 50°. the viewer is 40 ft away and the viewers eyes are 5.5 ft f

rom the ground. how high is the pole to the nearest tenth of a foot?

Mathematics
1 answer:
Margarita [4]3 years ago
3 0

Answer:

53.2 feet

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle ABC

tan(50^o)=\frac{AC}{BC} -----> by TOA (opposite side divided by the adjacent side)

substitute the values

tan(50^o)=\frac{h}{40}

solve for h

h=(40)tan(50^o)

h=47.7\ ft

therefore

The height of the pole is

h+5.5=47.7+5.5=53.2\ ft

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Help meez 40 pts use surface area formula of cylinder that is for Lateral surface area and for total surface area
jeka94

Answer:So the radius of the cylinder is 2.65 cm.

A cylinder can be defined as a solid figure that is bound by a curved surface and two flat surfaces. The surface area of a cylinder can be found by breaking it down into 2 parts:

1.  The two circles that make up the caps of the cylinder.

2.  The side of the cylinder, which when "unrolled" is a rectangle.

The area of each end cap can be found from the radius r of the circle, which is given by:

A = πr2

Thus the total area of the caps is 2πr2.

The area of a rectangle is given by:

A = height × width

The width is the height h of the cylinder, and the length is the distance around the end circles, or in other words the perimeter/circumference of the base/top circle and is given by:

P = 2πr

Thus the rectangle's area is rewritten as:

A = 2πr × h

Combining these parts together we will have the total surface area of a cylinder, and the final formula is given by:

A = 2πr2 + 2πrh

where:

π  is Pi, approximately 3.142

r  is the radius of the cylinder

h  height of the cylinder

By factoring 2πr from each term we can simplify the formula to:

A = 2πr(r + h)

The lateral surface area of a cylinder is simply given by: LSA = 2πr × h.

Example 1: Find the surface area of a cylinder with a radius of 4 cm, and a height of 3 cm.

Solution:

SA = 2 × π × r2 + 2 × π × r × h

SA = 2 × 3.14 × 42 +  2 × 3.14 × 4 × 3

SA = 6.28 × 16 + 6.28 × 12

SA = 100.48 + 75.36

SA = 175.84

Surface area = 175.84 cm2

Example 2: Find the surface area of the cylinder with a radius of 5.5cm and height of 10cm.

Solution:

The radius of cylinder = 5.5 cm.

The height of cylinder = 10 cm.

The total surface area of the cylinder is therefore:

TSA = 2πr(r+h)

TSA = 11π (5.5+10)

TSA = 170.5 π

TSA = 535.6 cm2

Example 3: Find the total surface area of a cylindrical tin of radius 17 cm and height 3 cm.

Solution:

Again as in the previous example:

TSA = 2πr(r+h)

TSA = 2π× 17(17+3)

TSA = 2π×17×20

TSA = 2136.56 cm2

Example 4: Find the surface area of the cylinder with radius of 6 cm and height of 9 cm.

Solution:

The radius of cylinder: r = 6 cm

The height of cylinder: h = 9 cm

Total surface area of cylinder is therefore:

TSA = 2πr(r + h)

TSA = 12π (6+9)

TSA = 180 π

TSA = 565.56 cm2

Example 5: Find the radius of cylinder whose lateral surface area is 150 cm2 and its height is 9 cm.

Solution:

Lateral surface area of cylinder is given by:

LSA = 2πrh

Given that:

LSA = 150cm2

h = 9cm

π is the constant and its value = 3.14

Substitute the values in the formula and find the value of r by isolating it from the equation:

LSA = 2πrh

150 = 2× π × r × 9

r = 150 / (2×9× π)

r = 2.65cm

So the radius of the cylinder is 2.65 cm.

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2 years ago
All Five of these Questions = 90 Points. Need done ASAP.
vichka [17]

Answer:

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3 years ago
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gulaghasi [49]

I believe the answer to this is:

Mean: <u>8.7</u> minutes

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5 0
3 years ago
An object at the top of a building with height 110 feet is thrown upward with an initial speed of 23 ft/s. Find its position z(t
alina1380 [7]

Answer:

Step-by-step explanation:

Given

Height of building is h=110\ ft

Initial upward velocity u=23\ ft/s

height of object is given by

z(t)=ut+\frac{1}{2}gt^2

but building is already at a height of 110 ft so z(t) must be given by

Z(t)=ut+\frac{1}{2}(-g)t^2+110

Z(t)=23\times t-\frac{1}{2}\times 9.8\times t^2

Z(t)=-16t^2+23t+110

Time when it hits is given by when Z(t)=0[/tex]

-16t^2+23t+110=0

t=\frac{-23\pm \sqrt{(23)^2-4\times (-16)\times 110}}{2\times (-16)}

t=\frac{-23\pm 87}{-32}

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6 0
3 years ago
An airplane cruises 1 kilometer in 1 12 of a minute. What is its cruising speed?
Aleonysh [2.5K]

Answer:

Step-by-step explanation: 12 ur welcome

4 0
3 years ago
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