I need help pleaseeee

hram777 [196]

We have been given a circle H, in which length of arc XY is 78 miles and measure of arc XY is 70 degrees. We are asked to find the radius of circle.

We will use arc length formula to solve our given problem.

$\text{Arc length}=2\pi r\cdot \frac{\theta}{360^{\circ}}$ , where,

r = Radius of circle,

$\theta$ = Central angle corresponding to arc.

We know that the measure of central angle that corresponds to arc XY will be equal to measure of arc XY.

$78=2\cdot 3.14\cdot r\cdot \frac{70^{\circ}}{360^{\circ}}$

$78=2\cdot 3.14\cdot r\cdot \frac{7}{36}$

$78= 3.14\cdot r\cdot \frac{7}{18}$

$78= r\cdot \frac{21.98}{18}$

$r\cdot \frac{21.98}{18}=78$

$r\cdot \frac{21.98}{18}\cdot \frac{18}{21.98}=78\cdot \frac{18}{21.98}$

$r=63.8762511373$

Upon rounding to nearest hundredth, we will get:

$r\approx 63.88$

Therefore, the radius of circle H is approximately 63.88 miles.

7 0

3 years ago

The surface area of a square pyramid 360 square meters. The base length is 12 meters. Determine the slant height.

garri49 [273]

Answer:

The slant height is 9 meters.

Step-by-step explanation:

To determine the slant height, we will follow the steps below;

First, write down the formula:

Surface area = 2bs + b²

where b= the length of the base of the square pyramid

s = the slant height of the square pyramid

From the question given,

surface area of a square pyramid = 360 square meters

base length = 12 meters

We can now proceed to insert the values into the formula and then solve for s

Surface area = 2bs + b²

360 = 2(12)s + (12)²

360 = 24s + 144

subtract 144 from both-side of the equation

360 - 144 = 24s

216 = 24s

Divide both-side of the equation by 24

216/24 = 24s/24

9 = s

s = 9 meters

The slant height is 9 meters.

7 0

3 years ago

Read 2 more answers

The value of y is directly proportional to the value of x. If y = 45 when x = 180, what is the

vaieri [72.5K]

Answer:

The value of y when x = 90

y = 22.5

Step-by-step explanation:

Step(i):-

The value of y is directly proportional to the value of x.

Y∝ X

y = k x

If y = 45 when x = 180

45 = k ( 180)

$k = \frac{45}{180} = 0.25$

Step(ii):-

The value of y when x = 90

y = 0.25 × 90 = 22.5

y = 22.5

3 0

3 years ago

You can ride a bicycle 15 mph. Your sister

igor_vitrenko [27]

Answer:

4

Step-by-step explanation:

Find the LCM of 12 and 15.

LCM = 60.

Now divide the LCM by the two numbers.

60/12 = 5, 60/15 = 4.

As the sister got an hour head start, subtract one.

5-1=4.

Therefore it will be 4 hours.

5 0

4 years ago

Felix and Oscar are standing on a tower that is 112 feet high. Felix drops his penny while Oscar throws his penny down and it hi

creativ13 [48]

Answer:

It will take 2.64 s for Felix's penny to hit the ground.

Initial velocity of Oscar's penny is 7.27 m/s or 23.85 ft/s

Step-by-step explanation:

Given:

Height of the tower is, $h=112\ ft$

Felix drops the penny while Oscar throws his penny.

Time taken by Oscar's penny to reach ground is, $t_o=2\ s$

Now, as Oscar throws his penny, there will be some initial velocity of his penny. Let the initial velocity of his penny be $u_o$ .

As the penny is falling vertically, acceleration of the penny is due to gravity and is equal to -9.8 m/s².

Now, displacement of the penny is equal to the height of the tower = -112 ft = -34.14 m (1 ft = 0.3048 m)

Using equation of motion,

$y=u_ot+\frac{1}{2}at_o^2\\\\-34.14=2u_o-\frac{1}{2}\times9.8\times 2^2\\\\-34.14=2u_o-19.6\\\\2u_o=-34.14+19.6\\\\2u_o=-14.54\\\\u_o=\frac{-14.54}{2}=-7.27\ m/s$

Now, 1 m/s = 3.28 ft/s

So, 7.27 m/s = $7.27\times 3.28 = 23.85\ ft/s$

Therefore, the initial velocity of Oscar's penny is 7.27 m/s or 23.85 ft/s in the downward direction.

Now, Felix drops the penny. So, initial velocity of Felix's penny is 0 m/s.

Displacement of the penny is same and equal to -112 ft = -34.14 m

Using the same equation of motion,

$y=ut+\frac{1}{2}at^2\\\\-34.14=0-\frac{1}{2}\times9.8\times t^2\\\\-34.14=-4.9t^2\\\\t^2=\frac{-34.14}{-4.9}\\\\t=\sqrt{\frac{-34.14}{-4.9}}\\\\ t=2.64\ s$

Therefore, time taken by Felix's penny to reach ground is 2.64 s.

8 0

4 years ago