Solution :
Give that, a 72° sector in a circle ,
Area of Sector in a circle =
[tex] \pi \times r^{2} \times( \frac{\theta}{360} )\\ \:\: where, r = radius\, of\, the\, circle\ \\ \theta = angle \,in \, degrees [/tex]
Suppose radius of circle is r .
then Volume of sector of circle
[tex] \pi \imes r^{2} \times (\frac{72}{360} )= 16.4\pi\\\\r^{2} = \frac{16.4 \pi}{\pi \times \frac{72}{360} } = \frac{16.4 \times 360}{72} [/tex]
Area of a Circle of radius, r, [tex] A = \pi\times r^{2} [/tex]
Put [tex] r^{2} = \frac{16.4 \times 360}{\times 72} [/tex]
Area of Circle, A = [tex] \pi \times \ \frac{16.4 \times 360}{72} =82 \pi[/tex]
given, [tex] \pi =3.14 [/tex]
[tex] volume =82 \times 3.14 = 257.48 [/tex]
Hence, Area of circle= 257.48
Answer:257.48 yd sq
Step-by-step explanation: took de quiz
what is the solution of this equation x + 6 =24
Roasting meats at high temperatures makes them moist and tender.
True False
Answer:
False
Step-by-step explanation:
Just did the Culinary Quiz 2021
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<Jayla>
help please!!!
In Angle ABC, C is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth.
a = 3, c = 19
A. M
B. M
C. M
D M
Amys class is selling books to raise money for a field trip. If each book sells for $7, how many books will they need to sell to raise $125?
Two angle measures in a scaled Triangle are 77 and 62 what is the measure of the third angle
The area of a triangle is 40sq inches. If the base of the triangle is 10 inches what is it’s height?
Answer:
Step-by-step explanation: 8 inches
When calculating the successive discounts of 15% and 10% on a $100 item, _____. a. take 10% of $85 b. take 10% of $90 c. take 15% of $85 d. take 25% of $100
Answrer
Option (a) is correct .
i.e take 10% of $85
Reason
As given
15% and 10% on a $100 item i.e first applied 15 % discount on $ 100 and than apply 10% discount .
15 % is written in the decimal form
[tex]= \frac{15}{100}[/tex]
= 0.15
Amount becomes when 15 % discount on$100 = 100 - 0.15 × 100
= 100 - 15
= $ 85
Now apply 10 % discount on $ 85.
10 % is written in the decimal form
[tex]= \frac{10}{100}[/tex]
= 0.1
Amount becomes when 15 % discount on$100 = 85- 0.1 × 85
= 85 - 8.5
= $ 76.5
Therefore the option (a) is correct about the successive discounts of 15% and 10% on a $100 item is $76.5 .
Please help asap!!!!!!!!!!18 points
Someone help me ASAP!!!!!!
One angle of atriangle measures 12 degrees. the second angle's measurements is five times the third. what is the measure of the third angle
The measure of the third angle is; 28 degrees.
How does an angle form?An angle requires two straight line/ line segments/rays, such that they're connected on one of their endpoints.
The point of their joint is called vertex of that angle.
Those two line segments forming it are called arms of that angle.
The angle is the degree of rotation that it will take for the moving side to go from initial side to the position it is currently on.
Let the third angle be x
Given that One angle of a triangle measures 12 degrees. the second angle's measurements is five times the third.
We know that in a triangle the angles add up to 180 degrees.
so, 12 + 5x + x = 180.
Then we get
6x =168
x =28 degrees.
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A car dealership has seven cars in the lot. Unfortunately, the keys to the cars have been mixed up. The manager randomly grabs a key and tries to start a car salesman also randomly picks a different key and tries to start another car. What is the probability that both cars start?
A ball is thrown into the air from the edge of a 48 foot cliff so that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds.
For which interval is the ball’s height always decreasing?
A. 48
B.0
C.2.5
D.146
2.5 < x < 5.5 seconds is the time interval when ball's height always decreasing.
What is time interval?" Time interval is the division of time into small equal intervals to have a proper observation of any data."
According to the given graph,
x represents time in seconds along x-axis
y represents height in foot of the ball along y-axis
As per observation,
Height of the ball increasing from 48 to 146 in the time interval
0< x < 2.5.
Height of the ball decreasing from 146 to 0 in the time interval 2.5< x < 5.5.
Hence, we conclude that 2.5 < x < 5.5 seconds is the time interval when ball's height always decreasing.
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A ball is thrown straight up with a initial velocity of 56 feet per second . The height , h , of the ball t seconds after it is thrown is given by the formula h(t)=56t-16t^2 . What is the maximum height of the ball?
Formula: H(t) = 56t – 16t^2
H(t) = - 16t^2 + 56t
A. What is the height of the ball after 1 second? H (1) = 56(1) – 16(1) ^2 = 40 pt.
B. What is the maximum height? X = - (56)/2(- 16) = 1.75 sec h (1.75) = 56(1.75) – 16(1.75) ^2 h (1.75) = 49ft.
C. After how many seconds will it return to the ground? – 16t^2 + 56t = 0 - 8t =0 t = 0
- 8t (2 + - 7) = 0 2t – 7 = 0 t = 7/2 Ans: 3.5 seconds
The maximum height achieved by the ball is 49 meters at time t = 7/4 seconds.
What is time dependent function?
The time dependent function is the function whose values vary with change in time. For example - f(t) = 3t + 5.
Given is a ball is thrown straight up with a initial velocity of 56 ft/s. The height (h) , of the ball (t) seconds after it is thrown is given by the formula h(t) = 56t - 16t²
The given function is -
h[t] = 56t - 16t²
Now, for maximum height -
dh/dt = 0
d/dt ( 56t - 16t²) = 0
d/dt (56t) - d/dt (16t²) = 0
56 - 16 d/dt (t²) = 0
56 - 16 x 2t = 0
56 = 32t
t = 56/32
t = 7/4 seconds
Now, at t = 7/4 seconds, the height is maximum. Substituting the value
t = 7/4 seconds, we get -
h(7/4) = 56 x 7/4 - 16 x 49/16
h(7/4) = 14 x 7 - 49
h(7/4) = 98 - 49
h(7/4) = 49 meters
Therefore, the maximum height achieved by the ball is 49 meters at time t = 7/4 seconds.
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PLEASE HELP ME ON THIS QUESTION
THX~ BRANiLiEST AVAILABLE
PLZ EXPLAIN IF U COULD
Speed = distance divided by time taken. car 1 travels 10 miles every 5 minutes. car 2 travels 30 miles every 20 minutes. what is the difference of speed between these two cars in mph?
PLEASE HELP ME WITH THIS QUESTION AND DON'T FORGET TO EXPLAIN
Porters family ordered 4 pizzas. They ate 2 3/8 of pizza how much pizza is left?
There are three consecutive odd integers. Three times the largest is seven times the smallest. What are the integers?
In the right triangle shown, AC = BC = 7? What is AB?
explanation and answer
please help asap! match equation to the graph
Answer:
B) -7x + 7y= -49
Step-by-step explanation:
Using the general equation for a line
y=mx+b
where m is the slope (positive if the line goes up from left to right and negative is it goes down from left to right)
and b is the point where the line crosses the y-axis
By th graph we can see that the line goes up from left to right, so the slope is positive, and that it crosses the y axis in -7, b= -7 and x is positive.
Solving for y in all the options
A) y = -x
B) y = x - 7
C) y = -x +7
D) y= x+7
the option that describes the line in the graph is B) -7x + 7y= -49 since when clearing for y we get y = x - 7 wich has a positive slope, and has an interception b = -7.
Find the length of the side labeled x round to the nearest 10th
John let out 50 foot of kite string when he observes that his kite is directly above a point on the ground 30 feet away from him, how high is the kite ?
Answer:
the answer is 40 i had it on USATestPrep
Step-by-step explanation:
ion need one lml
I️ need to find the answer
An airplane takes off from the ground and reaches a height of 500 feet after flying 2 miles. given the formula h = d tan θ, where h is the height of the plane and d is the distance (along the ground) the plane has flown, find the angle of ascent θ at which the plane took off.
Please help! I'm very confused. 20 points.
If 5x^2 + y^4 = −9 then evaluate d^2y/dx^2 when x = 2 and y = 1. Round your answer to two decimal places.
Using complete sentences, explain the key features of the graph of the sine function.
1/3 math questions. pls help! 20 pts!
Or an angle θ with the point (−20, −21) on its terminating side, what is the value of cosine?
Answer:
The value of cosine is [tex]\cos \theta=-\frac{20}{29}[/tex].
Step-by-step explanation:
It is given that an angle θ with the point (−20, −21) on its terminating side.
It means the right angle triangle is formed in third quadrant where length of the perpendicular is 21 and the base is 20.
According to the Pythagoras theorem,
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
[tex]hypotenuse^2=(20)^2+(21)^2[/tex]
[tex]hypotenuse^2=400+441[/tex]
[tex]hypotenuse^2=841[/tex]
Taking square root both the sides.
[tex]hypotenuse=\sqrt{841}[/tex]
[tex]hypotenuse=29[/tex]
In a right angled triangle,
[tex]\cos \theta=\frac{base}{hypotenuse}[/tex]
[tex]\cos \theta=\frac{20}{29}[/tex]
θ lie in the third quadrant and cosine is negative in third quadrant.
[tex]\cos \theta=-\frac{20}{29}[/tex]
Therefore the value of cosine is [tex]\cos \theta=-\frac{20}{29}[/tex].