Answer:
Step-by-step explanation:
80 minutes.......8 minutes played commercials....that means (80 - 8) = 72 minutes played music
so the ratio of music to commercials is : 72/8 which reduces to 9/1...so the ratio is 9:1 <=== ur answer
** pay attention to the wording, because if it would have asked for the ratio of commercials to music, it would have been 8/72....ratio would be 1:9
Answer:
![\bold{495\pi} \approx \bold{1555.088 cm^3}](https://tex.z-dn.net/?f=%5Cbold%7B495%5Cpi%7D%20%5Capprox%20%5Cbold%7B1555.088%20cm%5E3%7D)
Step-by-step explanation:
There was no figure but the question is clear
Volume of a cylinder is given by the formula
where r is radius of base of cylinder, h is the height
Volume of a cone is given by ![\bold{\frac{1}{3} \pi r^2 h}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20h%7D)
where r is the radius of base of cone, h is the height
The radius of the cylinder =
(diameter) =
(12) = 6cm
Height of cylinder = 15cm
Volume of cylinder ![V_{cyl} = \pi (6)^2 15 = \pi (36)15 = \bold{540\pi}](https://tex.z-dn.net/?f=V_%7Bcyl%7D%20%3D%20%5Cpi%20%286%29%5E2%20%2015%20%3D%20%5Cpi%20%2836%2915%20%3D%20%5Cbold%7B540%5Cpi%7D)
Radius of cone =
(radius of cylinder) =
(6) = 3 cm
Height of cone same as height of cylinder = 15cm
Volume of cone, ![V_{cone} = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (3)^2 15 = \frac{1}{3}(9)15\pi = \bold{45\pi}\\](https://tex.z-dn.net/?f=V_%7Bcone%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%283%29%5E2%2015%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%289%2915%5Cpi%20%3D%20%5Cbold%7B45%5Cpi%7D%5C%5C)
Difference is the volume of the remaining solid
![V_{cyl} - V_{cone} = 540\pi - 45\pi = \bold{495\pi} \approx \bold{1555.088 cm^3}](https://tex.z-dn.net/?f=V_%7Bcyl%7D%20-%20V_%7Bcone%7D%20%3D%20540%5Cpi%20-%2045%5Cpi%20%3D%20%5Cbold%7B495%5Cpi%7D%20%5Capprox%20%5Cbold%7B1555.088%20cm%5E3%7D)
If the angle G is moved to a different spot in the circle the angle FGH and angle FEH in the cyclic quadrilateral will change to make it supplementary.
<h3>How to find angles of cyclic quadrilateral?</h3>
A cyclic quadrilateral is inscribed in a circle. It has all its vertices on the circumference of the circle.
Opposite angles in a cyclic quadrilateral are supplementary angles. That means they add up to 180 degrees.
Therefore,
∠F + ∠H = 180°
∠G + ∠E = 180°
Hence, if we moved ∠G to a different spot on the circle, angle FGH would change but angle FEH will also change to make the two opposite angles supplementary.
Therefore, Felix was wrong.
learn more on cyclic quadrilateral here: brainly.com/question/21208662
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Answer:
y = 3x+2
Step-by-step explanation:
First find the slope using the slope formula
m= (y2-y1)/(x2-x1)
= ( -1 - -4)/(-1 - -2)
= (-1 +4)/ (-1 +2)
= 3/1
= 3
The slope intercept formula is
y = mx+b where m is the slope and b is the y intercept
y = 3x+b
Using the point (-1,-1) and substituting into the equation
-1 = 3(-1)+b
-1 = -3+b
-1+3 = b
2 = b
y = 3x+2