Hey there! I'm happy to help!
Hey there! I'm happy to help!
First, let's find the area of the circle of the first cylinder. To do this, we square the radius and multiply by 3.14.
3²=9
9×3.14=28.26
Now we multiply by our height of 49 cm to see how much water there is.
28.26×49=1384.74
Now, let's find the area of the circle of the 7 cm cylinder.
7²=49
49×3.14=153.86
Now, we will take our liquid amount (volume) and divide by this circle amount (base) to find the number of centimeters of height of the water column.
1384.74÷153.86=9
So, the height of our water column will be 9 cm.
Have a wonderful day and keep on learning! :D
an equation for a circle has formula
(x-m)² + (y-n)² = r²
where (m,n) is its center
and r is its radius
so, the equation has center (4,3) and radius 4
the equation is derived from the pythagorean theorem
-12x² + 11x - 3 = 0
x = <u>-(11) +/- √((11)² - 4(-12)(-3))</u>
2(-12)
x = <u>-11 +/- √(121 - 144)</u>
-24
x = <u>-11 +/- √(-23)
</u> -24
x = <u>-11 +/- i√(23)</u>
-24
x = <u>-11 + i√(23</u>) x = <u>-11 - i√(23)</u>
-24 -24
x = ¹¹/₂₄ - 0.0416√(23) x = ¹¹/₂₄ + 0.0416√(23)
<u />
m<ACB = 65°
m<BCD and m<ACB are supplementary
Sum of supplementary angles = 180
so
m<BCD = 180 - 65
m<BCD = 115
Answer
A. 115
The length of the sky lift is 3.387.05 ft
Step-by-step explanation;
By an online search, i found that the sky lift
rises at an angle of 20.75 degrees.
Then we can think on a triangle rectangle, such
that:
One cathetus is 1200ft, this is the opposite
cathetus to the angle of 20.75°
The length of the ski lift would be the
hypotenuse of this triangle rectangle.
Then we can use the relationship:
Sin(a) = opposite cathetus/hypoteuse.
such that:
a = 20.75°
opposite cathetus=1200ft
then:
sin(20.75°) = 1200ft/hypotenuse
hypotenuse =1200ft/sin(20.759) =3.387.05 ft
The length of the sky lift is 3.387.05 ft