surface area of cylinder = 2 π r h + 2π r²
plug in values of pi, radius and area
2,461.76 = 2× 3.14 × 14 × h + 2× 3.14 × 14 × 14
2,461.76 = 87.92 h + 1,230.88
2,461.76 – 1,230.88 = 87.92h
1,230.88 = 87.92h
1,230.88 ÷ 87.92 = h
h = 14 ft
Answer:
(1)
Donna = Pounds 180
Kyra = Pounds 240
(2)
Kelly = Pounds 225
Nelly = Pounds 175
Step-by-step explanation:
(1)
Donna = x
Kyra = x + 60
If Donna spends 1/3 of her money she is left with 2/3 of her money;
2/3 x
Kyra now has twice as much money as Donna can be represented as;
X + 60 = 2 * 2/3 x
X + 60 = 4/3 x
(x + 60)3 = 4x
3x + 180 = 4x
180 = 4x – 3x
180 = x
Donna = 180
Kyra = 180 + 60 = 240
(2)
Kelly = x
Ned = y
Kelly spends 40% of her money. Therefore he is left with 60%;
60/100 x
Nelly spends Euros 40 of his money. Therefore he is left with;
y- 40
If they now have the same amount of money;
60/100 x = y – 40
3/5 x = y – 40
3x = 5y – 200
3x – 5y = -200
Remember Kelly & Ned has Euros 400 in total;
x + y = 400
Now we can solve the simultaneous equation by substitution;
x + y= 400
3x – 5y = -200
3x + 3y = 1200
-
3x – 5y = - 200
=
8y = 1400
Y = 175
X = 225
Kelly = 225
Nelly = 175
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Answer:
y=-2x+2
Step-by-step explanation:
okay?.......................
Answer:
V = 2000r³/3
Step-by-step explanation:
We know that the base is a circular disk, so it creates a circle on the xy plane. It would be in the form x² + y² = r². In other words x² + y² = (5r)². Let's isolate y in this equation now:
x² + y² = (5r)²,
x² + y² = 25r²,
y² = 25r² - x²,
y = √25r² - x² ---- (1)
Now remember that parallel cross sections perpendicular to the base are squares. Therefore Area = length^2. The length will then be = 2√25r² - x² --- (2). Now we can evaluate the integral from -5r to 5r, of [ 2√25r² - x² ]² dx.
![\int _{-5r}^{5r}\:\left[\:2\sqrt{\left(25r^2\:-\:x^2\right)}\:\right]\:^2\:dx\\=\int _{-5r}^{5r}4\left(25r^2-x^2\right)dx\\\\= 4\cdot \int _{-5r}^{5r}25r^2-x^2dx\\\\= 4\left(\int _{-5r}^{5r}25r^2dx-\int _{-5r}^{5r}x^2dx\right)\\\\= 4\left(250r^3-\frac{250r^3}{3}\right)\\\\= 4\cdot \frac{500r^3}{3}\\\\= \frac{2000r^3}{3}](https://tex.z-dn.net/?f=%5Cint%20_%7B-5r%7D%5E%7B5r%7D%5C%3A%5Cleft%5B%5C%3A2%5Csqrt%7B%5Cleft%2825r%5E2%5C%3A-%5C%3Ax%5E2%5Cright%29%7D%5C%3A%5Cright%5D%5C%3A%5E2%5C%3Adx%5C%5C%3D%5Cint%20_%7B-5r%7D%5E%7B5r%7D4%5Cleft%2825r%5E2-x%5E2%5Cright%29dx%5C%5C%5C%5C%3D%204%5Ccdot%20%5Cint%20_%7B-5r%7D%5E%7B5r%7D25r%5E2-x%5E2dx%5C%5C%5C%5C%3D%204%5Cleft%28%5Cint%20_%7B-5r%7D%5E%7B5r%7D25r%5E2dx-%5Cint%20_%7B-5r%7D%5E%7B5r%7Dx%5E2dx%5Cright%29%5C%5C%5C%5C%3D%204%5Cleft%28250r%5E3-%5Cfrac%7B250r%5E3%7D%7B3%7D%5Cright%29%5C%5C%5C%5C%3D%204%5Ccdot%20%5Cfrac%7B500r%5E3%7D%7B3%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B2000r%5E3%7D%7B3%7D)
As you can see, your exact solution would be, V = 2000r³/3. Hope that helps!
