Answer:
12g
Step-by-step explanation:
Answer: 30% of decrease
Step-by-step explanation:
$13.95 - $10 = $3.95
$13.95___100%
$3.95___x= 28.31%
(3.95*100) / 13.95 = 28.31 = 30
13x - y = 3 .....(1)
x - 6y = -33 ......(2)
eqn (2) × 13
13x - 78y = -429 .....(3)
(3) - (1)
13x - 78y = -429
13x - y = 3
(-). (+). (-)
_________________
- 77y = 431
_________________
-77y = 431
y = 431 ÷ -77
y = -5.5
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!
Answer:
The answer to your question is:
x = 1
Square's perimeter = 12
Rectangle perimeter = 12
The value of x is one and the perimeter of the square and the rectangle is the same.
Step-by-step explanation:
Data
Side of Square = 4x - 1
Length of rectangle = 2x + 1
Width = x + 2
Perimeters are the same
Process
Square perimeter = 4(4x - 1)
Rectangle's perimeter = 2(2x + 1) + 2(x+ 2)
Then
4(4x - 1) = 2(2x + 1) + 2(x+ 2) Equation
16x - 4 = 4x + 2 + 2x + 4
16x - 4 = 6x + 6
16x - 6x = 6 + 4
10x = 10
x = 10 / 10
x = 1
Perimeter of the square = 4(4(1) - 1)
= 4(3)
= 12
Perimeter of the rectangle = 2(2(1) + 1) + 2((1)+ 2)
= 2(3) + 2(3)
= 6 + 6
= 12
