Surface Area of a Sphere = 4π(d/2)²
Let the smaller sphere's diameter be just a sample of 4 units in diameter and let the large spheres diameter be 4 times that of the smaller sphere.
Small Sphere: 4π(4/2)² = 16π units²
Large Sphere: 4π(16/2)² = 256π units²
256π / 16π = 16 times
The large sphere has a surface area 16 times that of the smaller one.
Answer:
Step-by-step explanation:
The secants form a proportion where the full length of the secant is the denominator of a fraction where the numerator is the external part of the secant.
7/(x + 7) = 6/(15 + 6) Cross Multiply after combining
7 / (x + 7) = 6/(21)
6 * (x + 7) = 7 * 21 Remove the brackets
6x + 42 = 147 Subtract 42
6x = 147 - 42
6x = 105 Divide by 6
x = 17.5
I think I've done this correctly. If you find an error, please let me know and I'll open it for editing.
Answer:
Mean: 5.5555555555556
Median: 6
Mode: 6
Step-by-step explanation:
Answer:
The coordinates of E are 
.
Step-by-step explanation:
The triangle ABC represents a right triangle as both sides AB and AC are orthogonal to each other. The side AB is in the y axis, whereas the side AC is in the x axis. The triangle is dilated with respect to the origin, in which point A is set.
Vectorially speaking, dilation is defined by the following operation:
![P'(x,y) = O(x,y) + k\cdot [P(x,y) - O(x,y)]](https://tex.z-dn.net/?f=P%27%28x%2Cy%29%20%3D%20O%28x%2Cy%29%20%2B%20k%5Ccdot%20%5BP%28x%2Cy%29%20-%20O%28x%2Cy%29%5D)
(1)
Where:
- Point of reference.
- Original point.
- Dilated point.
- Dilation factor.
By applying this operation, point B becomes point D:
, 
![D(x,y) = (0,0) + k\cdot [(0,4)- (0,0)]](https://tex.z-dn.net/?f=D%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B%20k%5Ccdot%20%5B%280%2C4%29-%20%280%2C0%29%5D)
Lastly, we transform point C into point E by applying the same operation: 
, 
and
![E(x,y) = (0,0) + \frac{3}{2}\cdot [(3,0)-(0,0)]](https://tex.z-dn.net/?f=E%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5Ccdot%20%5B%283%2C0%29-%280%2C0%29%5D)
The coordinates of E are .
