Answer:
Step-by-step explanation:
The general equation of a sphere is as follows:
In which the center is , and r is the radius.
In this problem, we have that:
So
Interior contained in the first octant:
The first octant is bounded by:
The xy plane, in which z is 0. The distance from the center of the sphere to the xy plane is 9.
The xz plane, in which y is 0. The distance from the center of the sphere to the xz plane is 4.
The yz plane, in which x is 0. The distance from the center of the sphere to the yz plane is 5.
This means that if the radius is higher than four, the sphere will cross into a different octant.
So the radius for the largest sphere is 4.
The equation is
Answer:
x=38
Step-by-step explanation:
First, know that the sum of the angles in a triangle is 180.
Then, add the angles. 2x+38+x+x-10.
Make them equal to 180.
2x+38+x+x-10=180
Simplify.
4x+28=180
Subtract 28 from 180.
4x=152
Divide 4 from 152 to make x alone.
x=38
There you go!
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Part I)
The module of vector AB is given by:
lABl = root ((- 3) ^ 2 + (4) ^ 2)
lABl = root (9 + 16)
lABl = root (25)
lABl = 5
Part (ii)
The module of the EF vector is given by:
lEFl = root ((5) ^ 2 + (e) ^ 2)
We have to:
lEFl = 3lABl
Thus:
root ((5) ^ 2 + (e) ^ 2) = 3 * (5)
root ((5) ^ 2 + (e) ^ 2) = 15
Clearing e have:
(5) ^ 2 + (e) ^ 2 = 15 ^ 2
(e) ^ 2 = 15 ^ 2 - 5 ^ 2
e = root (200)
e = root (2 * 100)
e = 10 * root (2)
Answer:
B
Step-by-step explanation:
The proportional equation for the the number of gallons of yellow paint, y needed for any amount of blue paint, b is:
<h3>Proportional equation:</h3>
- A <em>proportional equation</em> is modeled by:
- In which a is the constant of proportionality.
In this problem, the parameters are:
- of a gallon of blue paint, hence
- of a gallon of yellow paint, hence .
Then, to find the constant of proportionality:
Hence, the equation is:
You can learn more about proportional equation at brainly.com/question/13112448