The price p based on the equation given is p = 3000 - 0.1x.
<h3>How to express the price?</h3>
The equation given in the question is x = 3000 - 10p. The price(p) will be:
x = 3000 - 10p.
Make p the subject of the formula
x + 10p = 3000
10p = 3000 - x
p = (3000 - x)/10
p = 3000 - 0.1x
The revenue will be price multiplied by quantity. This will be:
= (3000 - 0.1x) × x
= 3000x - 0.1x²
The marginal revenue will be calculated after differentiating. This will be:
= 3000x - 0.1x²
= 3000 - 0.2x
The demand which is the quantity based on the information will be:
3000 - 0.2x = 0
0.2x = 3000
x = 1500
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Given:
The inequalities are:
a) 
b) 
To find:
The solution of inequalities by substituting the given values.
Solution:
a) We have,
After substituting the given values one by one, we get
False statement.
False statement.
True statement.
True statement.
Therefore the solutions of 
are 
.
b)
We have,
After substituting the given values one by one, we get
True statement.
False statement.
False statement.
False statement.
Therefore, the solution of 
is 
.
The volume of a sphere is defined as:
V=(4*pi*r^3)/3
then, if we double the radius of the sphere (r=2r):
V=(4*pi*(2r)^3)/3
V=(4*pi*(2^3*r^3))/3
V=(4*pi*r^3)/3*8
Then, the answer is that if you double the radius of the sphere, its volume is increased 8 times.
The maximum monthly rent that she should pay is 2,784.
Solution:
1,082 x 12 months = 12,984
1,648 x 12 months = 19,776
1,933 x 12 months = 23,196
2,784 x 12 months = 33,408
Since her annual salary is 46,392, she can still afford to pay the rent for 2,784 per month, which equals to 33,408 annually.
