Answer:
The Principle of Zero Products states that if the product of two numbers is 0, then at least one of the factors is 0. (This is not really new.) If ab = 0, then either a = 0 or b = 0, or both a and b are 0.
hope it helped
Hello from MrBillDoesMath!
Answer:
12/5
Discussion:
Note that 10 is a common denominator of both denominators:
9/5 = (9*2)/(5*2) = 18/10
- ( -6/10) = + (6/10)
So the original problem is equivalent to
18/10 + 6/10 =
(18 +6)/10 =
24/10 =
(2*12)/ (2*5) => cancelling the common factor "2"
12/5 =
2 and 2 fifths =
22/5 (though this looks like (22)/5!)
Thank you,
MrB
Answer:
Explanation:
You need to use derivatives which is an advanced concept used in calculus.
<u>1. Write the equation for the volume of the cone:</u>
<u />
<u>2. Find the relation between the radius and the height:</u>
- r = diameter/2 = 5m/2 = 2.5m
<u>3. Filling the tank:</u>
Call y the height of water and x the horizontal distance from the axis of symmetry of the cone to the wall for the surface of water, when the cone is being filled.
The ratio x/y is the same r/h
The volume of water inside the cone is:
<u>4. Find the derivative of the volume of water with respect to time:</u>
<u>5. Find x² when the volume of water is 8π m³:</u>
m²
<u>6. Solve for dx/dt:</u>
<u />
<u>7. Find dh/dt:</u>
From y/x = h/r = 2.08:
That is the rate at which the water level is rising when there is 8π m³ of water.
The first step to solving this is to use tan(t) =
to transform this expression.
cos(x) ×
Using cot(t) =
,, transform the expression again.
cos(x) ×
Next you need to write all numerators above the least common denominator (cos(x)sin(x)).
cos(x) ×
Using sin(t)² + cos(t)² = 1,, simplify the expression.
cos(x) ×
Reduce the expression with cos(x).
Lastly,, use
= csc(t) to transform the expression and find your final answer.
csc(x)
This means that the final answer to this expression is csc(x).
Let me know if you have any further questions.
:)