Please solve this question the answer is 45 degree
1 answer:
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Answer:
x^4 -53x^2 +108x +160
Step-by-step explanation:
If <em>a</em> is a zero, then (<em>x-a</em>) is a factor. For the given zeros, the factors are ...
p(x) = (x +8)(x +1)(x -4)(x -5)
Multiplying these out gives the polynomial in standard form.
= (x^2 +9x +8)(x^2 -9x +20)
We note that these factors have a sum and difference with the same pair of values, x^2 and 9x. We can use the special form for the product of these to simplify our working out.
= (x^2 +9x)(x^2 -9x) +20(x^2 +9x) +8(x^2 -9x) +8(20)
= x^4 -81x^2 +20x^2 +180x +8x^2 -72x +160
p(x) = x^4 -53x^2 +108x +160
_____
The graph shows this polynomial has the required zeros.
Answer:
The quantity of salt at time t is , where t is measured in minutes.
Step-by-step explanation:
The law of mass conservation for control volume indicates that:
Where mass flow is the product of salt concentration and water volume flow.
The model of the tank according to the statement is:
Where:
- The salt concentration in the tank, as well at the exit of the tank, measured in
.
- Concentration rate of change in the tank, measured in
.
- Volume of the tank, measured in gallons.
The following first-order linear non-homogeneous differential equation is found:
This equation is solved as follows:
The initial concentration in the tank is:
Now, the integration constant is:
The solution of the differential equation is:
Now, the quantity of salt at time t is:
Where t is measured in minutes.