Please help ASAP. Quadrilateral CDEF is inscribed in circle A. If the m∠C = 7x + 11° and m∠E = 7x + 1°, what is the measure of ∠
2 answers:
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Answer:
The amount of salt in the tank when it is full of brine is 393.75 pounds.
Step-by-step explanation:
This is a mixing problem. In these problems we will start with a substance that is dissolved in a liquid. Liquid will be entering and leaving a holding tank. The liquid entering the tank may or may not contain more of the substance dissolved in it. Liquid leaving the tank will of course contain the substance dissolved in it. If Q(t) gives the amount of the substance dissolved in the liquid in the tank at any time t we want to develop a differential equation that, when solved, will give us an expression for Q(t).
The main equation that we’ll be using to model this situation is:
Rate of change of <em>Q(t)</em> = Rate at which <em>Q(t)</em> enters the tank – Rate at which <em>Q(t)</em> exits the tank
where,
Rate at which Q(t) enters the tank = (flow rate of liquid entering) x
(concentration of substance in liquid entering)
Rate at which Q(t) exits the tank = (flow rate of liquid exiting) x
(concentration of substance in liquid exiting)
Let y<em>(t)</em> be the amount of salt (in pounds) in the tank at time <em>t</em> (in seconds). Then we can represent the situation with the below picture.
Then the differential equation we’re after is
is the volume of brine in the tank at time <em>t. </em>To find it we know that at time 0 there were 100 gallons, 5 gallons are added and 3 are drained, and the net increase is 2 gallons per second. So,
We can then write the initial value problem:
We have a linear differential equation. A first-order linear differential equation is one that can be put into the form
where <em>P</em> and <em>Q</em> are continuous functions on a given interval.
In our case, we have that
The solution process for a first order linear differential equation is as follows.
Step 1: Find the integrating factor, , using
Step 2: Multiply everything in the differential equation by and verify that the left side becomes the product rule
and write it as such.
Step 3: Integrate both sides.
Step 4: Find the value of the constant and solve for the solution y(t).
Now, the tank is full of brine when:
The amount of salt in the tank when it is full of brine is
Answer:
Given Polynomial:
Factors of Coefficient of terms
80 = 5 × 16
32 = 2 × 16
48 = 3 × 16
Common factor of the coefficient of all term is 16.
Each term contain variable. So the Minimum power of b is common from all terms.
Common from all variable part comes b².
So, Common factor of the polynomial = 16b²
⇒ 16b² ( 5b² ) - 16b² ( 2c³ ) + 16b² ( 3b²c )
⇒ 16b² ( 5b² - 2c³ + 3b²c )
Therefore, Statements that are true about David's word are:
The GCF of the coefficients is correct.
The variable c is not common to all terms, so a power of c should not have been factored out.
In step 6, David applied the distributive property