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1 Find The Value Of U That Makes Q A Maximum When They Are Related By The Equation Q = 10u

Maximizing profits solution?

Here is how I set it up

u: number of small sofas

v: number of large sofas

w: number of chairs

The objective is to maximize the profit. So the objective function is

z = 60 * u + 60 * v + 50 * w

The constraints given your info above

10u + 10v + 10w< = 1200

30u +30v + 10w <= 3000

20u + 10w < = 1800

[where < = means less than or equal to]

If you solve the system of equations as a system of equalities you will get the maximum profit

This is the system of equations in equality form (using equal signs vs. less than or equal to)

10u + 10v + 10w = 1200

30u +30v + 10w = 3000

20u + 10w = 1800

Once you get the values for u,w, and v then plug them into the z-function (the objective function) and you will get the value for the maximum profit.

How do I measure total capacitance using Wheatstone bridge?

How do I use concept of Wheatstone bridge in solving circuit of capacitance?A Wheatstone Bridge is used to measure small changes in a much larger signal, either a voltage or a resistance ratio. It can also be used to measure small changes in capacitance, such as for a sensor that changes capacitance to indicate the quantity it is measuring.A garden variety Wheatstone Bridge from Electronics-Tutorials dot com:Or R3 may be fixed, and R2 made a variable resistor.To measure capacitance, you must use an AC voltage source. Then you use resistors on the left, and the other a reference capacitor and the capacitance you are measuring. On the left side, there is no phase shift because it is pure resistance, on the right, there is no phase shift because it is pure capacitance. Assuming a very low impedance AC driving source.Thanks to Play-Hookey dot com for the image:Or both along the top are resistors, and the bottom elements are the reference capacitor and the capacitance you are measuring.Thanks again to Play-Hookey dot com:Here, C1 is a variable, but it could be a fixed reference and make R2 a variable resistor. Don’t make R1 the variable, because R1C1 and R2Cx make a shift in phase, and by making R2 variable, you are making the phase shift equal when the voltages are equal.If you make R1 variable, then except for the special case of R1 and R2 being equal and C1 and Cx being equal, you’ll never get both phase and voltage equal at the same time and so the null will be shallow and inaccurate.

Find the value of C that will make the polynomial a perfect square trinomial.?


Let me try and explain this problem to you.

The problem says,

49x^2 + 70x + C

We have to find the value of C such that the expression is a complete square.

(7x)^2 + 7x(10) + C

Let 7x = m

Now, the expression can be written as m^2 + 10m + c.

m^2 + 10m + c

= m^2 + 2(5)m + c

= m^2 + 2(5)(1)m + c

Formula: (a + b)^2 = a^2 + 2(a)(b) + b^2

Now compare the expression with the perfect square formula.

So, c = b^2 = 5^2 = 25

c = 25.

Hope the above solution makes it clear!

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