Evaluate the given expression for x = 4 and y= 3. 7x2 + 6xy + 6y?The answer is: _____
1 answer:
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Answer:
E = 64.05
NG = 52.29
O = 35.15
Step-by-step explanation:
With the statement we can create a system of 3X3 equations that would be as follows:
E = electricity
NG = natural gas
O = oil
0.35 * E + 0.15 * NG + 0.25 * O = 25
0.35 * E + 0.15 * NG + 0.2 * O = 15
0.1 * E + 0.1 * NG + 0.1 * O = 20
If we pass this system equations to matrix and subtract it from the identity matrix we would have the following:
0.65 * E - 0.15 * NG - 0.25 * O = 25
-0.35 * E + 0.85 * NG - 0.2 * O = 15
-0.1 * E - 0.1 * NG + 0.9 * O = 20
Solving this system of equations around here can be very long and impractical, therefore, I attach a photo of the process:
And the answer is:
E = 64.05
NG = 52.29
O = 35.15
Take an arbitrary interval [<em>a</em>, <em>b</em>], where <em>a</em> < <em>b</em>.
Compute the arc length <em>L</em> of <em>y</em> = <em>f(x) </em>over [<em>a</em>, <em>b</em>] :
Now comptue the area <em>A</em> under the curve <em>y</em> = <em>f(x)</em> over [<em>a</em>, <em>b</em>] :
We have
<em>f</em> (<em>x</em>) = 1/4 <em>e</em> ⁻ˣ + <em>e </em>ˣ → <em>f ' </em>(<em>x</em>) = -1/4 <em>e</em> ⁻ˣ + <em>e </em>ˣ
Then
√(1 + (<em>f '</em> (<em>x</em>))²) = √(1 + (-1/4 <em>e</em> ⁻ˣ + <em>e </em>ˣ)²)
… = √(1 + 1/16 <em>e</em> ⁻²ˣ - 1/2 + <em>e </em>²ˣ)
… = √(1/16 <em>e</em> ⁻²ˣ + 1/2 + <em>e </em>²ˣ)
… = 1/4 √(<em>e</em> ⁻²ˣ + 8 + 16<em>e </em>²ˣ)
… = 1/4 √((<em>e</em> ⁻ˣ + 4 <em>e</em> ˣ)²)
… = 1/4 (<em>e</em> ⁻ˣ + 4 <em>e</em> ˣ)
… = 1/4 <em>e</em> ⁻ˣ + <em>e</em> ˣ
… = <em>f</em> (<em>x</em>)
so both <em>A</em> = <em>L</em> for any choice of interval [<em>a</em>, <em>b</em>].