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Evaluate 3.2 divided m for m=2?

Updated: 4/28/2022
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Daviongocrazy 12

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Queenie Botsford

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Q: Evaluate 3.2 divided m for m=2?
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35 * * * * * How about 3.2*10 = 32 m2 instead?


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What is the answer of 15 divided by m - m plus 8 equals 10?

(15/m) - m + 8 = 1015/m - m = 215 - m2 - 2m = 0 or m2 +2m - 15 = 0This factoises as (m +5)( m - 3), so m = 3 or -5


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-the sum of one number and four times another number is 64 Find the value of the numbers so that their product is a maximum?

The numbers are 8 and 32 and the max product is 256.Let one number be mLet the other be nWe have m + 4n = 64So 4n = 64 - mor n = 16- m/4We want mn = m(16 - m/4) to be a max value.That is to say the product of these two numbers equals -(1/4)m2 + 16m.Now depending on you level of math there are many ways to do this.If you know calculus, you can take the derivative of f(m)= -(1/4)m2 + 16mand you find it as -(1/2)m + 16.Now you would set that equal to zero which will indicates m = 32.So you have:-(1/2)m + 16 = 0m = 32To find the other number, substitute 32 for m into the equation n = 16 - m/4 and solve for n.So that the other number is 16-32/4 or 8.Thus, the numbers are 8 and 32, and their product is 256.Since f(m)=16m-m2 /4, we can also look at f(32)= 16(32)-322 /4=512-256=256METHOD TWONow if you don't know calculus, here is another way to do it.You can see that f(m)= -(1/4)m2 + 16m is a quadratic function written in standard form asax2 + bx + c, where a = -1/4, b = 16, and c = 0.The graph is a parabola which opens down since the sign of the coefficient of m2 is negative (a = -1). We need to find the vertex of the parabola where the y-coordinate will be the max value.The formula for the vertex is (-b/2a, f(-b/2a)), so we have-b/2a = -16/(2(-1/4)) = 32, andf(m) = -(1/4)m2 + 16mf(-b/2a) = f(32) = -(1/4)(32)2 + 16(32) = 256Therefore, the vertex of the parabola is at (32, 256) and the maximum value of 256 happens when m = 32. Since this max value is the product of m and n, then n = 8 (256/32).METHOD THREEOnce again look at the function f(m)=16m-m2 /4 and write it in standard formf(m)=-m2 /4 +16mNow complete write this as -1/4(m2 -64m) and complete the square.We havef(m)=-1/4(m -32)2 +256This tells us the graph is a parabola with vertex (32, 256)Since the parabola opens downward, 256 is the max.


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