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Garnet H.'s Resources

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find profit (answer)

okay, that's an upside-down U and the maximum value is at the top  if you put the function in vertex form you can easily find the vertex: group the first two terms and factor out the negative (essentially factoring out -1): p = - (x²-14x) + 54 complete the square by taking...

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4n^2=-12n-6 (answer)

bring all terms to one side and set equal to 0 4n²+12n+6=0 factor out 2 2(2n²+6n+3)=0 ===> 2n²+6n+3=0   complete the square 2(n²+3n+9/4) + 3 = 0 + 9/2 ===> 2(n+3/2)² = 3/2 ===> (n+3/2)² = 3/4 take square root of...

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5m^2+12m+6=0 complete the square (answer)

separate the first two terms on the left and factor out 5 5(m² + (12/5)m ) + 6 = 0 take half the middle coefficient (12/5), square it, and add it to the terms in parentheses 5(m² + (12/5)m + 36/25) + 6 = 0 + 36/5 (this has the effect of adding 36/5 to both sides) simplify...

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9/2x+1=4/x (answer)

assuming those are 3 terms and not 2 you should start by noting all restrictions for x. In this case, x cannot be 0 because we can't divide by 0. multiply both sides by the lcm (2x) 9 + 2x = 8 ===> 2x = -1 ===> x = -1/2

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Which equation has roots of -3 and 5 (answer)

if the roots are r1 and r2, then the simplest equation is the quadratic: (x-r1)(x-r2) = 0 since yours are -3 and 5, the simplest (quadratic) equation is: (x - -3)(x - 5) = 0 (x+3)(x-5) = 0 which expands to x²-2x-15 = 0

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How do you find the answer? (answer)

check the number of digits in the number you have 3 possibilities: 1-digit numbers 2-digit numbers 3-digit numbers the only 3-digit candidate you have is 100 and that results in a 1, so this is an easy case for a 1-digit number the only way for the digits to add to 1 is for that number to be =...

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what are four consecutive integers whose sum is 86? (answer)

suiye is right, and that way is probably even quicker, but another way to arrive at the answer is to set up an equation four consecutive integers: x, (x+1), (x+2), and (x+3) sum them up and get 86 x + x+1 + x+2 + x+3 = 86 now solve for x, the smallest...

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Parametric equations (answer)

they ask for parametric equations and they give you the speed this is really projectile motion (the ball is moving both in the x and y dir. due to downward acceleration) but to answer the question you only need the quantities for the x-dimension: v(t) = 140           x(t)...

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2 dimensional motion problem (answer)

(a) from  a = v²/r  we get  0.86 = v²/3.6 which leads to v = 1.76 m/s period is the time it takes to complete a full cirle (your distance) from v = d/t we get 1.76 = 2π(3.6) / T which leads to T = 12.9s     (b) again from...

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f(x)=-2x^2+12x-22 (answer)

(1) y = -2(x²-6x ) - 22         (rewrite) (2) y = -2(x²-6x+9) - 22      (take half the coeff of -6 (-3), square it, and add it to the expression (3) y = -2(x²-6x+9) -22 + 18   (u essentially subtracted...

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How do you ask a question in Chinese? (answer)

depends on the type of question. if it's a yes/no question (in other words it requires only a yes or no for an answer), then you use the word -ma (this is toneless) at the end. there are other type of questions, (like when, who, what, how)....these questions have their chinese counterparts what -...

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