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Natalija [7]
1 year ago
9

Help:

D0" id="TexFormula1" title="1.\ &x^4-61x^2+900=0 \\ 2. \ & x^4-25x^2+144=0" alt="1.\ &x^4-61x^2+900=0 \\ 2. \ & x^4-25x^2+144=0" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
yawa3891 [41]1 year ago
7 0

\bf{1) \  x^4-61x^2+900=0 }

Applying the factorization method, for example:

      \bf{ 0=(x^2)^2-61(x^2)+900=(x^2-36)(x^2-25)}

               \bf{\\ &=(x+6)(x-6)(x+5)(x-5);    }

              \bf{ x_1=6 \quad x_2=-6 \quad \ \ \ x_3=5 \quad x_4=5  }

\bf{2) \  x^4-25x^2+144=0  }

Applying the factorization method:

          \bf{0&=(x^2)^2-25(x^2)+144=(x^2-16)(x^2-9) }

             \bf{ =(x-4)(x+4)(x-3)(x+3); }

            \bf{ x_1=4 \quad x_2=-4 \quad x_3=3 \quad x_4=-3  }

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Answer:

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3 0
3 years ago
Read 2 more answers
Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value
MArishka [77]

Answer:

  • y = 81-x
  • the domain of P(x) is [0, 81]
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Step-by-step explanation:

<u>Given</u>

  • x plus y equals 81
  • x and y are non-negative

<u>Find</u>

  • P equals x squared y is maximized

<u>Solution</u>

a. Solve x plus y equals 81 for y.

  y equals 81 minus x

__

b. Substitute the result from part a into the equation P equals x squared y for the variable that is to be maximized.

  P equals x squared left parenthesis 81 minus x right parenthesis

__

c. Find the domain of the function P found in part b.

  left bracket 0 comma 81 right bracket

__

d. Find dP/dx. Solve the equation dP/dx = 0.

  P = 81x² -x³

  dP/dx = 162x -3x² = 3x(54 -x) = 0

The zero product rule tells us the solutions to this equation are x=0 and x=54, the values of x that make the factors be zero. x=0 is an extraneous solution for this problem so ...

  P is maximized at (x, y) = (54, 27).

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2 years ago
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____ [38]

If an object has a density of less than 1 g/ml, the object will float in water.

So, fourth option is correct

Density = \frac{Mass}{Volume}

The object with density less than 1 g/ml will float, and the object with a density more than 1 g/ml will sink.

So, if an object has a density of less than 1 g/ml, the object will float in water.

Therefore, fourth option is correct

Learn more about density here:

brainly.com/question/3049000?referrer=searchResults

4 0
2 years ago
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