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kirill [66]
3 years ago
8

Without doing the math, determine which is greater, 40. 1/4 or 40÷ 1/4. Explain your reasoning.

Mathematics
2 answers:
nevsk [136]3 years ago
8 0

When you divide by a fraction, in this case 40 divided by 1 over 4, you multiply by the reciprocal of what you're dividing by, so:

\frac{40}{1} ÷ \frac{1}{4}

turns into...

\frac{40}{1} · \frac{4}{1}, or 40 * 4, which equals 160.

With this knowledge, whenever given a set of numbers like you were given, we know that 40 ÷ \frac{1}{4} must be the larger, and 40 · \frac{1}{4} must be the smaller.

Therefore, 40 ÷ \frac{1}{4} is the greater number.

<em>Hope this helps! :)</em>

maw [93]3 years ago
4 0

40 ÷ \frac{1}{4} is greater

multiplying a whole number by a fraction  reduces the size of the whole number

dividing a whole number by a fraction increases the size of the number


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Answer:

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box  has largest volume.

Step-by-step explanation:

Given that,

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The length of the one side of the squares which are cut out of the each corners of the metal sheet be x.

The length of the metal box be = (15-2x) inches.

The width of the metal box be =(10-2x) inches

The height of the metal box be =x inches

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Differentiating with respect to x

V'=12x²-100x+15

Again differentiating with respect to x

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For maximum or minimum value, V'=0

12x²-100x+15=0

Apply quadratic formula x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}, here a=12, b= -100 and c=15

x=\frac{-(-100)\pm\sqrt{(-100)^2-4.12.15}}{2.12}

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For x= 8.18, The value of (15-2x) and (10-2x) will negative.

∴x=0.1528 .

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∴At x=0.1528 inch, the volume of the metal box will be maximum.

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box  has largest volume.

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Step-by-step explanation:

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Answer:

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General Formulas and Concepts:

<u>Pre-Algebra</u>

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Step-by-step explanation:

<u>Step 1: Identify</u>

<em>a</em> = x + 3

<em>b</em> = x

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<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Substitute [PT]:                                                                                                (x + 3)² + x² = (√117)²
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  3. Combine like terms:                                                                                       2x² + 6x + 9 = (√117)²
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  6. Factor out GCF:                                                                                               2(x² + 3x - 54) = 0
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Since we are dealing with positive values, we can disregard the negative root.

∴ x = 6

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3 years ago
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