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3 years ago

Haily walked 15 miles in 9 hours. What was her walking rate in miles per hour? Express your answer in simplest form

Mathematics

2 answers:

SVEN [57.7K]3 years ago

7 0

Answer: 1 2/3 miles

Step-by-step explanation:

Hsiky walked 15 miles in 9 hours.

For 1 hour, Haily will walk, (15/9) miles which gives 1 6/9 miles. Reducing it to lowest term equals 1 2/3 miles

Pachacha [2.7K]3 years ago

6 0

Answer:

1.67

Step-by-step explanation:

you should do 15 ÷ 9 and you get 1.6666666667 and when you simplify that you get 1.67

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Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 181.5 square cen

3241004551 [841]

Answer:

The base and height of the solid is 5.5cm

Step-by-step explanation:

Given

$Surface\ Area = 181.5cm^2$

Required

Determine the dimensions that maximizes the volume

Let the base dimension be x and the height be h

The volume is calculated as:

$Volume =x^2 * h$

$Volume =x^2h$

181.5 =x^2h

The surface area (S) is calculated as this:

$S = 2(x^2 + xh + xh)$

$S = 2(x^2 + 2xh)$

$S = 2x^2 + 4xh$

Substitute 181.5 for S

$181.5 = 2x^2 + 4xh$

Make h the subject:

$4xh = 181.5 - 2x^2$

$h = \frac{181.5 - 2x^2}{4x}$

Substitute $h = \frac{181.5 - 2x^2}{4x}$ in $Volume =x^2h$

$V = x^2(\frac{181.5 - 2x^2}{4x})$

$V = x(\frac{181.5 - 2x^2}{4})$

$V = \frac{1}{4}(x)(181.5 - 2x^2)$

$V = \frac{181.5x}{4} - \frac{2x^3}{4}$

$V = \frac{181.5x}{4} - \frac{x^3}{2}$

To get the maximum, we differentiate V with respect to t and set the differentiation to 0

$dV = \frac{181.5}{4} - \frac{3x^2}{2}$

Set to 0

$0 = \frac{181.5}{4} - \frac{3x^2}{2}$

$\frac{3x^2}{2} = \frac{181.5}{4}$

Multiply through by 4

$4 * \frac{3x^2}{2} = \frac{181.5}{4} * 4$

$2*3x^2 = 181.5$

$6x^2 = 181.5$

$x^2 = \frac{181.5}{6}$

$x^2 = 30.25$

$x = \sqrt{30.25$

$x = 5.5$

Recall that:

$h = \frac{181.5 - 2x^2}{4x}$

$h = \frac{181.5 - 2 * 5.5^2}{4 * 5.5}$

$h = \frac{181.5 - 60.5}{22}$

$h = \frac{121}{22}$

$h = 5.5$

So, we have:

$h = 5.5$

$x = 5.5$

Hence, the base and height of the solid is 5.5cm

7 0

3 years ago

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Maru [420]

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Artyom0805 [142]

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4 years ago

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Jackson's robot moved 5 meters in 2 seconds How far did he move in 30 sec? (please explain and use fractions)

tatyana61 [14]

75 meters

Step-by-step explanation:

5 x 30/2

= 5 x 15

= 75 meters

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3 years ago

Need help with this

Leya [2.2K]

Answer:

Step-by-step explanation:

The least common denominator of the fractions is the least common multiple of the denominators.

Multiples of 3: 3, 6, 9, 12, 15, 18, ...

Multiples of 4: 4, 8, 12, 16, 20, 24, ...

The lowest multiple that is common to 3 and 4 is 12.

LCD of 1/3 and 3/4 is 12.

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3 years ago

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