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Varvara68 [4.7K]

3 years ago

5

Angelica uses the point (4,3) to represent the location of her house and uses the point (10,8) to represent the location of a ga

s station. Each unit on the graph represents 1 mi. How far is the gas station from Angelica's house? Show your work.

2 answers:

Mamont248 [21]3 years ago

7 0

Answer: The distance between the 2 locations is 7.81 miles

Step-by-step explanation:

Allushta [10]3 years ago

5 0

Answer:

Distance between Gas Station and House = 7.81 miles.

Step-by-step explanation:

Given: House location ( 4, 3 ) and Gas station location ( 10, 8)

On graph 1 unit = 1 mile.

To find: Distance between Gas Station and House

We use the Distance formula to find the distance between two points $(x_1,y_1)\:and\:(x_2,y_2)$

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

From given points and formula,

$Distance\:between\:house\:and\:gas\:station=\sqrt{(10-4)^2+(8-3)^2}$

= $\sqrt{(6)^2+(5)^2}$

= $\sqrt{36+25}$

= $\sqrt{61}$ units

Since, 1 unit = 1 mile

⇒ $\sqrt{61}\:unit=\sqrt{61}miles=7.81 miles$

Therefore, Distance between Gas Station and House = 7.81 miles.

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Ne4ueva [31]

Answer:

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Step-by-step explanation:

Let's C be the circumference of the circle and S be the circumference of the square. If we cut the string into 2 pieces the total circumferences would be the string length 100cm.

S + C = 100 or S = 100 - C

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So the area of the square is

$A_S = \frac{S^2}{4^2} = \frac{S^2}{16}$

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Therefore the total area is

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We can substitute 100 - C for S

$A = \frac{(100 - C)^2}{16} + \frac{C^2}{4\pi}$

$A = \frac{100^2 - 200C + C^2}{16} + \frac{C^2}{4\pi}$

$A = 625 -12.5C + \frac{C^2}{16} + \frac{C^2}{4\pi}$

$A = 625 -12.5C + C^2(\frac{1}{16} + \frac{1}{4\pi})$

To find the maximum and minimum of this, we can take the first derivative and set that to 0

$A^{'} = -12.5 + 2C(\frac{1}{16} + \frac{1}{4\pi}) = 0$

$C(\frac{1}{8} + \frac{1}{2\pi}) = 12.5$

$C \approx 44 cm$

If we take the 2nd derivative:

$A^{''} = \frac{1}{8} + \frac{1}{2\pi} > 0$

We can see that this is positive, so our cut at 44 cm would yield the minimum area.

The maximum area would be where you not cut anything and use the total string length to use for either square or circle

if C = 100 then $A_C = \frac{C^2}{4\pi} = \frac{100^2}{4\pi} = 795.77 cm^2$

if S = 100 then $A_S = \frac{S^2}{16} = \frac{100^2}{16} = 625 cm^2$

So to yield maximum area, you should not cut at all and use the whole string to form a circle

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4 years ago

The area of a rectangle is 0.8 square units. The length is 3.2 units and the width is x units. What is the value of x?

zhannawk [14.2K]

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Step-by-step explanation:

To find the area of a rectangle ,we need to multiply the length by the width.

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3.2 * x = 0.8 Now solve for x.

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