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Sophie [7]
3 years ago
8

You have to order fencing for a 25-acre, rectangular field. One side of the field measures exactly ¼ mile. How many yards of fen

cing will you need to enclose the field completely?
Mathematics
1 answer:
zysi [14]3 years ago
3 0

Answer:

1430 yards

Step-by-step explanation:

Note that 1\text{ acre}=\dfrac{1}{640}\text{ square mile}. Then

25\text{ acres}=\dfrac{25}{640}\text{ square mile}.

If one side of the restangular field measures exactly \dfrac{1}{4} mile, then let the second side be x miles and

\dfrac{25}{640}=\dfrac{1}{4}\cdot x,\\ \\x=\dfrac{\frac{25}{640}}{\frac{1}{4}}=\dfrac{25}{640}\cdot \dfrac{4}{1}=\dfrac{25}{160}=\dfrac{5}{32}\ mile.

The perimeter of the rectangle will be

P=2\cdot \dfrac{1}{4}+2\cdot \dfrac{5}{32}=\dfrac{2\cdot 8+10}{32}=\dfrac{26}{32}=\dfrac{13}{16}\ mile.

Since 1\ mile=1760\ yards, then \dfrac{13}{16}\ mile=\dfrac{13}{16}\cdot 1760=1430\ yards.


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Given:

A line through the points (7,1,-5) and (3,4,-2).

To find:

The parametric equations of the line.

Solution:

Direction vector for the points (7,1,-5) and (3,4,-2) is

\vec {v}=\left

\vec {v}=\left

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Now, the perimetric equations for initial point (x_0,y_0,z_0) with direction vector \vec{v}=\left, are

x=x_0+at

y=y_0+bt

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The initial point is (7,1,-5) and direction vector is \vec {v}=\left. So the perimetric equations are

x=(7)+(-4)t

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y=1+3t

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Therefore, the required perimetric equations are x=7-4t, y=1+3t and z=-5+3t.

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3 years ago
In performing a chi-square goodness-of-fit test for a normal distribution, a researcher wants to make sure that all of the expec
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Answer:

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In your own words, explain how to find the incenter and the circumcenter of a triangle and what the Circumcenter Theorem and Inc
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Step-by-step explanation:

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To find Circumcenter:

Construct perpendicular bisectors of all sides of triangle and their intersection point gives the circumcenter.

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I feel like it’s B but I’m not sure
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F(x+h) = (x+h)² + 3(x+h)^3<br><br> How would I distribute this?
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Answer:

f(x + h) = 3x³ + x² + 9h²x + 3h³ + h² + 9hx² + 2hx

General Formulas and Concepts:

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  • Distributive Property
  • Expand by FOIL (First Outside Inside Last)
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Step-by-step explanation:

<u>Step 1: Define function</u>

f(x) = x² + 3x³

f(x + h) is x = x + h

<u>Step 2: Simplify</u>

  1. Substitute:                              f(x + h) = (x + h)² + 3(x + h)³
  2. Expand by FOILing:               f(x + h) = (x² + 2hx + h²) + 3(x + h)³
  3. Rewrite:                                  f(x + h) = (x² + 2hx + h²) + 3(x + h)²(x + h)
  4. Expand by FOILing:               f(x + h) = (x²+2hx+h²) + 3(x² + 2hx + h²)(x+h)
  5. Distribute/Expand:                 f(x + h) = (x²+2hx+h²) + 3(x³+3hx²+3h²x+h³)
  6. Distribute 3:                            f(x + h) = (x²+2hx+h²)+(3x³+9hx²+9h²x+3h³)
  7. Combine like terms:               f(x + h) = 3x³+x²+9h²x+3h³+h²+9hx²+2hx
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