Unit 1250 unit 2825 what the ratio for each unit a day

Problem: A piece of farmland is a watering plot of land in a circular pattern. A sewer line needs to be installed from a new hou

Musya8 [376]

The entry and exit points of (2, 3), and (12, 6), and 200 ft. extension of the sprinkler system gives;

(1) The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)

(2) The longest installable sprinkler system is approximately 172.4 feet

<h3>How can the points where the line crosses the farmland be found?</h3>

1. The slope of the sewer line is found as follows;

m = (6 - 3)/(12 - 2) = 3/10 = 0.3

The equation of the sewer line can be expressed in point and slope form as follows;

(y - 3) = 0.3×(x - 2)

y = 0.3•x - 0.6 + 3

y = 0.3•x + 2.4

The equation of the circumference of the sprinkler can be expressed as follows;

(x - 8)² + (y - 3)² = 2²

Therefore;

(x - 8)² + (0.3•x + 2.4 - 3)² = 2²

Solving gives;

x= 6.53, or x = 8.48

y = 0.3×6.53 + 2.4 = 4.36

y = 0.3×8.48 + 2.4 = 4.9

Therefore;

The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)

2. When the farmland does not cross the sewer line, we have;

sewer line is tangent to circumference of farmland

Slope of radial line from center of the land is therefore;

m1 = -1/0.3

Equation of the radial line to the point the sewer line is tangent to the circumference is therefore;

y - 3 = (-1/0.3)×(x - 8)

Which gives;

y = (-1/0.3)×(x - 8) + 3

The x-coordinate is therefore;

0.3•x + 2.4 = (-1/0.3)×(x - 8) + 3

x ≈ 7.5

y = 0.3 × 7.5 + 2.4 ≈ 4.65

The longest sprinkler system is therefore;

d = √((7.5 - 8)² + (4.65 - 3)²) ≈ 1.724

Which gives;

The longest sprinkler system is 1.724 × 100 ft. ≈ 172.4 ft.

Learn more about the equation of a circle here:

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3 0

1 year ago

The average homicide rate for the cities and towns in a state is 10 per 100,000 population with a standard deviation of 2. If th

zlopas [31]

Answer:

$P(X>8)=P(\frac{X-\mu}{\sigma}>\frac{8-\mu}{\sigma})=P(Z>\frac{8-10}{2})=P(Z>-1)$

And we can find this probability with the complement rule:

$P(Z>-1)=1-P(Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the average homicide rate for the cities of a population, and for this case we know the distribution for X is given by:

$X \sim N(10,2)$

Where $\mu=10$ and $\sigma=2$

We are interested on this probability

$P(X>8)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>8)=P(\frac{X-\mu}{\sigma}>\frac{8-\mu}{\sigma})=P(Z>\frac{8-10}{2})=P(Z>-1)$

And we can find this probability with the complement rule:

$P(Z>-1)=1-P(Z$

5 0

3 years ago

Which of the following polygons is a quadrilateral

saw5 [17]

Answer:

C

Step-by-step explanation:

A quadrilateral is a shape with 4 sides.

A is a triangle, 3 sides

B is a pentagon, 5 sides

D is a hexagon, 6 sides

C is a quadrilateral, 4 sides

4 0

1 year ago

Read 2 more answers

An entry code into a building is a 5-digit number.

lakkis [162]

Answer:B

Step-by-step explanation:

5 0

3 years ago

List 5 fractions between 4/5and 10/11

snow_tiger [21]

Step-by-step explanation:

if we simply add 1 to numerator and denominator (top and bottom of the fraction), we get a fraction that is bigger than the original fraction and smaller than the fraction that added 2 to numerator and denominator.

so, my choice would be

4/5

5/6

6/7

7/8

8/9

9/10

10/11

6 0

2 years ago