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3 years ago

Which is the distance between parallel lines with the equations 3x-5y=1 and 3x-5y=-3

Mathematics

1 answer:

jonny [76]3 years ago

8 0

Answer:

The distance between parallel lines is $0.6860\ units$

Step-by-step explanation:

we have

$3x-5y=1$ -----> equation A

$3x-5y=-3$ -----> equation B

Line A and Line B are parallel lines, because their slopes are equal

Step 1

Find the slope of the given lines

isolate the variable y in the equation A

$5y=3x-1$

$y=(3/5)x-1/5$

The slope is $m=(3/5)$

Step 2

Find the slope of the perpendicular line to the given lines

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

$m1*m2=-1$

we have

$m1=3/5$ -----> given lines

substitute

$(3/5)*m2=-1$

$m2=-5/3$

Step 3

Find the equation of the perpendicular line that pass though the origin

with the slope $m2=-5/3$ and the point (0,0) Find the equation of the line

$y-y1=m(x-x1)$

$y-0=(-5/3)(x-0)$

$y=-(5/3)x$

Step 4

Using a graphing tool

Graph the two parallel lines and the perpendicular line

The intersection points are

$A(-0.2647,0.4412)$ and $B(0.0882,-0.1471)$

see the attached figure

we know that

the distance between the points A and B is the distance between parallel lines

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute the values

$d=\sqrt{(-0.1471-0.4412)^{2}+(0.0882+0.2647)^{2}}$

$d=\sqrt{(-0.5883)^{2}+(0.3529)^{2}}$

$d=0.6860\ units$

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nikdorinn [45]

Answer:

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Step-by-step explanation:

Data given and notation

$\bar X=95$ represent the sample mean

$\sigma=5$ represent the population standard deviation

$n=210$ sample size

$\mu_o =94$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is different from 94, the system of hypothesis are :

Null hypothesis: $\mu = 94$

Alternative hypothesis: $\mu \neq 94$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{95-94}{\frac{5}{\sqrt{210}}}=2.898$

P-value

Since is a two-sided test the p value would be:

$p_v =2*P(Z>2.898)=0.0038$

Conclusion

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let father's age be f yr old and son age be s yr old

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jenyasd209 [6]

Answer:

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