All categories

4 years ago

Fine the exact distance between the line 6x-y=-3 and the point (6,2). Show your work. Explain your answer.

Mathematics

1 answer:

AVprozaik [17]4 years ago

6 0

Answer:

$\sqrt{37}$ units

Step-by-step explanation:

If we draw a perpendicular from point (6,2) on the line 6x - y = - 3, then we have to find the length of the perpendicular.

We know the formula of length of perpendicular from a point $(x_{1}, y_{1} )$ to the straight line ax + by + c = 0 is given by

$\frac{|ax_{1} + by_{1} +c |}{\sqrt{a^{2}+b^{2}}}$

Therefore, in our case the perpendicular distance is

$\frac{|6(6)-2+3|}{\sqrt{6^{2} +(-1)^{2} } } = \frac{37}{\sqrt{37} } = \sqrt{37}$ units. (Answer)

You might be interested in

A manager at a local company asked his employees how many times they had given blood in the last year. The results of the survey

Lubov Fominskaja [6]

Answer:

$Var(X) = E(X^2) -[E(X)]^2 = 4.97 -(1.61)^2 =2.3779$

And the deviation would be:

$Sd(X) =\sqrt{2.3779}= 1.542 \approx 1.54$

Step-by-step explanation:

For this case we have the following distribution given:

X 0 1 2 3 4 5 6

P(X) 0.3 0.25 0.2 0.12 0.07 0.04 0.02

For this case we need to find first the expected value given by:

$E(X) = \sum_{i=1}^n X_i P(X_I)$

And replacing we got:

$E(X)= 0*0.3 +1*0.25 +2*0.2 +3*0.12 +4*0.07+ 5*0.04 +6*0.02=1.61$

Now we can find the second moment given by:

$E(X^2) =\sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2)= 0^2*0.3 +1^2*0.25 +2^2*0.2 +3^2*0.12 +4^2*0.07+ 5^2*0.04 +6^2*0.02=4.97$

And the variance would be given by:

$Var(X) = E(X^2) -[E(X)]^2 = 4.97 -(1.61)^2 =2.3779$

And the deviation would be:

$Sd(X) =\sqrt{2.3779}= 1.542 \approx 1.54$

8 0

3 years ago

parking garage has 5 floors. If 117 cars can be parked on each floor, how many total cars can park in the garage? Drag numbers t

mr Goodwill [35]

Answer:

585 cars

Step-by-step explanation:

Given

$Floors = 5$

$Cars = 117$ per floor

Required

Determine the total number of cars

This is calculated by multiplying number of cars per floor by number of floors.

$Total = Floors*Cars$

$Total = 5 * 117$

$Total = 585$

<em>Hence, there are 585 cars in total</em>

6 0

3 years ago

0.5 to the second power x (20-2 to the third power x 3)x(2/5x25)

lesantik [10]

Answer:

489

Step-by-step explanation:

4 0

3 years ago

List the next four multiples of 4/8

8090 [49]

Next four multipules of 4/8
to keep the value of 4/8 the same, we must multiply the top number and bottom number by the same thing
4/8 times 2/2=8/16
4/8 times 3/3=12/24
4/8 times 4/4=16/32
4/8 times 5/5=20/40

next 4 multipulees are
8/16, 12/24, 16/32, 20/40

5 0

3 years ago

The Sydney Morning Herald - February 8, 2004 reported that in 1961, the average number of children born to Australian women (3.5

Alborosie

Answer:

<h2>A. Agree, 4 children is the most typical number of children.</h2>

Step-by-step explanation:

By analysis the problem, we can make our decision by first determining the percent of 3.55 of 4

therefore the percentage can be computed as

=(3.55/4)*100

=0.8875*100

=88.75%

The analysis above it shows that 88.75 percent of the women who give birth to children give birth to 4 children.

This number is very close to a hundred percent hence the statistical claim is "Agree, 4 children is the most typical number of children."

3 0

3 years ago