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grandymaker [24]
3 years ago
11

Find the equation of the line that passes through (1,3) and is perpendicular to y=1−2x. Leave your answer in the form y=mx+c

Mathematics
1 answer:
IgorLugansk [536]3 years ago
7 0

Answer:

The equation of the line  that passes through (1,3) and is perpendicular to y=1−2x is y=1/2x+5/2

Step-by-step explanation:

We can rewrite the original equation as y=-2x+1

To find an equation's perpendicular slope, you take the reciprocal of it and negate it, therefore the perpendicular slope is -2 -> 1/-2 -> 1/2

So far, we have y=1/2x+b, but to find the y-intercept, b, we would need to plug in (1,3) and solve for b:

y=1/2x+b

3=1/2(1)+b

3=1/2+b

5/2=b

Therefore, your final equation is y=1/2x+5/2

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Let C be the positively oriented square with vertices (0,0), (1,0), (1,1), (0,1). Use Green's Theorem to evaluate the line integ
liq [111]

Answer:

1/2

Step-by-step explanation:

The interior of the square is the region D = { (x,y) : 0 ≤ x,y ≤1 }. We call L(x,y) = 7y²x, M(x,y) = 8x²y. Since C is positively oriented, Green Theorem states that

\int\limits_C {L(x,y)} \, dx + {M(x,y)} \, dy = \int\limits^1_0\int\limits^1_0 {(Mx - Ly)} \, dxdy

Lets calculate the partial derivates of M and L, Mx and Ly. They can be computed by taking the derivate of the respective value, treating the other variable as a constant.

  • Mx(x,y) = d/dx 8x²y = 16xy
  • Ly(x,y) = d/dy 7y²x = 14xy

Thus, Mx(x,y) - Ly(x,y) = 2xy, and therefore, the line ntegral is equal to the double integral

\int\limits^1_0\int\limits^1_0 {2xy} \, dxdy

We can compute the double integral by applying the Barrow's Rule, a primitive of 2xy under the variable x is x²y, thus the double integral can be computed as follows

\int\limits^1_0\int\limits^1_0 {2xy} \, dxdy = \int\limits^1_0 {x^2y} |^1_0 \,dy = \int\limits^1_0 {y} \, dy = \frac{y^2}{2} \, |^1_0 = 1/2

We conclude that the line integral is 1/2

4 0
2 years ago
Read the following excerpts from the New York Times (December 17, 1996) article Chance of Heart Attack Increases for Those Who S
nataly862011 [7]

Answer:

1. B

2. A

3. A

4. A

Step-by-step explanation:

Hello!

The study claimed that subjects who suffer depression are more likely to have a heart attack than those who are not depressed.

1551 persons were interviewed as part of the experiment and classified according to their answers in two groups "suffered depression" and "didn't suffer depression"

Afterward, the researchers looked up the medical history of all 1551 subjects and recorded how many of them had heard issues.

1.

An observational study is one where the researcher only determines the variables he wants to study without controlling or influencing any factor of the population of interest. Because there is no interference from the researchers, there is a high risk that confounding factors may affect the conclusions of it. These studies are usually precursors to experimental tests, it allows the researcher to have an idea of the association between the two variables but you cannot establish causal relationships from them.

This is an example of an observational study, the researcher merely recorded the variables of interest without interfering with any aspects that may influence them. (For example diet or exercise habits of the subjects)

2. and 3.

The objective of the study is to determine if "depression" causes "disposition to heart attacks"

The explanatory variable is "depression status of the subject" since it is what is suspected to influence over the heart condition of said subject and "heart attack status" is the response variable.

4.

Of the 1551 subjects originally studied, 444 were classified as depressed, of these 27 had heard attacks. You can calculate the "proportion of subjects that suffered depression and had heart attacks" as:

p': 27/444= 0.06 ⇒ 6%

Since this value was obtained from the sample, it is an estimation of the population parameter, also called statistic.

I hope it helps!

4 0
2 years ago
Which soap deal has the lowest price per ounce?
Tom [10]
It’s 5.75 for 14 oz. It’s answer is 0.41 which is the lowest out of all of them.
7 0
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A ______ is a rule that pairs each element in one set with exactly one element from a second set.​
Cloud [144]

Answer:

function

Step-by-step explanation:

A <u>function</u> is a rule that pairs each element in one set with exactly one element from a second set.​

3 0
3 years ago
X^2-2x+15 in quadratic equation​
Arturiano [62]

Answer:

No solution

Step-by-step explanation:

There is not a real nor an imaginary solution to this equation. You can use a radical calculator to verify.

3 0
2 years ago
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