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3 years ago

write an equation of the line passing through the pair of points or state that the slope is undefined. (-3,5) and (3,-7)

Mathematics

1 answer:

AveGali [126]3 years ago

7 0

Step-by-step explanation:

equation of a line = y-y1=m(x-x1)

but we have to find the slope

so slope=y2-y1 = -7-5

x2-x1. 3--3

-12

-2

1. =-2

y-5=-2(x-3)

y-5=-2x+6

y=-2x+6-5

y=2x+1

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Two streams flow into a reservoir. Let X and Y be two continuous random variables representing the flow of each stream with join

zlopas [31]

Answer:

c = 0.165

Step-by-step explanation:

Given:

f(x, y) = cx y(1 + y) for 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3,

f(x, y) = 0 otherwise.

Required:

The value of c

To find the value of c, we make use of the property of a joint probability distribution function which states that

$\int\limits^a_b \int\limits^a_b {f(x,y)} \, dy \, dx = 1$

where a and b represent -infinity to +infinity (in other words, the bound of the distribution)

By substituting cx y(1 + y) for f(x, y) and replacing a and b with their respective values, we have

$\int\limits^3_0 \int\limits^3_0 {cxy(1+y)} \, dy \, dx = 1$

Since c is a constant, we can bring it out of the integral sign; to give us

$c\int\limits^3_0 \int\limits^3_0 {xy(1+y)} \, dy \, dx = 1$

Open the bracket

$c\int\limits^3_0 \int\limits^3_0 {xy+xy^{2} } \, dy \, dx = 1$

Integrate with respect to y

$c\int\limits^3_0 {\frac{xy^{2}}{2} +\frac{xy^{3}}{3} } \, dx (0,3}) = 1$

Substitute 0 and 3 for y

$c\int\limits^3_0 {(\frac{x* 3^{2}}{2} +\frac{x * 3^{3}}{3} ) - (\frac{x* 0^{2}}{2} +\frac{x * 0^{3}}{3})} \, dx = 1$

$c\int\limits^3_0 {(\frac{x* 9}{2} +\frac{x * 27}{3} ) - (0 +0) \, dx = 1$

$c\int\limits^3_0 {(\frac{9x}{2} +\frac{27x}{3} ) \, dx = 1$

Add fraction

$c\int\limits^3_0 {(\frac{27x + 54x}{6}) \, dx = 1$

$c\int\limits^3_0 {\frac{81x}{6} \, dx = 1$

Rewrite;

$c\int\limits^3_0 (81x * \frac{1}{6}) \, dx = 1$

The $\frac{1}{6}$ is a constant, so it can be removed from the integral sign to give

$c * \frac{1}{6}\int\limits^3_0 (81x ) \, dx = 1$

$\frac{c}{6}\int\limits^3_0 (81x ) \, dx = 1$

Integrate with respect to x

$\frac{c}{6} * \frac{81x^{2}}{2} (0,3) = 1$

Substitute 0 and 3 for x

$\frac{c}{6} * \frac{81 * 3^{2} - 81 * 0^{2}}{2} = 1$

$\frac{c}{6} * \frac{81 * 9 - 0}{2} = 1$

$\frac{c}{6} * \frac{729}{2} = 1$

$\frac{729c}{12} = 1$

Multiply both sides by $\frac{12}{729}$

$c = \frac{12}{729}$

$c = 0.0165 (Approximately)$

8 0

3 years ago

The number of cable TV systems recently decreased from 16,300 to 16,020. Find the percent decrease.

irga5000 [103]

Percent decrease = (change in value) / (original value)

change in value = 9965-10100 =-135

We will just use 135 because the negative just that the value decreased

original value = 10100

So 135 / 10100 = .0134

This is a decrease of 1.34%

8 0

2 years ago

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Identify coordinate point A. (0, 2) (6, 7) (1, 5) (7, 3)

Novosadov [1.4K]

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2 years ago

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H(x)=2x^2+3x-7 find h(-1)

nata0808 [166]

Answer:

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Step-by-step explanation:

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3 years ago

Which values of c will cause the quadratic equation –x2 3x c = 0 to have no real number solutions? check all that apply.

nika2105 [10]

The given quadratic equation will not have any real solution for c<-9/4.

The given quadratic equation is:

$-x^{2} +3x+c=0$

<h3>What is a quadratic equation?</h3>

Any equation of the form $ax^{2} +bx+c=0$ is called a quadratic equation with a≠0.

In order to have no real solution, the discriminant of a quadratic equation will be less than zero.

$D < 0$

$3^{2} -4(-1)(c) < 0$

$9+4c < 0$

$c < -\frac{9}{4}$

For $c < -\frac{9}{4}$ the given quadratic equation will have no real solutions.

Hence, the given quadratic equation will not have any real solution for c<-9/4.

To get more about quadratic equations visit:

brainly.com/question/1214333

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2 years ago