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3 years ago

Which equation is not a linear equation

Mathematics

1 answer:

Misha Larkins [42]3 years ago

4 0

Answer:

1+1=2 is not linear a+b=c is linear

Step-by-step explanation:

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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

4 years ago

I NEED THIS ANSWERED AS SOON AS POSSIBLE! How much material is needed to construct a triangular tent that is 6 feet wide, 4 feet

Elena-2011 [213]

To figure out this problem, you need to find the surface area of a triangular prism.

a=5ft

b=5ft

c=6ft

h=8ft

A= (a*h) + (b*h) + (c*h) + 1/2√-a⁴ + 2(a*b)² + 2(a*c) - b⁴ + 2(b*c) - c⁴

=152 square feet

5 0

4 years ago

Sam and Bethan share £54 in the ratio 5:4<br> Work out how much each person gets.

jeyben [28]

Answer:

Sam: $30; Bethan: $24

Step-by-step explanation:

Since the ratio is 5:4 Sam has to pay 5/9 of the total which is 54. To find how much he pays set up the equation like this.

$\frac{x}{54} =\frac{5}{9}$

Cross Multiply

54(5)=9x

270=9x

Divide by 9

30=x

So Sam pays $30. To find out how much Bethan pays simply subtract 30 from 54

54-30=24

So Bethan pays $24

5 0

3 years ago

A triangular prism is 18 feet long and has a triangular face with a base of 9 feet and a height of 14 feet. What is the volume o

tangare [24]

The answer is 1,134.

6 0

3 years ago

Read 2 more answers

If the area of a park is exactly halfway between 2.4 and 2.5 acres, what is the area of the park? Explain. Please if you know th

grandymaker [24]

"If the area of a park is exactly halfway between 2.4 and 2.5 acres, what is the area of the park" its 2.45 acres.

8 0

3 years ago