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3 years ago

What is the equation of a line that passes through (6,3) and has a slope of -2/3

Mathematics

1 answer:

goldenfox [79]3 years ago

6 0

Answer:

y=mx+b = 3y=6x+-2/3

Step-by-step explanation:

hope this is better

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The perimeter of a bedroom is 88 feet. The ratio of the width to the length is 5:6. What are the dimensions of the bedroom?

Elza [17]

Answer:

20 feet wide, 24 feet long

Step-by-step explanation:

Let x - width, y - length.

The perimeter is given by the formula:

P = 2*(width + length) or using x, y

P = 2*(x + y) = 88

x + y = 44

And we know that the ratio between the sides is 5/6:

x/y = 5/6. x is on top because the length is bigger than the width

x = 5y/6

Plug this in the first expression:

y + 5y/6 = 44. Muliply by 6

6y + 5y = 264

11y = 264

y = 264/11 = 24.

So x = 5(24)/6 = 20

7 0

3 years ago

1. (a) Solve the differential equation (x + 1)Dy/dx= xy, = given that y = 2 when x = 0. (b) Find the area between the two curves

erastova [34]

(a) The differential equation is separable, so we separate the variables and integrate:

$(x+1)\dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x+1} \, dx = \left(1-\dfrac1{x+1}\right) \, dx$

$\displaystyle \frac{dy}y = \int \left(1-\frac1{x+1}\right) \, dx$

$\ln|y| = x - \ln|x+1| + C$

When x = 0, we have y = 2, so we solve for the constant C :

$\ln|2| = 0 - \ln|0 + 1| + C \implies C = \ln(2)$

Then the particular solution to the DE is

$\ln|y| = x - \ln|x+1| + \ln(2)$

We can go on to solve explicitly for y in terms of x :

$e^{\ln|y|} = e^{x - \ln|x+1| + \ln(2)} \implies \boxed{y = \dfrac{2e^x}{x+1}}$

(b) The curves y = x² and y = 2x - x² intersect for

$x^2 = 2x - x^2 \implies 2x^2 - 2x = 2x (x - 1) = 0 \implies x = 0 \text{ or } x = 1$

and the bounded region is the set

$\left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^2 \le y \le 2x - x^2\right\}$

The area of this region is

$\displaystyle \int_0^1 ((2x-x^2)-x^2) \, dx = 2 \int_0^1 (x-x^2) \, dx = 2 \left(\frac{x^2}2 - \frac{x^3}3\right)\bigg|_0^1 = 2\left(\frac12 - \frac13\right) = \boxed{\frac13}$

7 0

3 years ago

Is 3/7 and 18/42 equivalent ratios

nignag [31]

Yes they are. if you multiply numerator and denominator of 3/7 by 6, you get 18/42

7 0

3 years ago

Read 2 more answers

ABCD=STQR. What is CD?

ololo11 [35]

Answer:

CD = QR because abcd= star then last 2 are answer

8 0

3 years ago

Read 2 more answers

At the city museum, child admission is $6.10 and adult admission is $9.30 . On Sunday, four times as many adult tickets as child

dalvyx [7]

Answer:

21 child tickets

Step-by-step explanation:

For this problem, you'd use a system of equations.

First, define your variables.

x = # of child tickets sold

y = # of adult tickets sold

There were 4 times as many adult tickets (y) as child tickets (x) sold, so:

4 x = y

4 x - y = 0

93 (4 x - y = 0)

372 x - 93 y = 0

The total revenue was $909.30, adult tickets were $9.30 each, child tickets were $6.10 each, so:

6.10 x + 9.30 y = 909.30

10 (6.10 x + 9.30 y = 909.30)

61 x + 93 y = 9093

372 x - 93 y = 0

433 x = 9093

433 x / 433 = 9093 / 433

x = 21

3 0

3 years ago