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3 years ago

Cameron adds 4 new hats to his collection each year. He started with only 3. Find slope and the y intercept.

Mathematics

1 answer:

pantera1 [17]3 years ago

3 0

The slope is 4. The y intercept is 3.

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A rare book was purchased for $200 and then it was sold for $400. What percent increase was that

hram777 [196]

Answer:

100% increase

Step-by-step explanation:

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2 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

2 years ago

Determine the circumference of a circle with a radius of 6.8. Round your answer to the tenths place.

Eva8 [605]

Answer:

42.73

Step-by-step explanation:

2*pi*r = 2*pi*6.8=42.73

5 0

2 years ago

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Four times the difference of a number and 5 is the same as 5 increased by four times the number plus five times the number

asambeis [7]

4*(x-5)+5=5+(4*x)+(5*x)

4x-20+5=5+4x+5x

-20+5=5+5x

-15=5+5x

-20=5x

-4=x

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2 years ago

Craig opened a bank account with $500 in it when his son was born. Each birthday since, Craig has deposited $100. There is now $

OleMash [197]

Answer:

Step-by-step explanation:

$1300 - $500 = $800

He put in $100 on

1st birthday = $600

2nd birthday = $700,

3rd = 800

4th = 900

5th = 1000

6th = 1100

7th = 1200

8th = 1300

6 0

3 years ago

Read 2 more answers