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3 years ago

Does the equation x^2 -4x + y^2 = -3 intersect the x-axis?

2 answers:

5 0

We can rewrite the equation into:
(x-2)^2+y^2=1

Therefore the circle's centre is that (2,0). Since the circle's centre lies on the x axis, the circle must intersect the x-axis.

olya-2409 [2.1K]3 years ago

3 0

Answer:

Yes, because the center is on the x-axis?

Step-by-step explanation:

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bija089 [108]

Answer:

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Step-by-step explanation:

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2 years ago

HELP ASAPPPP!!! Question in pic. Find the value of x

erik [133]

Answer:

x = 14

Step-by-step explanation:

30 = 3x - 12 (vertically opp)

30 + 12 = 3x

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42÷3 = x

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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

Which of the following are square roots of 64? (check all that apply)

Angelina_Jolie [31]

The square roots of 64 is A B and C.

3 0

3 years ago

Simplify the expression. 7x^2+3-5(x^2-4) edguneity

Law Incorporation [45]

Answer:

2x^2+23.

Step-by-step explanation:

Combine like terms.

This expression simplified is 2x^2+23.

4 0

2 years ago