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Lapatulllka [165]

3 years ago

9

How to graph X = (-1/6) y

1 answer:

jenyasd209 [6]3 years ago

8 0

Answer:

X=(-1/6)y

Step-by-step explanation:

You might be interested in

A cone has a height of 1 meter and a diameter of 2 meters. What is it’s volume

Ber [7]

Cone volume formula: V = πr²h/3

r = radius

h = height

The radius is half the diameter, so, we can divide.

2 / 2 = 1

Now, solve with the given values.

V = π(1)²(1)/3

V = π(1)(1/3)

V = 3.14(1/3)

V ≈ 1.05

Therefore, the volume is roughly 1.05m^3

Best of Luck!

6 0

3 years ago

Evaluate the function. f(x) = 3x² – x Find f(10)

kirill [66]

Answer:

<em>f(10)=290</em>

Step-by-step explanation:

<u>Function Evaluation</u>

Given a function f(x) as an explicit expression, finding f(x=a) implies substituting the value of x by a in every instance it occurs.

We are given the function:

$f(x)=3x^2-x$

It's required to find f(10). We replace the x for 10:

$f(10)=3*10^2-10$

Operating:

$f(10)=3*100-10$

$f(10)=300-10$

$f(10)=290$

Thus, f(10)=290

4 0

3 years ago

Solve the Differential equation (x^2 + y^2) dx + (x^2 - xy) dy = 0

natita [175]

Answer:

$\frac{y}{x}-2ln(\frac{y}{x}+1)=lnx+C$

Step-by-step explanation:

Given differential equation,

$(x^2 + y^2) dx + (x^2 - xy) dy = 0$

$\implies \frac{dy}{dx}=-\frac{x^2 + y^2}{x^2 - xy}----(1)$

Let y = vx

Differentiating with respect to x,

$\frac{dy}{dx}=v+x\frac{dv}{dx}$

From equation (1),

$v+x\frac{dv}{dx}=-\frac{x^2 + (vx)^2}{x^2 - x(vx)}$

$v+x\frac{dv}{dx}=-\frac{x^2 + v^2x^2}{x^2 - vx^2}$

$v+x\frac{dv}{dx}=-\frac{1 + v^2}{1 - v}$

$v+x\frac{dv}{dx}=\frac{1 + v^2}{v-1}$

$x\frac{dv}{dx}=\frac{1 + v^2}{v-1}-v$

$x\frac{dv}{dx}=\frac{1 + v^2-v^2+v}{v-1}$

$x\frac{dv}{dx}=\frac{v+1}{v-1}$

$\frac{v-1}{v+1}dv=\frac{1}{x}dx$

Integrating both sides,

$\int{\frac{v-1}{v+1}}dv=\int{\frac{1}{x}}dx$

$\int{\frac{v-1+1-1}{v+1}}dv=lnx + C$

$\int{1-\frac{2}{v+1}}dv=lnx + C$

$v-2ln(v+1)=lnx+C$

Now, y = vx ⇒ v = y/x

$\implies \frac{y}{x}-2ln(\frac{y}{x}+1)=lnx+C$

5 0

3 years ago

????⃗ (x,y)=(3x−4y)????⃗ +2x????⃗ F→(x,y)=(3x−4y)i→+2xj→ and ????C is the counter-clockwise oriented sector of a circle centered

Karolina [17]

By Green's theorem, the integral of $\vec F$ along $C$ is

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_D\left(\frac{\partial(2x)}{\partial x}-\frac{\partial(3x-4y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=6\iint_D\mathrm dx\,\mathrm dy$

which is 6 times the area of $D$ , the region with $C$ as its boundary.

We can compute the integral by converting to polar coordinates, or simply recalling the formula for a circular sector from geometry: Given a sector with central angle $\theta$ and radius $r$ , the area $A$ of the sector is proportional to the circle's overall area according to

$\dfrac A{\frac\pi3\,\rm rad}=\dfrac{16\pi}{2\pi\,\rm rad}\implies A=\dfrac{8\pi}3$

so that the value of the integral is

$\dfrac{6\times8\pi}3=\boxed{16\pi}$

6 0

3 years ago

Which of the following statements is not true?

Nat2105 [25]

X5y5z5 = xyz5 is not true

6 0

3 years ago

Read 2 more answers