How do you find measures using postulates and theorems?

1 answer:

8 0

Just use the definitions and put them in order to explain the problem.m. for instance. why are angles a and b vertical angles? they are adjacent and they are supplementary.

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Find an equation for the surface consisting of all points p for which the distance from p to the x-axis is 5 times the distance

guajiro [1.7K]

Distance from P to the x-axis = 2x distance from P to the yz-plane

Distance to the x-axis of a point P=(x,y,z) is (y^2+z^2)^1/2 
Distance to the yz-plane of a point P=(x,y,z) is x 

So your equation is: 
(y^2+z^2)^1/2 = 2x 
=> y^2 + z^2 = 4x^2 
=> y^2 + z^2 - 4x^2 = 0

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.

6 0

3 years ago

If m∠JKP=3r+12 and m∠2=4r−2, what is ∠JKN?

Leokris [45]

The answer seems to be 108

8 0

3 years ago

F⃗ (x,y)=−yi⃗ +xj⃗ f→(x,y)=−yi→+xj→ and cc is the line segment from point p=(5,0)p=(5,0) to q=(0,2)q=(0,2). (a) find a vector pa

DerKrebs [107]

a. Parameterize $C$ by

$\vec r(t)=(1-t)(5\,\vec\imath)+t(2\,\vec\jmath)=(5-5t)\,\vec\imath+2t\,\vec\jmath$

with $0\le t\le1$ .

b/c. The line integral of $\vec F(x,y)=-y\,\vec\imath+x\,\vec\jmath$ over $C$ is

$\displaystyle\int_C\vec F(x,y)\cdot\mathrm d\vec r=\int_0^1\vec F(x(t),y(t))\cdot\frac{\mathrm d\vec r(t)}{\mathrm dt}\,\mathrm dt$

$=\displaystyle\int_0^1(-2t\,\vec\imath+(5-5t)\,\vec\jmath)\cdot(-5\,\vec\imath+2\,\vec\jmath)\,\mathrm dt$

$=\displaystyle\int_0^1(10t+(10-10t))\,\mathrm dt$

$=\displaystyle10\int_0^1\mathrm dt=\boxed{10}$

d. Notice that we can write the line integral as

$\displaystyle\int_C\vecF\cdot\mathrm d\vec r=\int_C(-y\,\mathrm dx+x\,\mathrm dy)$

By Green's theorem, the line integral is equivalent to

$\displaystyle\iint_D\left(\frac{\partial x}{\partial x}-\frac{\partial(-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=2\iint_D\mathrm dx\,\mathrm dy$

where $D$ is the triangle bounded by $C$ , and this integral is simply twice the area of $D$ . $D$ is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.