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2 years ago

For an angle θ, tan(θ) is a negative number. Which quadrants might θ be in?

Mathematics

2 answers:

Norma-Jean [14]2 years ago

6 0

θ will be in quadrants II and IV for an angle θ, tan(θ) is a negative number.

Hope it helps.

Klio2033 [76]2 years ago

4 0

So for this question, we're asked to find the quadrant in which the angle of data lies and were given to conditions were given. Sign of data is less than zero, and we're given that tangent of data is also less than zero. Now I have an acronym to remember which Trig functions air positive in each quadrant. . And in the first quadrant we have that all the trig functions are positive. In the second quadrant, we have that sign and co seeking are positive. And the third quadrant we have tangent and co tangent are positive. And in the final quadrant, Fourth Quadrant we have co sign and seeking are positive. So our first condition says the sign of data is less than zero. Of course, that means it's negative, so it cannot be quadrant one or quadrant two. It can't be those because here in Quadrant one, we have that all the trick functions air positive and the second quadrant we have that sign. If data is a positive, so we're between Squadron three and quadrant four now. The second condition says the tangent of data is also less than zero now in Quadrant three. We have that tangent of data is positive, so it cannot be quadrant three, so our r final answer is quadrant four, where co sign and seek in are positive.

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Use Stokes' Theorem to evaluate C F · dr F(x, y, z) = xyi + yzj + zxk, C is the boundary of the part of the paraboloid z = 1 − x

Serggg [28]

I assume $C$ has counterclockwise orientation when viewed from above.

By Stokes' theorem,

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

so we first compute the curl:

$\vec F(x,y,z)=xy\,\vec\imath+yz\,\vec\jmath+xz\,\vec k$

$\implies\nabla\times\vec F(x,y,z)=-y\,\vec\imath-z\,\vec\jmath-x\,\vec k$

Then parameterize $S$ by

$\vec r(u,v)=\cos u\sin v\,\vec\imath+\sin u\sin v\,\vec\jmath+\cos^2v\,\vec k$

where the $z$ -component is obtained from

$1-(\cos u\sin v)^2-(\sin u\sin v)^2=1-\sin^2v=\cos^2v$

with $0\le u\le\dfrac\pi2$ and $0\le v\le\dfrac\pi2$ .

Take the normal vector to $S$ to be

$\vec r_v\times\vec r_u=2\cos u\cos v\sin^2v\,\vec\imath+\sin u\sin v\sin(2v)\,\vec\jmath+\cos v\sin v\,\vec k$

Then the line integral is equal in value to the surface integral,

$\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}(-\sin u\sin v\,\vec\imath-\cos^2v\,\vec\jmath-\cos u\sin v\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{\pi/2}\int_0^{\pi/2}\cos v\sin^2v(\cos u+2\cos^2v\sin u+\sin(2u)\sin v)\,\mathrm du\,\mathrm dv=\boxed{-\frac{17}{20}}$

6 0

3 years ago

a positive number is 7 times another number if 3 is added to both the numbers then one of the new number becomes 5 by 2 times th

Neko [114]

Answer:

7 and 1

Step-by-step explanation:

Let the numbers be a and b.

A positive number is 7 times another number:

a = 7b

If 3 is added to both the numbers then one of the new number becomes 5 by 2 times the other new number:

a+3 = 5/2 × (b +3)

To solve this we substitute a with 7b in the second equation:

7b + 3 = 5/2 × (b +3) ⇒ multiplying both sides by 2
14b + 6 = 5b + 15 ⇒ collecting like terms
14b - 5b = 15 - 6
9b = 9
b = 1 ⇒ solved for b

Then, finding a:

a= 7b
a=7*1
a= 7 ⇒ solved for a

So the numbers are 7 and 1

3 0

3 years ago

Headshots question please help big points

stiv31 [10]

Answer:

Step-by-step explanation:

Graph f = x^2. Then the graph of g = (x + 3)^2 has the same shape, BUT its graph is that of f shifted 3 units to the LEFT. C is correct

6 0

3 years ago

Use the table to work out the values of a, b, c, and d.

Phoenix [80]

Answer:

aaaaaaaaa x=3-2y

7 0

2 years ago

Read 2 more answers

What is the remainder of 10^2017 divided by 1001?

pashok25 [27]

Note: When I use the double equal sign, I mean the triple bar used with modular arithmetic

10^3 = 1000 == -1 (mod 1001)
10^3 == -1 (mod 1001)
(10^3)^672 == (-1)^672 (mod 1001)
(10^(3*672) == 1 (mod 1001)
10^2016 == 1 (mod 1001)
10*10^2016 == 10*1 (mod 1001)
10^2017 == 10 (mod 1001)

Final Answer: 10

5 0

3 years ago