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4 years ago

Pls answer WILL VOTE UP BEST ANSWER FOR FIRST PERSON \/ question is in attached file \/

Mathematics

1 answer:

Anna007 [38]4 years ago

6 0

Your answer is D ................

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Is 68 prime because i am doing homework and im stuck on this and it is very hard so help me please

BlackZzzverrR [31]

If 68 is a prime number, then the only factors it has are 1 and 68.
If it has any other factors besides 1 and 68, then it's NOT prime.

Right away, without any higher math, you can look at just the last digit
in 68 . The last digit is '8'. That tells you that '68' is an even number,
and THAT tells you that '2' must be one of its factors. So '68' is not a
prime number.

The factors of 68 are 1, 2, 4, 17, 34, and 68 .

68 has four more factors besides 1 and 68, so it's not a prime number.

8 0

3 years ago

Read 2 more answers

For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential f

Phantasy [73]

The key idea is that, if a vector field is conservative, then it has curl 0. Equivalently, if the curl is not 0, then the field is not conservative. But if we find that the curl is 0, that on its own doesn't mean the field is conservative.

$\mathrm{curl}\vec F=\dfrac{\partial(5x+10y)}{\partial x}-\dfrac{\partial(-6x+5y)}{\partial y}=5-5=0$

We want to find $f$ such that $\nabla f=\vec F$ . This means

$\dfrac{\partial f}{\partial x}=-6x+5y\implies f(x,y)=-3x^2+5xy+g(y)$

$\dfrac{\partial f}{\partial y}=5x+10y=5x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=10y\implies g(y)=5y^2+C$

$\implies\boxed{f(x,y)=-3x^2+5xy+5y^2+C}$

so $\vec F$ is conservative.

$\mathrm{curl}\vec F=\left(\dfrac{\partial(-2y)}{\partial z}-\dfrac{\partial(1)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x)}{\partial z}-\dfrac{\partial(1)}{\partial z}\right)\vec\jmath+\left(\dfrac{\partial(-2y)}{\partial x}-\dfrac{\partial(-3x)}{\partial y}\right)\vec k=\vec0$

Then

$\dfrac{\partial f}{\partial x}=-3x\implies f(x,y,z)=-\dfrac32x^2+g(y,z)$

$\dfrac{\partial f}{\partial y}=-2y=\dfrac{\partial g}{\partial y}\implies g(y,z)=-y^2+h(y)$

$\dfrac{\partial f}{\partial z}=1=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=z+C$

$\implies\boxed{f(x,y,z)=-\dfrac32x^2-y^2+z+C}$

so $\vec F$ is conservative.

$\mathrm{curl}\vec F=\dfrac{\partial(10y-3x\cos y)}{\partial x}-\dfrac{\partial(-\sin y)}{\partial y}=-3\cos y+\cos y=-2\cos y\neq0$

so $\vec F$ is not conservative.

$\mathrm{curl}\vec F=\left(\dfrac{\partial(5y^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial x}\right)\vec\jmath+\left(\dfrac{\partial(5y^2)}{\partial x}-\dfrac{\partial(-3x^2)}{\partial y}\right)\vec k=\vec0$

Then

$\dfrac{\partial f}{\partial x}=-3x^2\implies f(x,y,z)=-x^3+g(y,z)$

$\dfrac{\partial f}{\partial y}=5y^2=\dfrac{\partial g}{\partial y}\implies g(y,z)=\dfrac53y^3+h(z)$

$\dfrac{\partial f}{\partial z}=5z^2=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=\dfrac53z^3+C$

$\implies\boxed{f(x,y,z)=-x^3+\dfrac53y^3+\dfrac53z^3+C}$

so $\vec F$ is conservative.

4 0

4 years ago

Simplify expression 8x-6+x-1

charle [14.2K]

Answer:

9x -7

Step-by-step explanation:

8x-6+x-1

Combine like terms

8x +x -6-1

9x -7

8 0

3 years ago

A square is cut from a rectangle. The side length of the square is half of the unknown width w. The area of the shaded region is

Virty [35]

Answer:

See below

Step-by-step explanation:

The side of the square is w/2, then its area is:

A = (w/2)² = w²/4

The shaded area is the difference of areas of the rectangle and the square:

14w - w²/4 = 84

This can be simplified:

56w - w² = 336
w² - 56w + 336 = 0

8 0

3 years ago

If cos(x)=1/4 what is sin(x) and tan(x)

anygoal [31]

You can use the identity
cos(x)² +sin(x)² = 1
to find sin(x) from cos(x) or vice versa.

(1/4)² +sin(x)² = 1
sin(x)² = 1 - 1/16
sin(x) = ±(√15)/4

Then the tangent can be computed as the ratio of sine to cosine.
tan(x) = sin(x)/cos(x) = (±(√15)/4)/(1/4)
tan(x) = ±√15

There are two possible answers.
In the first quadrant:
sin(x) = (√15)/4
tan(x) = √15

In the fourth quadrant:
sin(x) = -(√15)/4
tan(x) = -√15

3 0

3 years ago