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3 years ago

Help? ( picture below)

Mathematics

2 answers:

Gnesinka [82]3 years ago

8 0

Cross multiply 9/c=6/d.

This would be 9d=6c.

Your answer is 6c.

Hope this helps :)

balu736 [363]3 years ago

3 0

The correct answer is is 6c

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For each vector field f⃗ (x,y,z), compute the curl of f⃗ and, if possible, find a function f(x,y,z) so that f⃗ =∇f. if no such f

butalik [34]

$\vec f(x,y,z)=(2yze^{2xyz}+4z^2\cos(xz^2))\,\vec\imath+2xze^{2xyz}\,\vec\jmath+(2xye^{2xyz}+8xz\cos(xz^2))\,\vec k$

Let

$\vec f=f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k$

The curl is

$\nabla\cdot\vec f=(\partial_x\,\vec\imath+\partial_y\,\vec\jmath+\partial_z\,\vec k)\times(f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k)$

where $\partial_\xi$ denotes the partial derivative operator with respect to $\xi$ . Recall that

$\vec\imath\times\vec\jmath=\vec k$

$\vec\jmath\times\vec k=\vec i$

$\vec k\times\vec\imath=\vec\jmath$

and that for any two vectors $\vec a$ and $\vec b$ , $\vec a\times\vec b=-\vec b\times\vec a$ , and $\vec a\times\vec a=\vec0$ .

The cross product reduces to

$\nabla\times\vec f=(\partial_yf_3-\partial_zf_2)\,\vec\imath+(\partial_xf_3-\partial_zf_1)\,\vec\jmath+(\partial_xf_2-\partial_yf_1)\,\vec k$

When you compute the partial derivatives, you'll find that all the components reduce to 0 and

$\nabla\times\vec f=\vec0$

which means $\vec f$ is indeed conservative and we can find $f$ .

Integrate both sides of

$\dfrac{\partial f}{\partial y}=2xze^{2xyz}$

with respect to $y$ and

$\implies f(x,y,z)=e^{2xyz}+g(x,z)$

Differentiate both sides with respect to $x$ and

$\dfrac{\partial f}{\partial x}=\dfrac{\partial(e^{2xyz})}{\partial x}+\dfrac{\partial g}{\partial x}$

$2yze^{2xyz}+4z^2\cos(xz^2)=2yze^{2xyz}+\dfrac{\partial g}{\partial x}$

$4z^2\cos(xz^2)=\dfrac{\partial g}{\partial x}$

$\implies g(x,z)=4\sin(xz^2)+h(z)$

Now

$f(x,y,z)=e^{2xyz}+4\sin(xz^2)+h(z)$

and differentiating with respect to $z$ gives

$\dfrac{\partial f}{\partial z}=\dfrac{\partial(e^{2xyz}+4\sin(xz^2))}{\partial z}+\dfrac{\mathrm dh}{\mathrm dz}$

$2xye^{2xyz}+8xz\cos(xz^2)=2xye^{2xyz}+8xz\cos(xz^2)+\dfrac{\mathrm dh}{\mathrm dz}$

$\dfrac{\mathrm dh}{\mathrm dz}=0$

$\implies h(z)=C$

for some constant $C$ . So

$f(x,y,z)=e^{2xyz}+4\sin(xz^2)+C$

3 0

3 years ago

Como puedo poner 2 3/5 en decimal

Alex73 [517]

When turning a fraction into a decimal, any whole numbers comes before the "." and the fraction will become after the ".".

To make it simple, turn the fraction into a "over 100" fraction to make it easier.

Multiple both numeriator and denominator by a specific number, to turn the denominator into a 100. You must times the numeriator as well since your changing the denominator.

100 / 5 = 20

So now, multiple both sides of the fraction by 20.

3 x 20 = 60

5 x 20 = 100

2 60/100

Now, put the whole number in front of the decimal symbol.

2.___

Now, take the numeriator and put it behind the decimal symbol.

2.60

So, when turning 2 3/5 into a decimal, it is 2.60.

8 0

3 years ago

Which expression is equivalent to (q6)2

Nat2105 [25]

Answer:

q¹²

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Exponential Rule [Powering]: $\displaystyle (b^m)^n = b^{m \cdot n}$

Step-by-step explanation:

Step 1: Define

Identify

(q⁶)²

Step 2: Simplify

Exponential Rule [Powering]: q⁶⁽²⁾
[Exponents] Multiply: q¹²

8 0

3 years ago

Read 2 more answers

Marcus earns 15% commission on his total sales at work.

IrinaVladis [17]

Answer:

Option C

Step-by-step explanation:

Given the following question:

Total cost is $725
15% Marcus makes in commission.

In order to find the answer, we have to find 15% of $725 and that number will be the total in commissions he earned that week.

$\frac{15\times725}{100} =15\times725=10875\div100=108.75$

Marcus makes "$108.75" or option C in commissions last week.

Hope this helps.

5 0

2 years ago

Solve 1.3 - 5g = 7.4 Show all work and check the solution

Ronch [10]

Answer:

1.22

Step-by-step explanation:

Subtract 1.3 from each side, so it now looks like this: 5g = 6.1
Divide each side by 5, so it now looks like this: g = 1.22

I hope this helps!

8 0

3 years ago

Read 2 more answers