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3 years ago

Simplify the expression below. 45 × 43

Mathematics

2 answers:

m_a_m_a [10]3 years ago

6 0

The answer to 45 x 43 is 1,935.

x 43

135

+1800

1935

N76 [4]3 years ago

4 0

The answer is 1,935. There really is no expression, it is just a simple multiplication problem.

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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

3 years ago

In a game experience, the level of monsters, L, is measured by the formula L=25M/E , where M= the number of monsters, and E= the

timama [110]

Answer:

E = \frac{25M}{L}

Step-by-step explanation:

To solve this, we can multiple each side by E and then divide each side by L:

$L*E=\frac{25M}{E}*E\\ L*E=25M\\\frac{L*E}{L}=\frac{25M}{L}\\ E = \frac{25M}{L}$

3 0

3 years ago

Read 2 more answers

- 7x + 12 - 2x = 23+13x

SpyIntel [72]

Hello, the answer is x=-1/2
Here are the steps....
−7x+12+−2x=23+13x(−7x+−2x)+(12)=13x+23(Combine Like Terms)−9x+12=13x+23−9x+12=13x+23
−9x+12−13x=13x+23−13x−22x+12=23
−22x+12−12=23−12−22x=11
−22x−22‌=‌11−22‌x=‌−12
Hope this helps you!!

6 0

3 years ago

What is −5 1/3 ÷ 2 3/4? a. −12 5/6 b. −7 5/12 c. −1 31/33 d. −1 11/12

julia-pushkina [17]

I hope this helps you

-( 3.5+1/3) ÷ 2.4+3/4

- 16/3 ÷ 11/4

-16/3 × 4/11

- 64 / 33

- 1 31 /33

7 0

3 years ago

Yolanda, Hong, and Ahmad served a total of 70 orders Monday at the school cafeteria. Yolanda served 6 fewer orders than Ahmad. H

irina [24]

Answer:Yolanda served 13 orders.

Ahmad served 19 orders.

Hong served 38 orders.

Step-by-step explanation:

Let x represent the number of orders that Ahmad served.

Yolanda served 6 fewer orders than Ahmad. This means that the number of orders that Yolanda served is x - 6

Hong served 2 times as

many orders as Ahmad. This means that the number of orders that Hong served is 2x

Yolanda, Hong, and Ahmad served a total of 70 orders Monday at the school cafeteria. This means that

x - 6 + x + 2x = 70

4x - 6 = 70

4x = 70 + 6 = 76

x = 76/4 = 19

Hong served 2 × 19 = 38

Yolanda served 19 - 6 = 13

5 0

4 years ago