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ExtremeBDS [4]
3 years ago
5

If 1/3 is 0.333 then 3/3 is 0.999 that means 1 doesnt actually equal 1​

Mathematics
2 answers:
sergejj [24]3 years ago
7 0

Answer:

Correct

Step-by-step explanation:

When you type 1/3 into a calculator it should give you something along the lines of .333333334. If you continue to round, eventually you will get 1.

zimovet [89]3 years ago
3 0

Answer:

Correct.

Step-by-step explanation:

On the off chance that 1/3 is 0.333 then 3/3 is 0.999 that implies 1 doesnt really equivalent 1. But if you continue to round, you will eventually get 1.

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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.

1.

\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.

2.

\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.

3.

\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.

4.

\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
When n basketball uniforms are purchased, the cost, C, of each uniform is given by the equation.
balandron [24]

Answer:

D. Subtraction property of equality; n = 15

Step-by-step explanation:

Given equation that shows the cost of n basketballs uniforms,

C = 40n + 260

According to the question,

Total cost = $ 860,

⇒ 40n + 260 = 860

Using subtraction property of equality, subtract 260 on both sides,

⇒ 40n = 860 - 260

⇒ 40n = 600

Using division property of equality, divide both sides by 40.

⇒ n = \frac{600}{40} = 15.

Hence, 15 uniforms were purchased.

i.e. Option D is correct.

5 0
3 years ago
If f(x)=3x+1 and g(x)=x^2-6 find (f-g)(x)
8090 [49]
Hi there!

• f(x) = 3x + 1
• g(x) = x² - 6

Then,
According to th' question :-

(f - g)(x) = f(x) - g(x)

= 3x + 1 - (x² - 6)

= 3x + 1 - x² + 6

= -x² + 3x + 7

Hence,
Option 2ⁿᵈ : -x² + 3x + 7 is Correct.

~ Hope it helps!
6 0
3 years ago
Read 2 more answers
Missing the y-value in the table?
jeyben [28]

Answer:

-1

Step-by-step explanation:

The constant rate of change is -y for every one x.

3 0
3 years ago
Help me!!!!!!!!!!!!!!
MA_775_DIABLO [31]

11. sin A = 7/25

cos A = 24/25

tan A = 7/24

3 0
3 years ago
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