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3 years ago

7

The temperature inside a classroom y is recorded each hour of the school day x . is that a function

1 answer:

musickatia [10]3 years ago

4 0

Answer:yes

Step-by-step explanation:

You might be interested in

How many triangles can be constructed with sides measuring 5 m, 16 m, and 5 m?

stepladder [879]

None i hope it helped

3 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.

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

Can someone please help me with these math problems please!

mr_godi [17]

Answer:

Step-by-step explanation:

8 0

2 years ago

A car traveled 330 miles during a 5½ hour period. If the speed at which the car traveled can be represented in the equation d=rt

Alina [70]

Answer:

The car was travelling at a speed of 60 miles per hour.

Step-by-step explanation:

Given:

Distance traveled = 330 miles

Time Period = $5 \frac12\ hr$

we need to find the speed of the car .

Solution:

Time Period = $5 \frac12\ hr$

Now we can say that;

$\frac12\ hr =0.5\ hr$

So Time period = $5+0.5 =5.5\ hr$

Now we know that;

Distance traveled $(d)$ is equal to Speed $(r)$ multiplied by Time Period $(t)$ .

framing in equation form we get;

$d=rt\\\\330 =r\times 5.5$

Dividing both side by 5.5 we get;

$\frac{330}{5.5}=\frac{5.5r}{5.5}\\\\r = 60\ mi/hr$

Hence The car was travelling at a speed of 60 miles per hour.

6 0

3 years ago

Equation of a straight line (see attached)

Viefleur [7K]

Answer:

y = 2x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = A(4, 7) and (x₂, y₂ ) = B(2,3)

m = $\frac{3-7}{2-4}$ = $\frac{-4}{-2}$ = 2 , thus

y = 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, 3), then

3 = 4 + c ⇒ c = 3 - 4 = - 1

y = 2x - 1 ← equation of line

8 0

3 years ago

Read 2 more answers