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gizmo_the_mogwai [7]

2 years ago

12

Ramona is counting the posts between mile markers on the highway. In 1 mile, she counts 33 posts if the posts are evenly spaced,

how many feet apart are they?
(1 mile = 5,280 feet)

1 answer:

goldfiish [28.3K]2 years ago

3 0

Answer:

it would be 5 divided by 280 and then that would tell u the answer 56 so it would be 56 feet. I hope this worked have a nice day.

Step-by-step explanation:

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Write the equation of a line with a slope of −2 and a y-intercept of 5. (2 points) Question 1 options: 1) −2x + y = 5 2) 2x − y

aleksandr82 [10.1K]

Answer:

3 is the answer

Step-by-step explanation:

8 0

3 years ago

How do I solve this problem

guapka [62]

You first subtract 1/5 from both sides
3/4-1/5 = 11/20
3/2x=11/20

now you multiply 2/3 on both sides since you have to get x

11/20 * 2/3
x = 11/30

3 0

3 years ago

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

Find the shaded area of each figure, round your answer to one decimal place if necessary

Annette [7]

<h2>area of shaded portion = 49.5 yd²</h2><h2>____________________</h2>

<u>Step-by-step explanation:</u>

radius of circle = 5 yd ------ ( <em>g</em><em>i</em><em>v</em><em>e</em><em>n</em><em> </em><em>)</em>

height of triangle = 16 yd --- ( <em>g</em><em>i</em><em>v</em><em>e</em><em>n</em><em> </em><em>)</em>

base of triangle = 16 yd ----- ( <em>g</em><em>i</em><em>v</em><em>e</em><em>n</em><em> </em><em>)</em>

area of triangle = 1/2 × base × height

= 1/2 × 16 × 16

= 128 yd²

area of circle = π × radius²

= 3.14 × 5 × 5 --- ( π = 3.14 )

= 78.5 yd²

<h2>---------------------------------------</h2>

area of shaded portion = area of triangle - area of circle

area of shaded portion= 128 yd²-78.5 yd²

area of shaded portion = 49.5 yd²

<h2>--------------------------------------</h2><h2>PLEASE FOLLOW ME</h2>

8 0

2 years ago

-0.26<br> 0.5<br> Select one:<br> -0.052<br> 0.052<br> -0.52<br> -0.51

erik [133]

Answer:

-0.51

Step-by-step explanation:

4 0

3 years ago