All categories

3 years ago

A constant force F=47i+30j moves an object along a vector D=13i-8j. find the work done

Mathematics

2 answers:

Nikitich [7]3 years ago

3 0

$W=(47\,\mathbf i+30\,\mathbf j)\cdot(13\,\mathbf i-8\,\mathbf j)=371$

WINSTONCH [101]3 years ago

3 0

Answer: The correct answer is 371 J.

Step-by-step explanation:

The expression for work done in terms of force and displacement is as follows;

W=F.D

Here, F is the applied force and D is the displacement.

Here, the work done is equal to the dot product of force and displacement. The dot product of i.i=j.j=k.k=1.

Calculate the work done.

W=F.D

Put F=47i+30j and D=13i-8j.

W=(47i+30j).(13i-8j)

W=611-240

W= 371 J

Therefore, the work done is 371 J.

You might be interested in

A barista averages making 16 coffees per hour. At this rate, how many hours will it take until she’s made 1,200 coffees?

nignag [31]

Answer:

75 hours

Step-by-step explanation:

16 times x=1200 or

16x=1200

divide both sides by 16

1200/16

so we simplify 1200/16 by factoring out the ones (4/8=1/2 times 4/4 since 4/4=1)

1200=3*2*2*2*2*5*5

16=2*2*2*2*1

so we notice that there are four 2's in both so those are the 'ones' so cross them off and get

3*5*5/1 or 75/1 or 75 hours

5 0

3 years ago

Parallelogram PARL is similar to parallelogram WXYZ. If AP = 7, PL = 15, and WZ = 45, find the value of c.

Angelina_Jolie [31]

Answer:

c = 21

Step-by-step explanation:

<u>**I assume that side WX in my diagram (attached as an image below) is the value of C that we're looking for. ALSO, the sizes and lengths of the parallelograms are NOT to scale.**</u>

If two parallelograms are similar, that means the lengths of the corresponding sides have EQUAL ratios.

PL corresponds with WZ. To get from 15 to 45, you would multiply 15 by 3, so the ratio of the legnths of the corresponding sides between these two parallelograms is 1:3.

With that in mind, we can apply this ratio to find WX.

We know that AP has a length of 7, so we will multiply that by 3, getting a value of 21, and 7:21 ratio is the same as 1:3.

c = 21

Hope this helps (●'◡'●)

7 0

2 years ago

1. Let f(x, y) be a differentiable function in the variables x and y. Let r and θ the polar coordinates,and set g(r, θ) = f(r co

Olenka [21]

Answer:

$g_{r}(\sqrt{2},\frac{\pi}{4})=\frac{\sqrt{2}}{2}\\$

Step-by-step explanation:

First, notice that:

$g(\sqrt{2},\frac{\pi}{4})=f(\sqrt{2}cos(\frac{\pi}{4}),\sqrt{2}sin(\frac{\pi}{4}))\\$

$g(\sqrt{2},\frac{\pi}{4})=f(\sqrt{2}(\frac{1}{\sqrt{2}}),\sqrt{2}(\frac{1}{\sqrt{2}}))\\$

$g(\sqrt{2},\frac{\pi}{4})=f(1,1)\\$

We proceed to use the chain rule to find $g_{r}(\sqrt{2},\frac{\pi}{4})$ using the fact that $X(r,\theta)=rcos(\theta)\ and\ Y(r,\theta)=rsin(\theta)$ to find their derivatives:

$g_{r}(r,\theta)=f_{r}(rcos(\theta),rsin(\theta))=f_{x}( rcos(\theta),rsin(\theta))\frac{\delta x}{\delta r}(r,\theta)+f_{y}(rcos(\theta),rsin(\theta))\frac{\delta y}{\delta r}(r,\theta)\\$