All categories

1 year ago

GIVING BRAINLIEST TO THE PERSON THAT CAN EXPLAIN THIS THE BEST (:

Mathematics

1 answer:

scZoUnD [109]1 year ago

4 0

Answer:

14w

Step-by-step explanation:

Width = w

Length is 6 time its width. so, multiply w by 6

length = 6*w = 6w

Perimeter of rectangle = 2* (length + width)

= 2*(6w + w)

= 2*7w

= 14w

You might be interested in

Consider the line integral Z C (sin x dx + cos y dy), where C consists of the top part of the circle x 2 + y 2 = 1 from (1, 0) t

pashok25 [27]

Direct computation:

Parameterize the top part of the circle $x^2+y^2=1$ by

$\vec r(t)=(x(t),y(t))=(\cos t,\sin t)$

with $0\le t\le\pi$ , and the line segment by

$\vec s(t)=(1-t)(-1,0)+t(2,-\pi)=(3t-1,-\pi t)$

with $0\le t\le1$ . Then

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)$

$=\displaystyle\int_0^\pi(-\sin t\sin(\cos t)+\cos t\cos(\sin t)\,\mathrm dt+\int_0^1(3\sin(3t-1)-\pi\cos(-\pi t))\,\mathrm dt$

$=0+(\cos1-\cos2)=\boxed{\cos1-\cos2}$

Using the fundamental theorem of calculus:

The integral can be written as

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=\int_C\underbrace{(\sin x,\cos y)}_{\vec F}\cdot\underbrace{(\mathrm dx,\mathrm dy)}_{\vec r}$

If there happens to be a scalar function $f$ such that $\vec F=\nabla f$ , then $\vec F$ is conservative and the integral is path-independent, so we only need to worry about the value of $f$ at the path's endpoints.

This requires

$\dfrac{\partial f}{\partial x}=\sin x\implies f(x,y)=-\cos x+g(y)$

$\dfrac{\partial f}{\partial y}=\cos y=\dfrac{\mathrm dg}{\mathrm dy}\implies g(y)=\sin y+C$

So we have

$f(x,y)=-\cos x+\sin y+C$

which means $\vec F$ is indeed conservative. By the fundamental theorem, we have

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=f(2,-\pi)-f(1,0)=-\cos2-(-\cos1)=\boxed{\cos1-\cos2}$

3 0

2 years ago

Find the difference between 1, 407 and 699

Rus_ich [418]

Answer:708

Step-by-step explanation:

7 0

3 years ago

Which expressions are equivalent to 3x+3(x+y)?

storchak [24]

Answer: 6x+3y

Step-by-step explanation:

3x+3(x+y)= 3x+3x+3y=6x+3y

6 0

3 years ago

3. A vehicle uses 15 gallons of gasoline to travel 13 miles. At this rate, how many miles can the

Tems11 [23]

1. Start by identifying what the question wants so we are looking for miles per 1 gallon.
2. Set up a statement. When the word “per” is being used it relates to a fraction or a ratio. In this question we need to find how many miles a single gallon will give us. So set it up as miles/gallons
3. Plug in your numbers. Now our statement is 13 miles/15 gallons
4. Calculate. So do 13/15 which equals 0.86 miles per 1 gallon.
Tip: always add in words into your calculations. Mainly the units you are using so you can quickly look and know what the units will be. This will help you in upper placement math as well

5 0

3 years ago

Read 2 more answers

Write the sentence as an equation.<br> 367 is 2 divided by a

Andrej [43]

Answer:

Step-by-step explanation:

183.5

5 0

3 years ago

Read 2 more answers

￼ GIVING BRAINLIEST TO THE PERSON THAT CAN EXPLAIN THIS THE BEST (:

GIVING BRAINLIEST TO THE PERSON THAT CAN EXPLAIN THIS THE BEST (: