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Rom4ik [11]
3 years ago
5

Can someone isolate the variable “n” and show steps?

Mathematics
1 answer:
oee [108]3 years ago
5 0

Answer:

n= s/180 +2

Step-by-step explanation:

s=(n-2)180

/180

s/180=n-2

+2

s/180 +2 =n

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A man invests some money at 10% interest for 1 year
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Answer:

investment=£3000

Step-by-step explanation:

let ; principal amount (investment)=p ,

simple interest = p*t*r/100

£3300-p=p*1*10/100

(3300-p)100/10= p

33000-10p=p

33000=11p

33000/11 = p

£3000=p

3 0
3 years ago
Here we will study the function f (x) = e ^ x sin (x), where x ∈ [0, 2π]. a) Determine where the function is decreasing and incr
Semmy [17]

fff

f(x) = e^x sin (x)

To find increasing and decreasing intervals we take derivative

f'(x) = e^xsin(x)+e^x(cosx)= e^x(sinx+cosx)

Now we set the derivative =0  and solve for x

e^x(sinx+cosx)=0

sinx + cosx =0

divide whole equation by cos x

\frac{sinx}{cosx} + \frac{cosx}{cosx} =0

tanx +1 =0

tanx = 1

x=\frac{3\pi }{4} and  x=\frac{7\pi}{4}

Now we pick a number between 0 to  \frac{3\pi }{4}

Lets pick  \frac{\pi }{2}

Plug it into the derivative

f'(x) =e^{\frac{\pi }{2}}(sin(\frac{\pi}{2})+cos(\frac{\pi }{2}))

= 4.810 is positive

So the graph of f(x) is increasing on the interval [0, x=\frac{3\pi }{4})

Now we pick a number between   \frac{7\pi}{4} to 2pi

Lets pick  \frac{11\pi}{6}

Plug it into the derivative

f'(x) =e^{\frac{11\pi}{6}}(sin(\frac{11\pi}{6})+cos(\frac{11\pi }{6}))

= 116 is positive

So the graph of f(x) is increasing on the interval (\frac{7\pi }{4}, 2\pi)

Increasing interval is (0,\frac{3\pi }{4}) U (\frac{7\pi }{4}, 2\pi)

Decreasing interval is (\frac{3\pi}{4}, \frac{7\pi}{4})

(b)

The graph of f(x) increases and reaches a local maximum at x=\frac{3\pi}{4}

The graph of f(x) decreases and reaches a local minimum at x=\frac{7\pi}{4}

(c)

f(0) = 0

f(2\pi)=0

f(\frac{3\pi }{4})=7.46

f(\frac{7\pi}{4})=-172.64

Here global maximum at x=\frac{3\pi}{4}

Here global minimum at x=\frac{7\pi}{4}


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vivado [14]

Answer:

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