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9966 [12]
3 years ago
13

3. two lines, a and b, are represented by the following equations:

Mathematics
1 answer:
Sveta_85 [38]3 years ago
3 0
2x + y = 6 . . . . . (1)
x + y = 4 . . . . . (2)

(1) - (2) => x = 2

From (2): 2 + y = 4 => y = 4 - 2 = 2

Therefore, the solution is (2, 2)
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Mike can do 126 sit-ups in six minutes. how many sit-ups is that per minute?
qaws [65]

Answer:

21

Step-by-step explanation:

126/6= 21 sit ups per minute

8 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}


3 0
3 years ago
Read 2 more answers
How do you multiply 45 times 52
ser-zykov [4K]
Put in the calculator 45x52
7 0
3 years ago
Read 2 more answers
DaVonne and Tom picked up candy off from the ground when a pinata was
Tpy6a [65]
It’s correct answer believe me
8 0
2 years ago
MATH HELP WILL MARK BRAINLIEST !!!!!!!!
Leokris [45]

1. sum of a number plus 6 is 7 times the number:

n+6 = 7n


2. qoutent of a number and 5 is 8

n/5 =8

n = 5*8

n = 40


3. distance = speed times time

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3 years ago
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