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Monica [59]
3 years ago
11

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating

rectangle. y = 3/x, y = 3/x2, x = 7 Find the area of the region

Mathematics
1 answer:
MakcuM [25]3 years ago
6 0

Answer:

A=8.4063u^{2}

Step-by-step explanation:

Be the functions:

y=\frac{3}{x};y=\frac{3}{x^{2}}:x=7

according the graph:

\int\limits^1_7 {\frac{3}{x} } \, dx -\int\limits^1_7 {\frac{3}{x^{2} } } \, dx =3\int\limits^1_7 {\frac{1}{x} } \, dx -3\int\limits^1_7 {\frac{1}{x^{2} } } \, dx=3(\int\limits^1_7 {\frac{1}{x} } \, dx -\int\limits^1_7 {\frac{1}{x^{2} } } \, dx)=3[lnx-\frac{1}{x}](1-7)=3[(ln7-ln1)-(\frac{1}{7}-1)]=3[(1.945-0)-(0.1428-1)]=3*(1.945+0.8571)=3*2.8021=8.4063u^{2}

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3.f(-4) - 3.(2) =<br> Int<br> GA<br> SS
Doss [256]

Answer:

1.7. 9 () “ -- .3 .3 .4 . .9 F 5 XXX Ammo. Phosphate., 1916. . .8 10 0 “ -- .4 .2 .4 . . .9 Essex Fertilizer Co. E 7 Grain, Grass & Potato Fert. . . . . .8 12 0 Yes Passed .

Step-by-step explanation:

1.7. 9 () “ -- .3 .3 .4 . .9 F 5 XXX Ammo. Phosphate., 1916. . .8 10 0 “ -- .4 .2 .4 . . .9 Essex Fertilizer Co. E 7 Grain, Grass & Potato Fert. . . . . .8 12 0 Yes Passed .

8 0
3 years ago
List all your possibility of outcomes (there are 36 outcomes) if you roll a dice containing numbers 1-6 two times. Determine the
Talja [164]
Check the table attached. 

The first coordinates of each pair represent the 1.roll, and the second coordinates the 2nd, roll.

All the possible outcomes are {(1, 1), (1, 2).... (6, 5), (6, 6)}, a total of 36, as can be seen in the table.

Each outcome has a chance of 1 out 36 total possible outcomes of occurring.

So the probability is 1/36=0.02778



8 0
3 years ago
The function f(x)=2/3x-4 was replaced with f(x+k)=2/3x-6 what is the value of k
HACTEHA [7]

Answer:

The given function f(x)=\frac{2x}{3}-4 was replaced with f(x+k)=\frac{2x}{3}-6 then the value of k is -3

that is k=-3.

Step-by-step explanation:

The given function is f(x)=\frac{2x}{3}-4\hfill (1)

and when x=x+k then f(x+k)=\frac{2x}{3}-6\hfill (2)

Now to find the value of k:

Put x=x+k in the function f(x)

f(x)=\frac{2x}{3}-4

f(x+k)=\frac{2(x+k)}{3}-4

f(x+k)=\frac{2x+2k}{3}-4\hfill (3)

Now comparing equations (2) and (3) we get

f(x+k)=\frac{2x+2k}{3}-4=\frac{2x}{3}-6

\frac{2x+2k}{3}-4=\frac{2x}{3}-6

\frac{2x+2k}{3}-4-\frac{2x}{3}+6=0

\frac{2x}{3}+\frac{2k}{3}-4-\frac{2x}{3}+6=0

\frac{2k}{3}+2=0

\frac{2k}{3}=-2

k=\frac{-2\times 3}{2}

k=-3

Therefore k=-3

Therefore the given function f(x)=\frac{2x}{3}-4 was replaced with  f(x+k)=\frac{2x}{3}-6 then the value of k is -3

that is k=-3.

7 0
3 years ago
Sarah wants to arrive at her friends wedding at 3:00 pm. The distance from Sarah’s house to the wedding is 85 miles. Based on us
Mrrafil [7]

Answer:

(A) 15 minutes

(B) 10 minutes

(C) 1 hour

(D) 1:35 pm

Step-by-step explanation:

<em>Question:</em>

Sarah wants to arrive at her friend’s wedding at 3:00 PM. The distance from Sarah’s house to the wedding is 85 miles. Based on usual traffic patterns, Sarah predicts she can drive the first 15 miles at 60 miles per hour, the next 5 miles at 30 miles per hour, and the remainder of the drive at 65 miles per hour.

(A) how many minutes will it take Sarah to drive the first 15 miles?

(B) how many minutes will it take Sarah to drive 5 miles?

(C) how many hours will it take Sarah to drive the rest of the trip?

(D) what time should Sarah leave her house? (Give your answer using standard hour:minute clock format.)

<em>Solution:</em>

Total distance = 85 miles

There are three segments of this trip, each one with its own speed.

<em>1) 15 miles at 60 mph</em>

<em>2) 5 miles at 30 mph</em>

Up to here, the distance is 15 miles + 5 miles = 20 miles.

The total distance is 85 miles, so the last segment of the trip is 85 miles - 20 miles = 65 miles.

<em>3) 65 miles at 65 mph</em>

The equation for speed is:

speed = distance/time

Now we solve it for time:

speed * time = distance

time = distance/speed

To find a time, divide the distance by the speed.

Part (A)

distance = 15 miles; speed = 60 mph; find time

time = distance/speed = 15 miles/60 mph = 0.25 hours

Since 1 hour = 60 minutes,

time = 0.25 hours * 60 minutes/hour = 15 minutes

Part (B)

distance = 5 miles; speed = 30 mph; find time

time = distance/speed = 5 miles/30 mph = 1/6 hour

Since 1 hour = 60 minutes,

times = 1/6 hour * 60 minutes/hour = 10 minutes

Part (C)

distance = 65 miles; speed = 65 mph; find time

time = distance/speed = 65 miles/65 mph = 1 hour

Part (D)

The driving times for the three segments are 15 minutes, 10 minutes, and 1 hour. The total driving time is

15 minutes + 10 minutes + 1 hour = 1 hour and 25 minutes

Now we subtract 1 hour 25 minutes from 3:00 pm.

3:00 pm is the same as 2:60 pm

2:60 pm - 1:25 = 1:35 pm

She needs to leave at 1:35 pm

5 0
3 years ago
How do you find a mean?
kherson [118]

Answer:

Add up all the numbers, then divide by how many numbers there are.

Step-by-step explanation:

7 0
3 years ago
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