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solniwko [45]
3 years ago
7

Determine whether the following statements are true and give an explanation or counterexample.

Mathematics
1 answer:
Furkat [3]3 years ago
5 0

Answer:

A) When using the shell​ method, the axis of the cylindrical shells is parallel to the axis of revolution. True.

The Shell method is a technique used to find the volume of a solid of revolution. Here, we take thin shells with axis coinciding with the axis about which the region whose volume is to be found, is revolved.

B) If a region is revolved about the​ y-axis, then the shell method must be used. False.

This method can be used with any axis of rotation.

C) If a region is revolved about the​ x-axis, then in principle it is possible to use the​ disk/washer method and integrate with respect to x or the shell method and integrate with respect to y. True.

The washer method uses thin disks with infinite width but the shell method uses thin concentric shells with infinite width about the axis of revolution. So, the statement is true.

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A ladder is placed 5 feet away from a house. The ladder comes up to 12 feet on the side of the house. How long is the ladder? Pl
LuckyWell [14K]
Answer: A. 13ft

Explanation:

a^2 + b^2 = c^2
a = 5, b = 12

5^2 = 25, 12^2 = 144

25 + 144 = 169

Square root of 169 = 13
3 0
2 years ago
Read 2 more answers
Which of the following is a solution to the inequality below? 12 - x/11 > 8
n200080 [17]

Answer:

12 - x/11 > 8

12 -8 - x/11 > 8 -8

4 -x/11 > 0

4 -x/11  + x/11> 0 + x/11

4 > x/11

44 > x

x is less than 44

Step-by-step explanation:

7 0
2 years ago
When running a 100 meter race Bill reaches his maximum speed when he is 45 meters from the starting line and 5 seconds have elap
Mkey [24]

Bill's speed is constant after 5 seconds and 45 meters into the race.

Correct responses:

a. Bill's maximum speed is 8 m/s

b. 24 meters

c. 57 meters

<h3>Methods used to calculate speed and distance traveled</h3>

Given parameters are;

The distance of the race = 100 meter

Distance at which Bill reaches maximum speed = 45 meters

Speed Bill maintains after 5 seconds = The maximum speed

Time at which Bill is 85 meters from the starting line = 10 seconds after start

a. Required;

Bill's maximum speed in meters.

Solution:

Distance Bill runs at maximum speed, d = 85 m - 45 m = 40 m

Time at which Bill runs the 40 m at maximum speed, <em>t</em> = 10 s - 5 s = 5 s

Speed = \mathbf{\dfrac{Distance}{Time}}

Therefore;

  • Bill's \  maximum \ speed = \dfrac{40 \ m}{5 \ s} = \underline{8 \ m/s}

b. i. Required:

The distance Bill will run for 3 seconds at the maximum speed;

Solution:

Distance,<em> s</em> = Speed, <em>v</em> × Time, <em>t</em>

<em />

The distance traveled at maximum speed in 3 seconds is therefore;

Distance = 8 m/s × 3 s = 24 m

The distance Bill travels in 3 seconds at the maximum speed is 24 meters.

ii) The distance Bill travels at 8 seconds after start, is given as follows;

Distance traveled in the first 5 seconds = 45 meters

Distance traveled in the next 3 seconds = 24 meters

Therefore;

  • Bill's distance from the starting line 8 seconds after start is 45 meters + 25 meters = <u>69 meters</u>

c. Bill's distance 6.5 seconds after the start of the race is given as follows;

Distance traveled in the first 5 seconds = 45 meters

Distance traveled in the next 1.5 seconds = 1.5 s × 8 m/s = 12 meters

  • Bill's distance from the starting line 6.5 seconds after start of the race = 45 meters + 12 meters = <u>57 meters</u>

Learn more about distance, speed, time, relationship here:

https://brainly.in/question/49075584

6 0
2 years ago
Name the slope and the y intercept for the equation y= 5x -7
NeTakaya

Answer:

The slope is 5x and the y-intercept is -7

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Question 1 (1 point)
sergey [27]

Answer:

10

Step-by-step explanation:

2 1/2 ÷ 1/4 reduce

5/2 × 4/1 = 20/2

20 ÷ 2 = 10 pounds of flour per sugar

(I'm not very good at math so this might be wrong)

4 0
3 years ago
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