Answer:
Exercise (a)
The work done in pulling the rope to the top of the building is 750 lb·ft
Exercise (b)
The work done in pulling half the rope to the top of the building is 562.5 lb·ft
Step-by-step explanation:
Exercise (a)
The given parameters of the rope are;
The length of the rope = 50 ft.
The weight of the rope = 0.6 lb/ft.
The height of the building = 120 ft.
We have;
The work done in pulling a piece of the upper portion, ΔW₁ is given as follows;
ΔW₁ = 0.6Δx·x
The work done for the second half, ΔW₂, is given as follows;
ΔW₂ = 0.6Δx·x + 25×0.6 × 25 = 0.6Δx·x + 375
The total work done, W = W₁ + W₂ = 0.6Δx·x + 0.6Δx·x + 375
∴ We have;
W = [tex]2 \times \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= 2 \times \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 750[/tex]
The work done in pulling the rope to the top of the building, W = 750 lb·ft
Exercise (b)
The work done in pulling half the rope is given by W₂ as follows;
[tex]W_2 = \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 562.5[/tex]
The work done in pulling half the rope, W₂ = 562.5 lb·ft
16
15. The dimensions of a triangle
with base 4 m and height
5 m are multiplied by 3. How
is the area affected?
Answer:
It increases it by 9.
Step-by-step explanation:
Given the following data;
Base = 4m
Height = 5m
Area of triangle = ½*base*height
Area of triangle = ½*4*5
Area of triangle = 2 * 5
Area of triangle = 10 m²
Multiplying the parameters by 3, we have;
Base = 4 * 3 = 12m
Height = 5 * 3 = 15m
To find the area of triangle;
Area of triangle = ½*base*height
Area of triangle = ½*12*15
Area of triangle = 6 * 15
Area of triangle = 90 m²
Therefore, multiplying the dimensions by a factor of 3 increases the area by 9.
If John gets paid $45.00 an hour and works 10 hours, how much does he earn?
PLEASE HELP!! WILL MARK AS BRAIN LIST
Write the inequality shown by the graph
Find the surface area of a basketball with a diameter of 10 in.
400π in²
10π in²
100π in²
25π in²
Answer:
100 pie
Step-by-step explanation:
Find the surface area of a basketball with a diameter of 10 in.
100π in²
10π in²
400π in²
25π in²
The surface area of the basketball is 100π square inches.
The correct option is C.
What is the surface area of a sphere?The area of the outer surface of a sphere is the surface area of a sphere.
And its formula:
The surface area of the sphere is 4πr².
Where r is the radius of the sphere.
Given:
The shape of the basketball is spherical.
The diameter of the basketball is 10 inches.
So, the radius of the basketball = 10/2 = 5 inches.
The surface area of the basketball,
= the surface area of the sphere.
= 4πr²
= 4π(5)²
= 2π25
= 4 x 25π
= 100π square inches.
Therefore, the surface area is 100π square inches.
To learn more about the surface area of the sphere;
https://brainly.com/question/14692728
#SPJ6
PLEASE I NEED HELP CLICK ON THIS IMAGE
Answer:
Its 10, because it repeats the most
Step-by-step explanation:
50 POINTS + BRAINLIEST
PLEASE DONT STEAL POINTS
Answer:
80-89
Step-by-step explanation:
When you put it in a stem- and - leaf plot, you'll see that 80-89 is the mode interval.
Answer:
80-89
Step-by-step explanation:
That is the range that most students got.
The measure of an angle is 165. What is the measure of its complementary angle?
Answer:
15
Step-by-step explanation:
!!BRAINLIEST!! Is the opposite of I-5I 5?
Answer:
No. It is not. The opposite is -5
Step-by-step explanation:
I -5 I
The symbols; | | represents absolute value.
It gives the non negative value of that number irrespective of the sign of the number.
That is;
| -a | = a and | a | = a
So in this case;
| -5 | = 5
Opposite of 5 = -5
So the answer is FALSE!
A bike was on sale for $3600 Sam makes an offer equal to 3/4 of the price how much does Sam offer
Hellen is using 3.508 grams of copper for her science experiment. How many kilograms of copper did Hellen use for her science experiment?
Answer:
.003508 kg of copper
Step-by-step explanation:
1000 grams = 1 kg
3.508 g/1000 g = .003508 kg
Help me with this please
Answer:
x = 37.5
Step-by-step explanation:
The easiest way to solve this is to realize that the bottom triangle is a an Isosceles triangle, with the upper angle being equal to 180 - 75 degrees. That gives us the number 105°
Because it's an Isosceles triangle, we can simply say that the bottom angles, including the one we want to calculate are equal and both add up 105 (again, because the angles in a triangle add up to 180, and we know the top one is 105).
That gives us:
(180 / 105) / 2
= 75 / 2
= 37.5
help please hurry it not a test be hurry no links please
Answer:
65%
Step-by-step explanation:
Answer:
65%
Step-by-step explanation:
Also I know that's iready test
Find the slope of the line.
Answer:
1/3
Step-by-step explanation:
It takes 3 spots for the line to hit an intersection of y and x axis so therefore the slope is 1/3
Prove that the sum of three successive even integers is always a multiple of 6.
Answer:
if you see three consecutive numbers you can figure out that at least one of them is divisible by 6
Step-by-step explanation:
you can use mathematical induction by proving it mathematically. for a number to be divisible by 6, it should be divisible by 2. Since all are even numbers the number will be divisible by 2.
Can anyone help me I would really appreciate it.
Answer:
7c + 4 = 8
7c = 8 -4
7c = 4
c=4/7
Lucy started to run on a treadmill after setting its timer for 77 minutes. The display says that she has finished 79% of her run. How many minutes have gone by? Round your answer to the nearest tenth.
Answer:
60.8
Step-by-step explanation:
Step 1: Go on g oogle
Step 2: Type "79% of 77"
Step 3: Round your answer 60.83 to 60.8 because it said round to the nearest tenth.
Lamont wants to buy raspberries and apples to make a fruit tart raspberries cost $3.50 per pound and apples cost $3.75 per pound. How much dose he spend if he buys 3 pounds Aurora has been losing 2 pounds of apples ?how much does he spend if he buys X pounds of raspberries and Y pounds of apples ?
Complete question :
Lamont wants to buy raspberries and apples to make a fruit tart raspberries cost $3.50 per pound and apples cost $3.75 per pound. How much dose he spend if he buys 3 pounds raspberry and 2 pounds of apples ?how much does he spend if he buys X pounds of raspberries and Y pounds of apples ?
Answer:
$18.00 ;
3.50x + 3.75y
Step-by-step explanation:
Given that:
Cost per pound of raspberry = $3.50
Cost per pound of apple = $3.75
Cost of 2 pounds of raspberry = 3 * $3.50 = $10.50
Cost of 2 pounds of apple = 2 * $3.75 = $7.50
Total spent = $(10.50 + 7.50) = $18.00
Cost of X pounds of raspberry and Y pound of apple
.
(3.50 * X) + (3.75 * Y)
3.50x + 3.75y
hey so i need help on my khan so please please please help
Answer:
Step-by-step explanation:
Mario Works in a bakery He made 90 more loaves of bread on Saturday then he did on Sunday he made 70 more loaves of bread on Monday that he did on Sunday if he made 340 loaves off Bread on Monday how many lobes are friendly do you make on Saturday
Hi can u tell me whats going on here?
work out the circumference of this circle
give your answer in terms of pi
Answer:
37.68
Step-by-step explanation:
Well, the first thing first is to know the outline of the question. So I made sure I knew the diameter. In this case we didn't, so I multipilied 6 by 2 and got 12. Then I multipyed 12 by 3.14 to get 37.68
in a company 75% of the workers are men if 725 people work for the company who aren't men how many workers are there in all
Answer:
544 are men 181 are women
Step-by-step explanation:
725/4 =181x3
does 12, 24, 36 form a right triangle
Explanation is in the file
tinyurl.com/wpazsebu
I need help with this problem??!?!
Answer:
155
Step-by-step explanation:
<MEY= <PEX because they are vertical angles
<PEY = 180 because it is a straight angle, so 180-25 = 155
Answer:
155
Step-by-step explanation:
yup
A circle has a radius of 6 inches and a central angle of 60°. What is the measure of the arc length associated with this angle?
Answer:
[tex]2\pi[/tex]
Step-by-step explanation:
first you take 60°/360°= 1/6 then you take 1/6 and multiple it by [tex]2\pi[/tex] and that equals [tex]\frac{\pi }{3}[/tex] finally take [tex]\frac{\pi }{3}[/tex] times the radius (6) and that should equal [tex]2\pi[/tex]
PLATO USERS #platolivesmatters
The measure of the arc length associated with the angle is 2π inches OR 6.28 inches
Calculating the length of an arcFrom the question, we are to determine the measure of the arc length
The measure of the arc length can be calculated by using the formula,
[tex]l = \frac{\theta}{360 ^\circ}\times 2\pi r[/tex]
Where [tex]l[/tex] is the length of the arc
θ is the central angle
r is the radius of the circle
From the given information,
r = 6 inches
θ = 60°
Putting the parameters into the formula, we get
[tex]l = \frac{60 ^\circ}{360 ^\circ}\times 2 \pi \times 6[/tex]
[tex]l = \frac{1}{6}\times 2 \pi \times 6[/tex]
[tex]l =2\pi[/tex] inches OR 6.28 inches
Hence, the measure of the arc length associated with the angle is 2π inches OR 6.28 inches
Learn more on Calculating the length of an arc here: https://brainly.com/question/12541510
A scientist is experimenting with bacteria growth populations. He starts with 100 bacteria in a petri dish and estimates that the population will triple each day
Chloe biked the same distance each day for 9 days. If she traveled 513 kilometers altogether, how many kilometers did she travel each day?
Answer:
57 kilometers a day.
Step-by-step explanation:
I just divided 513 by 9 and got that.
Richard took a trip from Montreal to Vancouver, a distance of 2,937.67 miles. John went from Chicago to Denver, a distance of 1,014.9 miles. Richard went how much farther than John?
use photomath it helps a lot
What is 3x3/6 because I can’t figure it out
Answer:
its 48
Step-by-step explanation:
Answer: 1.5
Step-by-step explanation:
i dont know the answer to this so i am asking yall guys and girls.
which number will make the two fractions equivalent? 6/7=?/21
Answer:
18/21
Step-by-step explanation:
7x3 = 21
6x3=18
Answer:
18
Step-by-step explanation:
[tex]\frac{6}{7} =\frac{x}{21} \\\\\frac{6}{7} =\frac{18}{21}[/tex]
Multiply 3 to 6 since 7 x 3 is 21,
so 6 x 3 = 18
What is the slope of the line that passes through the points (-20, 18) and (30, 14)?
25
2
5
2
2
5
2
25
Answer:
[tex]-\frac{2}{25}[/tex]
Step-by-step explanation:
slope is the change in y over the change in x.
change in y is 14-18= -4
change in x is 30-(-20)= 50
so the answer is -4/50
we can factor out 2 from both equations to simplify the fraction. this gives us -2/25