A cart weighing 60 lb is placed on a ramp inclined at 15° to the horizontal. The cart is held in place by a rope inclined at 60° to the horizontal, as shown in the figure. Find the force that the rope must exert on the cart to keep it from rolling down the ramp. (Round your answer to one decimal place in lbs.)
Answers
I assume you ignore friction. The cart is held in equilibrium, so the net force on the cart is zero.
There are 3 forces acting on the cart:
• weight (magnitude w, pointing down)
• normal force (mag. n, pointing perpendicular to the ramp)
• tension in the rope (mag. t, pointing 60º from the horizontal, or equivalently 60º - 15º = 45º from the parallel direction)
Split up the forces into horizontal and vertical components. We have
• horizontal:
t cos(60º) + n cos(105º) = 0
• vertical:
n sin(105º) + (-w) = 0
(the normal force has a direction of 105º from the horizontal because it's perpendicular to the ramp, so it forms an angle of 90º with the ramp, plus the 15º inclination of the ramp itself)
We're given that w = 60 lb, so
n sin(105º) = 60 lb
n ≈ 62.1 lb
Solve for t :
t cos(60º) = -n cos(105º)
t = -n cos(105º)/cos(60º)
t ≈ 32.2 lb
Related Questions
IM DUMB HELP ME WAAAAAAAAA
Answers
Answer:
Sales tax (6.5% of Subtotal) would be
The total amount comes out to
Step-by-step explanation:
The first step is to add the sales tax percentage to the gratuity percentage. In this example, that would equal 24.5%. Next, we must divide the sum of the sales tax percent and the gratuity percent by 100 to convert to a decimal. So, 24.5% divided by 500 comes out to 0.245. Then, multiply the result by the amount of the bill to find what the sales tax and gratuity add to the bill. However, we do not have the bill amount given, so we must figure that out. In order to do this,
Solve the equation and describe what your answer. What happens? 5x-7=2x+1+3x
Answers
Answer: The Answer is 0
Step-by-step explanation:
The key here is combining like terms. Here:
1) 5x-7=2x+1+3x
2) 5x-7=5x+1
Then you add 7 to both sides anywhere that there is no variable. You also subtract 5x to the other 5x
3) 0x=8
When you divide by zero on both sides, your answer should be 0
Selecting which is the digit six is 10 times the value of the digit six in 3.161
Answers
Step-by-step explanation:
All the answers which apply are D and F
Answer:
I think it is d but I am now overthinking it so don't put too much trust in that
[tex](a) { - (b)}^{2} [/tex]
Answers
Answer:
a - b2
Step-by-step explanation:
STEP 1 :
Trying to factor as a Difference of Squares:
1.1 Factoring: a-b2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : a1 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares
Final result :
a - b2
HOPE THIS HELPS!
PLEASE MARK BRAINLIEST! :)
PLEASE ANSWERRRRRRRRRRRR
Answers
Answer:
Bertha picked up more than anica.
Step-by-step explanation:
10 1/3 = 10.33333 which is greater than anica
How much would $700 invested at 3% interest compounded annually be worth after 10 years
Answers
Answer: $940.74
Step-by-step explanation: Use the Calculator provided on money chimp or you can look up the formula. I like using the calculator
Please help I’m stuck on this question
Answers
Answer:
C. a => c
Step-by-step explanation:
a b c a => b a => c (not C)
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0 F F
1 0 1 F
1 1 0 F
1 1 1
¬a b c a => b ¬a => c (not B)
1 0 0 F F
1 0 1 F
1 1 0 F
1 1 1
0 0 0
0 0 1
0 1 0
0 1 1
a b c a => b c => a (not D)
0 0 0
0 0 1 F
0 1 0
0 1 1 F
1 0 0 F
1 0 1 F
1 1 0
1 1 1
¬a b ¬c a => b ¬a => ¬c
1 0 1
1 0 0 F
1 1 1
1 1 0 F
0 0 1 F
0 0 0 F
0 1 1
0 1 0
answer: everything is false lol
what is the missing value in the table below?
Answers
3 * 60 = 180
The missing number in the given table is 180 minutes.
To find the value of x in the equation 2/120 = 3/x, we can use cross multiplication.
First, we multiply both sides of the equation by 120
(2/120) * 120 = (3/x) * 120
To simplify, we have:
2 = 3 * (120/x)
2/3 = (120/x)
To solve for x, we can multiply both sides of the equation by x:
(x) * (2/3) = (120/x) * (x)
2x/3 = 120
To isolate x, we can multiply both sides of the equation by 3/2:
(2x/3) * (3/2) = 120 * (3/2)
x = 180
Therefore, the value of x in the equation 2/120 = 3/x is x = 180.
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ6
7. You bought three erasers and a magazine for $6. You spent a total of $18. How much did
each eraser cost?
Answers
Answer:
each eraser cost $4
Step-by-step explanation:
Answer:
$12
Step-by-step explanation:
The science center has 200 people in attendance on Monday. The center expects Saturday's attendance to be 140
percent of Monday's attendance. Natasha is trying to figure put how many people will be in attendance. Her work is
shown below.
part 140
whole 100
140-2 ?
100x2200
140-2-70
70 people will be in attendance.
Answers
Answer:
Natasha should have multiplied 140 by 2
Answer:
A
Step-by-step explanation:
(((click on the image to see it all))))
I need the answers to number 2 and 4 asap
Answers
Answer:
2.Matrices and Linear Algebra. 2.1 Basics. Definition 2.1.1. A matrix is an m × n array ... aij = 0 i = j. (1b) A diagonal matrix A may be denoted by diag(d1,d2,... ,dn) ... space of A. With r1 (A),...,rm (A) denoting the rows of A the row space
4.Introduces reflections in the x- and y-axes. Demonstrates the ... This leaves us with the transformation for doing a reflection in the y-axis. For this transformation, I'll switch ... Many textbooks don't get any further than this. If these are all the rules ...
Celeste wants to have her hair cut and
permed and also go to lunch. She knows
she will need $95. The perm costs twice
as much as her haircut and she needs $5
for lunch.
How much does the perm cost?
Answers
Answer:
the perm will cost $60
Step-by-step explanation:
take away $5 from the total because Its a set amount that's already known
which leaves 90 which if you take 30 away you are left with 60 its twice the amount of the haircut, I didn't really do any math techniques so I'm sorry that my explanation is weird, I hope this helped
con las medidas de los lados 8cm , 9cm ,2cm se existe un triángulo ?
Answers
Answer:
si
Step-by-step explanation:
la longitud mayor es menor que la suma de las otras 2 longitudes que es 10
A police radar gun is used to measure the speeds of cars on a highway. The speeds of cars are normally distributed with a mean of 55 mi/hr and a standard deviation of 5 mi/hr. Roughly what proportion of cars are driving between 60 and 70 mi/hr? Round to the nearest thousandth) Group of answer choices
Answers
Answer:
Approximately [tex]0.157[/tex].
Step-by-step explanation:
Let [tex]X[/tex] denote the speed of a car. The question is asking for [tex]P(60 \le X \le 70)[/tex].
That probability is equal to [tex]P(X \le 70)- P(X \le 60)[/tex].
Find each of [tex]P(X \le 60)[/tex] and [tex]P(X \le 70)[/tex] using a [tex]Z[/tex]-table.
Calculate the [tex]Z[/tex] value for [tex]x = 70[/tex] and [tex]x = 60[/tex]:
At [tex]x = 70[/tex], [tex]\displaystyle z = \frac{x - \mu}{\sigma} = \frac{60 - 55}{5} = 3[/tex].
At [tex]x = 60[/tex], [tex]\displaystyle z = \frac{x - \mu}{\sigma} = \frac{70 - 55}{5} = 1[/tex].
In other words: [tex]P(X \le 70) = P(Z \le 3)[/tex] whereas [tex]P(X \le 60) = P(Z \le 1)[/tex].
Look up [tex]P(Z \le 3)[/tex] and [tex]P(Z \le 1)[/tex] on a [tex]Z[/tex]-table. The question is asking that the answer be rounded to the nearest thousandth. Therefore, keep at least more decimal places than that in intermediate values.
[tex]P(Z \le 3) \approx 0.9987[/tex] and [tex]P(Z \le 1) \approx 0.8413[/tex].
Therefore:
[tex]\begin{aligned}P(60 \le X \le 70) &= P(X \le 70)- P(X \le 60) \\ &= P(Z \le 3) - P(Z \le 1) \approx 0.157\end{aligned}[/tex].
Becky read 10 books in 4 days.Sarah reads 50 books in 20 days. Are the two girls reading at the same rate
Answers
10 x 5 = 50
4 x 5 = 20
They both have equal multiples.
Andre filled 4 jars using a total of 10 cups of blackberry jam how many did cups of jam is in each jar
Answers
Answer:
2.5 cups in each jar
Step-by-step explanation:
10/4 is 2.5
In a group of 343 children, 104 have a swing set, 126 have a trampoline and 42 have a swing set and trampoline. How many have a swing set only?a. 20b. 72c. 62d. 54e. 52f. none of above
Answers
Answer:
None of the above
In circle K with \text{m} \angle JKL= 138^{\circ}m∠JKL=138
∘
, find the angle measure of minor arc \stackrel{\Large \frown}{JL}.
JL
⌢
.
Answers
The probability of a person being left-handed is about 11%. Suppose you interview 500 people. About how many people would you expect to be left-handed? Group te?
Answers
Answer:
78
Step-by-step explanation:
Hi
There is 5 *100 people and so 11 every 100 is left handed so within 500 people there is 5*11 people left handed = 55
you can also do 500 * 11/100 = 55
determine the intersepts of the lines
Answers
Answer:
Y-intercept is (0, 100) and the X-intercept is (-250, 0)
Step-by-step explanation:
For the y-intercept the line from the origin does not move left or right and stays at 0 but it goes up by 100.
For the x-intercept the line does not go up and down but it goes to the left -250.
I will give branliest to the first person to answer!
Simplify the following expressions
Please include the work its greatly appriciated!
1. 8x - 5 + 2x
2. 2.5w - 3y + 4w
3. 3(5 - 2n) + 9n
4. 5/7x + 15 = 9/14x - 9
Answers
Answer:
1: 10x-5
2: 6.5w-3y
3: 15+3n
4: not sure
41 divide by 278.8 hi my name chavoria
Answers
I believe u might of meant 278.8 divided by 41 which equals 6.8
Please help I’m stuck on this question
Answers
the answer is b. the rest is so it can be enough charecters so i can post this answer
Please help asap
What is 3/5 simplified
Answers
Answer: Its already in its simple form
Step-by-step explanation:
can you please help me with this question
Answers
Answer:
D
Step-by-step explanation:
4 * 20 = 80
Write the equation of the line that is parallel to the line y = -3x + 12 and passes through the point (-1, 6). (2 points)
Answers
Answer:
x=−9. Explanation: x=12 is a line parallel to the y-axis passing through all points in the plane with an x-coordinate of 12. therefore a line ...
x=−9 Explanation: x=12 is a line parallel to the y-axis passing through all points in the plane with an x-coordinate of 12 therefore a line parallel ... More
Miguel is designing shipping boxes that are rectangular prisms. One shape of the box with height h in feet, has a volume defined by the function V(h)=h(h-10(h-8). What is the height that would produce the maximum volume for the domain 0
Answers
Answer: 105ft^3
Step-by-step explanation:
Answer:
[tex]105ft^{3}[/tex]
Step-by-step explanation:
V(h) = h(–h + 10)(–h + 8)
Apply the distributive property to the right side and simplify.
V(h) = h(–h + 10)(–h + 8)
V(h) = {h(-h) + h(10)}(-h+8)
V(h) = (-h²+10h)(-h+8)
V(h) = (-h²)(-h) + (-h²)(8) + (10h)(-h) + (10h)(8)
V(h) = -8h² -10h² + 80h
V(h) = -18h² + 80h
Plug in the value of h from 1 to 9 (since 0<h<10) into the function V(h) = -18h² + 80h and create a table
h | V(h)
1 | 63
2 | 96
3 | 105 <------maximum volume is the highest y-value
4 | 96
5 | 75
6 | 48
7 | 21
8 | 0
9 | -9
The maximum volume for the domain 0<h<10 is 105 cubic feet.
Ellen borrowed some money from her brother. She paid him back by giving him the same amount every week.The graph shows how much DO after each week.
A. 18 weeks
B.6 weeks
C.12 weeks
D. She will never pay it back
Answers
I’m 100% sure!
Point A is at (3, - 8) and point B is at (7, 3)
What is the midpoint of line segment overline AB ?
Please help
Answers
need help on this 1 its really hard but i stilll can get it please help
Answers
Answer:
A.
92%
Step-by-step explanation: