The picture shows a cement bag of weight Fg hanging from a rope which itself is supported by two other ropes attached to a ceiling. The latter two ropes make an angle θ1 and θ2 with the ceiling. Determine the tension in each rope. Use the angle addition identity to simplify your result: sin(α ± β) = sin α cos β ± cos α sin β
Answers
Answer:
[tex]T_1= \dfrac{F_gcos \theta_2}{sin (\theta_1+\theta_2)}[/tex]
Step-by-step explanation:
From the free body diagram attached below; we will see that
T₃ = Fg ------ (1)
Thus; as the system is in equilibrium, the net force in the x and y direction shows to be zero
Then;
[tex]\sum F_x= 0 \to T_2 Cos \theta _2 - T_1 cos \theta _1[/tex]
[tex]T_2 Cos \theta _2 = T_1 cos \theta _1 \ \ \ \ \ - - - (2)[/tex]
Also;
[tex]\sum F_y =0 \to T_2sin \theta_2+T_1sin \theta_1 - T_3 = 0[/tex]
[tex]T_3 = T_2sin \theta_2+T_1sin \theta_1[/tex] ---- (3)
From equation (2):
[tex]T_2 = \dfrac{T_1cos \theta_1}{cos \theta_2}[/tex]
Replacing the above value for T₂ into equation 3; we have
[tex]T_3 = \dfrac{T_1cos \theta_1}{cos \theta_2}sin \theta_2+T_1sin \theta_1[/tex]
[tex]T_3 cos \theta_2 = {T_1cos \theta_1}{}sin \theta_2+T_1sin \theta_1 cos \theta_2[/tex]
[tex]T_3 cos \theta_2 = T_1(cos \theta_1 sin \theta_2+sin \theta_1 cos \theta_2)[/tex] ---- (4)
Using trigonometric identity Sin (A+B) = SIn A cos B + Cos A sin B
So ; equation 4 can now be:
[tex]T_3 cos \theta_2 = T_1sin(\theta _1 + \theta_2)[/tex] --- (5)
replacing equation (1) into equation (5) ; we have:
[tex]F_g}cos \theta_2 =T_1 sin (\theta_1+\theta_2)[/tex]
Hence; the tension in the string is:
[tex]T_1= \dfrac{F_gcos \theta_2}{sin (\theta_1+\theta_2)}[/tex]
Related Questions
اذا كانت س زاويه حاده و كان جاس= ٣/٥ فان ظا س=؟؟
Answers
Carla Ridley is a high school algebra teacher. Her annual salary is $38,625.00. If she receives a pay check every month of the year, what is her monthly salary?
Answers
Answer:
3218.75 a month
Step-by-step explanation:
Tate is paid $17.35 per hour with time and a half overtime. What will his gross pay period in which he worked 35 hours one week and 44 hours next week for a total 79 hours?
Answers
Answer:
The new rule has a higher salary level for exemption from overtime, at $684 a week. This means that lower-pay exempt employees may qualify for overtime.
Step-by-step explanation: this is your answer plz rate e the most brainlest
Find z1z2 if z1 = 3(cos37° + isin37°) and z2 = 2/3(cos53° + isin53°).
Answers
Answer:
[tex]z_{1}\cdot z_{2} = 2\cdot (\cos 90^{\circ} + i \cdot \sin 90^{\circ})[/tex]
Step-by-step explanation:
Both variable can be rewritten into polar form:
[tex]z_{1} = 3\cdot e^{i\cdot 0.205\pi}[/tex] and [tex]z_{2} = \frac{2}{3}\cdot e^{i\cdot 0.294\pi}[/tex]
The complex product is equal to:
[tex]z_{1}\cdot z_{2} = (3)\cdot \left(\frac{2}{3}) \cdot e^{i\cdot (0.205\pi+0.294\pi)}[/tex]
[tex]z_{1}\cdot z_{2} = 2 \cdot e^{i\cdot 0.499\pi}}[/tex]
The resultant expression in rectangular form is:
[tex]z_{1}\cdot z_{2} = 2\cdot (\cos 90^{\circ} + i \cdot \sin 90^{\circ})[/tex]
Answer:
The correct question is:
Find [tex]z_{1}.z_{2}[/tex] if [tex]z_{1}= 3(cos37 + isin37)[/tex] and [tex]z_{2}= \frac{2}{3} (cos53 + isin53)[/tex].
(Note: the angles mentioned in the equations above are in degrees)
The answer is [tex]z_{1}.z_{2}= 2i[/tex]
Step-by-step explanation:
[tex]z_{1}.z_{2}= 3(cos37 + isin37)* \frac{2}{3} (cos53 + isin53)[/tex]
[tex]z_{1}.z_{2}= (3cos37 + 3isin37)* (\frac{2}{3} cos53 + \frac{2}{3}isin53)[/tex]
[tex]z_{1}.z_{2}= 3cos37*\frac{2}{3} cos53 + 3cos37*\frac{2}{3}isin53+3isin37*\frac{2}{3} cos53+3isin37*\frac{2}{3}isin53[/tex]
[tex]z_{1}.z_{2}= 0.961+1.275i+0.724i-0.961[/tex] (Because [tex]i*i=i^{2}=-1[/tex] & [tex]i=\sqrt{-1}[/tex])
[tex]z_{1}.z_{2}= 0.961+1.275i+0.724i-0.961[/tex]
[tex]z_{1}.z_{2}= 2i[/tex]
What is the quotient?
(6 * 108) = (1.5 x 10-4)
4 x 1012
4 x 104
4 x 10-32
4 * 10-2
Answers
Answer:
The first choice.
Step-by-step explanation:
6 * 10^8 / 1.5 * 10^-4
= (6/1.5) * (10^(8 - (-4))
= 4 * 10^12.
Answer:
4 x 1012
Step-by-step explanation:
The quarterback Tom Brady completes 60% of his passes. To simulate the outcome of a single pass we use the digits 0, 1, 2, 3, 4, and 5 to represent the outcome "the pass is completed" and the digits 6, 7, 8, and 9 to represent the outcome "the pass is not completed." To be confident that our simulation is accurate, one needs to :
A. Repeat the simulation several more times
B. Assign new digits to represent outcomes
C. Take the average of the results of Line 134 and Line 101
Answers
Answer:
A. Repeat the simulation several more times
Step-by-step explanation:
The purpose of the simulation model is to represent the effectivity of the passes.
The proportion of successful passes is 60%.
As we have 10 digits available, 6 (digits from 0 to 5) are used for the outcome "the pass is completed" and 4 (digits 6, 7, 8, and 9) to represent the outcome "the pass is not completed". This is correct, as it represents a probability of 60% of having a successful pass.
But to have a representative distribution of the possible and probable results, the simulation have to run enough times to have a stable distribution of the results.
We conduct a study to determine whether the majority of community college students plan to vote in the next presidential election. We choose a significance level of 0.05. We survey 650 randomly selected community college students and find that 54% of them plan to vote. The P-value is 0.02. H0: 50% of community college students plan to vote in the next presidential election. Ha: More than 50% of community college students plan to vote in the next presidential election. What can we conclude
Answers
Answer:
we can conclude that more than 50% of community college students plan to vote in the next presidential election
Step-by-step explanation:
Decision Rule
If;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
Z score > Z(at 95% confidence interval) ---- reject Null hypothesis
Z score < Z(at 95% confidence interval) ------ accept Null hypothesis
Null hypothesis H0: 50% of community college students plan to vote in the next presidential election
H0: p = 0.50
Ha: More than 50% of community college students plan to vote in the next presidential election
Ha: p > 0.50
P-value = 0.02
From the decision rule;
Since the p-value for this study is less than the significance level.
0.02 < 0.05
So, we reject the null hypothesis, there is enough evidence to reject the null hypothesis. We thereby accept the alternative hypothesis.
Therefore, we can conclude that more than 50% of community college students plan to vote in the next presidential election
If you flipped a fair coin 18 times about how many times would you expect heads to appear?
Answers
Answer:
9 times
Step-by-step explanation:
hope this helps
Answer:
9
Step-by-step explanation:
Mathematically, 9, although reality wise, you could flip the coin and get heads every time, or the opposite.
I think you mean mathematically though, so yes, it would be 9.
A bag contains 10 Yellow, 4 Green and 7 Blue marbles. Find the following probabilies.
P(blue)
Answers
Answer:
1/3
Step-by-step explanation:
The total number of marbles
10+4+7 = 21
P(blue) = blue marbles / total marbles
= 7 / 21
= 1/3
Simplify (-2x^3)2•y•y^9
Answers
-2x^3 • 2 = 4 (because 2•2 is 4, they don’t share the same variable so you just multiply the base)
y^9 • y^1 (9+1=10)
-4x^3 y^10
Simplify (-2x^3)^2 •y•y^9 Answer 4x^6y^10
which is equivalent to sin^-1 ( sqrt 3/2 )? Give your answer
Give your answer in radians.
Answers
Answer: pi/3
Step-by-step explanation:
correct on edge 2020
The equivalent value of trigonometric relation sin⁻¹ ( √3/2 ) = π/3
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the trigonometric relation be represented as A
Now , the value of A is
sin⁻¹ ( √3/2 ) = θ
Now , the value of θ is calculated by
In a triangle , sin θ = opposite / hypotenuse
So , sin θ = √3/2
The value of θ = 60°
So , the measure of 60° in radians is θ = π/3
Hence , the value of θ from the trigonometric relation is π/3
To learn more about trigonometric relations click :
https://brainly.com/question/14746686
#SPJ7
(13 – 6)^2 (5 + 2)^2÷(5 – 2)^3
Answers
Answer:
88 25/27
Step-by-step explanation:
(13 – 6)^2 (5 + 2)^2÷(5 – 2)^3
PEMDAS
Parentheses first
(7)^2 (7)^2÷(3)^3
Then exponents
49*49 ÷27
Then multiply and divide from left to right
2401÷27
2401/27
88 25/27
88.92592593
Answer:
Step-by-step explanation:
(7)^2(7)^2 / (3)^3
49*49 / 27
2401/27
88 25/27
j+ 12 =25 find the solution to equation algebtaically
Answers
Answer:
j= 13
just subtract 12 from 25
Start by isolating the j.
Subtract 12 from both sides.
On the left, the 12 and -12 cancel.
On the right, 25 - 12 is 13.
So we have j = 13.
Find the area of the regular polygon.
Round your answer to the
nearest tenth if necessary.
Answers
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete as the dimension of the polygon is not given.
However, I'll give a general explanation of how to calculate the area of a regular polygon.
If you follow these simple steps, you'll arrive at your answer.
The area of a polygon is calculated as thus;
A = ½(nbh)
Where A represent the area
n represents the number of sides
b represents the length of the base
h represent the height of the polygon
Take for instance, the polygon is a regular pentagon.
This means n = 5.
Also assume that the base and the height are 5cm and 7cm respectively.
This means that
Area = ½ * (5 * 5 * 7)
Area = ½ * 175
Area = 87.5cm²
Hence, the area of the polygon is 87.5cm²
568,924,126 each digit stands for what
Answers
Answer:
500,000,00060,000,0008,000,000900,00020,0004,000100206Step-by-step explanation:
To find what a digit stands for, make all the other digits zero.
This is substantially what we do when we write the number in "expanded form."
568,924,126
= 500,000,000 +60,000,000 +8,000,000 +900,000 +20,000 +4,000 ...
... +100 +20 +6
The list of numbers in the sum is the list of numbers the digits stand for.
Livia eats a chicken drumstick with 11 grams of protein. She also eats x cheese sticks, each with 7 grams of protein. The table shows y , the total number of grams of protein that Livia will consume if she eats x cheese sticks. Livia may eat only part of a cheese stick, so x may not always be a whole number.
Answers
Step-by-step explanation:
C
Answer:
The answer is C
Step-by-step explanation:
I took the test and got it right :)
hopefully this helps you :)
pls mark brainlest ;)
What function has zeros at x=10 and x=2
Answers
Answer:
f(x) = x^2 -12x +20
Step-by-step explanation:
There are an infinite number of functions with zeros at those values of x. One simple polynomial function with those zeros is ...
f(x) = (x -10)(x -2) . . . . . each zero contributes a factor
f(x) = x^2 -12x +20
A spinner is divided into 8 equal sections numbered 1 to 8. About how many times would you expect the pointer to land on a number less than 6 if the pointer is spun 30 times.
Answers
Answer:
The answer is
6.25×30= 18.75
I'm not sure but this is what I think
Solve: 3x
+ 4 = 5x - 4x - 8
Answers
Answer:
3x = - 18
Step-by-step explanation:
1. Simplify this equation in terms of what is already provided:
3x + 4 = 5x - 4x - 8 ⇒ 3x + 4 = x - 8
2. Now subtract 3x from either side, at the same time adding 8 to either side: 3x + 4 = x - 8 ⇒ 4 = -2x - 8 ⇒ 12 = -2x
3. Divide -2 on either side to isolate the x, and recieve it's value:
12 = -2x ⇒ x = 12/-2 ⇒ x = -6
4. The question demads for the value of 3x, so simply multiply the known value of x by 3, as such: x = -6 ⇒ 3x = -6 * 3 = -18
Write the fraction from least to greatest: 1/8, 1/3, 1/8
Answers
Answer:
Start with making them equal.
1/8 --> 3/24
1/8 --> 3/24
1/3 --> 8/24
Now order them.
1/8, 1/8, 1/3.
Hope this helps ;)
. The pet store salesman told Evan to feed his dog 8 ounces of food per day. The food is sold in pounds. How many pounds does Evan need to buy for 2 weeks of feeding his dog? (16 ounces = 1 pound)?
Answers
It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is -4h. It can be described with the equation -4h=-14. What value of h makes the equation true?
Answers
The equation is -4h = -14
To find h, divide both sides of the equation by -4:
H = -14 / -4
H = 3.5 hours.
Cody paid $24.00 to join an online music service. If she purchases 15 songs each month at a cost of $1.25 per song, what will be the total amount she has spent after 6 months?
Answers
15 songs x 1.25 per song = $18.75 per month for songs.
18.75 per month x 6 months = $112.50
112.50 + 24.00 = $136.50 total
Consider the graph of the exponential function, y =3(2)^x. The x- intercept of the graph is
Answers
Answer:
the x intercept is 2
Step-by-step explanation:
I just went over this unit
Answer:
2
Step-by-step explanation:
A sphere is inscribed in a cube. Explain the relationship between the surface areas of the two solid figures
Answers
Answer:
No one knows. Jk just go look at the other brainly links. the question has already been asked and answered so you can go see them there.
Step-by-step explanation:
:)
7.6 cm
3.7 cm
Find the area of the parallelogram.
Answers
Answer:
7cm²
Step-by-step explanation:
g(t) = 6t - 1
g ( ) = -7
Answers
Answer:
g(-1) = -7
Step-by-step explanation:
Put the given value for g(t) into the first equation and solve for t.
-7 = 6t -1
-6 = 6t . . . . . . add 1
-1 = t . . . . . . . . divide by 6
g(-1) = -7
Answer: -1
Step-by-step explanation:
If you flip a coin 10 times, what is the best prediction possible for the number of times it will land on tails?
Answers
Answer:
5
Step-by-step explanation:
The probability of tails is 1/2, so the expected value is (1/2) (10) = 5.
Answer:
5
Step-by-step explanation:
Probability of land a tail when the coin is tossed once is 1/2 because a coin has two sides and contains one head
Then when it is tossed 10 times, the no of time a tail appears is. 1/2 * 10 =5
word problem of addition or subtraction
Answers
Answer:
subtraction
Step-by-step explanation:
In order to find out how many more flowers you need, you need to subtract both of the numbers to get the difference.
Answer:19
Step-by-step explanation:subtract 27 from 8.
Andre hit 46 balls at practice. He hit no fewer than 20 less than double the number of hits Jason had. Which inequality represents the situation if j represents the number of hits Jason had?
46 minus 20 less-than 2 j
2 j minus 20 less-than-or-equal-to 46
46 minus 20 less-than-or-equal-to 2 j
2 j minus 20 greater-than-or-equal-to 46
Answers
Answer:
2j -20 ≤ 46
Step-by-step explanation:
"20 less than double the number Jason [hit]" can be represented by 2j-20.
We are told that 46 is no fewer than this value, so it is greater than or equal to this value:
46 ≥ 2j -20
2j -20 ≤ 46 . . . . . swapping sides to match answer choices
Answer:
2j -20 ≤ 46
Step-by-step explanation:
