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
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]
What is the solution to the equation StartFraction m Over m + 4 EndFraction + StartFraction 4 Over 4 minus m EndFraction = StartFraction m squared Over m squared minus 16 EndFraction?
Answer: m = -2.
The given equation is: [tex]\frac{m}{m+4}+\frac{4}{4-m}=\frac{m^{2}}{m^{2}-16}[/tex].
The LCM of the denominators = [tex]m^{2}-16=(m+4)(m-4)[/tex].
We multiply both sides by LCM.
[tex]\left(m+4\right)\left(m-4\right)\left(\frac{m}{m+4}+\frac{4}{4-m}\right)=\left(m+4\right)\left(m-4\right)\cdot\frac{m^{2}}{m^{2}-16}[/tex]
[tex]m\left(m-4\right)-4\left(m+4\right)=m^{2}[/tex]
[tex]m^{2}-4m-4m-16=m^{2}[/tex]
[tex]8m=-16\\m=-2[/tex]
Learn more: https://brainly.com/question/13769924
Answer:
M=-2 B
Step-by-step explanation:
trust me i took the quiz
ice, as long as it stays in its frozen form, will not lose its shape or its volume. Why?
solid form
Step-by-step explanation:
it will not loose shape because it is in solid form
Answer:
It freezes it self in the solid state
Step-by-step explanation:
expand and simplify (2x-1)(x-3)
Answer:
Expand the polynomial using the FOIL method.
2 x 2 − 7 x + 3
Step-by-step explanation:
A technique for distributing two binomials. The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial, Outer means multiply the outermost terms in the product, Inner means multiply the innermost terms, and Last means multiply the terms which occur last in each binomial.
An algebraic expression consisting of one or more summed terms, each term consisting of a constant multiplier and one or more variables raised to integral powers.
This object is made with five identical cubes. each cube edge if 4 centimeters long, What is the surface area of this object in square centimeters.
Answer:
480 cm ^ 2
Step-by-step explanation:
To calculate the surface area of the figure, we must calculate the surface area of the cube, we know that they are identical, therefore, calculating the area of one is sufficient.
We have that the surface area of a cube is:
A = 6 * a ^ 2
where a is the edge, we know that if it is a cube all its sides are equal, in this case it is 4 centimeters, if we replace we have:
A = 6 * (4 ^ 2)
A = 96
96 square centimeters is the area of a cube, but since the area of the object would be the sum of the area of all the cubes, then:
AT = 96 * 5
AT = 480 cm ^ 2
The surface area of the object formed with the cubes is 480 cm ^ 2
Sandy does babysitting in her spare time. She gets $100 advance pay and $10 per hour for babysitting. She wants to earn enough to buy a new Iphone for $450. How many hours she needs to babysit to earn enough money to buy the Iphone?
Answer: 35 hours
Step-by-step explanation: 450-100 because of the advanced pay, then you dived 350 by ten so you get 35 hours
Answer:
Sandy needs to babysit for 35 hours to earn enough money to buy an Iphone.
Explanation:
Sandy gets $100 advance pay and $10 per hour for babysitting.
Let x denotes the number of hours then
10x + 100
Sandy wants to buy an Iphone for $450
10x + 100 = 450
Solving the above equation
10x = 450 - 100
10x = 350
x = 350/10
x = 35 hours
Therefore, Sandy needs to babysit for 35 hours to earn enough money to buy an Iphone.
A car travel 65kms from A to B in 70 minutes and 80 km from B to C in 75 minutes.
Find the average speed in km/h of the car for the whole journey?
Answer:
60 km/h
Step-by-step explanation:
The car has traveled a total distance of 65+80 = 145 km in 70+75 = 145 minutes. Then the average speed is ...
speed = distance/time = (145 km)/(145 min)·(60 min/h) = 60 km/h
The average speed for the journey is 60 km/h.
Given the formula, Sn=a 1-r^n/1-r, what is the sum of the first nine terms of the geometric series: 324, -108, 36, -12...
If necessary, round to the hundredths place. (2 places after the decimal)
Answer:
243.01.
Step-by-step explanation:
The first term (a) = 324.
The common ratio (r) = -108/324 = -1/3.
So sum of 9 terms is:
S(9) = 324 * (1 - (-1/3)^9) / ( 1 - (-1/3)
= 324 ( 1 - (-0.00005076)) / 4/3
= 324 * 1.00005076 / 1.33333
= 243.012.
A tree grows 20 percent taller every year after it is planted. The tree was 12 feet tall when planted. How tall will it be after 10 years?
a.) 74.3 feet
b.) 120 feet
c.) 144 feet
d.) 146.3 feet
Answer:
Option A; 74.3 feet
Step-by-step explanation:
~ Here we can see that this problem is set to be so that compound interest is applied ~
1. If compound interest is to be applied, it would be that the "20 percent" is the interest, the principle number ( start value ) ⇒ 12 feet in height, and the time is 10 years.
2. Let us approach this problem step by step. Instead of substiting values into a compound interest formula, let us simply attempt a variation of that process...
3. 20 percent is, in a decimal form, ⇒ 0.2
4. Now add 1 to this value 0.2, to get ⇒ 1.2
5. If we were to consider the formula, 1.2 would first be exponentially multiplied by itself 10 time, considering that it is to the power of 10 years. In other words ⇒ 1.2^10 = 6.191736422..........
6. Now let us multiply this infinite value 6.19...... by the principle quantity 12 feet ⇒ 6.191736422.......... * 12 = (About) 74.30083707.......
7. If we were to round this value, it would be to ⇒ 74.3 feet, or in other words the first option; Option A
Jacob rolls a number cube numbered 1 to 6. What is the likelihood Jacob rolls a number less than 7?
A wheel with radius 1 foot makes 1 revolution in 4 seconds. What is the linear velocity, in feet per second, of a point on the edge of the wheel?
In one revolution of the wheel, a point on the edge travels a distance equal to the circumference of the wheel.
The wheel has radius 1 ft, so its circumference is 2π (1 ft) = 2π ft.
Then the point has a linear speed of
(1/4 rev/s) * (2π ft/rev) = 2π/4 ft/s = π/2 ft/s
The linear velocity of a point on the edge of the wheel is π/2 feet per second.
In this case, the wheel has a radius of 1 foot and makes 1 revolution in 4 seconds.
The circumference of a circle is given by the formula
C = 2πr, where r is the radius of the circle.
So, the circumference of the wheel is 2π(1) = 2π feet.
Now, the linear velocity of the point on the edge of the wheel is the distance traveled (circumference) divided by the time taken, which is:
Linear velocity = Circumference / Time = 2π feet / 4 seconds
Linear velocity = π/2 feet per second
So, the linear velocity of a point on the edge of the wheel is π/2 feet per second.
Learn more about Circumference of circle here:
https://brainly.com/question/17130827
#SPJ2
Please help.
Thank you.
Answer:
The first option is not a function
Explanation:
A function is where there is no repeated x values
Just a reminder
Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x.The quantities xxx and yyy are proportional.
xxx yyy
777 353535
121212 606060
202020 100100100
Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x.
Answer:
5
Step-by-step explanation:
Solving the given equation for r, we get ...
y = rx
y/x = r
Then we can find r from any pair in the table:
r = 35/7 = 5
The constant of proportionality is 5.
Answer:
y=3
Step-by-step explanation:
i did it in khan academy :)
a roll of dimes is 5. if the diameter of a dime is 18 millimeters and the height of each dime is 1.4 millimeters, what is the approximate volume of the roll of dimes?
Answer:
17.8 cm³
Step-by-step explanation:
The radius of the roll is half the diameter, so is 9 mm. The length of the roll of 50 dimes is 1.4·50 mm = 70 mm. With these dimensions, we can use the formula for the volume of a cylinder:
V = πr²h = π(9 mm)²(70 mm) = 5670π mm³ ≈ 17,812.8 mm³
Perhaps a more convenient unit of measure is cm³. Each cm³ is 1000 mm³, so the volume of a roll of dimes is approximately ...
V ≈ 17.8 cm³
evaluate one third of the sum of 15 and 6
Answer:
7
Step-by-step explanation:
15 plus 6 equals 21
21 divided by 3 is 7
Answer:7
Step-by-step explanation:
sum of 15 and 6
15+6=21
1/3 Of The sum
1/3 of 21
1/3 x 21
(1x21)/3
21/3=7
What’s the correct answer for this?
Answer:
i think it's B
Step-by-step explanation:
hope this helps
Answer:
B
Step-by-step explanation:
A median cuts a triangle into half (2:1) so the triangle is divided into two equal parts.
The area of Jamie's square backyard is 64 square meters. What is the length of one side of Jamie's backyard? Please Answer this asap bc I have to get this turned in, in about 10 mins please hurry
Answer:
8 meters
Step-by-step explanation:
Since the 4 sides of a square are all equal, the area of a square can be found using:
a=s*s or
a=s^2
We know that the area is 64 square meters, so we can substitute 64 in for a
64=s^2
We are trying to find a side, s, so we have to get s by itself. Since s is being squared, take the square root of both sides. This will cancel out the exponent, and leave s by itself.
[tex]\sqrt{64}=\sqrt{s^2}[/tex]
8=s
So, one side of the backyard is 8 meters
What’s the correct answer for this?
Answer:
A.
Step-by-step explanation:
We would reflect the point P so that another point would be made of the same length from the line.
Lola has h hats. Polly has triple as many hats as Lola. Darla has eight less hats than Polly.
a. Write an expression for how many hats each person has in terms of h.
Answer:
number of Lola hats = h
number of Polly hats = 3h
number of Darla hats = 3h - 8
Step-by-step explanation:
Lola has h number of hats . Polly has triple as many as Lola . Then Darla has eight number of hat less than Polly. The expression for how many hat each person has in terms of h can be express below.
Let
number of Lola hats = h
number of Polly hats = 3h (recall Polly has triple as many as Lola)
number of Darla hats = 3h - 8(Note Darla has 8 number less of hats than Polly who already have 3h number of hats)
The simplest way to explain this is that Lola has h number of hats. This means she has h number of hats .Polly has triple of Lola hats, this implies that 3 times h of Lola hats is Polly hats. Then finally Darla hats is 8 less than Polly hats. This simply means if you subtract 8 from Polly's hats you have gotten Darla's hats.
What error did Mr. Sanders likely make, and what is the actual fraction of students who have
completed 12 or more paintings? Use the drop-down menus to explain his reasoning and correct
his mistake.
Mr. Sanders likely found that of the students have completed 12 or more paintings because
there are Choose... bars on the histogram, and Choose... of the bars represent
students with 12 or more completed paintings. The actual fraction of the students who have
completed 12 or more paintings is Choose...
Answer: (1st box) = 6 (2nd box) = 2 (3rd box) = 2/3
Step-by-step explanation:
Answer:
(1st box) = 6
(2nd box) = 2
(3rd box) = 2/3
Step-by-step explanation:
I got a big brain
Tony wants to estimate the number of bees in a beehive. He catches 100 bees from the hive and marks each one with a dye. He then lets the bees go. The next day, tony catches 60 bees from the hive. 15 of these bees have been marked with dye. A) using this information what is a good estimate for the number of bees in the beehive.
Answer:
Number of total bees = 400
Step-by-step explanation:
He catches 100 bees from the hive and marks each one with a dye.
He later catches 60 and 15 were marked with the dye.
Its very to estimate from the data given.
I'll answer it with ratio.
We'll ratio number of bees with dye to total he caught the second day.
I.e 15:60 = 1:4
We'll multiply this ratio with the number he caught the first day to know the total.
1/4x =100
X = 100*4
X= 400
Where x is the total number of bees in the bee hive.
Identify two Pythagorean triples using the known triple 9, 40 , 41. *
Your answer
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {9}^{2} + {40}^{2} = {41}^{2} \\ 81 + 1600 = 1681 \\ 1681 = 1681[/tex]
write it as a product: -[tex]ax^{6}[/tex]+[tex]\frac{1}{8}[/tex]
Answer:
[tex]\frac{-abx^{6}+1 }{b}[/tex]
Step-by-step explanation:
if a sample of 57 swimmers is taken from a population of 135 swimmers, the population mean is the mean of how many swimmers' times?
Answer:
135
Step-by-step explanation:
A P E X
heeeeeeeeeeeeeeellllllllllllllllllllpppppppppp
Answer:
Keep the circle closed like it is and draw an incresing line (towards the positive numbers)(basically towards the right) with the arrow at the end of it
Step-by-step explanation:
Write eight and fifteen hundredths in decimal notation
Answer:
8.15
Step-by-step explanation:
Answer:
0.08, 0.15
Step-by-step explanation:
what is the equation of the line in slope-intercept form?
Answer:
y = 5x
Step-by-step explanation:
Slope intercept form is y = mx + b
m is the slope
m = 5 on this graph
b is the y intercept which is 0 on this graph
A large trucking company wants to estimate the proportion of its tracker truck population with refrigerated carrier capacity. A random sample of 200 tracker trucks is taken and 30% of the sample have refrigerated carrier capacity. The 95% confidence interval to estimate the population proportion is _______.
Answer:
The 95% confidence interval to estimate the population proportion is (0.2365, 0.3635).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 200, \pi = 0.3[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 - 1.96\sqrt{\frac{0.3*0.7}{200}} = 0.2365[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 + 1.96\sqrt{\frac{0.3*0.7}{200}} = 0.3635[/tex]
The 95% confidence interval to estimate the population proportion is (0.2365, 0.3635).
if a cube measures 5.3 cm on each side and has a mass of 280 grams how much is its volume
Answer:
8.1 g/cm
Step-by-step explanation:
what is the sum of 21 and 5 times a number f is 61
Answer:
f = 8
Step-by-step explanation:
21 + 5f = 61
5f = 61 - 21
f = (61 - 21) / 5
f = 8
Answer:
f = 8
Step-by-step explanation:
"Sum" = addition
"Times" = multiplication
Write an equation to represent this scenario
21 + 5 * f = 61
Multiply 5 by f
21 + 5f = 61
Subtract 21 from both sides of the equation
5f = 40
Divide both sides of the equation by 5
f = 8
Hope this helps :)
