2/3x=4

Group of answer choices

a. x= 8

b. x= 6

c. x = 8/3

Answer:

c

Step-by-step explanation:

Answers:

T1 = 59.5677879151077 N

T2 = 45.7583538175564  N

The values are approximate. Round the values however you need to.

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Explanation:

Refer to the diagram below. I have added red and blue lines to break up each tension vector into the x and y components. For tension T1 in red, we have x1 and y1 as the horizontal and vertical components respectively. Note that x1 points to the left and y1 points upward.

For T2 in blue, we have x2 point to the right and y2 point upward. The horizontal components x1 and x2 must be equal, and point in opposite directions, so that we have horizontal balance. Otherwise, the object would accelerate to one side rather than be stationary.

Applying a bit of trig, we can say

cos(angle) = adjacent/hypotenuse

cos(45) = (x1)/(T1)

x1 = T1*cos(45)

and also

sin(angle) = opposite/hypotenuse

sin(67) = (x2)/(T2)

x2 = T2*sin(67)

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Again, the x1 and x2 vectors must be equal in magnitude, allowing us to say this

x1 = x2

T1*cos(45) = T2*sin(67)

T1 = T2*sin(67)/cos(45)

which we'll use later.

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Doing a bit more trig set up, we know that

sin(45) = (y1)/(T1)

y1 = T1*sin(45)

and

cos(67) = (y2)/(T2)

y2 = T2*cos(67)

Adding those two y components together will yield the total upward force that the ropes apply

y1+y2 = T1*sin(45)+T2*cos(67)

y1+y2 = (T2*sin(67)/cos(45))*sin(45)+T2*cos(67)

y1+y2 = T2*( sin(67)*sin(45)/cos(45) + cos(67) )

y1+y2 = T2*( sin(67)*tan(45) + cos(67) )

y1+y2 = T2*( sin(67)*1 + cos(67) )

y1+y2 = T2*( sin(67) + cos(67) )

This combined upward pull must be equal to 60 newtons or else we wouldn't have vertical equilibrium. If the upward pull was smaller than the downward pull, then the object would be falling. If the other way around, then the object would be pulled upward at some accelerated speed (think of a spring action).

So we'll set y1+y2 equal to 60 and solve for T2

y1+y2 = 60

T2*( sin(67) + cos(67) ) = 60

T2 = 60/( sin(67) + cos(67) )

T2 = 45.7583538175564

That value is approximate. The units for T2 are in newtons. This is the amount of pull or force along the T2 line in the upper right direction.

Side note: make sure your calculator is in degree mode.

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The last thing to do is to compute T1

T1 = T2*sin(67)/cos(45)

T1 = 45.7583538175564*sin(67)/cos(45)

T1 = 59.5677879151077

That value is approximate as well. The units are also newtons here. This represents the amount of pull in the upper left direction as the diagram shows.

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Finding such values for T1 and T2 is useful to determine if a rope can handle a certain stress load. Let's say we had a rope that was rated for only 40 newtons. Anything beyond 40 N for this hypothetical rope would mean the rope breaks. We found T1 and T2 beyond this threshold which would indicate that such a rope isn't up to the task of holding this object up (at least not with the angles shown in the diagram).

Answer:

676 pi

Step-by-step explanation:

208 ÷ 4 =52

(each length =52cm)

diameter = 52 cm

radius = 52÷2 = 26cm

area of circle = pi × radius ^2

pi × 26^2 = 676 pi

Answer: 135 degrees

Step-by-step explanation:

Answer:

135

Step-by-step explanation:

sum of triangle angles = 180

then JLK =. 180 -(70+65) = 180 - 135 = 45

then JLK = 45

since JLM = 180

then KLM = 180 - 45 = 135

Answer:

128 sq. ft.

Step-by-step explanation:

The outer sides of the walkway will have a length of 20 feet and the breadth will be 16 feet

The area of the pool along with the walkway will be 20 × 16 = 320 square feet.

Area of the pool without the walkway will be 16 × 12 = 192 square feet.

Therefore area of the walkway will be

352 - 216 = 128 square feet.

What question do you need help with

Answer: I would say 4

Step-by-step explanation:

Answer:

There are more factories in the city than in the country.

Step-by-step explanation:

Hope this helps!

Answer:

tip total = $25.13

total(bill+tip) = $114.88

Answer:

Step-by-step explanation:

Slope of perpendicular line = [tex]\frac{-1}{m}[/tex]

       = -1 ÷ [tex]\frac{-5}{3}[/tex]

        [tex]= -1 *\dfrac{-3}{5}\\\\=\dfrac{3}{5}[/tex]

Step-by-step explanation:

I got 98.1, not sure how she got her answer

Answer: 14:30

Step-by-step explanation:

19:13 - 4.43 looks easy, but time expressed in 24-hour format is a base 60 calculation in the decimal portion.  It only contains values between 0 and 59.

I broke it it down to simplify:

1)  Take 13 minutes off the 19:13 to make it 19:00.  

2)  Then take the same 13 minutes off the 4.43, which would make it 4.30 (4 1/2 hours)

3)  Now take off the 4.30 from the 19:00.  The 4 portion of 4.3 can be removed:  19:00 - 4:00 = 15:00.  Then remove the 0:30 portion (1/2 hour), which would leave 14:30.

14:30 plus 4:43 = 18:73, but the 0:73 must convert to 1:13 to account for the 60 minutes/hour format

Olivia started knitting a jumper at 13:30.

A 24-hour time format is similar regular AM/PM time, except that you keep counting up after you get past 12 PM (noon). So 1 PM in 24-hour format is 13:00, 2 PM is 14:00, and so on. All you need to do is add 12 to any time in the PM to get 24-hour format time.

The given time is 19:13 and Olivia started knitting a jumper

4 hours and 43 minutes before the given time.

Then he starts at  13:30 started knitting a jumper.

Learn more about what time Olivia started knitting the jumper here-brainly.com/question/25212957

#SPJ2

Answer:

x=-4

Step-by-step explanation:

Multiply both sides by 50 and you get

3-x =7,

so x= -4

Answer:

false, true, false

Step-by-step explanation:

9514 1404 393

Answer:

  6.39×10²³

Step-by-step explanation:

There are 23 digits to the right of the most significant digit (6), so it is in the number place with a place value of 10²³. The number in scientific notation is ...

  6.39×10²³ . . . . kg

Answer:

4500 gr

Step-by-step explanation:

4.5 kg equals some number (n) times one gram.  Solve this for n:

4.5 kg = n(1 gr)

Recall that 1 kg = 1000 gr.  Because of this, the equation above becomes

        4.5 kg          (4.5)(1000 gr)

n = --------------- or ------------------- or 4500 gr

       1000 gr                     1 gr

Answer:

x = 16

Step-by-step explanation:

m<B+m<C+m<D = 180°

5x + 14 + x + 19 + 2x + 19 = 180

8x + 52 = 180

8x = 180 - 52

x = 128/8

x = 16

Answer:

It's true, if that's what your asking.

Step-by-step explanation:

5/6 = 0.833 to 3 sig.fig.

4/5 = 0.800 to 3 sig.fig.

6/7 = 0.857 to 3 sig.fig.

0.833 is more than 0.800 and less than 0.857.

Answer:

Have a splendiferous day!

Hope this helps!

Step-by-step explanation:

Shopping at the grocery store

Rough calculations of math

Figuring out time it would take to reach a location

Making nearly accurate measurements

Trying to stay within a budget

Solving extremely complicated numbers

Dealing with decimals

For quick calculations in a business

To prepare ahead, e.g an overestimate

and so on.

Answer:

49 minutes

Step-by-step explanation:

7: 43

8: 32

17 minutes 'till 8:00

Another 32 'till 8:32

so add 17+32

Answer:

5)3/2

6) 7

7)16

8)13

9)27

10)17

Step-by-step explanation:

5) 4x+3=10x-1

x=3/2

6)9x-25=38

x=7

7)5x-7=

Answer:

5

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2..................

[tex]x = - \frac{2}{5} \\ x = \frac{1}{2} \\ \\ \\ hope \: \: it \: \: helps \: \\ \\ see \: \: the \: \: attachment[/tex]

Answer:

3

Step-by-step explanation: