Justin needs 9 pieces of rope that are
1 1/2 feet long each. He says he can cut the 9 pieces from a 12 3/4 foot long rope. Is Justin correct? Write an equation with a complex fraction to support your answer.​

Answers:

T1 = 59.5677879151077 N

T2 = 45.7583538175564  N

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

=========================================================

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)

----------------------

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.

----------------------

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.

----------------------

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.

----------------------

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:

If you can join the foreign language club then you know spanish.

Giving me brainlest or sth will be appreciated

Answer:

Counterclockwise rotation 90°

Step-by-step explanation:

first quadrant graph -> 2nd quadrant

Counterclockwise rotation 90° : (x,y) -> (-y , x)

The slope is [tex]-\frac{3}{7}[/tex]

Step-by-step explanation:

there seems to be something missing.

I assume the slope of the line is -2/3.

the slope of a line is always the factor of x in the equation.

the slope is the y/x ratio indicating how many units y changes, when x changes by a certain amount of units (e.g. when going from one point on the line to another).

the equation for the line looks like this then :

y = (-2/3)×x + b

to get b we use the provided point (-6, -5) and it's x and y values.

-5 = (-2/3)×-6 + b = 4 + b

b = -9

so, the full equation of the line is

y = (-2/3)×x - 9

Answer:

= 30,550 rupee owed

Step-by-step explanation:

yr1 = 50000 x 0.10^1 = 5000

5000 - 10000 = 5000 credit from debt.

yr 2 = 50000 x 1.10^2 = 500 debit from debt = 5000-15000= 10,000 credit from debt

yr 3 = 50000 x 1.10^3 = 50 debit from debt

5000 + 500 = 15000 where 50,000 owed initially and yr1 and yr 2 paid in full interest of 5500 and we deduct this from his payment = 25000-5500 =

19500 paid of initial and nothing owed on interest.

50000-19500= 30,500 rupees owed + 50 rupee interest.

= 30,550 rupee owed

The amount he should pay at the end of the three years to settle the loan is; 41,550 Rupees

We are given;

Investment = 50000 rupees

Annual Interest Rate = 10% = 0.1

Since the interest is compounded annually, then number of times of compounding = 3

Thus;

Amount to pay after 3 years is;

A = 50000(1 + 0.1)³

A = 50000 × 1.1³

A = 66500 Rupees

Now, we are told that he has already paid 10000 rupees after one year and 15000 rupees after two years. Thus, amount he now owes to settle the loan = 66500 - (10000 + 15000) = 41,550 Rupees

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Answer:

slope is positive 2/1

Step-by-step explanation:

Answer:

a) the slope is 2 because the line goes from (4,1) to (5,3)

I d k any of the bonus questions tho sorryyyy

Step-by-step explanation:

Answer:

15%

Step-by-step explanation:

4590 = 5400 - D% × 5400

4590 = 5400 - D/100 * 5400

4590 = 5400 - 54D

54D = 5400 - 4590

D = 810 / 54

D = 15%

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Answer: -0.432

Step-by-step explanation:

0.4*1.08 would be 0.432 add the negative sign to get -0.432

The product of 0.4 and -1.08 is -4.240.

Multiplication is a method of finding the product of two or more numbers

To multiply 0.4 and 1.08, we need to follow few steps

first multiply as if there is no decimal.

Next, count the number of digits after the decimal in each factor.

Finally, put the same number of digits behind the decimal in the product.

   0.40

    1.08

___________

     240

   000+

 040++

____________

    4.240

As there is a negative sign infront if 1.08, we will put minus sign to the product value

So 0.4(-1.08) is -4.240

Hence the product of 0.4 and -1.08 is -4.240.

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Answer:

42:30

Step-by-step explanation:

10 x 3 = 30

14 x 3 = 42

Answer:

The Tickets grow approximately ¢68 or $0.68 each year

Step-by-step explanation:

7% of 9.75 = 0.68

A percentage is out of a fraction of 100; 7/100

Hope This Helps!

Answer: 3 + 7i

Step-by-step explanation:

Equation expanded: 12 + 5i - 9 + 2i // now simplfy

12 - 9 = 3

5i + 2i = 7i

// together, we get

3 + 7i

Answer:

10i

Step-by-step explanation:

(12+5i) - (9-2i)

(17i) - (7i)

10i

Answer:

Step-by-step explanation:

2x - 3 = 135    {Corresponding angles are congruent}

2x = 135 + 3

2x = 138

Divide both sides by 2

x = 138/2

x = 69

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=================================

2× - 3 = 135

2× = 135 + 3

2× = 138

× = 138/2

× = 69

=================================

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Answer:

z. sjshshdbd.d.difffjfjfjf

Answer:

here's your answer

hope it helps

(look at attachment)

Answer:

SSS~

RQP

Step-by-step explanation:

36/15 = 2.4

48/20 = 2.4

72/30 = 2.4

Triangles are similar by SSS~.

triangle JKL is similar to triangle RQP

Answer:

YES!!

Step-by-step explanation:

All rational numbers can be expressed as a fraction whose denominator is non-zero. Here, the given number, 3 can be expressed in fraction form as 3⁄1. Hence, it is a rational number.

Answer:

1.3 x 10^6

8.825 x 10^8

1.25 x 10^4

5.167 x 10^7

Step-by-step explanation:

Answer:

-16

Step-by-step explanation:

multiply 4x4 and then determine if its negative or positive

clapped

Step-by-step explanation:

thanks for the points

Step-by-step explanation:

hehe

Answer:

Hi There,

Your answer is -926.318

Answer:

log

2

(

y

)

=

5

→

2

5

=

y

⇒

y

=

32

Step-by-step explanation:

The value of the stamp at the end of the third year is £976.31.

From the information, Sam buys a rare stamp for his stamp collection at an auction. he buys the stamp for 920£ the stamp increased in value by 7% in each of the first 2 years.

First year value:

= 920 + (2% × 920)

= 938.4

Second year value:

= 938.4 + (2% × 938.4)

= 957.168

Third year value:

= 957.168 + (2% × 957.168)

= £976.31

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Complete question

sam buys a rare stamp for his stamp collection at an auction. he buys the stamp for 920£ the stamp increased in value by 7% in each of the first 2 years decreased in value by 4% in the third year. What is the cost by the end of. the third year?

Answer:

AAS

Step-by-step explanation:

I'm pretty sure its this, but im sorry if im wrong!

Step-by-step explanation:

so levt's label the video games as "P"

if 6P=207.54$

1P= X

1P × 207.54$ = 6P × X

1P × 207.54$ = 6P × X => P eliminates P on the right side

6P 6P. => 6P eliminates 6P on the left side

207.54$ = X

6

X = 34.59$

Step-by-step explanation:

Let the cost of 1 video game = x

6 video games = $207.54

1 video game = x........cross multiply

6x = 207. 54............ divide both sides by 6

x = 34.59

therefore, 1 video game costs $34.59

The lowest point of the cables above the bridge is 48 feet above the bridge.

The statement give us a parabola equation in standard form, the vertical distance of the lowest point above the bridge is determined by the y-coordinate of the vertex. Hence, the lowest point of the cables above the bridge is 48 feet above the bridge.

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Answer:

b

Step-by-step explanation:

And since we're perpendicular to y is equal to 3x plus 9, we know the slope of the two lines that are perpendicular

K times 3 is minus 1, so k is minus 1/3,

Only b and c match. Plug in the point negative 6,5.

The answer is b.