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balandron [24]
3 years ago
10

Two ropes are attached to the bumper of a car. Rope A is pulled with a force of 60 pounds at an angle of 30° to the horizontal g

round, and rope B is pulled with a force of 80 pounds at an angle of 15° to the horizontal ground. The same effect can be produced by a single rope pulling with what force and at what angle to the ground?
Mathematics
1 answer:
lbvjy [14]3 years ago
8 0
<span>The forces caused by these two ropes could be equally produced by a single rope pulling at 138.82 pounds at an angle of 21.42 degrees to the horizontal ground. This can be found by considering each rope as the hypotenuse of a triangle. One leg of these triangles is the ground, and the other is perpendicular to the ground. Using Sine and Cosine you can find the components of the force in the horizontal and vertical directions. These are then added to find the resultant force components. The pythagorean theorem can then be used to find the net force of 138.82 pounds, and inverse tangent can be used to find the resultant angle of 21.42 degrees. *These calculations were done to two significant digits. If more precision is desired you can repeat these calculations to the desired number of significant digits.</span>
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aul bought 9 total shirts for a total of $72. Tee shirts cost $10 and long sleeve shirts cost $7. How many of each type of shirt
vodomira [7]

Set up a system of equations:


\text{Total shirts bought}

x + y = 9


\text{Total cost}

10x + 7y = 72


x represents how many tee shirts were bought, and y represents how many long sleeve shirts were bought.


For the first equation, subtract y from both sides to get x by itself:


x = 9 - y


We'll now use substitution. Since x is equal to a value, we can substitute this value for the other equation:


10(9-y) + 7y = 72


Distribute the 10 to both terms in parentheses:


10 \times 9 = 90

10 \times -y = -10y


90 - 10y +7y = 72


Combine like terms:


-10y + 7y = -3y

90 - 3y = 72


Subtract 90 from both sides:


-3y = -18


Divide both sides by -3 to get y by itself:


y = 6


6 long sleeve shirts were bought.


Now you have a value for y. Input this value into the first equation:


x + 6 = 9


Subtract both sides by 6 to get x by itself:


x = 3


3 tee shirts were bought.


The answer is B. 3 tee shirts and 6 long sleeve shirts.

4 0
3 years ago
Read 2 more answers
Gary earns $12 an hour plus $16 an hour for every hour of overtime. Overtime hours are any hours more than 30 hours for the week
hoa [83]

Part A.

Amount of money earned = Regular rate per hour * Number of working hours

M = 12 x

 

Part B.

Amount of wages earned = Regular rate per hour * Maximum number of regular working hours + Overtime rate per hour * Excess working hours

T = 12 * 30 + 16 * y

T = 360 + 16 y

or

T = 16 y + 360

 

Part C.

Given T = 408, find y:

408 = 16 y + 360

y = 3 hrs

Therefore the total hours Gary worked that week is,

<span>x + y = 30 + 3 = 33 hrs        </span>

<span>(x = 30 since that is the maximum limit for regular working hours)</span>

7 0
3 years ago
So far Monica has read 56 of a book she has read the same number of pages each day for five days what fraction of the book does
alexandr1967 [171]

Answer:

14/125

Step-by-step explanation:

56 % ÷ 5 days ie 11.2% per day ie 112/1000 or 14/125

4 0
2 years ago
Please answer letter c asap!!​
garri49 [273]

24.95 times 3 is $74.85

Your answer is $74.85

<em>Hope this helps!</em>

5 0
2 years ago
A board is 29ft long. The second piece is 4 times longer than the first. The third piece is 3 times longer than the second. What
Nady [450]

Answer:

Length of first piece = 1.7058823 ft

Length of second piece = 4(1.7058823) = 6.82352941 ft

Length of third piece = 12(1.7058823) = 20.47058823 ft

Step-by-step explanation:

As given, Total length of the board = 29 ft

Let the board is divided into 3 pieces

Suppose that the length of first piece = x ft

As given, the second piece is 4 times longer than the first

⇒Length of second piece = 4x ft

Also given, the third piece is 3 times longer than the second.

⇒Length of third piece = 3(4x) = 12x ft

Now,

As total length of board = 29

⇒ x + 4x + 12x = 29

⇒ 17x = 29

⇒ x = \frac{29}{17} = 1.7058823 ft

∴ we get

Length of first piece = 1.7058823 ft

Length of second piece = 4(1.7058823) = 6.82352941 ft

Length of third piece = 12(1.7058823) = 20.47058823 ft

5 0
3 years ago
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