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Ksenya-84 [330]
2 years ago
15

Two forces of 30 pounds and 40 pounds act upon a body, forming an acute angle with each other. The angle between the resultant a

nd the 30-pound force is 35degree 10'. Find, to the nearest ten minutes, the angle between the two given forces
Mathematics
1 answer:
tekilochka [14]2 years ago
8 0
Angles in the triangle are 
<span>35°10' </span>
<span>180° - A (with A = angle between the 2 forces) </span>
<span>A - 35°10' </span>

<span>40/sin35°10' = 30/sin(A-35°10') </span>
<span>sin(A-35.17) = 30sin35.17°/40 = 0.432 </span>

<span>A-35.17= 25.6 </span>
<span>A = 60.77° = 60°46' </span>
<span>60°50'</span>
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2. Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large
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Answer:

\boxed {\boxed {\sf 98 \ Small \ Cups}}\\\\\boxed {\boxed {\sf 57 \ Large \ Cups}}

Step-by-step explanation:

Let's make a system of equations.

First, define the variables.

Let s= small cups and g= large cups

Next, make 2 equations. 1 for the money and 1 for the number of cups.

<u>Money</u>

  • A small cup costs 1.25 and a large cup costs 2.50. The total money made is 265.
  • 1.25s+2.50g=265

<u>Number</u>

  • A total of 155 cups of lemonade were sold. The sum of small cups and large cups sold will equal 155.
  • s+g=155

Here is our system of equations:

1.25s+2.50g=265 \\s+g=155

Now, solve. Let's isolate a variable in the 2nd equation, so we can plug it in after.

  • Subtract g from both sides of the equation.
  • s+g=155
  • s+g-g=155-g
  • s=155-g

Now we know that s is equal to 155-g. We can substitute (155-g) in for s in the first equation.

1.25s +2.50g=265

1.25(155-g)+2.50g=265

Distribute the 1.25

  • 1.25(155-g)= (1.25*155)+ (1.25*-g)= 193.75-1.25g

193.75-1.25g+2.50g=265

Work to isolate the variable. Subtract 193.75 from both sides of the equation and combine like terms on the left.

193.75-1.25g+2.50g=265-193.75       (Subtract 193.75)

-1.25g+2.50g=265-193.75      

1.25g=71.25      (Combine like terms).

1.25 and g are being multiplied. The inverse of multiplication is division. Divide both sides by 1.25

1.25g/1.25=71.25/1.25\\g=71.25/1.25\\g=57

Now we know that 57 large cups were sold. Plug 57 back into the original second equation to find the small cups.

s+g=155

s+57=155

Subtract 57 from both sides of the equation to isolate the variable, s.

s+57-57=155-57\\s=155-57\\s=98

Ashley sold 57 large cups and 98 small cups.

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3 years ago
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beks73 [17]

Answer:

1.5 years

Step-by-step explanation:

She will give up making $28,000 per year for 2 years.  This means that she will give up making $56,000 in total.

$28,000 × 2 = $56,000

She also pay $34,000 in total to costs to get her degree.  She invested a total of $90,000.

$56,000 + $34,000 = $90,000

After graduating, she makes $60,000 a year.  It will take her 1.5 years to recover her investment.

90,000/60,000 = 1.5

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What is the volume of a cone with a radius of 18 cm and a height of 10 cm? Use 3.14 for pi. Round your answer to the nearest ten
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I hope this helps you




Volume of Cone = 1/3.pi.r^2.h



Volume=1/3.3,14.18^2.10


Volume=10173,6/3


Volume=3391,2
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