Five friends went to a restaurant and agreed to share the bill equally. however, one person forgot his wallet so the other four
2 answers:
Hey there :)
1 ) Five friends went to a restaurant with an agreement to share the bill
2 ) One forgets so four friends part of bill rose by $4 each
Let p represent the total amount of bill
Translating (1) into mathematics:
( Original agreement )
Translating (2) into mathematics:
( Share among four )
Portions of bill increases by
4
Therefore,
Change to same denominators
p = $80
The total bill was $80
1 ) Five friends went to a restaurant with an agreement to share the bill
2 ) One forgets so four friends part of bill rose by $4 each
Let p represent the total amount of bill
Translating (1) into mathematics:
Translating (2) into mathematics:
Portions of bill increases by
4
Therefore,
Change to same denominators
p = $80
The total bill was $80
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The perimeter of the area of the pen the farmer intends to build for his
ship includes the length of the permanent stone wall.
Response:
i) The length and width of the rectangular pen are; <em>x</em>, and , therefore;
- The area is;
iii) The value of <em>x</em> that makes the area as large as possible is x = 50
<h3>How is the function for the area and the maximum area obtained?</h3>Given:
The length of fencing the farmer has = 100 m
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Let <em>x</em> represent the length of the stone wall, we have;
2 × Width = 100 m - x
Therefore;
Width, <em>w</em>, of the rectangular pen,
Area of a rectangle = Length × Width
Area of the rectangular pen, is therefore;
, and
are found as follows;
iii) The value of <em>x</em> that makes the area as large as possible is given as follows;
Given that the second derivative, , is negative, we have;
At the maximum area, , which gives;
x = 50
- The value of x that makes the area as large as possible is <em>x</em> =<u> 50</u>
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The tension in the cable is given by the newton's first law will be 163.622 N.
<h3>What is newton's first law?</h3>The summation of the force is equal to zero.
The formula is given as
ΣF = 0
Where m is the mass of the body and a is the acceleration.
A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29 degrees and 53 degrees with the beam.
Then the tension in the cable will be
Let T be the tension in the cable.
T sin 29° + T sin 53° – 210 = 0
On simplifying, we have
T (sin 29° + sin 53°) = 210
T = 163.622 N
More about the newton's first law link is given below.
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