Using the slope line formula,
The slope of line y = mx is 1.0315.
We have given that,
parabola equation is y = 5x - 3x²
line passing through origin is in the form of y = mx
==> mx = 5x - 3x²
==> 3x²+ mx - 5x = 0
==> 3x² + x(m -5) = 0
==> x(3x + (m -5)) = 0
==> x = 0 , x = (5 -m)/3
The total area of the bounded region is then the integral of 5x - 3x² from x = 0 to x = (5-m)/3
Area under y = 5x - 3x2 and y = mx is (125/54)/2 = 125/108
==> [0 to (5 -m)/3] ∫(5x - 3x²-mx )dx = 125/108
==> [0 to (5 -m)/3]∫( (5 - m)x - 3x2 )dx = 125/108
==> [0 to (5 -m)/3] ((5 - m)x²/2 - x³ )= 125/108
==> (5 - m)[(5 -m)/3]²/2 - ((5 -m)/3)³ = 125/108
==> (5 -m)³/18 - (5 -m)³/27 = 125/108
==> (5 -m)³/54 = 125/108
==> (5 -m)³ = 125/2
==> (5 -m) = 3.9685
==> m = 5 - 3.9685
==> m = 1.0315
Hence slope of line = 1.0315
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Answer:
1 hour = 60 minutes
20 minutes = 1/4 of 60 minutes, which means 60 minutes = 4/4
when you write ratios, the larger number goes first - 60 minutes out of 15 minutes = 4/1, so the ratio in simplest form is 4:1
hope this helped!
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❖ The area of a square with lengths of 7 inches is 49 inches.
In a square, all sides are equal so if one side is 7 inches, the rest of the sides are 7 inches. You multiply 7 x 7 because you only need 2 sides to find the area because the area of a square is l x w. (If another sides length is stated, that is the length that you will use.
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Given that B lies on segment AC and AB=7.8cm , BC = 25mm
Let us convert AB to mm by multiplying with 10 that is AB = 78mm
There are totally 3 possible ways for B lying on segment AC.
Solution 1:- B lies in between A and C,
Then AC = AB+BC
=78+25 = 103 mm
Solution 2:- B lies to the right of C like ACB.
Then AB = AC+CB
78 = AC+25
AC = 78-25 = 53mm
Solution 3:- B lies to the left of A like BAC.
Then BC = BA+AC
25 = 78+AC
Since AC cannot be negative, this way is not possible.
Hence there are only 2 solutions possible.
If we are given that B lies on line joining A and C, then definitely B should lie between A and C. That means nothing but solution 1. So only one solution is possible in this case.
I believe it could be 19.5
