What is 5m - 3 = -3?
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The maximum angle of repose is the<span> maximum angle at which a material can be piled without slumping. The material piled up will form a cone.
If we project the situation on a 2D plane, we get a triangle rectangle (see picture attached). We know one angle and the Opposite side (height) and we need to find the Adjacent side (radius).
Recalling trigonometry formulae:
tan</span>α = O / A
Solving for A:
A = O / tan<span>α
We can now substitute our data (O = 20):
</span>1) Sand, Bank Damp
<span>α = 45°
A = 20 / tan(45)
= 20
The radius is 20 feet.
</span>
2)Sand, Bank Dry
α = 35°
A = 20 / tan(35)
= 28.5629
The radius is 28.6 feet.
3) Sand, core
α = 41°
A = 20 / tan(41)
= 23.0074
The radius is 23 feet.
4) Sand, foundry prepared
α₁ = 30°
A₁ = 20 / tan(30)
= 34.6410
α₂ = 44°
A₂ = 20 / tan(44)
= 20.7106
The radius is between 20.7 and 34.6 feet.
5) Sand, Foundry shakeout
α = 39°
A = 20 / tan(39)
= 24.6979
The radius is 24.7 feet<span>.</span>
If we project the situation on a 2D plane, we get a triangle rectangle (see picture attached). We know one angle and the Opposite side (height) and we need to find the Adjacent side (radius).
Recalling trigonometry formulae:
tan</span>α = O / A
Solving for A:
A = O / tan<span>α
We can now substitute our data (O = 20):
</span>1) Sand, Bank Damp
<span>α = 45°
A = 20 / tan(45)
= 20
The radius is 20 feet.
</span>
2)Sand, Bank Dry
α = 35°
A = 20 / tan(35)
= 28.5629
The radius is 28.6 feet.
3) Sand, core
α = 41°
A = 20 / tan(41)
= 23.0074
The radius is 23 feet.
4) Sand, foundry prepared
α₁ = 30°
A₁ = 20 / tan(30)
= 34.6410
α₂ = 44°
A₂ = 20 / tan(44)
= 20.7106
The radius is between 20.7 and 34.6 feet.
5) Sand, Foundry shakeout
α = 39°
A = 20 / tan(39)
= 24.6979
The radius is 24.7 feet<span>.</span>
The mathematical mistake that Riley made is that:
"She used the wrong common denominator." (Option A)
A common denominator is a factor that is similar to all the fractions in the sequence of equations.
Hence the correct answer is:
(2(2x² - 6x + 9))/((x-3) (x-2) (x+3))
See the correct sequence of steps below:
Step One - the Expression is given as:
(x/(x-3)(x-2)) + (3/(x+3))
Step 2 - Find the common denominator and rewrite the expression so that the numerators are above the common denominators.
Hence we have: (x (x+3) + 3(x-3) (x-2))/(x-3)(x-2)(x+3)
Step 3 Apply the Law of Multiplicative Distribution:
Hence we have (x² +3x+3x²-9x-6x+16)/(x-3)(x-2)(x+3)
Step 4 - Collect Like Items
This gives us: (x²+3x²)+(3x-9x-6x)+18/(x-3)(x-2)(x+3)
Step 5 Sort for like coefficients
This gives us: ((1+3)x² +(3-9-6) * x + 18)/(x-3)(x-2)(x+3)
Step 6 - check for the sum or difference
This gives us: (4x²+(3-9-6) * x+ 18)/(x-3)(x-2)(x+3)
We simplify and factor the expression to get
(2(2x²-6x+6)/(x-3)(x-2)(x+3).
See the attached for full question.
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