Raul simplified the expression, as shown below.
2 answers:
Answer:
Raul's errors are in the application of the distributive property(he applied it wrongly), in not respecting the precedence of operations, and in the multiplication of two terms with the same base(we add the exponent).
Step-by-step explanation:
Distributive property:
The distributive property of multiplication is:
a*(b + c) = a*b + a*c
Precedence of operations:
First multiplication, then addition.
Multiplication of terms with the same base:
The multiplication of h*h = h², which Raul missed.
The correct simplification is given by:
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Answer:
233 cartons of food; 467 cartons of clothing
Step-by-step explanation:
This linear programming problem can be formulated as two inequalities (in addition to the usual constraints that the variables be non-negative). One of these expresses the constraint on weight. Let f and c represent numbers of food and clothing containers, respectively.
40f +25c ≤ 21000
The other expresses the limit on volume.
20f + 5c ≤ 7000
_____
<u>Feasible Region vertex</u>
We can subtract the boundary line equation of the first inequality from that of 5 times the second to find f:
5(20f +5c) -(40f +25c) = 5(7000) -21000
60f = 14000
f = 233 1/3
The second boundary line equation can be rearranged to find c:
c = 1400 -4f = 466 2/3
The nearest integer numbers to these values are ...
(f, c) = (233, 467)
The other vertices of the feasible region are associated with one or the other variable being zero: (f, c) = (0, 840) or (350, 0).
<u>Check of Integer Solution</u>
Trying these in the constraint inequalities gives ...
- 40·233 +25·467 = 20,995 < 21000
- 20·233 +5·467 = 6995 < 7000
<u>Selection of the Answer</u>
The answer to the question will be the feasible region vertex that maximizes the number of people helped. That is, we want to maximize ...
p = 13f + 6c
The values of p at the vertices are ...
p = 13·233 + 6·467 = 5831
p = 13·0 + 6·840 = 5040
p = 13·350 + 6·0 = 2100
The most people are helped when the plane is filled with 233 food cartons and 467 clothing cartons.
Answer:
(i) ∠ABH = 14.5°
(ii) The length of AH = 4.6 m
Step-by-step explanation:
To solve the problem, we will follow the steps below;
(i)Finding ∠ABH
first lets find <HBC
<BHC + <HBC + <BCH = 180° (Sum of interior angle in a polygon)
46° + <HBC + 90 = 180°
<HBC+ 136° = 180°
subtract 136 from both-side of the equation
<HBC+ 136° - 136° = 180° -136°
<HBC = 44°
lets find <ABC
To do that, we need to first find <BAC
Using the sine rule
=
A = ?
a=6.9
C=90
c=13.2
=
sin A = 6.9 sin 90 /13.2
sinA = 0.522727
A = sin⁻¹ ( 0.522727)
A ≈ 31.5 °
<BAC = 31.5°
<BAC + <ABC + <BCA = 180° (sum of interior angle of a triangle)
31.5° +<ABC + 90° = 180°
<ABC + 121.5° = 180°
subtract 121.5° from both-side of the equation
<ABC + 121.5° - 121.5° = 180° - 121.5°
<ABC = 58.5°
<ABH = <ABC - <HBC
=58.5° - 44°
=14.5°
∠ABH = 14.5°
(ii) Finding the length of AH
To find length AH, we need to first find ∠AHB
<AHB + <BHC = 180° ( angle on a straight line)
<AHB + 46° = 180°
subtract 46° from both-side of the equation
<AHB + 46°- 46° = 180° - 46°
<AHB = 134°
Using sine rule,
=
AH = 13.2 sin 14.5 / sin 134
AH≈4.6 m
length AH = 4.6 m