2.2 - formulas example 1: using the given values, solve for the variable in each formula that was...
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2.2 - Formulas
Example 1:
9, 63d rt t d
63 9r
63 9
9 9
r
7 r
Using the given values, solve for the variable in each formula that was not assigned a value.
7r
Check:
63 9r
63 97
63 63
2.2 - Formulas
Example 2: Volume of a Pyramid1
40, 83
V Bh V h
40 81
3B 1
40 83
3 3 B
120 8B
15 B
120 8
8 8
B
15B
LCD: 3
2.2 - Formulas
Example 3: Solve for the requested variable.
1
22 2A bh
1
2A bh
Area of a Triangle β solve for b
2A bh
2A bh
h h
2Ab
h
LCD: 2
2.2 - FormulasExample 4: Solve for the requested variable.
932
532 32F C 9
325
F C
Celsius to Fahrenheit β solve for C
932
5F C
5 32 9F C
5 32
9
FC
932
55 5F C
5 32 9
9 9
F C
or 532
9F C
LCD: 5
2.2 - FormulasExample 6: Solve for the requested variable.
Solve for v
h=π£π‘β 16 π‘2
+16 π‘ 2+16 π‘2
h+16 π‘2=π£π‘
h+16 π‘ 2
π‘=π£
h+16 π‘ 2
π‘=π£π‘π‘
2.2 - FormulasExample 5: Solve for the requested variable.
Solve for x
ππ₯β5=ππ₯β2βππ₯βππ₯ππ₯βππ₯β5=β2
+5+5ππ₯βππ₯=3π₯ (πβπ)=3
π₯=3
πβπ
π₯ (πβπ)πβπ
= 3πβπ
2.3 - ApplicationsSimple Interest
Simple Interest .Principal= Interest Rate
π°=π·πΉπ»
Interest Rate is stated as a percent and converted to a decimal for calculation purposes.
. Time
Time is stated in years or part of a year.
61.25
Simple Interest
7%
Find the simple interest on a five year loan of $875 at a rate of 7%.
.$875
875 . 0.07
$306.25
. 5
. 5
. 5
306.25
π°=π·πΉπ»2.3 - Applications
You invest $8000 in two accounts and earn a total of $323 in interest from both accounts in one year. The interest rates on the accounts were 4.6% and 2.8%. How much was invested in each account?
Total Interest = Account 1 + Account 2
π°=π·πΉπ»
Account 1
Account 2
Principal Interest Rate Interest
x
8000-x
π .π%=π .πππ
π .π%=π .πππ
π .ππππ
π .πππ (ππππβ π)
πππ=π .ππππ+π .πππ (ππππβ π)πππ=π .ππππ+πππβπ .ππππππ=π .ππππππππ=π
Account 1: $5500
Account 2: 8000 β 5500
2.3 - Applications
Account 2: $2500
x + 7
ππ+ππ=ππx
2.3 - ApplicationsIn a right triangle, the length of the longer leg is 7 more inches than the shorter leg. The length of the hypotenuse is 8 more inches than the length of the shorter leg. Find the length of all three sides.
x + 8
(π)π+(π+π)π=(π+π)π
ππ+ππ+πππ+ππ=ππ+πππ+ππβππβπππβππβ ππβπππβππππβπ πβππ=π(π+π)(πβπ)ΒΏππ+π=π πβπ=ππ=βππ=π
π=π πππππππ+π=πππππππππ+π=ππππππππ
πΊπππππππππππΓπ ππππππππππππππππππππ=π ππππππππππ
2.3 - ApplicationsA family paid $26,250 as a down payment for a home. This represents 15% of the selling price. What is the price of the home?
πΓπ .ππΒΏππππππ .πππ=ππππππ .ππππ .ππ
=ππππππ .ππ
π=πππππππ=$πππ ,πππ
2.3 - Applications
ππ π+π
π+π π+π
Special Pairs of Angles
Complimentary angles: Two angles whose sum is 90Β°. They are compliments of each other.
Supplementary angles: Two angles whose sum is 180Β°. They are supplements of each other.
One angle is six more than five times the other angle. What are their measurements if the are supplements of each other?
ΒΏππππ π+π=ππππ π=ππππππ
=ππππ
π=ππ
π=ππΒ°π (ππ)+π=πππΒ°
ππΒ°+πππΒ°=πππΒ°
2.3 - ApplicationsA flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 30 feet more than the length of the shortest side. Find the dimensions if the perimeter is 102 feet.
x = the length of the shortest side
2x = the length of the second side
x + 30 = the length of the third side
x 2x
x + 30
P = a + b + c
102 = x + 2x + x + 30
102 = 4x + 30
102 β 30 = 4x + 30 β 30
72 = 4x
4
4
4
72 x
π₯=18 ππππ‘2(18)=36 ππππ‘
18+30=48 ππππ‘
β π₯=18
2.3 - ApplicationsThe length of a rectangle is 4 less than twice the width. The area of the rectangle is 70. Find the dimensions of the rectangle.
hπππππ‘ =2 π₯β 4
π΄=πΓπ€70=(2 π₯β 4 ) π₯70=2 π₯2 β 4 π₯0=2 π₯2β 4 π₯β 700=2 (π₯2 β2 π₯β35)0=2 (π₯+5)(π₯β 7)
(π₯+5 )=0 (π₯β7 )=0π₯=β5 π₯=7
hπππππ‘ =2 π₯β 4=2 (7 )β 4=10
2.3 - Applications
35 mph
π πππππππ=ππππΓ ππππ40 mph
Two cars leave an airport at the same time. One is traveling due north at a rate of 40 miles per hour and the other is travelling due east at a rate of 35 miles per hour. When will the distance between the two cars be 110 miles?
110 mi.π π=πππππ+ππ=ππ
(πππ )π+(πππ )π=ππππ
ππππππ
ππππ=πππππ
ππππ
π π=πππ
ππππ ππ+ππππππ=πππππππππ ππ=πππππ
ππ=π .πππ π=π .πππππ .β
2.2 - Formulas
It takes Karen 3 hours to row a boat 30 kilometers upstream in a river. If the current was 4 kilometers per hour, how fast would she row in still water?
Rate Equation:
Rate upstream: (π=ππ‘ ) 30=ππ’ (3) ππ’=10 hππ
Rate in still water: π π =10 hππ +4 hππ π π =14 hππ
How long would it take her to row 30 kilometers in still water? (π=ππ‘ ) 30=14 π‘ π‘=2.14 hππ .How long would it take her to row 30 kilometers downstream? (π=ππ‘ ) 30=(14+4)π‘ π‘=1.67hππ .30=18 π‘
2.3 - Applications