Construction
A warehouse is organized into rows (r) and lanes (L). At each position where a row and lane meet, three boxes are stacked.
Create a formula for the total number of boxes (B) in the warehouse.
B=3rL
Make y the subject of
3x+4y=20
y=5-3x/4
A car travels a distance (d) km in t hours. The speed (km/h) it travels is given by the formula
s=d/t
How fast did the car drive if it drove 250km in 3 1/2 hours?
s=71.43 km/h
What is the subject of a formula?
The isolated variable
You are a waffle vendor.
Each waffle (w) costs x kr to produce, and you just bought a new waffle machine for 290kr.
Write a formula for the total cost (C) of producing waffles.
C=wx+290
Make x the subject of
ax+by=c
x=(c-by)/a
When a stone is dropped from the top of a cliff, the distance fallen after t seconds is given by the formula
D=1/2 gt2, where g=9.8 m/s2
Find the distance fallen in the first 9 seconds.
D=396.9m
When a stone is dropped from the top of a cliff, the distance fallen after t seconds is given by the formula
D=1/2 gt2, where g=9.8 m/s2
Identify the variables in this formula.
D, g and t
You are a farmer, and fencing in your rectangular field. The fence will span the entirety of your field, and you will also install a gate that is 2m long (So you need less fencing).
Write a formula for how much fence (F) is needed to fence in your field.
F=2l+2w-2
Make k the subject of
T=2*c√ (k/g)
k=g*(T/2c)2
The kinetic energy of a object with mass m kg and speed v m/s is given by
E=1/2 mv2 J
What is the kinetic energy of a 2.9 kg ball thrown at 276 m/s?
E = 110 455.2 J
True or false; The steps taken in the following sequence are legal:
1. x2+6x=y ┃ +9
2. x2+6x+9=y+9
3. (x+3)2=y+9
True! You can add 9 to both sides of the equality to complete the square on the left hand side.
My garden exists in an interdimensional pocket, where distance is arbitrary.
It has width (w) equal to n+1
It has length (l) equal to 2n.
What is the area (A) of my garden?
A=lw=(2n)(n+1)=2n^2+2n
Make x the subject of
a(x+5)=b(x-1)
x = (5a+b)/(b-a)
You are given the formula
a=d2/(2bK)
Find the value of a when K=268, d=17, b=8
a=0.067
True or false; The steps taken in the following sequence are legal:
1. y=√ (a+b)
2. y=√ a + √ b
False!
Take a=4 and b=9
1. y=√ (4+9)=√ 13
2. y=√ 4 + √ 9 = 2+3=5
Two completely different answers.
You are a business owner, and produce small widget (w) and doodads (d).
Widgets cost x dollars to produce, and doodads cost y dollars.
A doodad sells for three times the production cost of a widget, and a widget sells for half the production cost of a doodad. You sell two doodads per widget.
Write a formula for how much money (M) the company earns. Assume you sell every unit you produce.
w = -x+1/2y
d = -y+2(3x)
M=w+d=5x+1/2y
Make x the subject of
y = (3x+7)/(3-2x)
x = (3y-7)/(3+2y)
The winning percentage of a tennis player who has won w matches and lost l matches is given by the formula
P = w/(w+l)*100
Find the winning percentage of a player who has won 19 matches, and lost 25.
P=43.2%
True or false; The steps taken in the following sequence are legal:
1. y=(x+1)/(x-1) ┃ * x
2. xy=(x+1)/-1 ┃ /y
3. x=(x+1)/(y-1)
False! The blood of a kitten is on your hands.
The denominator must be treated as a whole unit in the case of addition.
If the numbers in the denominator are multiplied with each other, then AND ONLY THEN, would this be allowed.