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| 10 Theory slides |
| 13 Exercises - Grade E - A |
| Each lesson is meant to take 1-2 classroom sessions |
Here is some recommended reading before getting started with this lesson.
Consider △ABC with side lengths a, b, and c.
Maya plans to jog 150 meters at a constant speed of 2.5 meters per second.
Equivalent equations have the same solution(s). Use the Properties of Equality and inverse operations to solve for the variable t.
Each equation will be solved for t, and then the solutions will be compared.
LHS−7=RHS−7
Commutative Property of Addition
Subtract terms
LHS/(-1)=RHS/(-1)
-b-a=ba
Put minus sign in front of fraction
1a=a
LHS/5=RHS/5
Calculate quotient
ca⋅b=ca⋅b
aa=1
Identity Property of Multiplication
Rearrange equation
While at the planetarium on Saturday, Dominika learns about Annie Jump Cannon, known as the census taker of the sky,
who introduced the Harvard Spectral Classification. In its simplest form, this system classifies stars according to their surface temperatures.
Stellar Classification | ||
---|---|---|
Class | Temperature (K) | Apparent Color |
O | ≥30000 | blue |
B | 10000−30000 | blue white |
A | 7500−10000 | white |
F | 6000−7500 | yellow white |
G | 5000−6000 | yellow |
K | 3500−5000 | light orange |
M | 2000−3500 | orange red |
LHS−273=RHS−273
LHS⋅59=RHS⋅59
LHS+32=RHS+32
Rearrange equation
K=3500
Subtract term
ca⋅b=ca⋅b
Calculate quotient
Add terms
Round to nearest integer
K=5000
Subtract term
ca⋅b=ca⋅b
Calculate quotient
Add terms
Round to nearest integer
Use the Properties of Equality to solve the given literal equation for the indicated variable. Some equations may require dividing both sides of the equation by a variable. Since division by zero is not defined, for these equations assume that the variable is not equal to 0.
On Sunday Dominika spends time on her hobby, which is candle making. She uses 170 cubic centimeters of wax to produce a cylindrical candle of radius 3 centimeters.
LHS/πr2=RHS/πr2
Cancel out common factors
Simplify quotient
Rearrange equation
Time (s) | Distance Traveled (m) |
---|---|
10 | 25 |
20 | 50 |
30 | 75 |
40 | 100 |
50 | 125 |
60 | 150 |
It takes Maya 60 seconds to run 150 meters.
Time (s) | Speed × Time | Distance Traveled (m) |
---|---|---|
10 | 2.5(10)=25 | 25 |
20 | 2.5(20)=50 | 50 |
30 | 2.5(30)=75 | 75 |
40 | 2.5(40)=100 | 100 |
50 | 2.5(50)=125 | 125 |
60 | 2.5(60)=150 | 150 |
Maya will run 150 meters in 60 seconds at a speed of 2.5 meters per second.
LHS/v=RHS/v
Cancel out common factors
Simplify quotient
Rearrange equation
We see that m is multiplied by g and h. We can isolate the variable m by first dividing the equation by g and then by h.
Therefore, the answer is B.
We first multiply the equation by 2 to get rid of the fraction on the right hand side. Then, we divide both sides by v^2.
This corresponds to A.
We equate the expressions of the different energies and solve for v.
We can exclude the negative solution because in this context the sign of the expression only indicates the direction. v=sqrt(2gh) The answer is D.
We will start by multiplying both sides by sqrt()μ_0 ε_0. Then we will raise both sides by 2 to get rid of the radical sign.
This equation matches with C.
The square shown has side lengths a and diagonal length d.
Notice that two sides of the square and the diagonal forms a right triangle. Since the whole figure is a square, the legs have length a. The diagonal is the hypotenuse of the right triangle.
For any right triangle, we can use the Pythagorean Theorem to relate its side lengths. Let's use it to see relationship between a and d. a^2+a^2=d^2 Now we will solve this equation for a.
Because a is a length, it is always positive. Therefore, we can ignore the negative root. a=d/sqrt(2)
We need to find an expression equivalent to r. To do so, we will use the Properties of Equality. Let's first multiply both sides by r^2, then isolate r.
Since distances are always positive, the negative solution is irrelevant in this context and thus we can remove it. r=sqrt(Gm_1m_2/F) The expression on the right-hand side corresponds to option C.