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Here are a few recommended readings before getting started with this lesson.
After becoming a subscriber of a streaming platform, Magdalena became interested in a particular crime series. While watching an episode, she found out that after an accident, police can determine the speed of a car before the driver started braking.
The speed of a car can be estimated by using the following formula.Magdalena shared her streaming account with Kriz so that they can watch a new nature documentary. The documentary is about the work of a Swiss agricultural biologist, Max Kleiber. He researched how the mass of an animal influences the animal's metabolic rate.
Metabolic Rate |
The rate at which a person or an animal burns calories to maintain its body weight. |
Mammal | Mass |
---|---|
Mouse | $20$ g |
Kriz | $81$ kg |
Horse | $625$ kg |
Mammal | Mass $(kg)$ | Metabolic Rate $(kcal/day)$ |
---|---|---|
Mouse | $0.02$ | $≈3.72$ |
Kriz | $81$ | $1890$ |
Horse | $625$ | $8750$ |
Multiply
$LHS/70=RHS/70$
$LHS_{4}=RHS_{4}$
$(ab)_{m}=a_{m}b_{m}$
$(na )_{n}=a$
$3LHS =3RHS $
$3a⋅b =3a ⋅3b $
$3a_{3} =a$
$na =a_{n1}$
$(a_{m})_{n}=(a_{n})_{m}$
$a_{n1}=na $
Calculate root
Calculate power and product
$LHS⋅32=RHS⋅32$
$32⋅32a =a$
Identity Property of Multiplication
$LHS−v=RHS−v$
Rearrange equation
$LHS_{2}=RHS_{2}$
$(a )_{2}=a$
Distribute $64$
$(a−b)_{2}=a_{2}−2ab+b_{2}$
$LHS−v_{2}=RHS−v_{2}$
$(ab)_{m}=a_{m}b_{m}$
Calculate power and product
$LHS−64s=RHS−64s$
$LHS/(-64)=RHS/(-64)$
Distribute $-641 $
$t=1$
$1_{a}=1$
Identity Property of Multiplication
Add terms
Next, the second equation $y=2t−16 $ will be graphed in the same coordinate plane by using a table of values. Remember to substitute $t≥8$ so that the square root can be calculated right away.
$t$ | $2t−16 $ | $y=2t−16 $ |
---|---|---|
$8$ | $2(8)−16 $ | $0 =0$ |
$10$ | $2(10)−16 $ | $4 =2$ |
$16$ | $2(16)−16 $ | $16 =4$ |
$26$ | $2(26)−16 $ | $36 =6$ |
$40$ | $2(40)−16 $ | $64 =8$ |
$58$ | $2(58)−16 $ | $100 =10$ |
All these points will be plotted and connected with a smooth curve.
According to the graph, Magdalena ran the first $2$ kilometers in $10$ minutes, while Kriz ran the first $2$ kilometers in $2$ minutes. They met $10$ minutes from the start of the marathon. After this time, Kriz was in front of Magdalena for a while.$x$ | $1.113+x $ | $T=1.113+x $ |
---|---|---|
$-3$ | $1.113+(-3) $ | $0$ |
$-2$ | $1.113+(-2) $ | $1.11$ |
$1$ | $1.113+1 $ | $2.22$ |
$6$ | $1.113+6 $ | $3.33$ |
$13$ | $1.113+13 $ | $4.44$ |
Next, the points from the table will be plotted on a coordinate plane and connected with a smooth curve.
Since the square root of a greater number is also greater, the function will increase to infinity. Additionally, the square root of a non-negative number is also non-negative. Consequently, the range of the function consists of numbers greater than or equal to $0.$ The obtained domain and range correspond to option C.
up.
In addition to watching TV, Magdalena also loves programming and developing simple applications for personal use in her spare time.
She has recently started thinking about doing a summer internship at one of the local start-up companies. The following radical function estimates the annual profit of the first company in millions of dollars.