Explain why it is important to be able to perform matrix operations by hand when a calculator can do them for you.
2 answers:
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The general form of a quadratic (second degree) equation is
, where
is called the Discriminant.
The Discriminant determines how many roots the equation will have as follows:
i) if D>0, the equation has 2 roots.
ii) if D=0, the equation has 1 double root.
iii) if D<0, the equation has no roots.
In our equation,
, a=1, b=-5, c=7
so the discriminant is D=(-5)^2-4*1*7=25-28<0
Thus the equation has no roots.
Remark: the equation has no roots in the Real numbers, but it has 2 roots in a larger set of numbers to be discussed in the future, the Complex numbers.
The Discriminant determines how many roots the equation will have as follows:
i) if D>0, the equation has 2 roots.
ii) if D=0, the equation has 1 double root.
iii) if D<0, the equation has no roots.
In our equation,
so the discriminant is D=(-5)^2-4*1*7=25-28<0
Thus the equation has no roots.
Remark: the equation has no roots in the Real numbers, but it has 2 roots in a larger set of numbers to be discussed in the future, the Complex numbers.
Answer:
The population will be 896 turtles 6 years later ⇒ B
Step-by-step explanation:
The exponential increasing formula is y = a, where
- y is the new value
- a is the initial value
- r is the rate of increase in decimal
- x is the time in years
∵ There are 300 turtles
∴ a = 300
∵ The population of the turtles exponentially increases 20% each year
∴ r = 20%
→ Divide it by 100 to change it to decimal
∵ 20% = 20 ÷ 100 = 0.2
∴ r = 0.2
∵ The time is 6 years
∴ x = 6
→ Substitute these values in the exponential formula above
∵ y = 300
∴ y = 300
∴ y = 895.7952
→ Round it to the nearest whole number
∴ y = 896
∴ The population will be 896 turtles 6 years later