Given:
The leading coefficient of a polynomial is 8.
Polynomial roots are 1 and 2.
The graph passes through the point (4,5).
To find:
The 3rd root and the equation of the polynomial.
Solution:
The factor form of a polynomial is:
Where, a is a constant and 
are the roots of the polynomial.
Polynomial roots are 1 and 2. So, 
and 
are the factors of the polynomial.
Let the third root of the polynomial by c, then 
is a factor of the polynomial.
The leading coefficient of a polynomial is 8. So, a=8 and the equation of the polynomial is:
The graph passes through the point (4,5). Putting 
, we get
Divide both sides by 48.
Therefore, the 3rd root on the polynomial is 
.
Answer:
option 1
option 3
option 4
Step-by-step explanation:
Inversely proportional means "one quality increases, the other decreases " or "one quantity decreases ,other increases. " Inverse relantionship, that's it.
option 1:
Since the volume is given as 56 and we know the volume is area of base * height, to keep the volume at constant [56], if height increases, area of base would need to decrease, and vice versa. So Inversely proportional.
option 2:
The time spend in plowing a field with a tractor with increase when we area using more fuel.So more fuel used means more time spent. So these are directly proportional, Not inverse.
option 3:
Since the price is a constant, the amount of length we buy more,the price per one yard HAS to decrease, and vice versa. So ,this is Inverse relantionship.
option 4:
If the number of identical tractors. increase, it will take less time to plow the set 358 acre farm. And vice versa. So this is Inversely proportional as well.
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Answer: 3,140 radians per minute.
Step-by-step explanation:
We know that the wheel does 500 revolutions per minute.
This is called the frequency of the wheel, and this is written as:
f = 500 rev/min = 500 RPM
The angular speed (or Angular velocity) is written as
ω = 2*pi*f
And this quantity is in radians/unit of time.
where pi = 3.14
then:
ω = 2*3.14*500 (rev/min)*(rad/rev) = 3,140 rad/min
This means that the angular velocity (or angular speed) is 3,140 radians per minute.
Answer:
Step-by-step explanation:
(27)^2/3=∛27²=∛3³*3³=3*3=9
√36³=√36*36*36=√6²*6²*6²=6*6*6=216
(-243)^3/5=5√2-42³=-27
Answer:
{48, 64, 81}
Step-by-step explanation:
