The number 12,300 is written 1.23 x 10⁴ as a scientific notation. It's coefficient is 1.23; base is 10⁴ in exponent form.
Scientific notation is a method developed by scientists to shorten the number that expresses a very large number. The scientific notation is based on powers of the base number 10.
Scientific notation has two numbers: coefficient and base. The coefficient must be greater than or equal to 1 and less than 10. The base is always 10 written in exponent form.
12,300 as coefficient in standard form in scientific notation.
1) put decimal after the first digit and drop the zeros. from 12,300 to 1.23 this is the coefficient.
2) to find the exponent, count the number of places from decimal to the end of the number.
1.2300 ; there are 4 places
So the scientific notation is 1.23 x 10⁴
Answer:
907.46 mm2
Step-by-step explanation:
Area of circle = (¶d^2)/4
d = 34 mm
Therefore
Area A = (3.14 x 34^2)/4
= 907.46 mm2
Answer:
Step-by-step explanation:
So, the function, P(t), represents the number of cells after t hours.
This means that the derivative, P'(t), represents the instantaneous rate of change (in cells per hour) at a certain point t.
C)
So, we are given that the quadratic curve of the trend is the function:
To find the <em>instanteous</em> rate of growth at t=5 hours, we must first differentiate the function. So, differentiate with respect to t:
![\frac{d}{dt}[P(t)]=\frac{d}{dt}[6.10t^2-9.28t+16.43]](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%5BP%28t%29%5D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5B6.10t%5E2-9.28t%2B16.43%5D)
Expand:
![P'(t)=\frac{d}{dt}[6.10t^2]+\frac{d}{dt}[-9.28t]+\frac{d}{dt}[16.43]](https://tex.z-dn.net/?f=P%27%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%5B6.10t%5E2%5D%2B%5Cfrac%7Bd%7D%7Bdt%7D%5B-9.28t%5D%2B%5Cfrac%7Bd%7D%7Bdt%7D%5B16.43%5D)
Move the constant to the front using the constant multiple rule. The derivative of a constant is 0. So:
![P'(t)=6.10\frac{d}{dt}[t^2]-9.28\frac{d}{dt}[t]](https://tex.z-dn.net/?f=P%27%28t%29%3D6.10%5Cfrac%7Bd%7D%7Bdt%7D%5Bt%5E2%5D-9.28%5Cfrac%7Bd%7D%7Bdt%7D%5Bt%5D)
Differentiate. Use the power rule:
Simplify:
So, to find the instantaneous rate of growth at t=5, substitute 5 into our differentiated function:
Multiply:
Subtract:
This tells us that at <em>exactly</em> t=5, the rate of growth is 51.72 cells per hour.
And we're done!
Answer:
40
Step-by-step explanation:
80/2=40
Answer
36/9= 4
Step-by-step explanation:
This is a fraction equal to
36 gallons ÷ 9 minutes
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 9
36 gallons ÷ 9
9 minutes ÷ 9
=
4 gallons
1 minute
=
4 gallons
minute
= 4 gallons per minute
