What is 9/10 of 80?
Solution:
The expression “9/10 of 80” can be written as
This is equal to 72.
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The expression “9/10 of 80” can be written as
This is equal to 72.
In the physical sciences, the amount of a sample is often given in terms of moles (i.e. Avogadro’s number, or 6.02214179 x 1023):
So, the probability that one of the trips takes more than 30 minutes is 0.05705343.
First write down the two equations and then pick several values of x and use those values to calculate the corresponding values of y. You can use the x,y pairs to then plot each line. You will see that the two lines intersect at 2,8 =i.e. x=2 and y=8).
First, let’s plot f(x) =
Here’s what the graph looks like:
Now, the definition of “domain of a function” as follows: The domain of a given function is the set of “input” values for which the function is defined.” For instance, the domain of cosine would be all real numbers, while the domain of the square root would be only numbers greater than or equal to 0 (ignoring complex numbers in both bases).
As you can see from the above graph, the function is valid for all “real” values of x, except for 0. The set of “real numbers”, as you may know, can be thought of as points on an infinitely long number line. The shorthand way of saying “all real numbers except for x” is as follows:
First, you have to have a clear idea what y = 2x^2+4x-5 means. This is an equation that tells you that, for any value of x, you can find y by dividing by multiplying x by x, and then multiplying that by two, adding 2 times x and finally subtracting 5. Does that sound familiar?
Now, what is the table you have to make? You will list several values of x (which you will be using as x-coordinates in your graph), and for each one use the equation to find what y is. We’ll show the work:
For x = 1, y = 2*1*1 + 4*1 – 5 = 1
For x = 2, y = 2*2*2 + 4*2 – 5 = 11
For x = 3, y = 2*3*3 + 4*3 – 5 = 25
For x = 4, y = 2*4*4 + 4*4 – 5 = 43
For x = 5, y = 2*5*5 + 4*5 – 5 = 65
Do you see what we did there? We just replaced x in the equation by each value of x, and did the multiplication and addition.
Now your table will look like this:
x | y
–+—–
1 | 1
2 | 11
3 | 25
4 | 43
5 | 65
We’ve only shown the x,y values for 1 through 5, out there are an infinite number of x values that you could plug in, including negative numbers and fractions. You can use the resulting T chart to help you create a graph, which will look like this:
First, let’s define what a Newton (N) is: “The Newton (N) is defined as the amount of force that, when acting on a 1 kg mass, produces an acceleration of 1 m/s/s (one meter per second per second). Therefore, 1 N = 1 kg =D7 1 m/s/s.”
The force of friction opposing the 325 N force is .25 * 925 N (which is equal to 231.25 N). The force pulling the crate is 325 N * cos(25), i.e. 294.55 N. (This is the component of force acting parallel to the floor.)
Take the difference between these two and you will have the net force pulling the crate (which is 63.3 N). Using Newton’s equation F = ma, you will find the acceleration by dividing the net force by the mass of the crate (the mass is 925 =/(one standard gravity [9.80665 m/s/s], or 94.32 kg). The acceleration is therefore 63.3 N / 94.32 kg, which equals 0.671 m/s/s.
The total area is 40π=2πrh+2πr^2
=2πr*8 + 2πr²
=16πr + 2πr²
=16r + 2r²
If we rearrange the terms and divide the terms by 2 (in order to simplify the equation), we get:
r2 + 8r – 20 = 0
(r+10) (r-2) = 0
r = 2 or -10
Therefore, r = 2 (assuming that -10 is not an option!).