I guess I can give a brief overview and then you can decide if I should go deeper into these meaning and use.
Complex numbers are useful because in a lot of cases we need to use the square root of a negative number. Ex.
Solve the quadratic equation x^2+x+1=0
We have to use the quadratic formula since its not factorable.
x=[-1+-sqrt(1-4*1*1)]/2
x=-1/2 + or - sqrt(-3)
If we don't have imaginary numbers, we would be stuck because sqrt(-3) wouldn't exist as you cannot take the square root of a negative number.
But with complex numbers we can actually get the answer for that equation as
x=-1/2 + or - sqrt3*i
Which would give us a mean of using this answer to calculate further to get other needs depending on the problem you are solving. If complex number is not a thing, about half of our equations will have undefined answers.
Now conjugates is a more interesting one, on the surface level we are discussing here there is not much its used for except if you have a complex number as a root of a quadratic equation, then the conjugate of that complex number must also be a solution. Again if you want me to go a more in depth just comment down below, because I could write an entire essay on this topic :-)
Answer:
V = 8,181.23
Step-by-step explanation:
Unfortunately, we are not given any answer choices to choose from but using the information provided we can find the actual volume of the basketball. A basketball is made in the shape of a sphere and the formula for the volume of a sphere is the following...
V =
radius of a circle/sphere is half of it's diameter. Since we are provided the diameter size we simply divide it by 2 which would give us 12.5cm. Now we simply plug this value into the formula and solve for V.
V =
V =
V = 8,181.23
Answer:
D) If an integer is NOT even then it is NOT divisible by 2.
Step-by-step explanation:
An inverse if/then statement is like an opposite statement. So the statement "if A happens, then B will happen" the opposite would be like saying "if A does NOT happen then B will NOT happen." Hopefully that makes sense :)
Answer:
y = -2x + 3
Step-by-step explanation:
The given equation is:
First we need to find the slope of the tangent line. This can be done by finding the derivative of the given function.
Slope of the tangent will be the value of the derivative at the given point. So the slope of tangent is:
Now we have slope of the tangent line and a point (0, 3) on the tangent. The point (0,3) is the y-intercept of the tangent line. So we can use slope-intercept form to directly write the equation of the line.
The slope intercept form of an equation is:
y = mx + c
where m is the slope and c is the y-intercept.
Using the values: m = -2 and c = 3, we get:
y = -2x + 3
This equation represents the tangent line