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Calculus
The branch of mathematics that deals with the study of continuously changing quantities, with the use of limits and the differentiation and integration of functions of one or more variables, is called Calculus. Calculus analyzes aspects of change in processes or systems that can be modeled by functions. The English physicist, Isaac Newton, and the German mathematician, G. W. Leibniz, working independently, developed calculus during the 17th century.
25,068 Questions
What is the value of f of x plus 7 if f of x equals -5x-9?
Let,
f (x) = - 5x - 9
Therefore,
f(x) + 7 = - 5x - 9 + 7
f(x) + 7 = - 5x - 2
What is the range of the function y equals -x?
The range depends on the domain, which is not specified.
What is lnx plus one half ln y minus 5ln z as a single logarithm?
lnx + .5lny - 5lnz
First, make the coefficients into exponents:
lnx + ln(y^.5) - ln(z^5)
ln[xy^.5] - ln(z^5)
ln[(xy^.5)/z^5]
There you go!
How do you solve 299 plus 156?
The answer is 455. Simply add the numbers together arithmetically as you would for the problem two plus two. To check your work, a calculator is the best option.
Which point lies on the graph of the line of y equals -2y shifted up 4 units?
y = -y implies the first line is y = 0 or the x axis.
Shifted up 4 units, it becomes the line y = 4.
It is math that was invented to solve physics problems.
If you're talking about food, it is fried fish, Angola-style.
What is 2 x 2 x 2 x 2 in standard form in math?
24
there are four twos therefore the index number is 4 and two is because they are the same whole number
What is the integral of 3 over 3x?
The 3s would cancel and it would become the integral of 1/x which is ln x.
This problem is difficult to answer without more information. Is the well filled with water? If so then you must know the size of the rock and the shape of the rock to calculate the affect of buoyancy and friction due to viscosity. If you assume the rock is dropping through air the only force is that of gravity. Therefore you can use the acceleration due to gravity and the following equation: D= Vinitial*t +(1/2)g*t^2 V initial = 0 here D=340 ft Than solving for time you get: t = 4.6 seconds However if you include all the forces you have the equation: (Mass of rock-density of fluid*volume of rock)*g -force viscosity = mass of rock*acceleration If you take the rock to be a sphere, stokes law under streamline conditions gives viscosity to be F=6*pi*viscosity*radius of sphere*velocity Plugging this in gives you a differential equation that can be solved however in order to solve this problem you would need to assume that the rock reaches terminal velocity before it hits the bottom. At this point the forces add up to zero and you can find a formulation for the terminal velocity and plug it into your differential equation. Sounds difficult but it is just simple mathematics.
Solve sin 5x plus sin x equals 0?
Assuming the angles are expressed in radians:
sin(5x) + sin(x) = 0
∴ sin(5x) = -sin(x)
∴ 5x = x + π
∴ x = π/4
On the other hand, if your angles are in degrees, then the answer would be:
sin(5x) + sin(x) = 0
∴ sin(5x) = -sin(x)
∴ 5x = x + 180
∴ x = 180°/4
∴ x = 45°
penumbra
The Latin word "umbra" means "shadow". The prefix "pen-" means "almost" or "partly", so "penumbra" means a partial shadow.
What ordered pairs satisfy the equation y equals 1 5x?
To find the ordered pairs in any equation, just plug in any number for x and solve for y.
If your equation is meant to be y=1+5x, then if x=0 then y=1+5*0, y=1 so the first ordered pair would be (0,1)
If your equation is meant to be y=(1/5)x, then if x=0 then y=(1/5)*0, y=0, so the first ordered pair would be (0,0)
Can't for the life of me rememer how to solve this equation. 155 equals 165 times .99x power?
Assuming the question is: 155 = 165 * 0.99x
155/165 = 0.99x
log(155/165) = x*log(0.99)
so x = log(155/165) / log(0.99) = -0.0272/-0.0044 = 6.2207 (approx).
How do you express sin x plus cos x divided by cos x in terms of tan x?
(sin x + cos x) / cosx
= sin x / cos x + cosx / cos x
= tan x + 1
