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Find three consecutive odd integers such that the sum of the first twice the second and three times the third is 70?

Let x, x+2 and x+4 be the three consecutive odd integers. x+2(x+2)+3(x+4)=70 x+2x+4+3x+12=70 6x+16=70 6x=54 x=9 The numbers are 9, 11, and 13 Check: 9+2(11)+3(13)= 9+22+39=70


Suppose that y varies directly as the cube of x If x is tripled what is the effect on y?

y will be multiplied by 27. Remember, whatever you do to one side of an equation, you must do to the other. In this case, the relationship between x and y would be expressed as y = x^3 To triple x would look like y = (3x)^3 ...b/c you're tripling the value x alone, not the entire term x^3 y = 27x^3 ...after distributing the exponent (3^3 = 27) In order to set both sides of the equation equal, y must be multiplied by 27... 27y = 27x^3 TADA!


Can you do 3x multiplied by 1?

Absolutely, friend! 3 times 1 is simply 3. Just like painting a happy little tree, sometimes the simplest things can bring the most joy. Keep up the good work!


What does a function multiplied by its inverse equal to?

The identity function.


What is the derivative of 3cosx?

The derivative of 3cos(x) is -3sin(x). This can be found using the chain rule, which states that the derivative of a composition of functions is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. In this case, the derivative of cos(x) is -sin(x), and when multiplied by the constant 3, we get -3sin(x) as the derivative of 3cos(x).