As you progress in math, it will become increasingly important that you know how to express exponentiation properly.
y = 2x3 – x2 – 4x + 5 should be written <span>y = 2^x3 – x^2 – 4^x + 5. The
" ^ " symbol denotes exponentiation.
I see you're apparently in middle school. Is that so? If so, are you taking calculus already? If so, nice!
Case 1: You do not yet know calculus and have not differentiated or found critical values. Sketch the function </span>y = 2x^3 – x^2 – 4^x + 5, including the y-intercept at (0,5). Can you identify the intervals on which the graph appears to be increasing and those on which it appears to be decreasing?
Case 2: You do know differentiation, critical values and the first derivative test. Differentiate y = 2x^3 – x^2 – 4^x + 5 and set the derivative = to 0:
dy/dx = 6x^2 - 2x - 4 = 0. Reduce this by dividing all terms by 2:
dy/dx = 3x^2 - x - 2 = 0 I used synthetic div. to determine that one root is x = 2/3. Try it yourself. This leaves the coefficients of the other factor, (3x+3); this other factor is x = 3/(-3) = -1. Again, you should check this.
Now we have 2 roots: -1 and 2/3
Draw a number line. Locate the origin (0,0). Plot the points (-1, 0) and (2/3, 0). This subdivides the number line into 3 subintervals:
(-infinity, -1), (-1, 2/3) and (2/3, infinity).
Choose a test number from each interval and subst. it for x in the derivative formula above. If the derivative comes out +, the function is increasing on that interval; if -, the function is decreasing.
Ask all the questions you want, if this explanation is not sufficiently clear.
Answer:
101430
Step-by-step explanation:
- 69000=100 what about 147%. 69000×147/100=101430
Based on the ratio of boys/girls We can infer that the only possibility for Ellen's math class would be answer B. 14/21
You can set up a proportion to solve for the percentage of the coins that are pennies. Of course, there are alternate methods as well, but this is one method. First, you define the percentage of the coins that are pennies to be equal to a variable, such as x. Next, you write 240/600 = x/100, due to how "x" is the amount out of 100 (since per cent is for every cent (out of 100)), and 240 would correspond to x while 600 would correspond to 100. This proportion may also be written as 100/x = 600/240, or 240/x = 600/100. In order to solve for x, you use cross-products, or you multiply each denominator by the numerator of the other fraction. You will be left with a numerical value that's equal to a number times x, and then you divide both sides of the equation by the coefficient of x in order to isolate x. As a result, you will have the percentage of the coins that are pennies to be your answer. Remember to write the units for every numerator and denominator in your proportion.
last one. i can do the first part. put x = distance from top of ladder to the floor, y = distance from base of ladder to the wall (draw a picture) then pythagoras sez
<span><span>x2</span>+<span>y2</span>=25</span>
calculus says
<span>2x<span>x′</span>+2y<span>y′</span>=0</span>
and you are told that
<span><span>y′</span>=2</span>
so you know
<span>2x<span>x′</span>+4y=0</span>
or
<span><span>x′</span>=−<span><span>2y</span>x</span></span>
