Find the average rate of change over the given interval: f(x) = 3x, [1, 4]
2 answers:
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Answer:
Step-by-step explanation:
When we multiply a polynomial by a specific monomial, all terms in the polynomial get multiplied by the monomial.
So we can do this by term.
Multiplying x by x to the something power will just increase the exponent on the x term by one (since powers are just x multiplied by itself). This means the exponent here will increase by 1, so this becomes .
Same logic applies to the second term: , raise the exponent by one,
.
For the third term, if there is no exponent on a term you can assume it's exponent is 1 (so in this case - as
). Again, using the same logic, this turns into
.
For the last term, when we multiply a constant by a variable, we get a term with a variable and a coefficient - the constant becomes the coefficient and the variable stays the variable. Therefore, .
Adding these terms all together gets us .
Hope this helped!
Answer:
the rectangle's width is approximately 3.39 inches
and the length is approximately 13.56 inches.
Step-by-step explanation:
Recall that the area of a rectangle is Length times Width
If we name the length "L" and the width "W", we have:
L * W = 46
Also: "the length is 4 times the width" can be written in math form as:
L = 4 * W
and now we can replace the length L by 4 * W in the formula for the area:
and now we find the value of L:
Therefore, the rectangle's width is approximately 3.39 inches
and the length is approximately 13.56 inches.