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Help on solving for x

Law Incorporation [45]

$\dfrac{x}{e^5}=e^{-4}|\cdot e^5\\
x=e^{-4}\cdot e^5\\
x=e\approx2.72


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4 0

3 years ago

Find f(a), f(a+h), and 71. f(x) = 7x - 3 f(a+h)-f(a) h if h = 0. 72. f(x) = 5x²

Leni [432]

Answer:

$71. \ \ \ f(a) \ = \ 7a \ - \ 3; \ f(a+h) \ = \ 7a \ + \ 7h \ - \ 3; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 7$

$72. \ \ \ f(a) \ = \ 5a^{2}; \ f(a+h) \ = \ {5a}^{2} \ + \ 10ah \ + \ {5h}^{2}; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 10a \ + \ 5h$

Step-by-step explanation:

In single-variable calculus, the difference quotient is the expression

$\displaystyle\frac{f(x+h) \ - \ f(x)}{h}$ ,

which its name comes from the fact that it is the quotient of the difference of the evaluated values of the function by the difference of its corresponding input values (as shown in the figure below).

This expression looks similar to the method of evaluating the slope of a line. Indeed, the difference quotient provides the slope of a secant line (in blue) that passes through two coordinate points on a curve.

$m \ \ = \ \ \displaystyle\frac{\Delta y}{\Delta x} \ \ = \ \ \displaystyle\frac{rise}{run}$ .

Similarly, the difference quotient is a measure of the average rate of change of the function over an interval. When the limit of the difference quotient is taken as h approaches 0 gives the instantaneous rate of change (rate of change in an instant) or the derivative of the function.

Therefore,

$71. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{(7a \ + \ 7h \ - \ 3) \ - \ (7a \ - \ 3)}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{7h}{h} \\ \\ \-\hspace{4.25cm} = \ \ 7$

$72. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{{5(a \ + \ h)}^{2} \ - \ {5(a)}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{{5a}^{2} \ + \ 10ah \ + \ {5h}^{2} \ - \ {5a}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{h(10a \ + \ 5h)}{h} \\ \\ \-\hspace{4.25cm} = \ \ 10a \ + \ 5h$

4 0

2 years ago

Which of the following best describes the algebraic expression x/3 -15

Dennis_Churaev [7]

Answer:

A. A number divided by three minus fifteen.

7 0

3 years ago

HELP QUICK! 20 POINTS PLEASE GET IT CORRECT

lyudmila [28]

We can conclude that Collin will have £3691.41 in his account after 10 years.

8 0

3 years ago

Which of the following constants can be added to x^2- 3x to form a perfect square trinomlal?

creativ13 [48]

Answer:

A 21/4

Step-by-step explanation:

When forming a perfect square trinomial you need to "complete the square".

All of the steps to completing the square when solving an equation:

1. The leading coefficient must be 1.

2. Divide b by 2.

3. Square (b/2)

4. Add (b/2)^2 to both sides to keep the polynomial balanced.

5. You can now write the perfect square trinomial and solve.

x^2 - 3x

-3/2

(-3/2)^2 = 9/4 = 2 1/4

8 0

2 years ago