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3 years ago

Can someone explain to me what a “derivative” means? How do you find the derivative of f(x)=x^3+1?

1 answer:

4 0

The derivative is the rate of change of a function, basically represents the slope at different points. To find the derivative of the given function you can use the power rule, which means, if n is a real number, d/dx(x^n)= nx^(n-1). This is a simplification of the chain rule based on the fact that d/dx(x)=1. Anyway, this means that d/dx(x^3 + 1)= 3x^2. Here n is 3 and so it is 3*x^(3-1)= 3x^2. The derivative of x^3+1 is 3x^2.

If you are wondering what happened to the 1, for any constant C, d/dx(C)=0.

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Braden bought a piece of commercial real estate for $101,234. The value of the real estate appreciated at a constant rate per ye

MrMuchimi

Answer:

f(t) = 101,234 $(1.03)^{t}$

Step-by-step explanation:

First, use FV formula to find the rate ;r given PV=101,234 and FV=104,271.02 and time= 1 year

$FV= PV (1+r)^{t}$

104,271.02 = 101,234 $(1+r)^{1}$

Divide both sides by 101,234 to get;

104,271.02 / 101,234 = 1+r

1.03 = 1+r

1.03 -1 =r

therefore r= 0.03 or 3%

Next, to get the function of FV of estate after t years; f(t) ;

Plug in the 3% rate found above into the FV formula with PV being the current value of 101,234 and it becomes;

f(t) = 101,234 $(1.03)^{t}$

5 0

2 years ago

Read 2 more answers

jerome tries to find the value of the expression 3-6+5 by first applying the communtative property. he rewrites the expression a

slega [8]

The commutative property is a property of <em>addition</em>, not of <em>subtraction</em>. It can work in a subtraction problem if you keep the sign with the number, so you're adding positive and negative numbers.

3 - 6 + 5

= (3) + (-6) + (5)

= (3) + (5) + (-6)

= 3 + 5 - 6

5 0

3 years ago

How to solve 4y-2/5y 4/5 = -3

lisabon 2012 [21]

One operator is missing. I will assume it is a + and that the equation is: 4y -2/5y +4/5 = -3

Solution step by step

1) Sum -4/5 to both sides

4y - 2/5y + 4/5 - 4/5 = -3 -4/5

2) Sum alike terms

18/5 y = -19/5

3) Multiply both sides by 5

18 y = -19

4) Divide both sides by 18

y = -19/18

5 0

2 years ago

Rewrite the expression below as the sum of one constant and one variable term 2(x-4)+6x-5x•3

Lorico [155]

Answer:

-7x-8

Step-by-step explanation:

First distribute the parenthesis:

2x-8+6x-5x·3

Following PEMDAS, Do multiplication next:

2x-8+6x-15x

Simplify:

-7x-8

6 0

3 years ago

A line with gradient of -3 passes through the points(3,k) and (k,8). Find the value of k and hence express the equation of the l

Kruka [31]

Answer:

3x + y = 9.5

Step-by-step explanation:

1) The equation of a line is in the form of y = mx + c, where m is the gradient and c is the y-intercept. Write the given values in that form.

y = -3x + c

2) Find the value of k by using the following formula: m = y2 - y1 / x2 - x1. We already know m.

-3 = 8 - k / k - 3

-3(k - 3) = 8 - k

-3k + 9 = 8 - k

-3k + k = 8 - 9

-2k = -1

k = -1/-2

k = 1/2

3) Therefore, a line with gradient of - 3 passes through the points (3, 1/2) and (1/2, 8). We can find the y-intercept (c). To do so, choose one of the coordinates and substitute.

y = -3x + c

1/2 = -3(3) + c

1/2 = -9 + c

1/2 + 9 = c

9.5 = c

Completed equation of the line: y = -3x + 9.5

4) Write it in the form of ax + by = c.

3x + y = 9.5

8 0

1 year ago