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3 years ago

No matter which natural number "n" that you choose, explain why the following statement can never be true:

1 answer:

3 0

First of all, 2^n and 3^n are exponentials with different bases, and thus their sum cannot be simplified beyond 2^n + 3^n. In other words, these two functions cannot be combined ino one function (such as 4^n).

You may gain much more insight by graphing 2^n, 3^n and 4^n to determine whether there is truth in the given statement or not.

You might be interested in

The formula for finding the perimeter of a rectangle with length, l, and width, w, is P = 2l + 2w.

user100 [1]

Perimeter of a rectangle:
P=2I+2W=2(I+w)

But if the length and width of a rectangle are both double, then we would have:
Length=2I
width=2w

Therefore, its perimeter would be:
P=2(2I+2w)=4(I+w)

the old perimeter was P=2(I+w) and the new perimeter is P=4(I+w)=2[2(l+w)]
There the perimeter is twice as great.

Answer: C) the perimeter is twice as great.

6 0

3 years ago

Given f(x) = (lnx)^3 find the line tangent to f at x = 3

kirill [66]

Explanation

We must the tangent line at x = 3 of the function:

$f(x)=(\ln x)^3.$

The tangent line is given by:

$y=m*(x-h)+k.$

Where:

• m is the slope of the tangent line of f(x) at x = h,

• k = f(h) is the value of the function at x = h.

In this case, we have h = 3.

1) First, we compute the derivative of f(x):

$f^{\prime}(x)=\frac{d}{dx}((\ln x)^3)=3*(\ln x)^2*\frac{d}{dx}(\ln x)=3*(\ln x)^2*\frac{1}{x}=\frac{3(\ln x)^2}{x}.$

2) By evaluating the result of f'(x) at x = h = 3, we get:

$m=f^{\prime}(3)=\frac{3}{3}*(\ln3)^2=(\ln3)^2.$

3) The value of k is:

$k=f(3)=(\ln3)^3$

4) Replacing the values of m, h and k in the general equation of the tangent line, we get:

$y=(\ln3)^2*(x-3)+(\ln3)^3.$

Plotting the function f(x) and the tangent line we verify that our result is correct:

Answer

The equation of the tangent line to f(x) and x = 3 is:

$y=(\ln3)^2*(x-3)+(\ln3)^3$

6 0

1 year ago

Logarithmic and Exponential Forms of Equations In Exercise,Write the logarithmic equation as an exponential equation,or vice ver

lesantik [10]

Answer:

e^-1.6094 = 0.2

Step-by-step explanation:

The inverse of In is e

If In 0.2 = -1.6094

Then e^-1.6094 = 0.2

4 0

3 years ago

I need help asap!!!

valentina_108 [34]

The answer is (7,6)

This is because a midpoint is in the exact middle, meaning that both sides are an equal distance away. You can find this by fining the difference between the two corresponding coordinates then adding that difference to the midpoint and that will give you your other endpoint.

Hope this helped !!

7 0

2 years ago

What is the answer to y+4>6

Svetach [21]

Answer:

y>2

Step-by-step explanation:

all you do is 6-4. and your welcome

5 0

3 years ago