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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.

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As part of an annual fundraiser to help raise money for diabetes research, Diane joined a bikeathon. The track she biked on was

Lyrx [107]

Answer:

$38.5\,\text{laps}\times\dfrac{1920\,\text{yd}}{1\,\text{lap}}\times\dfrac{3\,\text{ft}}{1\,\text{yd}}\times\dfrac{1\,\text{mi}}{5280\,\text{ft}}$
42 miles

Step-by-step explanation:

You know that fractions with the same value in numerator and denominator reduce to 1. This is true whether the value is a number, a variable expression, or some mix of those. That is ...

$\dfrac{1760}{1760}=1\\\\\dfrac{3\,\text{mi}}{1\,\text{mi}}=\dfrac{3}{1}\cdot\dfrac{\text{mi}}{\text{mi}}=3$

This example should show you that you can treat units as if they were a variable.

So, the unit conversion process is the process of choosing combinations of numerator and denominator units so that all the units you don't want cancel, leaving only units you do want.

You're starting with a number than has "laps" in the numerator. To cancel that, you need to find a conversion factor with "lap" in the denominator. On the list you are given, the one that has that is ...

$\dfrac{1920\,\text{yd}}{1\,\text{lap}}$

Now, you have canceled laps, but you have yards. Also on your list of conversion factors is a ratio with yards in the denominator:

$\dfrac{3\,\text{ft}}{1\,\text{yd}}$

This will cancel the yards in the numerator from the previous result, but will give you feet in the numerator. You want miles, so you look for a conversion factor between feet and miles, with miles in the numerator. The one you find is ...

$\dfrac{1\,\text{mi}}{5280\,\text{ft}}$

These three conversion factors go into the blanks. When you form the product, you will get ...

$\dfrac{38.5\cdot 1920\cdot 3}{1\cdot 1\cdot 5280}\cdot\dfrac{\text{laps$\cdot$yd$\cdot$ft$\cdot$mi}}{\text{lap$\cdot$yd$\cdot$ft}}=42\,\text{mi}$

7 0

3 years ago

Help ASAP, mathematics trig

GarryVolchara [31]

Answer:

Step-by-step explanation:

Using the tangent ratio in the right triangle

tanθ = $\frac{opposite}{adjacent}$ = $\frac{7}{4}$ , then

θ = $tan^{-1}$ ( $\frac{7}{4}$ ) ≈ 60° ( to the nearest degree )

8 0

3 years ago

The cost to rent a car at one agency is $24.50 per day plus an additional $15.99 fee for insurance. At a different agency, the c

Andru [333]

Answer:

Step-by-step explanation:

Formulas:

C = 24.50d + 15.99

C = 27.50d + 3.99

8 0

3 years ago

Read 2 more answers

How many change they give you for 5 dollar

grandymaker [24]

The answer is 25 quarters u will get back for change 5.00$ into change is 20 quarters

7 0

4 years ago

Find the compound interest earned by the deposit of $1800 at 6% compounded quarterly for 6 years.

Delvig [45]

For compound interest questions know the formula , after that just substitute accordingly
if the question is asking for the interest , do not forget to subtract off the amount you started with

8 0

4 years ago