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Ad libitum [116K]

2 years ago

15

Nick is undertaking an expedition across the desert from A to B. In order to complete his journey he starts at A, walks 7km West

and then 24km North until he arrives at B. How much shorter would Nick's journey have been if he had gone by the shortest route across the desert?

1 answer:

MaRussiya [10]2 years ago

7 0

Answer:

Shorting distance = 6 km

Step-by-step explanation:

Given:

Distance walk = 7 km west

Distance walk = 24 km north

Find:

Shorting distance

Computation:

Using Pythagorean theorem:

Magnitude AB = √AC² + BC²

Magnitude AB = √7² + 24²

Magnitude AB = √49 + 576

Magnitude AB = 25 Km

Total distance Nick walk = 7 km + 24 km

Total distance Nick walk = 31 km

Shorting distance = 31 km - 25 km

Shorting distance = 6 km

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2 years ago

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2 years ago

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What is the final amount if 784 is decreased by 1% followed by a 4% increase?

Iteru [2.4K]

Answer:

The final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.

Step-by-step explanation:

General Formula

<em>A way to solve this problem is as follows</em>:

The general formula for this is taking into account that:

$\\ percent\;change = \frac{change}{starting\;point}$

The <em>starting point</em> is number 784.

The most important key is the solution for this answer is that:

$\\ change = starting\;point - x$

Where <em>x</em> is a number that we need to find. Then

$\\ percent\;change = \frac{starting\;point - x}{starting\;point}$ [1]

Is 784 increased or decreased after all?

We also need to evaluate the following: if a quantity decreases a percentage, and then increases in another percentage, what is the final percentage? In this case, we have first that 784 decreases by 1% and then increases by 4%. As a result 784 will +4% - 1% = +3%, that is, 784 will increase in 3%.

Finding the result

If 784 increases by 3%, we have:

$\\ 3\% = \frac{784 - x}{784}$

Which is equal to

$\\ 0.03 = \frac{784 - x}{784}$

Solving for <em>x</em>, we first multiply by 784 to both sides of the previous formula:

$\\ 0.03 * 784 = \frac{784 - x}{784}*784$

$\\ 0.03 * 784 = (784 - x)*\frac{784}{784}$

$\\ 0.03 * 784 = (784 - x)*1$

$\\ 0.03 * 784 = (784 - x)$

Remember that if we add, subtract, multiply, divide... to both sides of the equation, we do not "alter" this equation.

Subtracting 784 to both sides:

$\\ (0.03 * 784) - 784 = (784 - 784 - x)$

$\\ (0.03 * 784) - 784 = (0 - x)$

$\\ (0.03 * 784) - 784 = - x$

$\\ 23.52 - 784 = - x$

$\\ -760.48 = - x$

Multiplying by -1 to both sides:

$\\ -1 * (-760.48) = -1 * (-x)$

We have to remember that:

$\\ +*+ = +; - * - = +; - * + = -; + * - = -$

$\\ 760.48 = x$

Then

$\\ x = 760.48$

Therefore, using formula [1], an increase of 3% is

$\\ 3\% = \frac{784 - 760.48}{784}$

$\\ change = 784 - 760.48$

$\\ change = 23.52$

Since an increase of 3% is 23.52, we have to add this to the starting point 784, and finally the amount is 784 + 23.52 = 807.52.

As a result, the final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.

In a more <em>terse way</em> of solving this problem, we can say that:

Increase of 4% = 784 * 0.04 = 31.36.

Decrease of 1% = 784 * 0.01 = 7.84.

Difference = 31.36 - 7.84 = 23.52.

Then, we need to add this value to 784, and 784 + 23.52 = 807.52 (the same result).

5 0

2 years ago

Which function has a range of y < 3?

Setler79 [48]

Using a graphing tool

Let's graph each of the cases to determine the solution of the problem

<u>case A)</u> $y=3(2^{x})$

see the attached figure N $1$

The range is the interval--------> (0,∞)

$y> 0$

therefore

the function $y=3(2^{x})$ is not the solution

<u>case B)</u> $y=2(3^{x})$

see the attached figure N $2$

The range is the interval--------> (0,∞)

$y> 0$

therefore

the function $y=2(3^{x})$ is not the solution

<u>case C)</u> $y=-2^{x}+3$

see the attached figure N $3$

The range is the interval--------> (-∞,3)

$y< 3$

therefore

the function $y=-2^{x}+3$ is the solution

<u>case D)</u> $y=2^{x}-3$

see the attached figure N $4$

The range is the interval--------> (-3,∞)

$y>-3$

therefore

the function $y=2^{x}-3$ is not the solution

<u>the answer is</u>

$y=-2^{x}+3$

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2 years ago

Read 2 more answers