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ICE Princess25 [194]
3 years ago
12

What is expanded form?

Mathematics
1 answer:
SashulF [63]3 years ago
4 0

Answer:

Expanded Form. When we write the number 521, what that number really means is that we have the total of 500 + 20 + 1. We've expanded the number to show the value of each of its digits. When we expand a number to show the value of each digit, we're writing that number in expanded form.



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Find the area of a square with 6 1/2
koban [17]

Answer:

I'm guessing the 6 1/2 means the length of one side so you would just multiply 6 1/2*6 1/2 and that equals 42.25 (or 169/4)

Step-by-step explanation:

6 0
2 years ago
You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along
sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}

Then, the time (speed divided by distance) is:

t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1

To optimize this function we have to derive and equal to zero:

\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\  \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\

x

As d_b=x, the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0
3 years ago
How big is the earth
melomori [17]
The 4th largest planet
7 0
3 years ago
Divide 20m^2n^3 - 10m^2n by 5mn
Sonja [21]

\frac{20 {m}^{2} {n}^{3}  - 10 {m}^{2}n  }{5mn}  \\  =   \frac{5mn(4m {n}^{2} - 2m) }{5mn}  \\  = 4 {m}^{2} n - 2m \\  = 2m(2mn - 1)

Hope this helps. - M
6 0
3 years ago
Using the numbers 5, 8, and 24, create a problem using no more than four operations (addition, subtraction, multiplication, divi
Oxana [17]

Answer:

There could be many answers to this problem, one being the √(24 x 5 - 8)

Step-by-step explanation:

Irrational numbers are classified as real numbers that are non-terminating and non-repeating decimals.  This means that the number will be a decimal that never ends and does not contain a pattern of any kind.  For example, a decimal that never ends is usually written as: 5.6789234...  This type of number is irrational because the decimal keeps going and shows no pattern of repetition. In the answer given, the value of (24 x 5 -8) is 112.  The square root of 112 is not a perfect square and thus you will get a non-terminating and non-repeated decimal as the final answer, thus making it irrational.

3 0
3 years ago
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