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Alecsey [184]
3 years ago
10

Mary walks 4 miles north and then turns and walks 5 miles west. How far is she from her original starting point?

Mathematics
1 answer:
dusya [7]3 years ago
5 0
Answer:  6.403 miles; or, write as:  6.403 mi.  .
__________________________________________________
Explanation:
_________________________________________________





                                5
--------------------------------------------
`                             right angle   |_ |
   `          (right triangle )                 |
         `                                               |    4 
             `                                           |
                      `    
       "c"                        `                  \        
 (hypotenuse)                          Starting point
                     
__________________________________________________
Since we have a "right triangle, we solve for "c"; using the 
"Pythagorean theorem" ; 
_______________________________________________________
→  a² + b² = c² ; Solve for "c" ; our answer (in "miles"; or, "mi.") ;
__________________________________________________
Given : a = 4; b = 5 ; 
____________________________
Plug these known values into our equation:
________________________________________
 → 4² + 5² = c² ; 
____________________________
 → 16 + 25 = c² ;  ↔  c² = 16 + 25 ;
______________________________
 → c² = 41 ; 
_______________________________
 → Take the positive square root of each side of the equation (since the side of a "triangle" cannot be "negative"; 
__________________________________
 → √(c²) = √(41) ; 
_____________________________
 → c =  √41 ; Use calculator;
________________________________
 → c =  6.40312423743 ; Round to:  

 → c = 6.403 miles; or, 6.403 mi. 
__________________________________________

 

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Without calculating, explain how many decimal places are in the product 0.6 X0.4 X 1.9. Rewrite the expression as the product of
Vladimir79 [104]
There's only one decimal point in the answer. This is quite obvious. Regardless of whether or not your adding, subtracting, dividing, or multiplying, there's really only going to be one decimal, ever. This doesn't change, However, what DOES change are decimal PLACES.

Looking at the problem, you see both .6 and .4 are placed to the right of the decimal, otherwise known as the tenths place (1/10). 

Looking at 1.9, you see you have one number (1) placed to the left of the decimal, the ones place, and another number placed to the right of the decimal (9), in the tenths place. 

Well, this is simple. You can look and see that your multiplying fractions against a whole number, which will of course make this whole number even smaller. By how much though??

Well, you can really tell this by looking at how MANY numbers are behind the decimal. You have .9, .4, and .6

That's 3 numbers behind the decimal place. This may not help you solve the problem itself, but this tells you here (ignoring the 1, that will be taken out immediately while solving and turned into a 0) that you will have 3 numbers placed from the tenths place all the way to the thousandths place.

Basically, this tells you that you'll have three decimal places to the right of the decimal. 

As for rewriting your problem to better show this, that's simple too.

All you have to do is simple multiplication, just in the tenths place. How? You know that 6*4 (referring to .6 and .4) is 24, that means that .6*.4 will be .24

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~Hope this helps!


4 0
3 years ago
Log 300 =<br> log 3.26 =<br> log 10,000 =<br> log 20 =
ehidna [41]

Answer:

Log300=2.4771

Log3.26=0.5132

Log10000=4

Log20=1.3010

Step-by-step explanation:

log300=2.4771

Log3.26=0.5132

Log10000=4

Log20=1.3010

4 0
3 years ago
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mezya [45]

Answer:

The bus travelled 60 miles in 1 hour.

Step-by-step explanation:

To solve this problem we need to calculate the average speed at which the bus travelled. This is given by the distance travelled divided by the time that they took to get there. So we have:

average speed = distance/time

average speed = 360/6

average speed = 60 miles/h

Therefore in 1 hour they travelled 60 miles.

4 0
2 years ago
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Andrew [12]

Answer:

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8 0
2 years ago
Read 2 more answers
An ice cube is melting, and the lengths of its sides are decreasing at a rate of 0.8 millimeters per minute At what rate is the
julia-pushkina [17]

Answer:

The rate of decrease is: 43.2mm^3/min

Step-by-step explanation:

Given

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Required

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The volume of the cube is:

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Differentiate

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Make dV the subject

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Divide both sides by dt

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Given that: l = 18mm and \frac{dl}{dt} = -0.8mm/min

\frac{dV}{dt} = 3 * (18mm)^2 * (-0.8mm/min)

\frac{dV}{dt} = 3 * 18 *-0.8mm^3/min

\frac{dV}{dt} = -43.2mm^3/min

<em>Hence, the rate of decrease is: 43.2mm^3/min</em>

8 0
2 years ago
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