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Dmitrij [34]
2 years ago
5

4,412.096 rounded to the nearest hundredth.

Mathematics
1 answer:
Mkey [24]2 years ago
8 0

We remember that when we round a decimal, we look the number to the right to the one we want to round (in this case, as we want to round to the nearest hundredth, we look at the thousandth position).

0. If the number ,is greater or equal than 5, we round up, (this is, we add 1 number to the position).

,

1. If the number, is less than 5, we round down, (we leave the same number)

In our exercise, we look at the thousandth position, which is 6. And as it is bigger than 5, we add 1 to the 9 (which is the hundredth position):

We obtain 10, but then as we can't put 10 on a digit, we add 1 to the tenth, and we obtain:

4,412.10

Thus, 4,412.096 rounded to the nearest hundredth is 4,412.1.

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Geometry problem: Find the distance between the parallel lines y=-3/2x+1 and 2y+3x=10
s344n2d4d5 [400]

Answer:

d = 1.847

Step-by-step explanation:

To avoid any ambiguity, please enclose the slope -3/2 inside parentheses:

y = (-3/2)x + 1.  Next, solve the 2nd equation for y:  2y = - 3x + 10 => y = (-3/2)x + 5.  Notice how these two lines have the same slope (-3/2)?  Thus, the two given lines are parallel.

It's important to realize that the distance between these two lines is a line segment with perpendicular to both lines.  Thus, the segment representing this distance has the form y = (2/3)x + c.  Let's say that this segment passes through the y-intercept of y = (-3/2)x + 1; it thus passes through (0,1), and thus has the equation y = (2/3)x + 1.  

Find the point at which this y = (2/3)x + 1 intersects the line y = (3/2)x + 5.  Note that the xresultant point

Setting these two equations = to one another results in (2/3)x + 1 = (-3/2)x + 5.

Multiplying both sides by the LCD (6) will eliminate the fractions:

4x + 6 = -9x + 30.  Combining like terms:  13x = 24, and x = 24/13 = 1.846.

Substitute this x-value into   y = (2/3)x + 1 to find the y-coordinate of the point of intersection of y = (2/3)x + 1 and y = (-3/2)x + 5:

When x = 1.846, y = (2/3)(1.846) + 1 = 1.231.

Thus, the desired distance is that between (0,1) and (1.846, 1.231), and is:

d = √ [ (1.846 - 0)^2 + (1.231 - 1)^2 ] = √ [ (1.846)^2 + (0.053)^2 ]

This simplifies to                              d = √ [ 3.408 + 0.003 ] = √3.411, or

                                                          d = 1.847   (answer)

7 0
3 years ago
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