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RideAnS [48]
3 years ago
10

The value of (2 x 10^4) + (9 x 10^4) - (3 x 10^3) in scientific notation?

Mathematics
1 answer:
Airida [17]3 years ago
8 0

Answer:

1.07 × 10^5

Step-by-step explanation:

First, let's start off by solving for the parentheses. So 2 × 10^4 is 20000, (I find it easier to solve by just adding however many zeros the exponet says with problems like that). 9 × 10^4 would be 90000. And lastly, 3 × 10^3 would be 3000. So now lets put it as our new equation. 20000 + 90000 - 3000. Don't forget about Pemdas (Parenthesis, exponet, multiplication, division, addition, subtraction). So now we have to add first before we subtract! 20000+90000 is 110,000. So now our new equation is 110,000 - 3000, which is 107,000. Now we have an awnser, let's make it in Scientific Notation form. So we would move the decimal point to the left in this case, to make it a number between 1 and 10. So we move to the left 5 times. Which gives us 1.07. Now what we would do is multiply it by 10 to an exponet of how much we moved the decimal point. So finally, we have 1.07 × 10^5. I hope this was helpful! Have a good rest of the day/evening.

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A parabolic arch has a height of 25 feet and a span of 40 feet. How high is the arch 8 feet from each side of the center?
Llana [10]

Answer:

The correct option is;

21 ft

Step-by-step explanation:

The equation of the parabolic arc is as follows;

y = a(x - h)² + k

Where the height is 25 ft and the span is 40 ft, the coordinates of the vertex (h, k) is then (20, 25)

We therefore have;

y = a(x - 20)² + 25

Whereby the parabola starts from the origin (0, 0), we have;

0 = a(0 - 20)² + 25

0 = 20²a + 25 → 0 = 400·a + 25

∴a = -25/400 = -1/16

The equation of the parabola is therefore;

y = (-\frac{1}{16})(x-20)^2 + 25

To find the height 8 ft from the center, where the center is at x = 20 we have 8 ft from center = x = 20 - 8 = 12 or x = 20 + 8 = 28

Therefore, plugging the value of x = 12 or 28 in the equation for the parabola gives;

y = (-\frac{1}{16})(12-20)^2 + 25 = (-\frac{1}{16})(-8)^2 + 25 = 21 \ ft.

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