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Law Incorporation [45]

3 years ago

12

A number changed to 12.6 after it was rounded. To what place was the number rounded? Explain how you know.

1 answer:

Anton [14]3 years ago

4 0

If 12.6 was rounded, that means that it was rounded to the tenths place.
You know this because the number has one decimal place, so that must be what it was rounded to.

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What is 7.27 times 1,000 i really need it fast!

gregori [183]

The answer would be 7,270.

Hope this helps, God bless.

8 0

2 years ago

Read 2 more answers

Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)

ELEN [110]

Question:

Find the point (,) on the curve $y = \sqrt x$ that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

Step-by-step explanation:

$y = \sqrt x$ can be represented as: $(x,y)$

Substitute $\sqrt x$ for $y$

$(x,y) = (x,\sqrt x)$

So, next:

Calculate the distance between $(x,\sqrt x)$ and $(3,0)$

Distance is calculated as:

$d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}$

So:

$d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}$

$d = \sqrt{(x-3)^2 + (\sqrt x)^2}$

Evaluate all exponents

$d = \sqrt{x^2 - 6x +9 + x}$

Rewrite as:

$d = \sqrt{x^2 + x- 6x +9 }$

$d = \sqrt{x^2 - 5x +9 }$

Differentiate using chain rule:

Let

$u = x^2 - 5x +9$

$\frac{du}{dx} = 2x - 5$

So:

$d = \sqrt u$

$d = u^\frac{1}{2}$

$\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}$

Chain Rule:

$d' = \frac{du}{dx} * \frac{dd}{du}$

$d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}$

$d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}$

$d' = \frac{2x - 5}{2\sqrt u}$

Substitute: $u = x^2 - 5x +9$

$d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}$

Next, is to minimize (by equating d' to 0)

$\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0$

Cross Multiply

$2x - 5 = 0$

Solve for x

$2x =5$

$x = \frac{5}{2}$

Substitute $x = \frac{5}{2}$ in $y = \sqrt x$

$y = \sqrt{\frac{5}{2}}$

Split

$y = \frac{\sqrt 5}{\sqrt 2}$

Rationalize

$y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$y = \frac{\sqrt {10}}{\sqrt 4}$

$y = \frac{\sqrt {10}}{2}$

Hence:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

3 0

3 years ago

What is 1.3742 rounded to the nearest tenth?

REY [17]

Answer:

1.4 that is the true answer

Step-by-step explanation:

go to the place right after the decimal and then look at the number next to it.if it is greater the 5 it goes up to 1.4 and it is

6 0

2 years ago

What is 6,400 in scientific notation

ch4aika [34]

The answer is 64*10^2

7 0

3 years ago

Read 2 more answers

Solve this question peasents nah jk lol

Zina [86]

v = √16 · √d

d = 300 ft

v = √16 · √300

v = √16 · √100 · √3

v = 4 · 10 · √3

<em>v = 40√3 ft/sec </em> <== simplified radical form

That's about 69.3 feet per sec, or 47.2 miles per hour.

5 0

2 years ago