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3 years ago

14

Nicholas wrote the steps below to simplify the fraction 20/30 divided the numerator and denominator of 20/30 by 2 to write the f

raction in simplest form explain and correct the error that each student made

1 answer:

iris [78.8K]3 years ago

7 0

Answer:

The answer is 2/3

Step-by-step explanation:

20 divided with 10

--

30 divideded with 10

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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

If your car can travel 20 miles on 1 gallon of fuel how many litres were used to travel 130 miles? Step by step

Bezzdna [24]

Answer:2600 Gallons

Step-by-step explanation: You first have to take 130 and times it by 20 then times it by 1. make sure you add labels

3 0

3 years ago

WILL GIVE BRAINLIEST

Andrei [34K]

Answer:

Hello, the answer would be A. ∠2

Step-by-step explanation:

Hope this helps!

Brainliest please.

6 0

3 years ago

Photo above need help

Ira Lisetskai [31]

Answer:

m = 0

Step-by-step explanation:

<u>If two lines are parallel, their slopes are equal. </u>

The slope of x - axis is 0

(why?)

because, slope of a line is given by

$\boxed{\mathsf{slope\:of\:a\:line=tan \theta}}$

Θ is the angle made by the line with the x- axis.

Here, the line in question is the x- axis itself, and every line makes an angle of 0° with itself.

=> Θ = 0

=> tan Θ = 0

=> slope = 0

and the line in blue is parallel to the X- axis, therefore, it's slope is also 0

(also, a line makes an angle of 0° with the line it's parallel to)

<u> </u>

$\mathfrak{\overline{There\:You\:Are!}}$

6 0

2 years ago

Read 2 more answers

Which statement is false?

Karolina [17]

Answer:

D is the correct answer

Step-by-step explanation:

Not all rectangles are squares.

4 0

3 years ago

Read 2 more answers