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Law Incorporation [45]
1 year ago
13

Questions are in the picture

Mathematics
1 answer:
gtnhenbr [62]1 year ago
3 0

The closest point is (3.5, 1.9) and the distance is 1.96 units

<h3>How to determine the point and the distance?</h3>

The coordinate is given as:

(4, 0)

The equation of the function is

y = √x

The distance between two points is calculated using

d = √(x2 - x1)^2 + (y2 - y1)^2

So, we have the following points

(x1, y1) = (4, 0) and (x2, y2) = (x, 0)

This gives

d = √(x - 4)^2 + (√x - 0)^2

Evaluate the difference

d = √(x - 4)^2 + (√x)^2

Evaluate the exponent

d = √x^2 - 8x + 16 + x

Evaluate the like terms

d = √x^2 - 7x + 16

Next, we differentiate using a graphing calculator

d' = (2x - 7)/[2√(x^2 - 7x + 16)]

Set to 0

(2x - 7)/[2√(x^2 - 7x + 16)] = 0

Cross multiply

2x - 7 = 0

Add 7 to both sides

2x = 7

Divide by 2

x = 3.5

So, we have:

Substitute x = 3.5 in y = √x

y = √3.5

Evaluate

y = 1.9

So, the point is (3.5, 1.9)

The distance is then calculated as:

d = √(x2 - x1)^2 + (y2 - y1)^2

This gives

d = √(3.5 - 4)^2 + (1.9 - 0)^2

Evaluate

d = 1.96

Hence, the closest point is (3.5, 1.9) and the distance is 1.96 units

Read more about distance at:

brainly.com/question/23848540

#SPJ1

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elena-14-01-66 [18.8K]

Given:

The complex number is:

z=1+i\sqrt{3}

To find:

The argument of the given complex number.

Solution:

If a complex number is z=x+iy, then the argument of the complex number is:

\theta=\tan^{-1}\dfrac{y}{x}

We have,

z=1+i\sqrt{3}

Here, x=1 and y=\sqrt{3}. So, the argument of the given complex number is:

\theta =\tan^{-1}\dfrac{\sqrt{3}}{1}

\theta =\tan^{-1}\sqrt{3}

\theta =\tan^{-1}\left(\tan \dfrac{\pi}{3}\right)

\theta =\dfrac{\pi}{3}

Therefore, the argument of the given complex number is \theta =\dfrac{\pi}{3}.

6 0
3 years ago
8. Sam divided a rectangle into 8 congruent
S_A_V [24]

Sam divided a rectangle into 8 congruent rectangles that each have a area of 5 cm2. what is the area of the rectangle before it is divided?

Answer:

Area\ of\ the\ rectangle = 40\ cm^{2}

Step-by-step explanation:

Given:

Sam divided a rectangle into 8 congruent  rectangles that each have an area of 5\ cm^{2}

We need to find the area of the rectangle before Sam divided it.

The area of the rectangle before Sam divided is 8 times of the area of the congruent rectangles.

Area of the rectangle = 8\times (area\ of\ congruent\ rectangles)

Area of the congruent rectangle is 5\ cm^{2}

So the area of the rectangle is

Area of the rectangle = 8\times 5

Area of the rectangle = 40\ cm^{2}

Therefore the area of the rectangle before divided is 40\ cm^{2}

4 0
3 years ago
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