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3 years ago

Which term is a perfect square of the root 3x4?

Mathematics

2 answers:

KiRa [710]3 years ago

5 0

Answer:

2√3

Step-by-step explanation:

√3x4 = √12 = 2√3

Leya [2.2K]3 years ago

4 0

Answer:

9x^8

Step-by-step explanation:

good luck!!

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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

What is the area of this figure? Enter your answer in the box. 8m 5 m 9m

Iteru [2.4K]

Answer:

314 feet

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

PLEASE HELP ILL GIVE MEDALS AND MARK BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!! NEEDS TO BE ALEGABRA 2 MEATHOD!!!!!!!!

mars1129 [50]

Hi there,
This is the original inequality equation:
$\frac{x}{x+1} \ \textless \ \frac{x}{x-1}$
So, we first need to find the critical points of equality, and we can do that by switching the less than sign to an equal sign.
$\frac{x}{x+1} = \frac{x}{x-1}$
Now, we multiply both sides by x + 1:
$x= \frac{x^{2} +x}{x-1}$
Then, we multiply both sides by x - 1:
$x^{2} -x= x^{2} +x$
Next, we subtract x² from both sides:
$-x=x$
After that, we solve for x. We do this by adding -x to both sides and dividing by 2. Doing so gives us x = 0, which is our first critical point. We need to find a few more critical points by testing x = -1 and x = 1. Here is how we do that:
x = −1 (Makes left denominator equal to 0)x = 1 (Makes right denominator equal to 0)Check intervals in between critical points. (Test values in the intervals to see if they work.)x <−1 (Doesn't work in original inequality)−1 < x <0 (Works in original inequality)0 < x < 1 (Doesn't work in original inequality)x > 1 (Works in original inequality)
Therefore, the answer to your query is -1 < x < 0 or x > 1. Hope this helps and have a phenomenal day!

4 0

3 years ago

Please answer. I will mark Brainliest

den301095 [7]

Statement: 1) Triangle ABC
2) 2x 3)x=52

Reason: I’m not sure but probably addition

4 0

3 years ago

U(-3,6), V(-8, 1), W(-3,1) 180° rotation about the origin

Ad libitum [116K]

Answer:

U'(3, -6), V'(8, -1), W'(3, -1)

Step-by-step explanation:

According to the 180°-rotation rule, you take the OPPOSITE of both the y-coordinate and x-coordinate:

Extended Rotation Rules

270°-clockwise rotation [90°-counterclockwise rotation] >> (x, y) → (-y, x)

270°-counterclockwise rotation [90°-clockwise rotation] >> (x, y) → (y, -x)

180°-rotation >> (x, y) → (-x, -y)

I am joyous to assist you anytime.

7 0

3 years ago

Which term is a perfect square of the root 3x4?​

Which term is a perfect square of the root 3x4?