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3 years ago

Which one is a scaled copy

Mathematics

1 answer:

Alexeev081 [22]3 years ago

3 0

Answer: D

Step-by-step explanation:

I believe it’s D because a scaled copy is similar to the original shape, but with different shapes. It might be C, but however in math, to make a scaled copy, you have to multiply length number with the same number. (Example: Length is 2, so the scaled copy is 4.)

I hope you have a good day.

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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

PLEASE HELP PICTURE SHOWN

Rainbow [258]

Your answer is B. 2
This is because to rationalise the denominator, we need to multiply it by (3 - √7), so we get:
(3 + √7)(3 - √7)
3 × 3 = 9
3 × √7 = 3√7
3 × -√7 = -3√7
√7 × -√7 = -7
So all in all you get 9 - 7 which is 2.

I hope this helps!

4 0

3 years ago

Read 2 more answers

A drink dispenser fills cups at a rate of 2 ounces per second. Adrain has 64 ounce cup that already contains 18 ounces of water.

diamong [38]

Answer:

23 seconds

Step-by-step explanation:

First, find out how many ounces left are needed to fill the water. Subtract the total, 64, by the already filled, 18. This should get you the answer of 46.

Since the dispenser fills 2 ounces per second, you need to divide the number 46 by 2 in order to find the amount of time in seconds it would take to fill the rest of the cup.

Therefore, your answer is 23 seconds.

Hope this helps!

3 0

3 years ago

Read 2 more answers

Please help it would be much appreciated!!

AlekseyPX

Answer:

a) P) 0.25 = 1/4 both

b) P) 0.75 = 3/4 one

c) P) 0.25 = 1/4 none

Step-by-step explanation: