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3 years ago

14

Martin lifted weights in the gym, Monday thru Friday, for 20 weeks. each day he did 25 repetitions. how many repetitions did he

do over the course of 20 weeks? then round the answer to the nearest thousand.

1 answer:

Ivan3 years ago

8 0

Answer:

3500

Step-by-step explanation:

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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

Can you help with a please on 46

valentina_108 [34]

3/5
Thats if u devide 9 by 3 and 15 by 5

5 0

3 years ago

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What's the area of a circle with a circumference of 10π

Gnesinka [82]

C=10pi
C=2(r)pi so r=5
A=pi(r)^2
so A=pi(5)^2

A=25pi

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3 years ago

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I need help with number 12!!

elixir [45]

Answer:

(4x + 2y)mi

Step-by-step explanation:

Check attachment

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3 years ago

Which inequality is shown in this graph? (0, 2) (-1,-2)

Juli2301 [7.4K]

Answer:

D) y = 4x + 2

Step-by-step explanation:

<u><em>Explanation</em></u>:-

Given ( 0, 2) ( -1 , -2 )

Given in equalities y = 4x + 2

put point (0,2) in equation y = 4x +2

2 = 4(0) +2

2 = 2

Therefore satisfies the point (0,2) equation y = 4x +2

put point (-1,-2) in equation y = 4x +2

-2 = 4(-1)+2

-2 = -2

Therefore satisfies the point (-1,-2) equation y = 4x +2

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3 years ago