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3 years ago

15

When parking parallel, it is best to leave the curb side wheels: just touching the curb 24 to 30 inches from the curb 18 to 24 i

nches from the curb 6 to 18 inches from the curb?

1 answer:

gtnhenbr [62]3 years ago

6 0

You would have to be At most 1 ft

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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

7- H ,0 am An average persons heart beats about 103,680 times a day and solve an equation to ﬁnd about how many times me average

Mrac [35]

103680÷24=4320
4320÷60=72
=72times/minute

8 0

3 years ago

Help plzz <br> 2decimal places<br> 165 x 0.38²

allsm [11]

Answer:

23.83

Step-by-step explanation:

3 0

2 years ago

What is the better buy?

White raven [17]

Answer: Option B is the cheaper deal (the 12 batteries for $14.76)

===========================================================

Explanation:

For the first deal we can say

3 batteries = 4.80 dollars

3/3 batteries = 4.80/3 dollars .... divide both sides by 3

1 battery = 1.60 dollars

The unit price for the first deal is $1.60 per battery.

----------------------------------

For the second deal we could say

12 batteries = 14.76 dollars

12/12 batteries = 14.76/12 dollars .... divide both sides by 12

1 battery = 1.23 dollars

The unit price for the first deal is $1.23 per battery.

This is the cheaper deal.

----------------------------------

So in short, you're dividing the total cost over the number of items to get the unit price.

4 0

3 years ago

Read 2 more answers

A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it in half with a fence parallel

pogonyaev

3x +2y A =xy = 6,000,000 y = 6,000, 000/x L = 2x + 12,000,000/x 3- (12,000,000/x^2) = 0 3 = 12, 000,000/x^2 sqrt x^2 = sqrt 4,000,000 x = 2,000 and y = 3,000 <span>
</span>

8 0

3 years ago