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3 years ago

11

How should the decimal point in 52.48 be moved to determine the product 52.48×105 ?

1 answer:

tensa zangetsu [6.8K]3 years ago

4 0

Answer:

5510.4

Step-by-step explanation:

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It takes Prakash 2 1/2 hours to paint a medium sized room. If he can work 50 minutes each day, how many days will it take to com

Aleksandr-060686 [28]

60 min in one hour so 60+60+30=150.
150 divided 50 mins = 3 days (50+50+50=150)

3 0

3 years ago

You decide to go to a summer camp and you have to choose five activities to do each day. Your choices include indoor activities

ehidna [41]

Answer: you would have to do alot of stuuff

Step-by-step explanation:

5 0

3 years ago

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

Brian pays £465.98 a year on his car insurance.

denpristay [2]

Answer:

<em>£ 449.20</em>

Step-by-step explanation:

We have to reduce 465.98 by 3.6%

Firstly, lets convert the percentage to decimal by dividing by 100. So we have:

3.6/100 = 0.036

Lets find 3.6% of 465.98

That is:

0.036 * 465.98 = 16.77528

This is the "LESSENED" amount. So the final amount would be:

465.98 - 16.77528 = 449.20472

<em>Rounding to 2 decimal places, £ 449.20</em>

8 0

3 years ago

I'll give brainlest to first correct answer!!!

zvonat [6]

Answer:

I think there both negative but I'm not sure

Step-by-step explanation:

if one is a positive and one is a negative then reflect over the y axis they should both turn negative

6 0

2 years ago