Ask question

Ask question

All categories

jek_recluse [69]

3 years ago

12

The Population of a town was

1 answer:

aliina [53]3 years ago

7 0

Answer:

33.3%

Step-by-step explanation:

Step one:

given data

Initial population (1980)= 12000

Final population(1990)= 16000

change in population= 16000-12000= 4000

Step two:

% increase= change in population/initail population *100

%increase= 4000/12000*100

%increase= 0.333*100

% increase= 33.3%

You might be interested in

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

bixtya [17]

Answer:

First day: 45x +20y = 875

Second day: 25x + 40y = 775

Adult ticket price: $15

Step-by-step explanation:

See paper attached. (:

8 0

3 years ago

Lily spent 1/6 of her free time practicing soccer and 3 of her

melomori [17]

Answer:

She spent 4/6 of her free time.

Step-by-step explanation:

1/6 + 3/6 = 4/6

4 0

3 years ago

Will mark brainliest, 60 points

il63 [147K]

Answer:

21 C

22 B

23 169

Step-by-step explanation:

21 3m mean 3 times a certain number

22 the negative make the 4 go negative and the -5 positive

23 i did 5^2-4^2= 9

then 6^2 divided by 9+9= 13 i took the 9 from the 5^2 problem then divided it by 6^2

then 13 x 13 = 169

8 0

3 years ago

How to solve Y = eight, X =2 and direct variation

rodikova [14]

Answer:

The answer is k = 4.

Step-by-step explanation:

Given:

Y = 8 and X = 2.

Now, to solve direct variation.

$y$ direct with $x$ .

Now, using equation to solve direct variation:

$y=kx$

$8=k\times 2$

Dividing both sides by 2 we get:

$4=k$ .

Therefore, the answer is k = 4.

5 0

3 years ago