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OverLord2011 [107]

2 years ago

13

Nonzero multiples of 12 and 15

1 answer:

Viefleur [7K]2 years ago

5 0

3 is a common multiple .. (3x4=12....3x5=15)

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Figure LMNP will be reflected across the y-axis. Place the point on the graph that represents

zimovet [89]

Answer:

If it's reflected on the y-axis, the answer for N would be (-2,-3).

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

PLEASE HELP THESE ARE MY ONLY POINT ;-; PLEASE

Zolol [24]

Answer:

a) max 12000 , min 0

b) no solution

c) pricing based on profit

Step-by-step explanation:

a) look at the parabola

b) there is more than one x (0)

c) the y intercepts represent his profit based on how much he priced the items at

3 0

2 years ago

The option for the first one is graph A or graph B

horrorfan [7]

First answer: Graph A

Second answer: E) Increase less

Graph A shows a flatter curve compared to B which is steeper. The steeper the curve, the faster the increase.

4 0

3 years ago

Write an equivalent expression by distributing the "-−" sign outside the parentheses:

charle [14.2K]

Answer:

6.6a+6b-7.1

Step-by-step explanation:

$-(-6.6a-6b)-7.1\\\\=-(-6.6a)-(-6b)-7.1\\\\=6.6a+6b-7.1$

7 0

2 years ago