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katen-ka-za [31]

2 years ago

14

PLEASE HELP!! if f(x)= 2x^2-11, find f(4)

2 answers:

Lemur [1.5K]2 years ago

4 0

Answer: f(4) = 21

Step-by-step explanation:

2(4)^2-11

4^2 = 16

2(16)-11

Multiply 2 and 16

32 - 11

Subtract

21

goldenfox [79]2 years ago

4 0

Answer:

21

Step-by-step explanation:

f(x)= 2x^2-11

Let x= 4

f(4)= 2*4^2-11

= 2 * 16 - 11

= 32 -11

21

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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

eden purchased a home for $156,200. The home appreciates about 4.5% each year. what is the value of the home after 17 years?

e-lub [12.9K]

Answer:

590,088

Step-by-step explanation:

So you divide 156,200 by 4.5 then once you have that times it bye the 17 years I think

6 0

2 years ago

Urrrrrrrrrrrrrrerrrrrr

Alenkasestr [34]

Answer:

answer = -12

Step-by-step explanation:

substitute y as -3 and z as 4

3(-3) - 2(4) + 5

-9-8+5

-17+5

-12

5 0

2 years ago

Read 2 more answers

Look at pic below... please do it.. need correct answer.. i will mrk brsinliest hurry.. need help..

galina1969 [7]

The answer to this question is B

5 0

3 years ago

Read 2 more answers

Which proportion could be used to determine if the figures represent a dilation? 2/3=5/8, 2/3=8/5, 2/8=5/3, or 2/8=3/5?

Maurinko [17]

Answer:

The answer is A. 2/3 =5/8

Step-by-step explanation:

5 0

3 years ago