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3 years ago

Trent is fishing from a pier.

Mathematics

1 answer:

iren [92.7K]3 years ago

3 0

Answer:

Trent is right because if you subtract 53 and 3/4 by 12 2/3 equals to 41 and 1/12.

Step-by-step explanation:

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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

The policy of the Kauderman's pawnshop is to lend up to 30% of the value of borrower's collateral. Tommy wants to use a pair of

lubasha [3.4K]

Answer:

30/100×$1500 = $450

Step-by-step explanation:

Tommy needs total capital of $1500 and he wants to lend 30% of loan from kaunderman, which is calculated as above.

8 0

3 years ago

What is the final amount of $70.00 that is put into a savings account with 16% interest rate for 25 years, if the interest is co

mylen [45]

PV × (1 + r/n)∧nt = FV
$70.00 × (1 + .16/4)∧4X25 = FV
$70.00 × (1 + .04)∧100 = FV
$70.00 × 50.50 = FV
$3535 =FV
The final amount is $3535

7 0

4 years ago

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Rachel tells Jonah that she can turn a square, but he won’t be able to tell that it was turned after she is finished turning it.

Dmitry [639]

ANSWER: it’s a square. All sides will look the same after turning because all sides LOOK THE SAME lol.

5 0

3 years ago

.question 9a data analyst is using statistical measures to get a better understanding of their data. what function can they use

MakcuM [25]

Planning, designing, gathering data, analyzing, creating relevant interpretations, and publishing the research findings are all statistical approaches that go into conducting a study.

The statistical analysis lends meaning to the abstract numbers, giving the data some life. Only when appropriate statistical tests are applied will the results and inferences be accurate. Science's field of statistics deals with gathering, organizing, analyzing, and extrapolating data from samples to the entire population. This necessitates the use of an acceptable statistical test, an adequate study design, and an appropriate study sample selection. However, if we want additional information about these, a consulting company may be able to assist us. we will benefit more from Silver Lake Consulting for our project.

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brainly.com/question/23091366

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6 0

1 year ago