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3 years ago

8

What is the height of a cylinder with a volume of 304 x cubic inches and a radius of 8 inches? Round to the nearest tenth of an

1 answer:

andreyandreev [35.5K]3 years ago

4 0

Answer:

1.5 inches

Step-by-step explanation:

V=pir^2h

304=pi8^2h

pi64h=304

pih=4.75

h=1.51197195937

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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

BRAINLIEST ASAP! PLEASE HELP ME :)

Irina-Kira [14]

Answer:

○ $\displaystyle 25\%$

Step-by-step explanation:

3 → 13 − 16

$\displaystyle \frac{Number\:of\:desired\:[favourable]\:outcomes}{Total\:number\:of\:possible\:outcomes} \\ \\ \frac{3}{12} = \frac{1}{4} = 25\%$

I am joyous to assist you anytime.

4 0

3 years ago

Kennedy has a gross income of $95,000. What is her total tax due?

ki77a [65]

Total tax due Answer: $27,000.

3 0

2 years ago

The table shows the number of diagonals that can be drawn from one vertex in polygon. Write an equation in function notation for

Reil [10]

Answer:

y = x - 3; 9 diagonals

Step-by-step explanation:

Find the equation: y = x - 3

Plug in 12: y = 12 -3

Solve: y = 9

9 diagonals

Hope this helps! Plz mark brainliest

3 0

2 years ago

Write two and forty-two thousandths in decimal notation.<br> please please

dem82 [27]

It’s 2.042

Have a great day! :D

8 0

3 years ago

Read 2 more answers