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Feliz [49]
3 years ago
5

Refer to the question below:

Mathematics
1 answer:
irakobra [83]3 years ago
7 0
∛(2x + 5) - 3 = 0
Add 3 to both sides
∛(2x + 5) = 3
Cube both sides
2x + 5 = 27
Subtract 5 from both sides
2x = 22
Divide both sides by 2
x=11
There's your answer. Have an awesome day! :)
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Anyone please???????
leva [86]

Answer:

\boxed{\sf B)\: x=\sqrt{17}}

Step-by-step explanation:

<u>Use the Pythagorean Theorem</u>

The equation for the Pythagorean Theorem is \tt a^2+b^2=c^2

* a and b are the lengths of the legs, and c is the hypotenuse.*

(To know which side is the hypotenuse look at longest side which is across the right angle).

a= x, b=8, c=9

\sf a^2+b^2=c^2

Let's Plug in the side lengths:

\sf x^2+8^2=9^2

Evaluate 8^2 and 9^2:

\sf x^2+64=81

Subtract 64 from both sides:

\sf x^2+64-64=81-64

\sf x^2=17

Take the square root of both sides:

\sf x=\sqrt{17}

___________________________

5 0
2 years ago
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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
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Genrish500 [490]

9514 1404 393

Answer:

  r = ±√47

Step-by-step explanation:

  -7r^2 = -329 . . . . given

  r^2 = 47 . . . . . divide both sides by -7 (multiplication property of equality)

  r = ±√47 . . . .  square root both sides (square root property of equality)

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2 years ago
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Helga [31]

Answer:

6%

Step-by-step explanation:

I asked this same exact question, no one got the right answer, so I just guessed, and what do you know, I got the answer right! So here you go.

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sergiy2304 [10]

Answer: Stephanie read more than 7 books because 8 points for 9 books each is equal to 72 points, which is the total amount of books she read.

Step-by-step explanation:

72 ÷ 8 × 9

x = 9

Hope this helped! :D

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2 years ago
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