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4 years ago

differentiate please.. y= √x +6 ÷ √x-6

1 answer:

4 0

$\bf y=\cfrac{\sqrt{x}+6}{\sqrt{x}-6}\implies \cfrac{dy}{dx}=\stackrel{quotient~rule}{\cfrac{\frac{1}{2}x^{-\frac{1}{2}}(\sqrt{x-6})~~-~~(\sqrt{x}+6)\frac{1}{2}x^{-\frac{1}{2}}}{(\sqrt{x}-6)^2}}$

$\bf \cfrac{dy}{dx}=\cfrac{\frac{1}{2}x^{-\frac{1}{2}}~(\underline{\sqrt{x}}-6~-~\underline{\sqrt{x}}-6)}{(\sqrt{x}-6)^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{1}{2}x^{-\frac{1}{2}}(-12)}{(\sqrt{x}-6)^2}
\\\\\\
\cfrac{dy}{dx}=\cfrac{\frac{-12}{2\sqrt{x}}}{(\sqrt{x}-6)^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{-6}{\sqrt{x}}}{(\sqrt{x}-6)^2}\implies 
\cfrac{dy}{dx}=\cfrac{-6}{\sqrt{x}(\sqrt{x}-6)^2}$

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Which of the following gives all of the sets that contain sqare root 9

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Answer:

4. the set of all natural numbers, the set of all whole numbers, the set of all integers, the set of all rational numbers, and the set of all real numbers

Step-by-step explanation:

√9 = 3

3 is every kind of number <em>except irrational</em>. It belongs to the sets of ...

natural numbers
whole numbers
integers
rational numbers
real numbers

6 0

4 years ago

A triangle has a hypotenuse that is 60 inches, and the length of one of its legs is 36 inches. What is the length, in inches, of

vodka [1.7K]

Answer:

Step-by-step explanation:

think of the a squared plus b squared equals c squared. plug in the 36 in either b or a. then plug in the 60 in c's spot. solve and get 48. you can check the answer by solving 48 squared plus 36 squared equals 60 squared. both sides are equal and both come out to be the 3600

4 0

3 years ago

Please help me thanks...

skad [1K]

144.44 in² is the closest amount of paper she will use to wrap the gift.

Solution:

The given net is the shape of the cylinder.

Diameter of the circle = 4 in

Radius of the circle = 4 ÷ 2 = 2 in

Width of the container = 10.5 in

Length of the container is same as the circumference of the circle.

Area of the circle = $\pi r^2$

= $3.14\times 2^2$

= 12.56 in²

Area of the 2 circles = 2 × 12.56 = 25.12 in²

Area of the rectangle = circumference × height

= $2 \pi r\times h$

= $2 \times 3.14 \times 2\times 10.5$

= 131.88 in²

Area of the net of the container

= Area of the circles + Area of the rectangle

= 12.56 in² + 131.88 in²

= 144.44 in²

Area of the net of the container = 144.44 in²

Hence 144.44 in² is the closest amount of paper she will use to wrap the gift.

8 0

3 years ago

If a game consists of picking a number from a bag of beans numbered 2, 2, 3, 4, and 5 and flipping a coin, which probabilities a

Semenov [28]

The true statement is (d) none of the above

<h3>Missing information</h3>

I. P(3 and tail)

II. P(even and head)

III .P(odd and head)

<h3>How to determine the equivalent probabilities?</h3>

We start by calculating each probability

There is only one 3 in the 5 numbers.

So:

P(3) = 1/5

The probability of a tail in a coin is:

P(Coin) = 1/2

So, we have:

P(3 and tail) = 1/5 * 1/2

P(3 and tail) = 1/10

There are three even numbers in the 5 numbers.

So:

P(even) = 3/5

The probability of a head in a coin is:

P(head) = 1/2

So, we have:

P(even and head) = 3/5 * 1/2

P(even and head) = 3/10

There are two odd numbers in the 5 numbers.

So:

P(odd) = 2/5

The probability of a head in a coin is:

P(head) = 1/2

So, we have:

P(odd and head) = 2/5 * 1/2

P(even and head) = 1/5

By comparing the results, none of the probabilities are equal.

Hence, the true statement is (d) none of the above

﻿﻿﻿differentiate please.. ﻿y= √x +6 ÷ √x-6

differentiate please.. y= √x +6 ÷ √x-6