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Answer:

[tex]\frac{1}{2\sqrt{5} }[/tex]

Step-by-step explanation:

Let, [tex]\text{sin}^{-1}(\frac{x}{6})[/tex] = y

sin(y) = [tex]\frac{x}{6}[/tex]

[tex]\frac{d}{dx}\text{sin(y)}=\frac{d}{dx}(\frac{x}{6})[/tex]

[tex]\frac{d}{dx}\text{sin(y)}=\frac{1}{6}[/tex]

[tex]\frac{d}{dx}\text{sin(y)}=\text{cos}(y)\frac{dy}{dx}[/tex] ---------(1)

[tex]\frac{1}{6}=\text{cos}(y)\frac{dy}{dx}[/tex]

[tex]\frac{dy}{dx}=\frac{1}{6\text{cos(y)}}[/tex]

cos(y) = [tex]\sqrt{1-\text{sin}^{2}(y) }[/tex]

          = [tex]\sqrt{1-(\frac{x}{6})^2}[/tex]

          = [tex]\sqrt{1-(\frac{x^2}{36})}[/tex]

Therefore, from equation (1),

[tex]\frac{dy}{dx}=\frac{1}{6\sqrt{1-\frac{x^2}{36}}}[/tex]

Or [tex]\frac{d}{dx}[\text{sin}^{-1}(\frac{x}{6})]=\frac{1}{6\sqrt{1-\frac{x^2}{36}}}[/tex]

At x = 4,

[tex]\frac{d}{dx}[\text{sin}^{-1}(\frac{4}{6})]=\frac{1}{6\sqrt{1-\frac{4^2}{36}}}[/tex]

[tex]\frac{d}{dx}[\text{sin}^{-1}(\frac{2}{3})]=\frac{1}{6\sqrt{1-\frac{16}{36}}}[/tex]

                   [tex]=\frac{1}{6\sqrt{\frac{36-16}{36}}}[/tex]

                   [tex]=\frac{1}{6\sqrt{\frac{20}{36} }}[/tex]

                   [tex]=\frac{1}{\sqrt{20}}[/tex]

                   [tex]=\frac{1}{2\sqrt{5}}[/tex]

Answer: 3y is the coefficient.

Step-by-step explanation: A coefficient is numerical or constant quantity placed before and multiplying the variable in an algebraic expression. Or, to put it simpler, a coefficient is a number with an variable next to it.

plzit explain question the get really don't I

Answer:

The answer is

[tex]y = - 3x + 1[/tex]

Step-by-step explanation:

❃Incase you forgot what the linear equation formula is ☟

[tex]y = mx + b[/tex]

❃Incase you also forgot, The is what the slope formula is ☟

[tex]m = \frac{y_2 - y_1 }{x_2 - x_1} [/tex]

➊ First: We are going to be solving for the slope.

[tex]m = \frac{ - 8 - 1}{3 - 0} = \frac{ - 9}{ \: \: \: 3} = - 3[/tex]

➋Second: We find the y-intercept.

[tex]y = mx + b \\ - 8 = - 3(3) + b \\ - 8 = - 9 + b \\ \frac{ + 9 = + 9 \: \: \: \: \: }{1 = b} [/tex]

➌Third: Plug in.

[tex]y = - 3x + 1[/tex]

Answer:

A = 31.68°

B = 109.45°

C = 38.92°

Step-by-step explanation:

Law of cosine: cosA = (b²+c²-a²) / 2bc

a = x = 10        b = 18        c = 12

cosA = (18² + 12² - 10²) / 2*18*12 = 368/432 = 0.851

A = 31.68

cosB = (10² + 12² - 18²) / 2*10*12 = -80/240 = -1/3 = -0.333

B = 109.45

cosC = (10² + 18² - 12²) / 2*10*18 = 280/360 = 0.778

C = 38.92

check: A+B+C = 31.68 + 109.45 + 38.92 =180.05 ≈ 80°

Wish this help!!

Answer:

[tex]x = \frac{ \sqrt{6} }{2} [/tex]

[tex]y = \frac{3 \sqrt{2} }{2} [/tex]

Step-by-step explanation:

[tex] \sin(theta) = \frac{opposite}{hypotenuse} [/tex]

[tex] \cos(theta) = \frac{adjacent}{hypotenuse} [/tex]

[tex] \tan(theta) = \frac{opposite}{adjacent} [/tex]

theta = 30°

hypotenuse = √6

opposite = x

adjacent = y

[tex] \sin(theta) = \frac{opposite}{hypotenuse} [/tex]

[tex] \sin(30) = \frac{x}{ \sqrt{6} } [/tex]

[tex] \sin(30) \times \sqrt{6} = x[/tex]

[tex] \frac{ \sqrt{6} }{2} = x[/tex]

[tex]x = \frac{ \sqrt{6} }{2} [/tex]

[tex] \cos(theta) = \frac{adjacent}{hypotenuse} [/tex]

[tex] \cos(30) = \frac{y}{ \sqrt{6} } [/tex]

[tex] \cos(30) \times \sqrt{6} = y[/tex]

[tex] \frac{3 \sqrt{2} }{2} = y[/tex]

[tex]y = \frac{3 \sqrt{2} }{2} [/tex]

Answer :

The probability that the coin will land on an area that is white is [tex]\dfrac{1}{2}[/tex]

Explanation :

Given that,

A 7-by-7 foot rug is shown in figure.

Suppose, all parts are equal.

The area of rug is

[tex]A_{r}=7\times7[/tex]

Area of one part of rug is

[tex]A'_{1}=3.5\times3.5[/tex]

We need to calculate the probability that the coin will land on an area that is white

Using formula of probability

[tex]P=\dfrac{Area\of\ white\ part}{Area\of\ total\ rug}[/tex]

Put the value into the formula

[tex]P=\dfrac{(3.5\times3.5)+(3.5\times3.5)}{7\times7}[/tex]

[tex]P=\dfrac{2\times3.5\times3.5}{7\times7}[/tex]

[tex]P=\dfrac{1}{2}[/tex]

Hence, The probability that the coin will land on an area that is white is [tex]\dfrac{1}{2}[/tex].

Answer:

F.-2...........................................

Answer:

$150

Step-by-step explanation: 11.25 divided by tax rate of 7.5 % equals 150

Answer:

16.

x<5

hope this helps!!:)

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Lmk if this was the right way to do it or not lol

Answer: 23 Yes

24. NO

25. Yes

26 yes

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

took the test

Answer:

it takes him 7/2 thirds to do 12 to find his average speed

Step-by-step explanation:

Well, if we use the Associative Property, we can switch around the positions of the 11, which is out of the parentheses. So, what we do is we put 11 and 3 into parentheses and r out of the parentheses, which makes:

r + (11 + 3)

So, now we solve the parentheses:

r + (14)

And finally, remove the parentheses. So, therefore, the answer is r + 14.

Answer:

300 tiles.

Step-by-step explanation:

First, you divide 195 by 65 to get what 1% is. 195/65 = 3. 1% is 3. Then you multiply 3x100 because there is 100%. So that is 300 and that's why there are 300 tiles in total. Hope this helped! :)

Answer:

A)ones

Step-by-step explanation:

a)How many days are there in one week?It is measured in the ones.

A.ones

Answer:

20

Step-by-step explanation:

4 * (2a − 1)

Let a=3

4 * (2*3 − 1)

Simplify inside the parentheses first

4 * (6 − 1)

4 * (5)

20

Answer:

Step-by-step explanation:

1)  5

2)  63

????

Answer:

Step-by-step explanation:

75+[(75*4)/100]=75+3=78

Answer: (5,3)

Step-by-step explanation:

Answer:

One-fifth plus one-fifth plus one-fifth plus one-fifth

Step-by-step explanation:

1/5 + 1/5 + 1/5 + 1/5 = 4/5 = 4 x 1/5

Answer:

5 'v'

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

The answer is A because 11+14=25 and you multiply 25 by 11 to see it equals 275.

Answer:

k = 2

Step-by-step explanation:

Based on the right triangle altitude theorem, thus:

4 = √(k*8)

Square both sides

4² = k*8

16 = 8k

Divide both sides by 8

16/8 = 8k/8

2 = k

k = 2