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3 years ago

A multivitamin tablet contains 18.5 mg of calcium. How much

Mathematics

1 answer:

Galina-37 [17]3 years ago

4 0

Answer:

740 mg of calcium is the correct answer

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Prove the formula for (d/dx)(cos−1(x)) by the same method as for (d/dx)(sin−1(x)). Let y = cos−1(x). Then cos(y) = and 0 ≤ y ≤ π

gtnhenbr [62]

Answer:

$\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }$

Step-by-step explanation:

Given the differential (d/dx)(cos−1(x)), to find the equivalent formula we will differentiate the inverse function using chain rule as shown below;

let;

$y = cos^{-1} x \\\\taking \ cos\ of\ both\ sides\\\\cosy = cos(cos^{-1} x)\\\\cosy = x\\\\x = cosy\\\\\frac{dx}{dy} = -siny\\$

$\frac{dy}{dx} = \frac{-1}{sin y} \\\\from\ trigonometry\ identity,\ sin^{2} x+cos^{2}x = 1\\sinx = \sqrt{1-cos^{2} x}$

Therefore;

$\frac{dy}{dx} = \frac{-1}{\sqrt{1-cos^{2}y } }$

Since x = cos y from the above substitute;

$\frac{dy}{dx} = \frac{-1}{\sqrt{1-x^{2}} }$

Hence, $\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }$ gives the required proof

5 0

4 years ago

An inlet pipe on a swimming pool can be used to fill the pool in 2020 hours. The drain pipe can be used to empty the pool in 212

boyakko [2]

Answer:

If the pool is 2/3 filled and then the inlet pipe and drain pipe are opened, it will take 140 hours to fill the pool

Step-by-step explanation:

An inlet pipe can fill the pool in hours = 20

Inlet pipe 1 hour work = $\frac{1}{20}$

A drain pipe can empty the pool in 21 hours

Drain pipe 1 hour work = $\frac{1}{21}$

Inlet pipe and drain pipe 1 hour together work = $\frac{1}{20}-\frac{1}{21}=\frac{1}{420}$

Now we are given that the pool is 2/3 filled

So, remaining portion to be filled = $1 - \frac{2}{3} = \frac{1}{3}$

So, Inlet pipe and drain pipe fill $\frac{1}{420}$ in hours = 1

So, they can fill 1/3 in hours = $\frac{1}{\frac{1}{420}} \times \frac{1}{3} =140 hours$

Hence If the pool is 2/3 filled and then the inlet pipe and drain pipe are opened, it will take 140 hours to fill the pool

6 0

3 years ago

Madison is thinking of a number.She states that the sum of her number , n,and 2/7,is equal to 3/4. write an equation that repres

zhannawk [14.2K]

Answer:

Step-by-step explanation:

If it has really helped u plz don't forget to thank me plz...

3 0

3 years ago

Please help asappp worth 20

Naily [24]

Answer:

Step-by-step explanation:

angles 1 and 2 are congruent, the lines in each side of the shape prove this.

another way to solve if you are not sure is to subtract all of the numbers from 360. all quadrilaterals equal 360 degrees, so if you subtract each of the three angles from 360, you will be left with the last angle.

360-120-44-98=98

5 0

3 years ago

Read 2 more answers

You move down 6 units. You end at (10, 4). Where did you start?

Alexandra [31]

Answer:

(10,10)

Step-by-step explanation:

coordinates are (x,y)

x is horizontal(left and right), y is vertical (up and down)

going down 6 means subtracting 6 from the second number

lets reverse that to go up and add 6 back

4+6=10

so the original point was (10,10)

8 0

3 years ago

Read 2 more answers