All Answers 352764 Answers

The area of the circle can be found, using \(\pi r^2\)

Since \(\frac{3}{4}\) is the diameter, then the radius should be \(\frac{1}{2}*\frac{3}{4}=\frac{3}{8}\)

Plugging the value into the formula, we have: \(\pi\frac{3}{8}^2=3.14*\frac{9}{64}\)

But, since the answer box wants the fraction, we get: \(\boxed{\frac{9}{64}}\)

See the answer here:

https://web2.0calc.com/questions/geometry-help-4-15-18

Sin(x) = 11.8 / 12

Sin(x) =0.98333.......

x = arcsin(0.98333.....)

x =79.52 degrees. Since the angle is greater than 75 degrees, the ladder is NOT safe at that angle.

3 x 3 = 9 inches - length of perforated crease on 1 side

9 x 2 = 18 inches - length of 3 x 3 perforated creases

6 x 6 = 36 - Length of perforated crease on 1 side

35 x 2 = 72 inches - Length of perforated creases on 6 x 6 sheet.

Area of Sector = θ/2 × r^2   (when θ is in radians)

A =[5pi/2] / 2 x 4^2

A =[5pi/4] x 16

A =80pi / 4

A =20pi

A =62.8 ft^2.

Area of circle = Pi x r^2

                      = Pi x [(3/4) / 2]^2

                      = Pi x [3/8]^2

                      =9/64Pi in^2

If you need anymore help let me know. I will be happy to help you with (or do your) work

The answer is the measure of ∠ABC is 58°.

It's the same length of ACB. 

Thank you!

It gives this answer using "Logarithmic Differentiation", but does not give step by step answer. Sorry about that:

Log(y'(x) = 2e^(x^2) x^(3/2) (x^2 + 1)^10 + (e^(x^2) (x^2 + 1)^10)/(2 sqrt(x)) + 20 e^(x^2) x^(3/2) (x^2 + 1)^9). Note: it uses natural logs.

in decimal form im pretty positive it would be .30 or .3

now in percentage form the answer would be 30%

if you want it in fraction form it would be 30/100 or 3/10

a fraction?

Arc Length = (θ × π/180) × r 
(when θ is in degrees)

Arc Length =(45 x pi/180) x 6 =6/4pi = 3/2pi - inches.

This may be the right answer; however, the instructions say to use logarithmic differentation.  If anyone knows how to solve for the answer usin logarithmic differentation, I would really appreciate it.  Thanks.

243 becomes 324

Take sqrt(324) = 18, then becomes:

81

Take the sqrt(81) = 9 - the original number that Thea started with.

Check:

9^2 = 81 this becomes:

18^2 =324 and this becomes:

243

Thats pretty cool i think mines better

https://gyazo.com/f148d753b8b48713cad5e440324b08ff

It uses implicit differentiation:

d/dx(y) = d/dx({e^(x^2) sqrt(x) (1 + x^2)^10})

The derivative of y is y'(x):

y'(x) = d/dx({e^(x^2) sqrt(x) (1 + x^2)^10})

Using the chain rule, d/dx({e^(x^2) sqrt(x) (x^2 + 1)^10}) = ( du)/( du) ( du)/( dx), where u = e^(x^2) sqrt(x) (x^2 + 1)^10 and d/( du)({u}) = {1}:

y'(x) = {d/dx(e^(x^2) sqrt(x) (1 + x^2)^10)}

Use the product rule, d/dx(u v) = v ( du)/( dx) + u ( dv)/( dx), where u = e^(x^2) and v = sqrt(x) (x^2 + 1)^10:

y'(x) = {sqrt(x) (x^2 + 1)^10 d/dx(e^(x^2)) + e^(x^2) d/dx(sqrt(x) (1 + x^2)^10)}

Using the chain rule, d/dx(e^(x^2)) = ( d e^u)/( du) ( du)/( dx), where u = x^2 and d/( du)(e^u) = e^u:

y'(x) = {e^(x^2) (d/dx(sqrt(x) (1 + x^2)^10)) + e^(x^2) d/dx(x^2) sqrt(x) (1 + x^2)^10}

Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 2.

d/dx(x^2) = 2 x:

y'(x) = {e^(x^2) (d/dx(sqrt(x) (1 + x^2)^10)) + 2 x e^(x^2) sqrt(x) (1 + x^2)^10}

Simplify the expression:

y'(x) = {2 e^(x^2) x^(3/2) (1 + x^2)^10 + e^(x^2) (d/dx(sqrt(x) (1 + x^2)^10))}

Use the product rule, d/dx(u v) = v ( du)/( dx) + u ( dv)/( dx), where u = sqrt(x) and v = (x^2 + 1)^10:

y'(x) = {2 e^(x^2) x^(3/2) (1 + x^2)^10 + (x^2 + 1)^10 d/dx(sqrt(x)) + sqrt(x) d/dx((1 + x^2)^10) e^(x^2)}

Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 1/2.

d/dx(sqrt(x)) = d/dx(x^(1/2)) = x^(-1/2)/2:

y'(x) = {2 e^(x^2) x^(3/2) (1 + x^2)^10 + e^(x^2) (sqrt(x) (d/dx((1 + x^2)^10)) + 1/(2 sqrt(x)) (1 + x^2)^10)}

Using the chain rule, d/dx((x^2 + 1)^10) = ( du^10)/( du) ( du)/( dx), where u = x^2 + 1 and d/( du)(u^10) = 10 u^9:

y'(x) = {2 e^(x^2) x^(3/2) (1 + x^2)^10 + e^(x^2) ((1 + x^2)^10/(2 sqrt(x)) + 10 (x^2 + 1)^9 d/dx(1 + x^2) sqrt(x))}

Differentiate the sum term by term:

y'(x) = {2 e^(x^2) x^(3/2) (1 + x^2)^10 + e^(x^2) ((1 + x^2)^10/(2 sqrt(x)) + d/dx(1) + d/dx(x^2) 10 sqrt(x) (1 + x^2)^9)}

The derivative of 1 is zero:

y'(x) = {2 e^(x^2) x^(3/2) (1 + x^2)^10 + e^(x^2) ((1 + x^2)^10/(2 sqrt(x)) + 10 sqrt(x) (1 + x^2)^9 (d/dx(x^2) + 0))}

Simplify the expression:

y'(x) = {2 e^(x^2) x^(3/2) (1 + x^2)^10 + e^(x^2) ((1 + x^2)^10/(2 sqrt(x)) + 10 sqrt(x) (1 + x^2)^9 (d/dx(x^2)))}

Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 2.

d/dx(x^2) = 2 x:

y'(x) = {2 e^(x^2) x^(3/2) (1 + x^2)^10 + e^(x^2) ((1 + x^2)^10/(2 sqrt(x)) + 2 x 10 sqrt(x) (1 + x^2)^9)}

Simplify the expression:

| y'(x) = {2e^(x^2) x^(3/2) (1 + x^2)^10 + e^(x^2) (20 x^(3/2) (1 + x^2)^9 + (1 + x^2)^10/(2 sqrt(x)))}  [Courtesy of Mathematica 11 Home Edition]

the answer is either 5 or 6

I suspect the 6 should be \(\theta\), in which case we have: \(f(\theta)=10(\cos\theta+i\sin\theta)\)

This is already in rectangular form!  In polar form it is: \(f(\theta)=10e^{i\theta}\)

CPhill made a small mistake in calculating the volume of the frustrum. It should be as follows:

V =1/3*Pi*Height*[R^2 + r^2 + R*r]

V =1/3*Pi*6[9^2 + 1^2 +(9*1) ]

V =1/3*Pi*6[81 + 1 + 9]

V =1/3*Pi*6[ 91]

V =1/3*Pi* 546

V = 182Pi - which is the correct answer.

They don't copy and paste so well, but here is a link to 3 of them

https://www.mathisfunforum.com/viewtopic.php?pid=363216

:)

Can you copy and paste the other solution so that they can be compared to see where the mistake is?

Just checking in, I see this question has been answered before only with a different answer of 182pi.  As far as I can tell the questions are identical, do you know why the answers are different?