61/100 in expanded form

If a bag contains 4 blue marbles, 8 red marbles, and 2 green marbles, what is the probability of pickibg a marble that is nit gr

SashulF [63]

The probability is 85.71%

7 0

3 years ago

Find the derivative dy, dx for y equals the quotient of the quantity x cubed minus 5 times x and the quantity x squared minus 1.

Elza [17]

Using the quotient rule

dy/dx = (x^-1) * (3x^2 -5 ) - (x^3 - 5x) * 2x
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(x^2 - 1)^2

You are correct

7 0

3 years ago

Let C be between D and E. Solve for x DC = 5x + 8 CE = 3x + 5 DE = 61

morpeh [17]

DE/2 = 30.5
CE=30.5
DC=30.5

3x + 5 = 30.5
3x = 30.5 - 5
3x = 25.5
25.5/3 =8.5
x=8.5

8 0

3 years ago

Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of f :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of g :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where n is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So f has a minimum of -7 and a maximum of 299.

4 0

3 years ago

The middle side of a triangle is half of 3 times the length of the shortest side. The longest side is 2 centimeters longer than

USPshnik [31]

Answer:

The difference between the longest and shortest sides of the triangle is 4 cm.

Explanation:

Step Number One:

Let the shortest side of the triangle have a length of x.

The middle side of the triangle has a length that is half of 3 times the length of the shortest side. This can be written as 1/2*3x, which equals 3/2x.

The longest side of the triangle has a length that is 2 centimeters longer than the length of the middle side. This can be written as 3/2x + 2.

Step Number Two:

The perimeter of the triangle, which can be found by adding the lengths of all of the sides of the triangle, is 18 centimeters. This can be shown by the following equations:

Shortest Side + Middle Side + Longest Side = Perimeter

x + 3/2x + 3/2x + 2 = 18

4x + 2 = 18

4x = 16

x = 16/4

x = 4

Step Number Three:

This means that the shortest side of the triangle has a length of 4 centimeters and the longest side of the triangle has a length of 8 centimeters.

8 cm - 4 cm = 4 cm

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Are you still confused? Not feeling confident in your ability to solve these types of problems? Some helpful topics to practice are listed below!

Still confused on ...

Step 1 - Practice equation solving!

Step 2 - Practice perimeter!

Step 3 - Practice addition and subtraction!

Remember: Certain problems may be tricky, but practice makes perfect!

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Answer by Math_Is_Me_123

7 0

3 years ago