What is 240.50 x 19.54

Use lagrange multipliers to find the maximum volume of a rectangular box that is inscribed in a sphere of radius r

vesna_86 [32]

For the derivative tests method, assume that the sphere is centered at the origin, and consider the circular projection of the sphere onto the xy-plane. An inscribed rectangular box is uniquely determined

1

by the xy-coordinate of its corner in the first octant, so we can compute the z coordinate of this corner by

x2+y2+z2=r2 =⇒z= r2−(x2+y2). Then the volume of a box with this coordinate for the corner is given by

V = (2x)(2y)(2z) = 8xy r2 − (x2 + y2),

and we need only maximize this on the domain x2 + y2 ≤ r2. Notice that the volume is zero on the boundary of this domain, so we need only consider critical points contained inside the domain in order to carry this optimization out.

For the method of Lagrange multipliers, we optimize V(x,y,z) = 8xyz subject to the constraint x2 + y2 + z2 = r2<span>. </span>

7 0

3 years ago

Allison is rolling her hula hoop on the playground. The radius of her hula hoop is 35 cm. What is the distance the hula hoop rol

lidiya [134]

Answer:

Distance covered by hula hoop rolls in 4 full rotations is 880 cm .

Step-by-step explanation:

Formula

$Perimeter\ of\ a\ circle = 2\pi r$

Where r is the radius of the circle.

As given

Allison is rolling her hula hoop on the playground.

The radius of her hula hoop is 35 cm.

r = 35 cm

$\pi = \frac{22}{7}$

Putting the value in the formula

$Perimeter\ of\ a\ hula hoop = 2\times \frac{22}{7} \times 35$

= 220 cm

As given

The hula hoop rolls in 4 full rotations.

Distance covered by hula hoop rolls in 4 full rotations = 220 × 4

= 880 cm

Therefore the Distance covered by hula hoop rolls in 4 full rotations is 880 cm .

6 0

3 years ago

The national average sat score (for verbal and math) is 1028. if we assume a normal distribution with standard deviation 92, wha

elena55 [62]

Let X be the national sat score. X follows normal distribution with mean μ =1028, standard deviation σ = 92

The 90th percentile score is nothing but the x value for which area below x is 90%.

To find 90th percentile we will find find z score such that probability below z is 0.9

P(Z <z) = 0.9

Using excel function to find z score corresponding to probability 0.9 is

z = NORM.S.INV(0.9) = 1.28

z =1.28

Now convert z score into x value using the formula

x = z *σ + μ

x = 1.28 * 92 + 1028

x = 1145.76

The 90th percentile score value is 1145.76

The probability that randomly selected score exceeds 1200 is

P(X > 1200)

Z score corresponding to x=1200 is

z = $\frac{x - mean}{standard deviation}$

z = $\frac{1200-1028}{92}$

z = 1.8695 ~ 1.87

P(Z > 1.87 ) = 1 - P(Z < 1.87)

Using z-score table to find probability z < 1.87

P(Z < 1.87) = 0.9693

P(Z > 1.87) = 1 - 0.9693

P(Z > 1.87) = 0.0307

The probability that a randomly selected score exceeds 1200 is 0.0307

5 0

3 years ago

What is the quotient of 42 divided by 9124

Sunny_sXe [5.5K]

<span>The answer is 0.0046032441911442</span>

4 0

4 years ago

HELP!!

Crazy boy [7]

Answer:

60

Step-by-step explanation:

45 divided by 9 is 5. So you multiply 4 times 5. Which equals 20. So 20 plus 45 is 65. Hope you understand it.

5 0

3 years ago