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Evaluate the expression 2x2 - yl yl + 3xº for x = 4 and y = 7​
Evaluate the expression 2x2 - yl yl + 3xº for - 1

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Answer 1
Answer:

Answer:

replace the given values of x and y

Step-by-step explanation:

hope it helped!!!

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Find the radius and height of a cylindrical soda can with a volume of 256cm^3 that minimize the surface area.B: Compare your answer in part A to a real soda can, which has a volume of 256cm^3, a radius of 2.8 cm, and a height of 10.7 cm, to conclude that real soda cans do not seem to have an optimal design. Then use the fact that real soda cans have a double thickness in their top and bottom surfaces to find the radius and height that minimizes the surface area of a real can (the surface area of the top and bottom are now twice their values in part A.

B: New radius=?

New height=?

Answers

Answer:

A) Radius: 3.44 cm.

Height: 6.88 cm.

B) Radius: 2.73 cm.

Height: 10.92 cm.

Step-by-step explanation:

We have to solve a optimization problem with constraints. The surface area has to be minimized, restrained to a fixed volumen.

a) We can express the volume of the soda can as:

V=\pi r^2h=256

This is the constraint.

The function we want to minimize is the surface, and it can be expressed as:

S=2\pi rh+2\pi r^2

To solve this, we can express h in function of r:

V=\pi r^2h=256\n\nh=(256)/(\pi r^2)

And replace it in the surface equation

S=2\pi rh+2\pi r^2=2\pi r((256)/(\pi r^2))+2\pi r^2=(512)/(r) +2\pi r^2

To optimize the function, we derive and equal to zero

(dS)/(dr)=512*(-1)*r^(-2)+4\pi r=0\n\n(-512)/(r^2)+4\pi r=0\n\nr^3=(512)/(4\pi) \n\nr=\sqrt[3]{(512)/(4\pi) } =\sqrt[3]{40.74 }=3.44

The radius that minimizes the surface is r=3.44 cm.

The height is then

h=(256)/(\pi r^2)=(256)/(\pi (3.44)^2)=6.88

The height that minimizes the surface is h=6.88 cm.

b) The new equation for the real surface is:

S=2\pi rh+2*(2\pi r^2)=2\pi rh+4\pi r^2

We derive and equal to zero

(dS)/(dr)=512*(-1)*r^(-2)+8\pi r=0\n\n(-512)/(r^2)+8\pi r=0\n\nr^3=(512)/(8\pi) \n\nr=\sqrt[3]{(512)/(8\pi)}=\sqrt[3]{20.37}=2.73

The radius that minimizes the real surface is r=2.73 cm.

The height is then

h=(256)/(\pi r^2)=(256)/(\pi (2.73)^2)=10.92

The height that minimizes the real surface is h=10.92 cm.

Final answer:

The minimal surface area for a cylindrical can of 256cm^3 is achieved with radius 3.03 cm and height 8.9 cm under uniform thickness, and radius 3.383 cm and height 7.14 cm with double thickness at top and bottom. Real cans deviate slightly from these dimensions possibly due to practicality.

Explanation:

For a cylinder with given volume, the surface area A, radius r, and height h are related by the formula A = 2πrh + 2πr^2 (if the thickness is uniform) or A = 3πrh + 2πr^2 (if the top and bottom are double thickness). By taking the derivative of A w.r.t r and setting it to zero, we can find the optimal values that minimize A.

For a volume of 256 cm^3, this gives us r = 3.03 cm and h = 8.9 cm with uniform thickness, and r = 3.383 cm and h = 7.14 cm with double thickness at the top and bottom. Comparing these optimal dimensions to a real soda can (r = 2.8 cm, h = 10.7 cm), we see that the real can has similar but not exactly optimal dimensions. This may be due to practical considerations like stability and ease of holding the can.

Learn more about Optimal Dimensions here:

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1. Simplify each of the following fractionsleaving each as an improper fraction, not a whole
number. Do not use your calculator!
4.50
5
3.2
8

Answers

Answers:

9/2

5/1

16/5

8/1
9/2
5/1
16/5
8/1
are the answers

Help asapppp pleaseeeeeee

Answers

3 and 4 , 3.872
5 and 6 , 5.292
7 and 8 , 7.874
8 and 9 , 8.718
10 and 11 , 10.247

What is the circumference, in centimeters, of the circle? Use 3.14 for pi (please!!)

Answers

Answer:

the diameter is 24 so the ray is 12

circonference = 2*pi*R = 2*3.14*12= 75.36
It should be 75 cm
Hope that helped

A survey of cars on a certain stretch of highway during morning commute hours showed that 70% had only one occupant, 15% had 2, 10% had 3, 3% had 4, and 2% had 5. Let Xrepresent the number of occupants in a randomly chosen car.a. Find the probability mass function of X.

b. Find P(X ≤ 2).

c. Find P(X > 3).

d. Find μX.

e. Find σX

Answers

Answer:

a) X    1       2      3       4       5

P(X) 0.7  0.15  0.10  0.03  0.02

b) P(X \leq 2) = P(X=1) +P(X=2) = 0.7+0.15=0.85

c) P(X >3) = 1-P(X \leq 3) = 1-[P(X=1) +P(X=2)+P(X=3)]=1-[0.7+0.15+0.1]= 0.05

d) E(X) = \sum_(i=1)^n X_i P(X_i) = 1*0.7 +2*0.15+ 3*0.1+4*0.03+ 5*0.02= 1.52

e) E(X^2) = \sum_(i=1)^n X^2_i P(X_i) = 1*0.7 +4*0.15+ 9*0.1+16*0.03+ 25*0.02=3.18

Var(X) = E(X^2) -[E(X)]^2= 3.18- (1.52)^2 = 0.8996

\sigma= √(Var(X))= √(0.8996)= 0.933

Step-by-step explanation:

Part a

From the information given we define the probability distribution like this:

X       1       2      3       4       5

P(X) 0.7  0.15  0.10  0.03  0.02

And we see that the sum of the probabilities is 1 so then we have a probability distribution

Part b

We want to find this probability:

P(X \leq 2) = P(X=1) +P(X=2) = 0.7+0.15=0.85

Part c

We want to find this probability P(X>3)

And for this case we can use the complement rule and we got:

P(X >3) = 1-P(X \leq 3) = 1-[P(X=1) +P(X=2)+P(X=3)]=1-[0.7+0.15+0.1]= 0.05

Part d

We can find the expected value with this formula:

E(X) = \sum_(i=1)^n X_i P(X_i) = 1*0.7 +2*0.15+ 3*0.1+4*0.03+ 5*0.02= 1.52

Part e

For this case we need to find first the second moment given by:

E(X^2) = \sum_(i=1)^n X^2_i P(X_i) = 1*0.7 +4*0.15+ 9*0.1+16*0.03+ 25*0.02=3.18

And we can find the variance with the following formula:

Var(X) = E(X^2) -[E(X)]^2= 3.18- (1.52)^2 = 0.8996

And we can find the deviation taking the square root of the variance:

\sigma= √(Var(X))= √(0.8996)= 0.933

A train leaves the station at time t=0. Traveling at a constant​ speed, the train travels 280 kilometers in 2 hours. Answer parts a and b.a. Write a function that relates the distance traveled d to the time t.

The function that relates the distance traveled d to the time t is

Answers

The function that relates the distance travelled d to the time t is d = f(t) = 140t.

What is Speed?

Speed is a scalar quantity which measures the rate of change of the position of an object without measuring on the direction.

In other words, it can be defined as the ratio of distance covered by an object to the time taken by the object to cover the distance.

The train leaves the station at time t = 0.

Distance travelled by the train = 280 kilometers

Time taken to travel the distance = 2 hours

Speed = Distance / Time

           = 280 / 2

           = 140 kilometers/ hour.

Given that train travels at a constant speed.

So for any distance 'd' and the time taken to travel the distance 't',

d / t = 140

d = 140t

d = f(t) = 140t

Hence the distance travelled by the train can be related to the time taken by the function, d = f(t) = 140t

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Answer:

d = 140t

Step-by-step explanation:
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