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777dan777 [17]
3 years ago
14

Translate each phrase into a variable expression. use n for the variable

Mathematics
2 answers:
gayaneshka [121]3 years ago
8 0
N + 2 that is correct
Svetllana [295]3 years ago
4 0
N + 2 is the answer to ur question
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Paul wants to know when gas would have cost about $1.50 per gallon. What step should he take?
EastWind [94]
 he should know how much gallons he need to fill his car up 
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3 0
3 years ago
Use Lagrange multipliers to find the dimensions of the box with volume 1728 cm3 that has minimal surface area. (Enter the dimens
Dima020 [189]

Answer:

(x,y,z) = (12,12,12) cm

Step-by-step explanation:

The box is assumed to be a closed box.

The surface area of a box of dimension x, y and z is given by

S = 2xy + 2xz + 2yz

We're to minimize this function subject to the constraint that

xyz = 1728

The constraint can be rewritten as

xyz - 1728 = 0

Using Lagrange multiplier, we then write the equation in Lagrange form

Lagrange function = Function - λ(constraint)

where λ = Lagrange factor, which can be a function of x, y and z

L(x,y,z) = 2xy + 2xz + 2yz - λ(xyz - 1728)

We then take the partial derivatives of the Lagrange function with respect to x, y, z and λ. Because these are turning points, each of the partial derivatives is equal to 0.

(∂L/∂x) = 2y + 2z - λyz = 0

λ = (2y + 2z)/yz = (2/z) + (2/y)

(∂L/∂y) = 2x + 2z - λxz = 0

λ = (2x + 2z)/xz = (2/z) + (2/x)

(∂L/∂z) = 2x + 2y - λxy = 0

λ = (2x + 2y)/xy = (2/y) + (2/x)

(∂L/∂λ) = xyz - 1728 = 0

We can then equate the values of λ from the first 3 partial derivatives and solve for the values of x, y and z

(2/z) + (2/y) = (2/z) + (2/x)

(2/y) = (2/x)

y = x

Also,

(2/z) + (2/x) = (2/y) + (2/x)

(2/z) = (2/y)

z = y

Hence, at the point where the box has minimal area,

x = y = z

Putting these into the constraint equation or the solution of the fourth partial derivative,

xyz - 1728 = 0

x³ = 1728

x = 12 cm

x = y = z = 12 cm.

7 0
3 years ago
Prove that XR is equivalent to YP by using the terms in geometry, its just proofs
Sophie [7]
PQRS is a parallelogram                   Given
SR=PQ                                               property of parallelogram
m∠S=m∠Q                                         property of parallelogram
SP=QR                                               property of parallelogram
XP=RY                                               given
SP-XP=QR-RY                                  substitution
SX=QY                                              segment subtraction
ΔSRX is conggruent to ΔQPY           SAS theorem (side-angle-side)
XR=YP                                              CPCTC (corresponding parts of                                                                          congruent triangles are congruent)

3 0
3 years ago
The batteries from a certain manufacturer have a mean lifetime of 850 hours, with a standard deviation of 70 hours, assuming tha
matrenka [14]

To answer (a), we will need to find the Z value for 710 hours and 990 hours.

\begin{gathered} For\text{ 710} \\ Z\text{ = }\frac{x-\mu}{\sigma} \\ \text{    = }\frac{710-850}{70} \\ \text{    = -2} \\ p\text{ =0.0228 } \\ For\text{ 990:} \\ Z\text{ = }\frac{990-850}{70} \\ \text{ =2} \\ p\text{ = 0.9772} \end{gathered}\begin{gathered} To\text{ find P \lparen–2 \le Z \le 2\rparen} \\ =\text{ 0.9772 -0.0228} \\ =\text{ 0.9544} \\ =95.44\% \end{gathered}

B) 68% of data lies between one standard deviation of the mean.

850 +70 = 920

850 - 70 = 780

5 0
1 year ago
They’ve had to write five pages for a book report. How many hours would it take him to write it if he wrote 1/6 of the page each
Katyanochek1 [597]
1/6 page = 1 hour
1page= 6 hours
5 pages would be 30 hours
6 0
3 years ago
Read 2 more answers
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