1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Free_Kalibri [48]
2 years ago
15

A tv has a height: width in ratio of 9:16. In a scale drawing the height is 4.5cm. What would the width be

Mathematics
1 answer:
Oksi-84 [34.3K]2 years ago
3 0
4.5 is half of nine, so simply divide 16 by 2 and your answer would be 8.

You might be interested in
What is equivalent to 4x-2=38
Tom [10]
2x4 is the answer to 4x-2=38
7 0
2 years ago
Sandy works at a clothing store. She makes $8 per hour plus earns 15% commission on her sales. She worked 80 hours over the last
Sergio [31]
C 1009 because with the 80 hours she makes 640 dollars and comissin will be another 369
4 0
3 years ago
EXAMPLE 5 Find the maximum value of the function f(x, y, z) = x + 2y + 11z on the curve of intersection of the plane x − y + z =
Taya2010 [7]

Answer:

\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}

<em>Maximum value of f=2.41</em>

Step-by-step explanation:

<u>Lagrange Multipliers</u>

It's a method to optimize (maximize or minimize) functions of more than one variable subject to equality restrictions.

Given a function of three variables f(x,y,z) and a restriction in the form of an equality g(x,y,z)=0, then we are interested in finding the values of x,y,z where both gradients are parallel, i.e.

\bigtriangledown  f=\lambda \bigtriangledown  g

for some scalar \lambda called the Lagrange multiplier.

For more than one restriction, say g(x,y,z)=0 and h(x,y,z)=0, the Lagrange condition is

\bigtriangledown  f=\lambda \bigtriangledown  g+\mu \bigtriangledown  h

The gradient of f is

\bigtriangledown  f=

Considering each variable as independent we have three equations right from the Lagrange condition, plus one for each restriction, to form a 5x5 system of equations in x,y,z,\lambda,\mu.

We have

f(x, y, z) = x + 2y + 11z\\g(x, y, z) = x - y + z -1=0\\h(x, y, z) = x^2 + y^2 -1= 0

Let's compute the partial derivatives

f_x=1\ ,f_y=2\ ,f_z=11\ \\g_x=1\ ,g_y=-1\ ,g_z=1\\h_x=2x\ ,h_y=2y\ ,h_z=0

The Lagrange condition leads to

1=\lambda (1)+\mu (2x)\\2=\lambda (-1)+\mu (2y)\\11=\lambda (1)+\mu (0)

Operating and simplifying

1=\lambda+2x\mu\\2=-\lambda +2y\mu \\\lambda=11

Replacing the value of \lambda in the two first equations, we get

1=11+2x\mu\\2=-11 +2y\mu

From the first equation

\displaystyle 2\mu=\frac{-10}{x}

Replacing into the second

\displaystyle 13=y\frac{-10}{x}

Or, equivalently

13x=-10y

Squaring

169x^2=100y^2

To solve, we use the restriction h

x^2 + y^2 = 1

Multiplying by 100

100x^2 + 100y^2 = 100

Replacing the above condition

100x^2 + 169x^2 = 100

Solving for x

\displaystyle x=\pm \frac{10}{\sqrt{269}}

We compute the values of y by solving

13x=-10y

\displaystyle y=-\frac{13x}{10}

For

\displaystyle x= \frac{10}{\sqrt{269}}

\displaystyle y= -\frac{13}{\sqrt{269}}

And for

\displaystyle x= -\frac{10}{\sqrt{269}}

\displaystyle y= \frac{13}{\sqrt{269}}

Finally, we get z using the other restriction

x - y + z = 1

Or:

z = 1-x+y

The first solution yields to

\displaystyle z = 1-\frac{10}{\sqrt{269}}-\frac{13}{\sqrt{269}}

\displaystyle z = \frac{-23\sqrt{269}+269}{269}

And the second solution gives us

\displaystyle z = 1+\frac{10}{\sqrt{269}}+\frac{13}{\sqrt{269}}

\displaystyle z = \frac{23\sqrt{269}+269}{269}

Complete first solution:

\displaystyle x= \frac{10}{\sqrt{269}}\\\\\displaystyle y= -\frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{-23\sqrt{269}+269}{269}

Replacing into f, we get

f(x,y,z)=-0.4

Complete second solution:

\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}

Replacing into f, we get

f(x,y,z)=2.4

The second solution maximizes f to 2.4

5 0
3 years ago
How to round 10.7703 to the nearest tenth.
xeze [42]
10.7703 to the nearest tenth is 10.8
5 0
2 years ago
Read 2 more answers
Helpppppppppppp me please
eimsori [14]

Answer: Y intercept: 5 The slope of the line is: 2

Step-by-step explanation:

Y=mx+b is y-intercept form

So you have to solve this equation for y.

This looks like:

-2x+y=5

+2x      +2x

y=2x+5


4 0
3 years ago
Other questions:
  • Given the relation y = -4x2 -8 if the input is 2 what is the output 8 -8 -16 -24
    10·2 answers
  • Changing the value of b in results in a _____ of the graph.
    13·1 answer
  • if there is 2/3 of a bag of jelly beans, and Danny ate 1/4 of the bag last night, what fraction of the bag is left?
    9·2 answers
  • ASAP need help
    14·1 answer
  • What is the degree of the polynomial below?<br>2х^2 + 3x +1​
    10·1 answer
  • What is 1 5/12 - 3 <br><br>A. 2 5/12<br><br>B. 2 7/12<br><br>C. 1 5/12<br><br>D. 1 7/12​
    7·1 answer
  • WHIHIHIHI ) Question 6 2 pts Given the first term and the recursive formula for a sequence generate the first five terms. f(1) =
    12·1 answer
  • Please help!! i need help with numbers 3 and 4.
    5·2 answers
  • What is the perimeter, in feet, a rectangle whose length is twice its width and whose width is 8 feet?
    10·1 answer
  • Type the correct answer in each box. Use numerals instead of words.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!