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olga2289 [7]
3 years ago
7

Find a positive angle less than 360° that is coterminal with the given angle -1031°

Mathematics
1 answer:
Studentka2010 [4]3 years ago
3 0

Answer:

To find a positive and a negative angle coterminal with a given angle, you can add and subtract 360° if the angle is measured in degrees or 2π if the angle is measured in radians .

Step-by-step explanation:

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A 6500 gallon storage tank is 2/13 full of oil. How many gallons of oil are in the tank
user100 [1]

The gallons of oil in the tank is 1000

A 6500 gallon storage tank is 2/13 full

The number of oil in the tank can be calculated by multiplying the amount of gallons in the tank which is 6500 by the measurement of the tank which is 2/13

= 2/13 × 6500

= 13,000/13

= 1,000

Hence 1000 gallons of oil are in the tank

Read more here

brainly.com/question/10373356?referrer=searchResults

#SPJ1

4 0
1 year 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
Witch statement best describes how to determine whether f(x) =x^3+5x+1 is an even function?
34kurt
A.Determine whether –(x3 + 5x + 1) is equivalent to x3 + 5x + 1. b.Determine whether (–x)3 + 5(–x) + 1 is equivalent to x3 + 5x + 1.
c. Determine whether –x3 + 5x + 1 is equivalent to –(x3 + 5x + 1).
d. Determine whether (–x)3 + 5(–x) + 1 is equivalent to –(x3 + 5x + 1)

A function is even if f(x) = f(-x) for all x.

f(-x) = -x³ + 5(-x) + 1
f(-x) = -x³ - 5x + 1

b.Determine whether (–x)3 + 5(–x) + 1 is equivalent to x3 + 5x + 1. 
3 0
3 years ago
12 quarts of soil are used to completely fill 5 flower pots. If each pot holds the same amount of soil, how many quarts will eac
Oksanka [162]

Answer:

2.4 or 12/5 or 2 2/5

Step-by-step explanation:

4 0
2 years ago
A gardener has 27 pansies and 36 daisies. He plants an equal number of flowers in each row. What is the greatest possible number
Serggg [28]
There would be a a row of seven and would be 9 in each row
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3 years ago
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