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Scorpion4ik [409]
3 years ago
9

36 jelly donuts is 200 percent of how many jelly donuts?

Mathematics
2 answers:
dlinn [17]3 years ago
8 0

Answer:

720 jelly donuts

hope it helps pls mark brainliest

Art [367]3 years ago
7 0

Answer:

18

Step-by-step explanation:

Equation

2x=36

Solve

x=18

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If 47400 dollars is invested at an interest rate of 7 percent per year, find the value of the investment at the end of 5 years f
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Answer:

Part A) Annual \$66,480.95  

Part B) Semiannual \$66,862.38  

Part C) Monthly \$67,195.44  

Part D) Daily \$67,261.54  

Step-by-step explanation:

we know that

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

so

Part A) Annual

in this problem we have  

t=5\ years\\ P=\$47,400\\ r=0.07\\n=1  

substitute in the formula above  

A=\$47,400(1+\frac{0.07}{1})^{1*5}  

A=\$47,400(1.07)^{5}  

A=\$66,480.95  

Part B) Semiannual

in this problem we have  

t=5\ years\\ P=\$47,400\\ r=0.07\\n=2  

substitute in the formula above  

A=\$47,400(1+\frac{0.07}{2})^{2*5}  

A=\$47,400(1.035)^{10}  

A=\$66,862.38  

Part C) Monthly

in this problem we have  

t=5\ years\\ P=\$47,400\\ r=0.07\\n=12  

substitute in the formula above  

A=\$47,400(1+\frac{0.07}{12})^{12*5}  

A=\$47,400(1.0058)^{60}  

A=\$67,195.44  

Part D) Daily

in this problem we have  

t=5\ years\\ P=\$47,400\\ r=0.07\\n=365  

substitute in the formula above  

A=\$47,400(1+\frac{0.07}{365})^{365*5}  

A=\$47,400(1.0002)^{1,825}  

A=\$67,261.54  

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Answer:

next Slopes are 4 and 20

Step-by-step explanation:

they are  

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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

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3 years ago
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