What is the surface area of the cylinder?

This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the ex

noname [10]

$L(x,y,z,\lambda)=10x+10y+2z+\lambda(5x^2+5y^2+2z^2-42)$

$L_x=10+10\lambda x=0\implies1+\lambda x=0$

$L_y=10+10\lambda y=0\implies1+\lambda y=0$

$L_z=2+4\lambda z=0\implies1+2\lambda z=0$

$L_\lambda=5x^2+5y^2+2z^2-42=0$

$\begin{cases}L_x=0\\L_y=0\\L_z=0\end{cases}\implies1+\lambda x=1+\lambda y=1+2\lambda z=0\implies x=y=2z$

$5x^2+5y^2+2z^2=5(2z)^2+5(2z)^2+2z^2=42z^2=42\implies z^2=1$

$z^2=1\implies z=\pm1\implies x=y=\pm2$

There are two critical points, at which we have

$f\left(2,2,1\right)=42\text{ (a maximum value)}$

$f\left(-2,-2,-1\right)=-42\text{ (a minimum value)}$

3 0

3 years ago

A grocery store bought milk for $2.50 per half gallon and stored it in two refrigerators. During the night, one refrigerator mal

daser333 [38]

In this problem, we let x be the number of half gallons of milk the store bought, and x-12 be the remaining half gallonsWe use the equation profit = revenue-cost
88.08=4.02(x-12)-2.60x88.08=4.02x-48.24-2.6x1.42x=88.08+48.24=136.32x=136.32/1.42=96Hence, the number of half gallons of milk the store bought is 96

4 0

3 years ago

The volume of the rectangular prism is 60x^3 + 145x^2 + 70x. Factor to find the possible expressions for length, width and heigh

tester [92]

The volume of the rectangular prism:
$V=length\cdot width\cdot height=lwh$

$60x^3 + 145x^2 + 70x=5x(12x^2+29x+14)\\\\=5x(12x^2+21x+8x+14)=5x[3x(4x+7)+2(4x+7)]\\\\=5x(4x+7)(3x+2)\\\\Answer:\\length=5x\\width=4x+7\\height=3x+2$

4 0

3 years ago

A poll found that 53% of a sample of 1170 teens in a certain large country go online several times a day. (Treat this sample as

posledela

Answer:(a) margin error = 2.4%

(b) The margin error gives the measure in percentage of how the population parameter determined differ from the real population statistics or value.

(c) in 90% of the samples of teens in the country, the percent who go online several times a day will be within 50.6% and 55.4%. of the estimated 100%

Step-by-step explanation:

Using the proportion formulae

Margin error = z √p(1-p)/n

n= 1170, p = 53% = 0.53, 1-p = 0.47

and the z value at 90% C.I = 1.645

M error= 1.645 √0.53×0.47/1170

Margin error = 0.024 = 0.024 ×100

Margin error = 2.4%

53 - 2.4 = 50.6% and 53 + 2.4 = 55.4%

In other words 90% of the time: the number of teens who go online several time a day will be between 50.6 and 55.4%.

8 0

3 years ago

Seven less than eight times a number is -12

aliina [53]

Answer:

19/8

Step-by-step explanation:

8x-7=-12

8x=19

x=19/8

5 0

3 years ago

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