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garri49 [273]
3 years ago
7

PLEASE HELP ME ASAP 50 POINTS AND BRAINLIEST!!!!!!

Mathematics
1 answer:
Virty [35]3 years ago
7 0

Answer:

The first shape is triangle; area of a triangle = 1/2*b*h

= 1/2*7*3

= 1/2*21

= 21/2

= 10.5

The second shape is rectangle; area of rectangle = l*b

= 7*3

= 21

Total area:

10.5+21

= 31.5

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This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the ex
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Answer with Step-by-step explanation:

We are given that

f(x,y,z)=10x+10y+3z

g(x,y,z)=5x^2+5y^2+3z^2=43

We have to find the extreme values of the function.

f_x(x,y,z)=10,f_y(x,y,z)=10,f_z(x,y,z)=3

g_x(x,y,z)=10x,g_y(x,y,z)=10y,g_z(x,y,z)=6z

\Delta f(x,y,z)=\lambda \Delta g(x,y,z)

Therefore,

10=\lambda 10x\implies x=\frac{1}{\lambda}

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z=\frac{1}{2\lambda}

Substitute the values in g(x)

Then, we get

\frac{5}{\lambda^2}+\frac{5}{\lambda^2}+\frac{3}{4\lambda^2}=43

\frac{20+20+3}{4\lambda^2}=43

\frac{43}{4\lambda^2}=43

\lambda^2=\frac{43}{4\times 43}

\lambda=\pm\frac{1}{2}

When \lambda=\frac{1}{2} then,

x=2,y=2,z=1

When \lambda=-\frac{1}{2}

Then, x=-2,y=-2,z=-1

f(2,2,1)=10+10+3=23

f(-2,-2,-1)=-10-10-3=-23

Hence, maximum value of f(x,y,z) is 23 at (2,2,1) and minimum value of f(x,y,z) is -23 at (-2,-2 ,-1).

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The removable discontinuity is at negative 6 and 6. Then the correct option is B.

<h3>What is a function?</h3>

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The function is given as

f\rm (x) =\rm  \dfrac{x^2-36}{x^3-36x}

The expression can be written as

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More about the function link is given below.

brainly.com/question/5245372

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Step-by-step explanation:

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