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3 years ago

Please very soon I offer the crown !!! + 10 points urgently !!!

Mathematics

2 answers:

KIM [24]3 years ago

4 0

Answer:

a. 3

b. 5

c. 4

d. 4

e. 10

Step-by-step explanation:

quester [9]3 years ago

3 0

Answer:

read below

Step-by-step explanation:

a.3

b.5

c.2

d.2

6. 8p

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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

velikii [3]

Answer:

The maximum value= 36

Minimum value = - 36

Step-by-step explanation:

Given that

f(x, y, z) = 8 x + 8 y + 4 z

h(x,y,z)=4 x² + 4 y² + 4 z² - 36

From Lagrange multipliers

Δf = λ Δh

Δf = < 8 ,8 , 4>

Δh = < 8 x ,8 y , 8 z>

Δf = λ Δh

< 8 ,8 , 4> = < 8 λ x ,8 λ y , 8 λ z>

8 = 8 λ x -------------1

8 = 8 λ y ---- ------2

4 = 8 λ z ----------------3

From equation 1 ,2 and 3

Now by putting the value of x,y and z in the following equation

4 x² + 4 y² + 4 z² = 36

$4\times \dfrac{1}{\lambda^2 }+4\times \dfrac{1}{\lambda^2 }+4\times \dfrac{1}{(2\lambda)^2 }=36$

$\dfrac{4}{\lambda^2 }+ \dfrac{4}{\lambda^2 }+ \dfrac{1}{\lambda^2 }=36$

So the value of λ is

$\lambda =\pm \dfrac{1}{2}$

When λ = 1/2

x = 1 / λ , y=1 / λ , z= 1 /2 λ

x= 2 , y = 2 , z=1

f(x, y, z) = 8 x + 8 y + 4 z

f(2, 2, 1) = 8 x 2 + 8 x 2 + 4 x 1

f(2, 2, 1) =36

When λ = - 1/2

x = 1 / λ , y=1 / λ , z= 1 /2 λ

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

f(x, y, z) = 8 x + 8 y + 4 z

f(-2, -2, -1) = 8 x (-2) + 8 x (-2) + 4 x (-1)

f(-2, -2, -1) = - 36

The maximum value= 36

Minimum value = - 36

7 0

3 years ago

Read 2 more answers

Verify sine law by taking triangle in 4 quadrant<br>Explain with figure.<br>

Ksivusya [100]

Proof of the Law of Sines

The Law of Sines states that for any triangle ABC, with sides a,b,c (see below)

 sin  A

 sin  B

 sin  C

For more see Law of Sines.

Acute triangles

Draw the altitude h from the vertex A of the triangle

From the definition of the sine function

 sin  B =

a n d  sin  C =

h = c  sin  B a n d h = b  sin  C

Since they are both equal to h

c  sin  B = b  sin  C

Dividing through by sinB and then sinC

 sin  C

 sin  B

Repeat the above, this time with the altitude drawn from point B

Using a similar method it can be shown that in this case

 sin  C

 sin  A

Combining (4) and (5) :

 sin  A

 sin  B

 sin  C

- Q.E.D

Obtuse Triangles

The proof above requires that we draw two altitudes of the triangle. In the case of obtuse triangles, two of the altitudes are outside the triangle, so we need a slightly different proof. It uses one interior altitude as above, but also one exterior altitude.

First the interior altitude. This is the same as the proof for acute triangles above.

Draw the altitude h from the vertex A of the triangle

 sin  B =

a n d  sin  C =

h = c  sin  B a n d h = b  sin  C

Since they are both equal to h

c  sin  B = b  sin  C

Dividing through by sinB and then sinC

 sin  C

 sin  B

Draw the second altitude h from B. This requires extending the side b:

The angles BAC and BAK are supplementary, so the sine of both are the same.

(see Supplementary angles trig identities)

Angle A is BAC, so

 sin  A =

h = c  sin  A

In the larger triangle CBK

 sin  C =

h = a  sin  C

From (6) and (7) since they are both equal to h

c  sin  A = a  sin  C

Dividing through by sinA then sinC:

 sin  A

 sin  C

Combining (4) and (9):

 sin  A

 sin  B

 sin  C

7 0

3 years ago

Graph 24 > - 3r 2 - 9

coldgirl [10]

Answer:

Solve for r

− √ 11 < r < √ 11

Step-by-step explanation:

7 0

3 years ago

(I NEED THIS ANSWERED SUPER SUPER FAST PLEASE IT'S IMPORTANT!!!!!!)<br><br> 6 7/8c =__ fl oz

Olegator [25]

1 cup = 8 fluid ounces.
6.875 cups = ? fluid ounces.
8*6.875=55.

Your answer would be 55 fluid ounces.

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3 years ago

Fruit Slice Flavor Small Bag Medium Bag Large Bag Orange 20 40 60 Grape 10 20 30 Cherry 5 10 15 Total Slices 35 70 105 Best Ever

Maksim231197 [3]

It depends on how much its the total

7 0

3 years ago

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