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2 years ago

Can I get Help on explaination of this?

Mathematics

1 answer:

storchak [24]2 years ago

7 0

Answer:

The measure of the outside angle is the sum of the two inside angles:

68+52=120

Or you could do it the long way and find the third angle inside the triangle then do 180 minus that but this is easier.

Step-by-step explanation:

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Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x,y)= e^xy; X

kotykmax [81]

Answer:

f(x,y) = $e^{xy}$ is maximum at x = 2 and y = 2 and f(2,2) = $e^{4}$

Step-by-step explanation:

Since f(x,y) = $e^{xy}$ and x³ + y³ = 16, Ф(x,y) = x³ + y³ - 16

df/dx = y $e^{xy}$ , df/dy = x $e^{xy}$ , dФ/dx = 3x² and dФ/dy = 3y²

From the method of Lagrange multipliers,

df/dx = λdΦ/dx and df/dy = λdΦ/dy

y $e^{xy}$ = 3λx² (1) and x $e^{xy}$ = 3λy² (2)

multiplying (1) by x and (2) by y, we have

xy $e^{xy}$ = 3λx³ (4) and xy $e^{xy}$ = 3λy³ (5)

So, 3λx³ = 3λy³

⇒ x = y

Substituting x = y into the constraint equation, we have

x³ + y³ = 16

x³ + x³ = 16

2x³ = 16

x³ = 16/2

x³ = 8

x = ∛8

x = 2 ⇒ y = 2, since x = y

So, f(x,y) = f(2,2) = $e^{2 X2}$ = $e^{4}$

We need to determine if this is a maximum or minimum point by considering other points that fit into the constraint equation.

Since x³ + y³ = 16 when x = 0, y is maximum when y = 0, x = maximum

So, 0³ + y³ = 16

y³ = 16

y = ∛16

Also, when y = 0, x = maximum

So, x³ + 0³ = 16

x³ = 16

x = ∛16

and f(0,∛16) = $e^{0X\sqrt[3]{16} } = e^{0} = 1$ .

Also, f(∛16, 0) = $e^{\sqrt[3]{16}X0 } = e^{0} = 1$ .

Since f(0,∛16) = f(∛16, 0) = 1 < f(2,2) = $e^{4}$

f(2,2) is a maximum point

8 0

3 years ago

between 9 p.m. and 6:36 a.m., the water level in a swimming pool decreased by 6/25. assuming that the water level decreased at

Licemer1 [7]

Answer:

The hourly drop between the two times is 1/40

Step-by-step explanation:

Firstly, we need to find the difference in time between 9 pm and 6:36 am

That would be 9 hours and 36 minutes

It would be needed to convert 36 minutes to hours

Mathematically, 60 minutes = 1 hour

So 36 minutes = (36 * 1)/60 = 36/60 = 0.6

So the difference between the two time is simple 9.6 hours

So the total drop during the time is given by 6/25

So the hourly drop will be 6/25 divided by 9.6

= 6/25 * 1/9.6 = 6/240 = 1/40

8 0

3 years ago

How do i solve <br> X^56 x X^14

sweet-ann [11.9K]

Answer:

x^70

Step-by-step explanation:

When multiplying exponents, you just add them up.

x^56+14= x^70

8 0

3 years ago

-9x-12=35-x

masya89 [10]

= -<span>9x-12=35-x

Put like terms together:

= -9x + x = 35 + 12

= -8x = 47

= x = -47/8

= x = -5.875

In short, Your Answer would be: -5.875

Hope this helps!</span>

6 0

3 years ago

The figure below shows a straight line AB intersected by another straight line t:

BaLLatris [955]

When two straight lines intersect, the pairs of nonadjacent angles in opposite posi-tions are known as vertical angles.

If a segment AB is intersected by a transversal labeled t, then ∠1 and ∠3 and ∠2 and ∠4 are vertically angles formed by the transversal t on the segment AB.

Angles ∠1 and ∠2 can be described as adjacent and supplementary angles, so

$m\angle 1+m\angle 2=180^{\circ}$ .

Angles ∠3 and ∠2 can be also described as adjacent and supplementary angles, so

$m\angle 3+m\angle 2=180^{\circ}$ .

Subtract from the first equation the second equation:

$m\angle 1+m\angle 2-(m\angle 3+m\angle 2)=180^{\circ}-180^{\circ},\\ m\angle 1-m\angle 3=0,\\ m\angle 1=m\angle 3$ .

Similarly you can prove that $m\angle 2=m\angle 4$ .

4 0

3 years ago