This is for my brother’s test What are the measures of L1 and L2? Show your work or explain your answers.

Answers

Answer 1

Answer:

Answer:

angle 2 is 75°

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Please help solve and explain this

Solve the differential equation x^2 y"-xy' +y 0

Answers

Answer:

$y(x)\ =\ √(x)[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

Step-by-step explanation:

Given differential equation is

$x^2y$ (1)

Let's assume that

$x=e^t$

$=>\ t\ =\ logx$

then,

$(dx)/(dt)=e^t$

$and\ (d^2x)/(dt^2)=e^t$

We can write,

$(dy)/(dx)=(dy)/(dt).(dt)/(dx)$

$=e^(-t)(dy)/(dt)$

Similarly,

$(d^2y)/(dt^2)=(d^2y)/(dt^2).(dt^2)/(dx^2)$

$=e^(-2t).(d^2y)/(dt^2)$

Putting these values in equation (1), we will get

$e^(2t).e^(-2t).(d^y)/(dt^2)-e^t.e^(-t)(dy)/(dt)+y=0$

$=>(d^2y)/(dt^2)-(dy)/(dt)+y=0$

So, the characteristics equation can be given as

$D^2-D+1=0$

$=>D\ =\ (1+√(1-4))/(2)\ or\ (1-1√(1-4))/(2)$

$=>D=\ (1)/(2)+i(√(3))/(2)\ or\ (1)/(2)-i(√(3))/(2)$

Hence, the general solution of the equation can be give by

$y(t)\ =\ e^{(t)/(2)}[C_1cos(√(3))/(2)t+C_2sin(√(3))/(2)t]$

Now, by putting the value of t in above solution, we will have

$y(x)\ =\ e^{(1)/(2)logx}[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

$y(x)=\ √(x)[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

Hence, the solution of above given differential equation can be given by

$y(x)=\ √(x)[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

Evaluate the limit, if it exists.
lim x2−11x+30x−5
x→5

Answers

Answer:

f(5) = 115

Given:

f(x) = x² - 11x + 30x -5

x⇒5

So,

f(x) = x² - 11x + 30x -5

f(5) = 5² - 11(5) + 30(5) -5

f(5) = 25 - 55 + 150 - 5

f(5) = 115

Solve the equation 15.6 + (-1.8) =

Answers

The solution to the equation 15.6 + (-1.8) is 13.8.

The equation to solve is 15.6 + (-1.8).

First, add the two numbers: 15.6 + (-1.8) = 13.8.

The result is 13.8.

In this equation, you're adding a positive value (15.6) and a negative value (-1.8), which results in a smaller positive value. When you add a positive number and a negative number, you can think of it as moving to the right on the number line (positive direction) but not as far as you would if you were only considering the positive value.

So, the solution to the equation 15.6 + (-1.8) is 13.8.

To know more about equation:

brainly.com/question/29657983

#SPJ3

Since +(-) becomes (-) we can write the given problem as

15.6-1.8

Subtraction gives us 13.8

Describe how to simplify the expression 3^-6/3^-4a. Divide the bases and then add the exponents.
b. Keep the base the same and then add the exponents.
c. Multiply the bases and then subtract the exponents.
d. Keep the base the same and then subtract the exponents.

Answers

Answer:

The correct option is d. To simplify the given expression we should keep the base the same and then subtract the exponents.

Step-by-step explanation:

The given expression is

$(3^(-6))/(3^(-4))$

In the above expression we have common base 3 but the exponents are different.

According to the rule of exponent, if the numerator and denominator have same base and different exponent, then the base remains the same and the exponent of denominator subtracted from exponent of numerator.

$(a^m)/(a^n) =a^(m-n)$

Use this rule in the given expression.

$(3^(-6))/(3^(-4))=3^(-6-(-4))$

$(3^(-6))/(3^(-4))=3^(-2)$

Therefore the correct option is d.

Answer:

d or Keep the base the same and then subtract the exponents.

Step-by-step explanation:

The planet Mars has a radius of 3400 km. What is the volume of Mars?Write your answer in scientific notation to three decimal places.

Answers

Answer:

1.646×10¹¹ km³.

Step-by-step explanation:

From the question given, we obtained the following information:

Radius (r) = 3400 km

Volume (V) =.?

The shape of a planet is spherical in nature. Thus, we shall apply the formula for calculating the volume of a sphere to obtain the volume of Planet Mar as illustrated below:

Radius (r) = 3400 km

Pi (π) = 3.14

Volume (V) =.?

Volume of a sphere = 4/3 πr³

V = 4/3 × 3.14 × (3400)³

V = 4/3 × 3.14 × 3.9304×10¹⁰

V = 1.646×10¹¹ km³

From the calculations made above, the volume of Planet Mar is 1.646×10¹¹ km³

Consider an optimization model with a number of resource constraints. Each indicates that the amount of the resource used cannot exceed the amount available. Why is the shadow price of such a resource constraint always zero when the amount used in the optimal solution is less than the amount available?

Answers

Shadow pricing refers to the practice of accounting the prince of securities not on their assigned market value (as might be expected) but by their amortized costs. This can also be considered an "artificial" price assigned to a non-priced asset or accounting entry.

In this optimization model, we find a number of resource constraints which limit the changes to the resources. It is expected that these resources would not exceed the amount allocated for each particular constraint. The shadow price of a resource constraint would be zero in this example because the amount used would be less than the amount available. This means that it can fit within the established parameters, and therefore, would not need to be assigned a shadow price.

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