At what angle does a diffraction grating produce a second-order maximum for light having a first-order maximum at 20.0 degrees?

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer:

a: 12 cm

b: I think it's 2.5 cm but someone might have to double check that

Step-by-step explanation:

A field that stores the value of a mathematical operation is calculated Field.

What does a mathematical operation mean?

The term "operation" in mathematics refers to the process of calculating a value utilizing operands and a math operator.

                       For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. They are: multiplication, division, addition, and subtraction.

What does the term "mathematical operator" mean?

In mathematics, an operator is typically a mapping or function that works on components of one space to produce elements of an other space (possibly and sometimes required to be the same space).

                              The most frequent operations are add, subtract, multiply, and divide (+,,, ). However, there are other others, like squaring, taking the square root, logarithms, etc. It is most likely an operation if it isn't a number.

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Answer:

  x = 9 inches

Step-by-step explanation:

You want the value of x in the similar triangles shown.

Corresponding sides are proportional. This means the ratio of the horizontal side of the triangle to the vertical side is the same for both.

  6/4 = (6+x)/10

  15 = 6 +x . . . . . . . . multiply by 10

  9 = x . . . . . . . . . subtract 6

The measure of x is 9 inches.

__

Additional comment

You could also write the proportion ...

  6/4 = x/(10 -4)

  x = 36/4 = 9 . . . . . . . multiply by 6

You can see this if you draw a horizontal line through the figure at the top of the side marked 4 in.

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Answer:

10 bars

Step-by-step explanation:

Given:

Ethan is 23 years older than Evan

So, let Ethan is (x) years old

And Evan is (y) years old

So, the difference between them is 23 years old

so, x - y = 23

And the sum of Ethan and Evan's age is 43

so, x + y = 43

So, we have the following system of equations:

add the equations to eliminate (y):

Now, substitute with (x) into the second equation to find (y):

So, the answer will be:

Ethan's age = x = 33

Evan's age = y = 10

Answer:

Step-by-step explanation:

favorable events for a sum of 3 are 12,21

P(sum 3)=2/36=1/18

favorable events for a sum of 9 are 36,63,45,54

P(sum of 9)=9/36=1/4

a = uk/b

u = ab/k

uk = ab

a = uk/b

Answer:

The original number is -22

Step-by-step explanation:

We'll label our mystery number x.

2x + 36 = 4x/11
Multiply both sides by 11
4x = 22x + 396
Isolate x to one side (for this I subtract 4x from both sides, but you can also subtract 22x if you'd like)
0 = 18x + 396
Isolate x pt 2
18x = -396
Divide both sides by 18 to find your answer!
x = -22

Plug in to confirm

-44 + 36 = -88/11S
8 = 8

Answer:

A= –5x2 + 4x – 7y + 14 = 0

C= 9x2 – 12xy + 4y2 + 4x – y + 5 = 0

D= 12x + 6y – 5y2 + 14 = 0

Step-by-step explanation:

I finished the assignment from Edge2020

The equation which would produce a parabola from the provided options are equation first and forth,

\(-5x^2 + 4x - 7y + 14 = 0\)

\(12x + 6y -5y^2 + 14 = 0\)

To of identify the type of conic section from an equation whether it is parabola, or not, let suppose the equation as,

\(Ax^2+By^2+Cx+Dy+E=0\)

If In this equation,

Either \(A=0\) or \(B=0\), but not both. Then it is the equation of parabola.

The first equation is,

\(-5x^2 + 4x - 7y + 14 = 0\)

There is no square term of y. Thus, this is the equation of parabola.

The second equation is,

\(-x^2 + 6x + y^2 - 8 = 0\)

This is not the equation of parabola, as there is two square terms of variable x and y.

The third equation is,

\(9x^2 - 12xy + 4y^2 + 4x - y + 5 = 0\)

Similar to the second equation, here is also two square terms of different variable. Thus, it is not a equation of parabola.              

The fourth equation is,

\(12x + 6y -5y^2 + 14 = 0\)

This equation is the equation of parabola, as there is only a single square term.

The fifth equation is,

\(20x^2 + 10xy - y^2 + 3x - 6y + 5 = 0\)

This is now the equation of parabola because of two square terms.

Hence, the equation which would produce a parabola from the provided options are equation first and forth,

\(-5x^2 + 4x - 7y + 14 = 0\)

\(12x + 6y -5y^2 + 14 = 0\)

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Answer:

X=2

Y=1

Step-by-step explanation:

........... Solution on the photo above

Answer:

f(3) = 3 + 1 = 4

Step-by-step explanation:

Since 3 > 0, we need to focus on the part of the function where x > 0. So:

f(3) = 3 + 1 = 4.

Answer:

  17 bars

Step-by-step explanation:

Peter wants to compute the maximum number of bars he can load safely if the load limit of 1200 kg and the bar weight of 60 kg are each rounded to the number of significant digits those numbers have.

The error in a rounded number is assumed to be as much as half of the least significant digit of the number.

Peter's load limit may actually be as low as ...

  1200 kg - (1/2)(100 kg) = 1150 kg . . . . . . . 1200 is rounded to nearest 100

Peter's bar weight might be as high as ...

  60 kg + (1/2)(10 kg) = 65 kg . . . . . . . . . . . 60 is rounded to nearest 10

If Peter has maximum-weight bars and does not want to exceed the minimum his load limit might be, the number of bars he can load is ...

  (1150 kg) / (65 kg/bar) ≈ 17.7 bars

The greatest number of bars Peter can load safely is 17.

Answer:

.......................

Answer:

x=-3

Step-by-step explanation:

We move all terms to the left:

7+2x/3-(5)=0

We add all the numbers together, and all the variables

2x/3+2=0

We multiply all the terms by the denominator

2x+2*3=0

We add all the numbers together, and all the variables

2x+6=0

We move all terms containing x to the left, all other terms to the right

2x=-6

x=-6/2

x=-3

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete but a possibility is that the given parameters are points  on a straight line.

I'll answer base on that assumption.

\(RS = 6y + 2\)

\(ST =2y + 7\)

\(RT =13y -21\)

To solve for y, we have that:

\(RT = RS + ST\)

This gives:

\(13y - 21 = 6y + 2 + 2y + 7\)

Collect Like Terms

\(13y - 6y - 2y = 21 +2+7\)

\(5y = 30\)

Divide both sides by 5

\(y = 6\)

To get the measure of each line. Substitute 6 for y in

\(RS = 6y + 2\)

\(ST =2y + 7\)

\(RT =13y -21\)

\(RS = 6 * 6 + 2 = 36 + 2 = 38\)

\(ST = 2*6 + 7 = 12 +7 = 19\)

\(RT = 13*6 - 21 = 78 - 21 = 57\)

Answer:

x = 0 , x = 2

Step-by-step explanation:

3x² = 6x ( subtract 6x from both sides )

3x² - 6x = 0 ← factor out 3x from each term

3x(x - 2) = 0

equate each factor to zero and solve for x

3x = 0 ⇒ x = 0

x - 2 = 0 ( add 2 to both sides )

x = 2

solutions are x = 0 , x = 2

Answer: 1/8

Step-by-step explanation:

First make the bottom half the same:

3/4*2/2=6/8

We don’t need to change the first portion since they have a common factor

7/8-6/8=1/8

Answer:

28  

Step-by-step explanation:

a = b * h

a = 4 * 7

4 acts as the base

7 acts as the height

there is a right angle to support this.

If Angel bought a $600 phone in Toronto instead of San Antonio, he pays $28.50 more sales tax, based on the subtraction operation.

Subtraction operation is one of the four basic mathematical operations, including addition, multiplication, and division.

Subtraction operation involves the subtrahend, the minuend, and the difference.

Sales tax rate in San Antonio Texas = 8.25%

Sales tax rate in Toronto Ontario = 13%

The cost of a phone bought by Angel = $600

The sales tax in dollars in San Antonio Texas = $49.50 ($600 x 8.25%)

The sales tax in dollars in Toronto Ontario = $78.00 ($600 x 13%)

The difference in tax between Toronto and San Antonio = $28.50 ($78.00 - $49.50).

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Answer: $25.2

Step-by-step explanation:

First, let's find out how many miles Andrew walked in total by multiplying the number of laps by the length of each lap:

24 laps * 1/5 mile/lap = 24/5 miles = 4.8 miles

Now, we can find out how much money Andrew's dad donated by multiplying the total miles walked by the donation per mile:

4.8 miles * $5.25/mile = $25.2

Andrew's dad donated $25.2 to the school's art department.

Given Information:  

Mean test score = μ = 77

Standard deviation of test score = σ = 6.5 seconds  

Answer:  

The lower limit represents those 34% test scores which are below the mean test score.

The range of test scores will be (70.5 to 77)

The upper limit represents those 34% test scores which are above the mean test score.

The range of test scores will be (77 to 83.5)  

Step-by-step explanation:  

Normal Distribution:

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

The Empirical Rule:

The empirical rule states that approximately 68% of all the data lie within 1 standard deviation from the mean, approximately 95% of all the data lie within 2 standard deviations from the mean and approximately 99.7% of all the data lie within 3 standard deviations from the mean.  

68% of all the data lie within 1 standard deviation from the mean, so that means 34% (half of 68%) of the test scores will be below the mean test score and remaining 34% of the test scores will be above the mean test score.

The confidence interval is given by

\(CI = \mu \pm 1 \cdot \sigma \\\\CI = 77 \pm 1 \cdot (6.5) \\\\CI = 77 \pm 6.5 \\\\Lower \: limit = 77 - 6.5 = 70.5 \\\\Upper \: limit = 77 + 6.5 = 83.5 \\\\\)

The lower limit represents those 34% test scores which are below the mean test score.

So the range of test scores will be (70.5 to 77)

The upper limit represents those 34% test scores which are above the mean test score.

So the range of test scores will be (77 to 83.5)

The length of one of the sides of the square base is 6 inches.

Let's denote the length of one of the sides of the square base by "s" and the height of the pyramid by "h". Then, the surface area of the pyramid can be expressed as:

Surface area = area of square base + sum of areas of four triangular faces

Surface area = s^2 + 4(1/2)(s)(h)

We know that the surface area is 116 in^2 and the sum of the areas of the four triangular faces is 80 in^2. So we can substitute these values into the equation:

116 = s^2 + 4(1/2)(s)(h)

80 = 4(1/2)(s)(h)

We can simplify the second equation to get:

20 = (1/2)(s)(h)

We can solve for h by substituting the value of (1/2)(s)(h) from the second equation into the first equation:

116 = s^2 + 4(20)

116 = s^2 + 80

s^2 = 36

s = 6

Therefore, the length of one of the sides of the square base is 6 inches.

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There were 21 questions in total in the test

From the question, we have the given parameters related to our computation are

Number of questions answered correctly = 15

Proportion of questions answered correctly = 70%

Represent the total number of questions with T

So, we have the following representation

Number of questions answered correctly = T * Proportion of questions answered correctly

Substitute the known values in the above equation

So, we have the following equation

70% * T = 15

Divide both sides by 70%

T =21

Hence, the total number of questions is 21

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The way that Zach would have avoided using a credit card and still paid for his large expenses and still get some time off work was by planning ahead and saving appropriately.

Zach had expected to spend money and take time off for the holidays. Zach may have saved some of his income and taken time off work if he had anticipated these costs and calculated the amount of money required to cover them.

This is why budgeting, planning, and saving is very important as they can help us avoid unnecessary expenses such as paying a higher interest on credit cards.

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Step-by-step explanation:

100 equals the exponential expression 10^2. So 100 times 100 can be written as an expression: 100 × 100

10^2 × 10^2

The product can be written as 10² x 10².

Any whole-valued (integer) power of 10 is the power of 10. To put it another way, when the power is any positive integer, the power of 10 indicates that the number 10 has been multiplied by itself n times. Therefore, the long-form 10 power is the number 1, followed by n zeros, where n is the number greater than or equal to 0.

Given 100 times 100

which is

100 x 100

to convert in power of 10,

Move the decimal point to the left side of its original position and place it after the first digit if the whole number greater than 10 is to be converted into the power of 10 Math. The number of places the original decimal point was moved will be represented by the power of 10, which will be positive as it moves to the left.

so 100 can be written as 10²,

and 100 x 100 is written as

10² x 10²

Therefore 100 times 100 is written as 10² x 10².

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The variables of the expression  4x-2y+3 are x and y

What is Variables?

Any qualities, quantity, or number that can be gauged or tallied qualifies as a variable. A data item is another name for a variable. Variables include things like age, sex, business revenue and expenses, country of birth, capital expenditures, class grades, eye color, and type of vehicle.

Given expression,

4x-2y+3

Variable is a representation of an unknown numerical value in an equation or algebraic statement by a symbol, typically a letter.

In this expression

4x - 2y + 3

The variable in this expression is x and y

Hence, the variables are x and y

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Answer: When there are n teams in a league and each team plays every other team twice, then each team will play a total of n-1 games (since they don't play against themselves). Therefore, the total number of games played in the league is the sum of all the games played by each team, which is:

Total number of games = (number of teams) × (number of games played by each team) / 2

The division by 2 is necessary since each game involves two teams, so counting each game twice would result in double counting.

For the given basketball league with 11 teams, the total number of games played would be:

Total number of games = 11 × (11-1) / 2

= 11 × 10 / 2

= 55 × 2

= 110

Therefore, 110 games would be played in the league.

Step-by-step explanation: