Problem 1 - If 1 radian = 206265 arcseconds, what is the resolution formula for arcseconds? Convert 1.22 Radian to arcseconds using ratio. Show your work with units.

Problem 2 - A biologist wants to study deforestation with a satellite camera with a pixel resolution of 10 meters/pixel, which at the orbit of the satellite corresponds to an angular resolution of 6 arcseconds. You have already determined the value for arc seconds from problem number one. To measure the loss of plant matter, she detects the reflection by the ground of chlorophyll, which is the most intense at a wavelength of ___________ (1 nanometer = 10-9 meters) [Use the Electromagnetic Spectrum Below to fill in the blank]. To determine the wavelength, use the electromagnetic spectrum visible light section; what color should chlorophyll reflect? Determine the wavelength using the diagram below. Calculate: What is the diameter of the camera lens that will ensure this resolution at the orbit of the satellite?
There are several steps you need to show for calculating the diameter of the camera lens to receive full credit for problem 2

a. Write the literal equation for the problem. What variable are you solving for? It would help if you manipulated the formula to solve this problem. Show your manipulation in steps.

How to solve literal equations help here.

b. What color should chlorophyll reflect? _____________ Where is the wavelength on the spectrum as far as nanometers? ___________ (this is the wavelength you will use for calculation). Not everyone will have the same wavelength, but it should be similar.

c. Use your literal equation and solve the diameter of the camera lens (You should show all work, and your answer should have one significant figure with units in your response). Circle the answer.
Problem 3 –Since you have already determined the diameter of a lens required for an object with your nanometers from problem #2, you can use this direct relationship to determine the necessary diameter to 10 microns (10 microns = 10,000 nanometers). Choosing the diameter of the lens depends on the wavelength. It would help if you constructed a graph showing the diameter of the lens or the mirror in meters needed to obtain a resolution of 1 arcsecond from far-ultraviolet wavelengths of 200 nanometers to infrared wavelengths of 10 micrometers.

Question: Construct a graph that shows the diameter of a lens or mirror needed to obtain a resolution of 1 arcsecond from far-ultraviolet wavelengths of 100 nanometers to infrared wavelengths of 10 microns (10,000 nanometers). From orbit, a human subtends an angle of 1 arcsecond and emits infrared energy at a wavelength of 10 microns. How large would the camera be to resolve a human by his heat emission?

To solve this problem, you will need to determine

1. Set up graph: Which variable would be on X and Y? Which variable is dependent/independent? Use units!

2. Label the graph with the appropriate scale, including a title.

3. Plot point versus draw a line of best fit starting at zero to determine the answer.
1. What does the spatial resolution of a telescope depend on?



2. The spatial resolution of a telescope is proportional to the wavelength of light being detected divided by the telescope's diameter. Is this a direct or inverse relationship? How does that relate to wavelength versus lens diameter?



3. What is the spatial resolution for our eyes?



4. How is spatial resolution related to remote sensing? (from Module 3 reading assignment)



5. How is the GOES satellite related to this lesson? What exactly does the GOES detect?

Answer:

Step-by-step explanation:

Q1)

A toffee costs $0.15 + $0.10 = $0.25

If you buy 15 candies, it will cost you 15* $0.15 = $2.25

If you buy 12 toffees, it will cost you 12* $0.25 = $3.00

So buying 15 candies is $3.00 - $2.25 = $0.75 cheaper than buying 12 toffees.

Q2)

The original price of two tennis rackets is $120 x 2 = $240

The original price of three cans of tennis balls is $15 x 3 = $45

So the original price of two tennis rackets and three cans of balls is $240 + $45 = $285

By buying two tennis rackets and three cans of balls at the sale price of $255, you save $285 - $255 = $30 off the original price.

The solution to the equation 5x + 9y = 561 and 5x + 6y = 276 is x = -58.8, y = 95

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Given the equation:

5x + 9y = 561    (1)

Let us assume the second equation is:

5x + 6y = 276     (2)

To solve using elimination method, subtract equation 2 from 1:

3y = 285

y = 95

Put y = 95 in equation 1:

5x + 9(95) = 561

5x = -284

x = -58.8

The solution is x = -58.8, y = 95

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Hope it helps.

Please send your query through comment section.

The value of x is 54/35 when y=12 and z=21. The solution is obtained using the concept of relations and functions.

What is relation and function?

A relation belongs to the Cartesian product's subgroup or just a lot of points (ordered pairs). In other words, the ordered pair collection, where the ordered pair is made up of an object from each set, is used to define the relationship between the two sets.

A function is a special sort of relation (a collection of ordered pairs) that adheres to the rule that every X-value should only be connected with one y-value.

We are given that x varies directly as y and inversely as z.

This means that x ∝ y and x ∝ 1/z

So, x ∝ y/z

=> x = k*y/z  ( k is a constant)

Now, it is given that x = 3 when y = 10 and z = 9

So,

=> 3 = k*10/9

=> k = 27/10

=> x = 27y/10z

When y=12 and z=21,

=> x = 27*12/10*21

=> x = 54/35

Hence, the value of x is 54/35 when y=12 and z=21.

Learn more about relation and function from the given link

https://brainly.com/question/29252006

#SPJ1

The total cost of the meal with the gratuity is $1.18p.

What is gratuity?

The amount that a company pays its employee as a "gratuity" for services rendered to it is referred to as a gratuity. The gratuity amount, however, is only given to employees who have worked for the business for five years or longer.

For each completed six-month period, the gratuity amount is equal to one-fourth of the employee's most recent basic salary.

Given:

A restaurant charges an automatic gratuity of 18% on tables with more than 6 people.

A party of 8 had a bill of p.

Since there are 8 people so, gratuity will be applied on the bill

Since bill is of amount p

So, gratuity of 18 % of p = 18% * p

                                      =  (18 / 100) *p

                                     =  0.18p

Now the total bill after adding gratuity = p + 0.18p

                                                               = 1.18p

Hence, the total cost of the meal with the gratuity is $1.18p.

To know more about gratuity, click on the link

https://brainly.com/question/2894582

#SPJ1

Answer:

Step-by-step explanation:

Solving by factoring is a strategy for solving a polynomial equation that is in quadratic form. Quadratic form means that the equation is of the form ax^2+bx+c=0, where a,b, and c are real numbers. When factoring, the goal is to express the equation as the product of two simpler equations. To do this, we must factor the quadratic equation into two linear equations, each with a single variable.

For example, consider the equation x^2+3x-4=0. To factor this equation, we can first rewrite it as (x+4)(x-1)=0. This is the same as x+4=0 and x-1=0. We can then solve each of these linear equations to find the solutions. In this case, the solutions are x=-4 and x=1.

Therefore, the strategy of solving by factoring is to rewrite a polynomial equation in quadratic form as the product of two simpler equations, and then solve each of these equations. The solutions to the original equation can then be found by solving each of the linear equations.

Hope it helps.

Please send your query through comment section.

Step-by-step explanation:

the funny thing with equations is we can transform them (as long as we do every operation in both sides), and we can even add them up or subtract from each other to get new equations that are maybe simpler to solve.

to eliminate x i would recommend to multiply the first equation by 4, and the second equation by 5 and then subtract equation 2 from equation 1 (comparable term by comparable term).

5x - 2y = 10

4x - 3y = 15

would then turn into

20x - 8y = 40

- 20x - 15y = 75

------------------------

0 7y = -35

y = -35/7 = -5

now we can pick any original equation to solve for x.

e.g.

5x - 2×-5 = 10

5x + 10 = 10

5x = 0

x = 0

Answer:

1

Step-by-step explanation:

(-1,2) and (2,6)

d=√[2-(-1)] ^+ [2-6]^

d=√3+(-4)^

d=√-1^

d=1

The number of goodie  bags she will need to sell is 107.

Breakeven is when profit is zero. it is the point where total cost is equal to total revenue.

Breakeven: Total cost = total revenue

fixed cost + variable cost = price x quantity sold

fixed cost + (cost per unit  x quantity sold)

$250 + (1.25 x q) = 3.60 x q

$250 + 1.25q = 3.60q

In order to determine the value of q, take the following steps:

Combine and add similar terms :

$250 = 3.60q - 1.25q

$250 = 2.35q

Divide both sides o the equation by 2.35

q = 250/2.35

q =  106.3 = 107

To learn m8re about breakeven, please check: https://brainly.com/question/10190285

SPJ1

Answer:

a)

i) To calculate the profit if 0 cakes are made per day, we can substitute x = 0 into the function:

P(x) = -x²+36x - 40

P(0) = -0² + 36(0) - 40 = -40 dollars

So, the profit from making 0 cakes per day is -40 dollars.

ii) To calculate the profit if 20 cakes are made per day, we can substitute x = 20 into the function:

P(x) = -x²+36x - 40

P(20) = -20² + 36(20) - 40 = 760 dollars

So, the profit from making 20 cakes per day is 760 dollars.

b) To find out how many cakes need to be made per day for the profit to be $270, we need to solve the equation P(x) = 270.

We can substitute the function P(x) into this equation:

-x²+36x - 40 = 270

Next we can solve this equation for x by using any method you prefer ( factoring, Quadratic formula, etc)

x = (36 +/- √(36² -4*(-40)(-1)))/ 2(-1)

x = (36 +/- √(1296 + 320))/ -2

x = (36 +/- √1616)/ -2

x = (36 +/- 40)/ -2

x = -2 +/- 20

x = 18 or -22

The number of cakes need to be made per day for the profit to be $270 is 18 or -22, but -22 is not a valid solution because the number of cakes must be a non-negative value, so the number of cakes need to be 18

Answer:

-27

Step-by-step explanation:

3a - 4b
-3 - 4b
-3 - 24
-27

If there are 135 people in a sport centre. The number of people  that use exactly one of these facilities is 49.

Number of people that uses gym= 73- ( 32-14+ 36-14 + 14)

Number of people that uses gym = 73 - 54

Number of people that uses gym = 19

Number of people that use pool only = 73-(36-14+35-14+14)

Number of people that use pool only= 73-57

Number of people that use pool only = 16

Number of people that use track only = 67-(32-14+35-14+14)

Number of people that use track only = 67-53

Number of people that use track only = 14

Number of people  that use exactly one of these facilities =19+16+14

Number of people  that use exactly one of these facilities = 49

Therefore we can conclude that the number of people  that use exactly one of these facilities is 49.

Learn more about probability here:https://brainly.com/question/29818698

#SPJ1

Answer:

128

Step-by-step explanation:

1.2*4 =4.8

so 32*4 = 128

The sum of A and B in the ten digits numbers is 6.

The ten-digit number 3872649A0B is divisible by 36 . Therefore, the ten digit number can divide 36 without any remainder.

Hence, the letters A and B each represent single digit even numbers. Even numbers are numbers that can divide 2 without remainders.

Therefore, let's find the sum of the numbers A and B.

Since, the numbers are single digits and even the numbers are 2, 4, 6 or 8.

Therefore, lets do trial and error to know what will be replaced in the ten digits to divide 36 without remainder.

Therefore, the numbers are 2 and 4.

Where,

A = 2

B = 4

3872649204 ÷ 36 = 107573589

Therefore,

A + B = 2 + 4 = 6

learn more on sum here: bhttps://brainly.com/question/122064

#SPJ1

Answer:

Step-by-step explanation:

a)24

b)4

c)10

d)16

e)172

Answer:

30 unit angles

Step-by-step explanation:

A unit angle is defined as an angle that measures 1 degree. To find the number of unit angles that the smaller angle 30° of a small pattern block goes through, we can divide the measure of the angle by the measure of a unit angle.

30° ÷ 1° = 30 unit angles

So, the smaller angle 30° of a small pattern block goes through 30 unit angles.

The interquartile range of the data given the first quartile and the third quartile is equal to 25.

The interquartile range is the difference between the third quartile and the first quartile.

The IQR is a measure of variability that is based on the division of a data set into quartiles.

The data arranged in ascending order as;

4,5, 6, 8, 9, 11, 13, 16, 16, 18, 20,21, 25,30, 33, 36, 37, 40, 41

Third quartile = 3/4(n + 1) = 3/4 x 20

= 15th term

= 50

First quartile = 1/4 x (n + 1) = 1/4 x 20

= 5th term

= 25

Thererfore, Interquartile range = 50 - 25 = 25

To learn more about interquartile range, please check:  brainly.com/question/3966385

#SPJ1

Two-variable linear equations have a line as their graph, which is why they are referred to as linear equations. Plotting (x1,y1) and (x2,y2), then creating a line that connects the two.

[tex]$\frac{d}{d x}\left(-(x-2)^2+1\right)$[/tex]

Domain of [tex]$-(x-2)^2+1:\left[\begin{array}{cc}\text { Solution: } & -\infty < x < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]

Range of [tex]$-(x-2)^2+1:\left[\begin{array}{cc}\text { Solution: } & f(x) \leq 1 \\ \text { Interval Notation: } & (-\infty, 1]\end{array}\right]$[/tex]

Interception zones on the axis [tex]$-(x-2)^2+1: \quad X$[/tex] Intercepts: [tex]$(3,0),(1,0), Y$[/tex]Intercepts: (0,-3) .

Vertex of [tex]$-(x-2)^2+1: \quad$[/tex] Maximum (2,1) .

The graph of the equation y=2x+1 shows a straight line, or it is a linear equation. When the value of x rises, eventually the value of y rises by twice the rise in x plus one. With a ruler and the specified amount as the starting point, draw a vertical line. From the line across to the -axis, create a horizontal line using a ruler. Look at the value on the -axis.

There are three fundamental ways to graph linear functions. The initial method involves charting points and then tracing a line through them. The second is by using the slope and y-intercept. The identity function f(x)=x is transformed as the third method.

To learn more about graph refer to :

https://brainly.com/question/19040584

#SPJ1

Answer:

Angle EBC = 88

because of the angle bisector theorem

44 + 44 = 88

Answer:88°

Step-by-step explanation:

EBD is equal to 44°, while DBC is also equal to 44° if you see it well.

So EBD and DBC together is 88°.

44°+44°=88°

The solution of 2³ + 7 x 4 using PEDMAS is 36.

According to the PEMDAS rule, the computation wrapped in brackets or the parenthesis comes first in the order of operation. Exponents (degrees or square roots) are then operated on, followed by multiplication and division operations, and finally addition and subtraction.

Given:

2to the 3rd power +7 x 4

The mathematical expression is

= 2³ + 7 x 4

We know by PEDMAS rule is one of the rules which is exactly equal to BODMAS rule. The full form of PEMDAS is given below:

P – Parentheses  [{()}]

E – Exponents (Powers and Roots)

MD- Multiplication and Division (left to right) (× and ÷)

AS – Addition  and Subtraction (left to right) (+ and -)

According to the rule

2³ + 7 x 4

= 8 + 7 x 4

= 8 + 28

= 36

Hence, the answer is 36.

Learn more about PEDMAS here:

https://brainly.com/question/24086845

#SPJ1

Step-by-step explanation:

let's start with combinations, where the order does not matter - the 4 basis are indistinguishable.

C(5, 4) = 5! / (4! × (5-4)!) = 5! / 4! = 5

that makes sense, of course, as we only need to trace the possibilities for the one empty box : 5 possibilities.

now, the order of the 4 balls matter.

the 4! term in the denominator was actually taking that away, so we need to remove it.

that turns the combinations into permutations, where the order matters.

P(5, 4) = 5! / (5 - 4)! = 5! = 5×4×3×2×1 = 120

4 distinguishable balls can be placed in 5 distinguishable boxes in 120 ways.

Answer:

10

Step-by-step explanation:

Maria has 12 bags of chocolate chips, and each batch of cookies requires 1/2 bag of chocolate chips, and she makes 8 complete batches of cookies. So we can calculate the number of bags of chocolate chips used by:

1/2 * 8 = 4 bags

The number of bags of chocolate chips left after making the cookies is:

12 - 4 = 8 bags

A batch of cupcakes requires 3/4 of a bag of chocolate chips, and Maria has 8 bags of chocolate chips left. So we can calculate the maximum number of complete batches of cupcakes that she can make by:

8 / (3/4) = 8 * (4/3) = 32/3 = 10.67

Maria can make a maximum of 10 complete batches of cupcakes. Since a batch of cupcakes cannot be fractional, it means Maria can't make any more cupcakes after using all the chocolate chips.

Answer:

[tex]y = 3x - 1[/tex]

Step-by-step explanation:

Let's define the terms we are given to understand what the question is asking us to do:

⭐What is a linear function?

⭐What is slope-intercept form?

Thus, we need to write the equation of the table in slope-intercept form.

To do so, we can first find the y-intercept (c).

When x = 0, y = -1.

Therefore, the y-intercept (c) of the equation is -1.

Substitute this value into the slope-intercept form equation.

[tex]y = mx - 1[/tex]

Next, to find the slope, we have to use this formula:

⭐[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

I am going to choose the coordinates (1,2) and (2,5), but you can choose any other coordinates you are given that ISN'T (0,-1).

Substitute these coordinates into the slope formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\m = \frac{5-2}{2-1}\\m = \frac{3}{1}\\m = 3[/tex]

Therefore, the slope of this line is 3.

Substitute this value into the slope-intercept form equation.

[tex]y = mx - 1\\y = 3x - 1[/tex]

Hence, the equation of the linear function represented by the table is:

[tex]y = 3x - 1[/tex]

⭐if this response helped you, please mark it the "brainliest"!⭐

Translating the statement "Babies are illogical" into symbolic form willoll be C. P➡️~Q

Symbols and logical connectors are used in symbolic sentences to represent the sentence's logic.

A letter, such as p, can represent an entire statement in symbolic logic.

In symbolic form, the argument is p → q ~p ∴ ~q It is in the form of the fallacy of the inverse and it is a fallacy, or invalid

In this case, it should be noted that since p is that you are a baby and Q be you are logical. The symbolic form will be C.

Learn more about symbolic form on:

https://brainly.com/question/29057571

#SPJ1

Answer:

4+3=7

-2+3=7

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation that models the scenario and number of years for the population to reach 656,000 will be option A.

i.e. y=100(3)^t and 8 years.

What are equations?

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

Here,

2x – 5 and 13 are expressions

The sign that connects these two expressions is “=”.

Algebra considers two prominent families of equations, namely polynomial equations and linear equations. Polynomial equations with one variable can be written in P(x) = 0, where P is a polynomial, and ax + b = 0 is the general form of linear equations. Here, a and b are parameters. We can practice geometric or algorithmic methods from linear algebra or mathematical analysis to solve these equations. Also, there are different types of equations, such as:

Linear equations

Quadratic equations

Cubic equations

Quartic equations

Differential equations

Parametric equations

Now,

The equation as the population is compounding annually for the scenario

will be y=P*(1+R)^t

Here p=Initial population

R=rate of increment/ decrement of population

t=time

Hence,

y=100*(1+2)^t                    (R=2 )

y=100*3^t

Time for which the population will be 656,000 will be

656000=100*3^t

6560=3^t

therefore,

t=8 years.

To know more about Equations visit the link given below

https://brainly.com/question/12788590?referrer=searchResults

#SPJ1

Circle the equation that models the scenario and the number of years it takes for the population to reach 656,000 is y = 100(3)^x, 8 years.

To learn more about equation refer:

brainly.com/question/22688504

#SPJ1

Answer:

Answer

Step-by-step explanation:

20s³ +50s²+32s+6

Answer:

1.80642 rounded to the nearest thousandth is 1.806.

Step-by-step explanation:

The guy above me is correct