Answer:
3 1/3 ft
Step-by-step explanation:
Let SHADOW and HEIGHT pertain to the building, and let shadow and height pertain to the tree.
The proportion is:
HEIGHT/SHADOW = height/shadow
Now we fill in with the numbers we know, and "shadow" for the shadow of the tree.
(36 ft)/(20 ft) = (6 ft)/(shadow)
Cross multiply.
36 × shadow = 6 × 20
36 × shadow = 120
shadow = 120/36 = 10/3
shadow = 3 1/3
Answer: 3 1/3 ft
?????????????????
???????
Answer:
he never made a mistake, so the answer is A
Step-by-step explanation:
these are in line with integers and their rules.
The rule that's being applied there's if numbers of the same base are being divided, maintain the base and subtract the powers.
A cylindrical jar contains three glass balls each has a diameter of 2cm and their surfaces touch the inner side of the jar as shown below. What is the volume of the gap in the jar?
6.28 cubic centimeters is the volume of the gap in the jar.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that cylindrical jar contains three glass balls each has a diameter of 2cm
Let us find the volume of each sphere.
Volume of sphere=4/3×πr³
As diameter is 2 then radius is 1.
Volume of each sphere=4.186
Volume of three spheres=3×4.186=12.56
Now let us find the volume of cylinder.
The diameter of cylinder will be 2 and height is 6 cmas there are 3 spheres of diameter 2cm.
Volume of cylinder=πr²h
=3.14×1×6
=18.84 cubic centimeters.
So the volume of the gap in the jar = 18.84-12.56
=6.28 cubic centimeters.
Hence, 6.28 cubic centimeters is the volume of the gap in the jar.
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HELPPP HHHEELOOOOOOO SCREENSHOT ATTACHED
Answer:
102 in.²
Step-by-step explanation:
the given figure is made up of a triangle and a rectangle. we can find out the areas of two of them separately and then add it up for the area of the whole figure as
area of rectangle:-
= length* breadth
= 15 * 5 in.²
= 75 in.²
area of triangle :-
= 1/2 *base*height
here base = 15 - 3 - 3 = 9in.and height= 11 -5 = 6 in.= 1/2*9*6in.²
= 27in.²
Total area
= 75 + 27 = 102in.² { required answer }
Answer:
D) 102 in²
Step-by-step explanation:
The given composite figure is made up of a triangle and a rectangle.
Rectangle
[tex]\begin{aligned}\textsf{Area of a rectangle}&=\sf length \times width\\&=15 \times 5\\&=75\; \sf in^2\end{aligned}[/tex]
Triangle
[tex]\begin{aligned}\textsf{Area of a triangle}&=\sf \dfrac{1}{2} \times base \times height\\\\&=\dfrac{1}{2} \times (15-3-3) \times (11-5)\\\\&=\dfrac{1}{2} \times 9 \times 6\\\\&=\dfrac{9}{2} \times 6\\\\&=\dfrac{54}{2} \\\\&=27\; \sf in^2\end{aligned}[/tex]
Therefore, the area of the given composite figure is:
[tex]\begin{aligned}\textsf{Area of composite figure}&=\textsf{Area of rectangle}+\textsf{Area of triangle}\\&=75+27\\&=102\; \sf in^2\end{aligned}[/tex]
Solve x/5-3<5 for oddesyywaree
Answer:
x < 40
Step-by-step explanation:
x/5-3<5
=5×x/5 -3×5 < 5×5
=x - 15 < 25
NOTE 5 will cancel 5 living x.
=x < 25 + 15
x < 40.
Therefore x is 40.
Debra is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Debra has been adding money. Suppose that x and y are related by the equation 650+20x=y.
Answer the questions below.
Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
The rate of change is $20 per week while the initial value is $650
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept.
Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Debra has been adding money.
Given the equation:
y = 20x + 650
The y intercept is $650 and the slope is $20 per week
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Express the trig ratios as fractions in simplest terms.
The value of trig in ratios as fraction are, sin X = 45/24 , cos W = 17/8
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle is shown in figure.
Now, we can find all the values as;
⇒ sin X = Perpendicular / Hypotenuse
⇒ sin X = 45 / 24
And, we get;
⇒ cos W = Base / Hypotenuse
⇒ cos W = 51 / 24
⇒ cos W = 17 / 8
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write the equation of the line that passes at the point ( 5 , 12 ) with the slope m = 3/5 in slope-intercept form.
Answer:
y = 3/5x + 7
Step-by-step explanation:
y = 3/5x + b
12 = 3/5(5) + b
12 = 5 + b
b = 7
y = 3/5x + 7
Find an ordered pair (x, y) that is a solution to the equation.
4x-y=3
(x, y) = (_, _)
Evaluate the expression if x = -3, y = 5, and z=2. (If an answer is undefined, enter UNDEFINED.)
x+y+z/
4y²x
The value of the expression (x + y + z) / (4xy²) at x = -3, y = 5, and z = 2 will be - 1/8.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ (x + y + z) / (4xy²)
The expression if x = -3, y = 5, and z = 2. Then the value of the expression is given as,
⇒ (-3 + 5 + 2) / (4 × (-2) × (2)²)
⇒ - 4 / 32
⇒ - 1 / 8
The value of the expression (x + y + z) / (4xy²) at x = -3, y = 5, and z = 2 will be - 1/8.
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Determine a series of transformations that would map Figure J onto Figure K. J
Figure.
Figure
Figure J is rotated 90° clockwise and then translated by 3 units toward the right.
What is a transformation of a shape?A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
The translation does not change the shape and size of the geometry. But changes the location.
Figure J is rotated 90° clockwise and then translated by 3 units toward the right.
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find the parametric equation of the conic.sections (x+1)²÷16-y²÷9=1
A circle with a radius of three and a center at (-1, 4) is a conic section with the parametric equations X=3cos(t)-1 and Y=3sin(t)+4.
Find the parametric equation of the conic sections ?The circle, the ellipse, the parabola, and the hyperbola are examples of conic sections.
Using a third variable (t or ), parametric equations are utilized to express the x and y variables in terms of a less complex way.
The parametric equation for a circle is given by: x=r cos(t) +h, y=r sin(t) +k, where r is the radius of the circle and (h, k) is the center of the circle. The equation for a circle is (x- h)2+(y- k)2 = r2.
A circle with a radius of three and a center at (-1, 4) is a conic section with the parametric equations X=3cos(t)-1 and Y=3sin(t)+4.
The circle's equation is (x + 1)2 + (y - 4)2 = 32.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
below
Step-by-step explanation:
The derivative of the given equation gives the RATE (slope) in the given year
Derivative = -.0102 t^2 +.232 t -.341
for t = 16 this equals .7598 <=====this one is greater
for t = 19 this equals .3848
Answer:
i xibfvlmow 10 seconds
Step-by-step explanation:
k
The test scores for the analytical writing section of a particular standardized test can be approximated by a normal distribution, as shown in the figure.
(a) What is the maximum score that can be in the bottom 5% of scores?
(b) Between what two values does the middle 90% of scores lie?
The maximum score that can be in the bottom 5% of scores is 2.64
The middle 90% of scores lie between 2.88 and 4.56.
What is the maximum score that can be in the bottom 5% of scores?(a) We must determine the score that corresponds to the 5th percentile of the normal distribution in order to determine the highest score that may fall inside the lowest 5% of scores.
We may use the standard normal table to determine that the 5th percentile corresponds to a standard normal score of -1.28 using the mean and standard deviation supplied (3.6 and 0.75, respectively). We may use the following formula to return to the original scale:
x = mu + z * sigma
Where
x is the original score, mu is the mean (3.6), z is the standard normal score (-1.28), and sigma is the standard deviation (0.75).Plugging in the values, we get:
x = 3.6 + (-1.28) * 0.75
x= 2.64
(b)
We must determine the 5th and 95th percentiles of the normal distribution in order to determine the range of scores that the middle 90% of scores fall inside.
The standard normal table may be used to determine that the 5th percentile corresponds to a normally distributed score of -1.28 and the 95th percentile corresponds to a standard normal rating of 1.28 using the mean and standard deviation supplied (3.6 and 0.75, respectively). We may use the following formula to return them to their original scale:
x = mu + z * sigma
Where
x is the original score, mu is the mean (3.6), z is the standard normal score, and sigma is the standard deviation (0.75).Plugging in the values, we get:
x = 3.6 + (-1.28) * 0.75
= 2.88 for the 5th percentile
x = 3.6 + 1.28 * 0.75
= 4.56 for the 95th percentile
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14. Ryan owns a small music store. He currently charges $10 for each CD. At this price, he sells about 80 CDs a week. Experience has taught him that a $1 increase in the price of a CD means a drop of about five CDs per week in sales. At what price should Ryan sell his CDs to maximize his revenue?
Answer: Ryan should sell his CDs for $13 to maximize his revenue.
Step-by-step explanation:
To find the price at which Ryan should sell his CDs to maximize his revenue, we need to use the information provided about the relationship between price and sales, and the formula for revenue (price x quantity sold).
Step 1: Identify the relationship between price and sales. We know that a $1 increase in the price of a CD leads to a drop of 5 CDs per week in sales.
Step 2: Create an equation that relates price, quantity sold, and revenue. Let P be the price of a CD, Q be the quantity sold, and R be the revenue. Then, we have R = P x Q
Step 3: Create a table that shows the relationship between price, quantity sold, and revenue.
Price Quantity Sold Revenue
10 80 800
11 75 825
12 70 840
13 65 845
14 60 840
15 55 825
16 50 800
17 45 785
18 40 720
19 35 665
20 30 600
Step 4: Identify the price that maximizes revenue. From the table we can see that the revenue is maximum at $13 which is 845 and this is the price at which Ryan should sell his CDs to maximize his revenue.
Therefore, Ryan should sell his CDs for $13 to maximize his revenue.
What’s the graph to t/3 - 1 > -3
Answer: The answer is C
Step-by-step explanation: This is because the equation has a greater than or equal to sign (≥). This mean that there will be a closed dot. Also, when it comes to inequalities, the sign points to where the line will be drawn, (greater than is to the right and less than is to the left), which indicates that the answer is C
Suppose that among the population of smartphone owners with
16
GB
16GB16, start text, G, B, end text of storage, the mean amount of storage used is
13
GB
13GB13, start text, G, B, end text and the standard deviation is
3
GB
3GB3, start text, G, B, end text. A consumer research group regularly takes random samples of
50
5050 of these customers and calculates the mean amount of storage
x
ˉ
x
ˉ
x, with, \bar, on top used in each sample.
The mean and standard deviation based on the information given will be 13gb and 0.4 gb.
How to calculate the mean?On average, smartphone owners have 13 GB of storage, with a 3 GB standard deviation. 50 smartphone owners are chosen at random as a sample from the general population.
Remember that the sampling distribution resembles the normal distribution if the sample size is large enough (n 30), according to the central limit theorem.
The sampling distribution's mean in this instance is given by because the sample size is sufficient (n = 50).The mean of the sampling distribution is 13 gb
The standard deviation will be:
= 3 / ✓50
= 3 / 5
= 0.4 gb.
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Complete question
Suppose that among the population of smartphone owners with 16 GB of storage, the mean amount of storage used is 13 GB and the standard deviation is 3 GB. A consumer research group regularly takes random samples of 50 of these customers and calculates the mean amount of storage Calculate the mean and standard deviation of the sampling distribution x bar.
A landscaping business is purchasing plants from a nursery to finish a project. It will
cost $14 each to buy each tree and $7 each to buy each bush. The landscaper wishes to
keep the spending to no more than $870. Let t be the number of trees and b be the
number of bushes.
Select the inequality that describes the situation.
14t7b870
14t+7b2870
14t+7b < 870
O14t+7b870
Answer: 818quuquqiqi$
Step-by-step explanation: because i dont wnna waycj brainly ads haha ok so you see this is shbwbwbwhjwwkkw because hwuqopqpoqiwnndncixo9nbccssioakaka.
What is the slope of the line?
Answer:
4/5
Step-by-step explanation:
rise over run
Suppose Fawn plans to take a sample to determine a 90 percent confidence interval for the population mean weight of chocolate in every package. She wishes the confidence interval to be of the form “plus or minus 3 grams,” and is willing to assume that the population standard deviation is equal to 12 grams. How large a sample should she take?
Suppose Fawn plans to take a sample to determine a 90 percent confidence interval for the population mean weight of chocolate in every package. Fawn should take a sample size of at least 43, to have a 90% confidence interval of plus or minus 3 grams in the weight of chocolate in every package.
What is the sample?Generally, Fawn can use the formula for the sample size needed to estimate a population mean with a certain level of confidence:
n = (z*σ / E)^2
Where:
n = sample size z = the z-score for the desired level of confidence (e.g., for 90% confidence, z = 1.645) σ = the population standard deviation (12 grams in this case) E = the margin of error (3 grams in this case)So the sample size needed is:
n = (1.645 * 12 / 3)^2
n= (5.48)^2
n = 43.296
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which graph best represents the function f(x)=1(1.5)^x
What is the surface area? 11 ft 26 ft 21 ft
The surface area of the triangular prism is 416 yd²
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The surface area of a solid object is the total area that the surface of the object occupies.
From the diagram:
Surface area = 2(10 yd * 10 yd) + 2(0.5 * 12 yd * 8 yd) + (10 yd * 12 yd) = 416 yd²
The surface area is 416 yd²
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Ali used 2/7 of a foot of ribbon to attach a decoration to his rearview mirror. Now, he has 10/21 of a foot of ribbon left.
QUESTION: How much ribbon did Ali start with?
The quantity of ribbon that Ali started with was 16/21 feet, based on the mathematical operation of addition.
What are mathematical operations?The basic mathematical operations include addition, subtraction, division, and multiplication.
In the addition operation, two or more addends are added to obtain a result called the sum or total using the equation symbol (=) and the addition operand (+).
The quantity of ribbon attached to the rearview mirror = 2/7
The remaining quantity of ribbon after the attachment = 10/21
The quantity of ribbon Ali started with = 16/21 (2/7 + 10/21)
Thus, using the addition operation, we can conclude that Ali started with 16/21 feet of ribbon.
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Please please look at the picture and answer the question thank you
Answer:
y = 3x -1
Step-by-step explanation:
You want the equation of the line through the points (0, -1) and (1, 2), among others.
Y-interceptThe y-value when x=0 is the y-intercept. The table shows you it is -1.
SlopeThe slope is the difference in y-values when x-values increase by 1. For the first two points in the table, the y-value shows an increase of ...
2 -(-1) = 3
This means the slope is 3.
Slope-intercept equationThe slope-intercept equation of a line is ...
y = mx +b . . . . . . . where m is the slope, and b is the y-intercept
For your line, we have determined m=3, b=-1, so the equation is ...
y = 3x -1
Use the circle Q shown below to answer the following questions:
4. Measure of arc AB = ______ 10. Measure of arc BAD = _____
5. Measure of arc DC = ______ 11. Measure of arc ADC = _____
6. Measure of arc BC = ______ 12. Measure of arc ACB = _____
7. Measure of arc AED =______ 13. Measure of arc ABD = _____
8. Measure of arc BD = ______ 14. Measure of arc CED = _____
9. Measure of arc AC =______ 15. Measure of arc BAC=_____
The measure of the arcs in relationship to the central angles measures are:
4. 40°
5. 50°
6. 90°
7. 180°
8. 140°
9. 130°
10. 220°
11. 230°
12. 320°
13. 180°
14. 310°
15. 270°
What is the Relationship between the Measure of the Central Angle and the Subtended Arc of a Circle?The relationship is that the measure of the central angle is the same as the measure of the arc it subtends in a circle.
4. Measure of arc AB = measure of central angle AOB
Substitute
Measure of arc AB = 40°
5. Measure of arc DC = measure of central angle DOC
Substitute
Measure of arc DC = 50°
6. Measure of arc BC = 180 - 40 - 50 = 90°
7. Measure of arc AED = 180°
8. Measure of arc BD = 90 + 50 = 140°
9. Measure of arc AC = 40 + 90 = 130°
10. Measure of arc BAD = 180 + 40 = 220°
11. Measure of arc ADC = 180 + 50 = 230°
12. Measure of arc ACB = 360 - 40 = 320°
13. Measure of arc ABD = 180°
14. Measure of arc CED = 360 - 50 = 310°
15. Measure of arc BAC = 40 + 180 + 50 = 270°
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Complete the following:
Write an exponential expression: choose a number between 0 and 10 to be the base and another number between 0 and 10, different from the base, to be the exponent.
Label the base and the exponent.
Then write the exponential expression in expanded form and standard form.
Essay
2 × 10³ is an exponential expression, which has a standard form as 2000.
What is exponential expression?Exponential expressions are just a way to write powers in short form. The exponent
indicates the number of times the base is used as a factor. So in the case of 32 it can
be written as 2 × 2 × 2 × 2 × 2 = 25, where 2 is the “base” and 5 is the “exponent”.
The expanded form comes in a variety of forms. Exponents are employed. The expanded form of that expression is what is stated above.
One more makes use of multipliers like 1, 10, 100, 1000, and so forth. The expression broadens in that form as...
10^2 = 1×100
Another expanded form uses the expanded form's individual digits, setting the others to zero.
10^2 = 100
The standard format is...
10^2 = 100.
Thus, 2 × 10³ is an exponential expression, which has a standard form as 2000.
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12.5
points
Skipped
eBook
Print
References
The cost per item at a supermarket
follows an exponential distribution.
There are many inexpensive items and
a few relatively expensive ones. The
mean cost per item is $10.5. What is the
percentage of items that cost:
a. Less than $7.5? (Round your answer
to 4 decimal places.)
Probability
Answer: 37.33 % of items cost less than $7.5
Step-by-step explanation:
To find the percentage of items that cost less than $7.5, we would need to know the probability distribution function of the cost per item, as well as the specific parameters of the distribution (such as the shape parameter).
Since the information provided is that the cost per item follows an exponential distribution and the mean cost per item is $10.5,
We can use the cumulative distribution function (CDF) of the exponential distribution which is
F(x) = 1 - e^(-λx)
where x is the cost of the item, λ is the rate parameter and e is the base of the natural logarithm.
We know the mean is $10.5 , and in an exponential distribution the mean and the rate parameter are equal, so we can say λ = 1/10.5
To find the percentage of items that cost less than $7.5, we need to find the probability that X < 7.5, which is the same as finding F(7.5)
So, F(7.5) = 1 - e^(-λ*7.5) = 1 - e^(-0.714)
Then, we need to convert this probability to percentage, so we need to multiply it by 100
F(7.5) = (1 - e^(-0.714)) * 100 = 37.33 %
Therefore, 37.33 % of items cost less than $7.5
3.8333 repeating as a fraction
Answer:
Answer and Explanation: As a fraction 3.83 (3 repeating) is 38399 3 83 99 . To convert 3.83 (3 repeating) to a fraction, we ignore the units as they will remain units. We then set up one equation of our unknown x being equal to 0.83333... and another that is 100 times greater, 100x=83.3333...
Regan won the grand prize at a store giveaway. The grand prize winner is guaranteed to win at least $500 in cash and prizes.
A. List three possible dollar amounts in cash and prizes Regan can win
B. Write an inequality to represent the dollar amounts d in cash and prizes Regan can win.
An inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, Regan won the grand prize at a store giveaway. The grand prize winner is guaranteed to win at least $500 in cash and prizes.
Let d represent the amount of cash in dollars and p represent the amount of prizes.
Since the grand prize winner is guaranteed to win at least $500,
So, p + d ≥ 500
Therefore, an inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.
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Please help thanks you
in word problems
each means multiply
3 tables each day means
3 times x or 3x
2 tables each day means
2x
the day that Miguel and Asia have the same number of tables means
38-3x=28-2x
x=10
y=38-3x
y=28-2x
y = 8
graph
y=38-3x
y=28-2x
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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:
Problem 1
The resolution formula for arcseconds is 1 radian = 206265 arcseconds.
To convert 1.22 radians to arcseconds, we can use the conversion ratio of 1 radian = 206265 arcseconds: 1.22 radians x 206265 arcseconds/radian = 252438.3 arcseconds
Problem 2
a. Literal equation: D = (Wavelength / (2* arcsecond))
Variable to solve for: D (diameter of camera lens)
b. Chlorophyll reflects green light. The wavelength of green light on the electromagnetic spectrum is approximately 550 nanometers.
c. D = (Wavelength / (2* arcsecond))
D = (550 x 10^-9 meters / (2* 6 x 10^-6 radians))
D = (550 x 10^-9 meters / 12 x 10^-6 radians)
D = (550 / 12) x 10^-9 meters / 10^-6 radians
D = 45.83 x 10^-3 meters or 0.04583 meters
Problem 3
The graph would have wavelength in nanometers on the x-axis and diameter of lens or mirror in meters on the y-axis.
The graph would start at 100 nanometers and end at 10,000 nanometers on the x-axis and the y-axis would start at 0 and end at the diameter of the lens or mirror needed to obtain a resolution of 1 arcsecond.
The graph would show that as the wavelength increases, the diameter of the lens or mirror needed to obtain a resolution of 1 arcsecond would decrease. At a wavelength of 10,000 nanometers (10 microns), the diameter of the camera would be 0.04583 meters.
The spatial resolution of a telescope depends on the size of the telescope's aperture and the wavelength of light being detected.
The spatial resolution of a telescope has an inverse relationship with the wavelength of light being detected and the telescope's diameter. As the wavelength increases, the spatial resolution decreases, and as the diameter of the telescope increases, the spatial resolution increases.
The spatial resolution for our eyes is about 1 arcminute.
Spatial resolution is related to remote sensing in that it refers to the ability of a sensor to distinguish between two objects that are close together. A higher spatial resolution allows for more detailed information to be gathered from an image.
The GOES (Geostationary Operational Environmental Satellite) detects weather patterns, temperature, humidity, and other atmospheric conditions. It uses remote sensing technology to gather and transmit data to meteorologists for weather forecasting and monitoring.
Answer:
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?
