The coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)).
What is meant by coordinates?A group of values that exhibit precise positioning The first number on a graph represents the distance along, while the second number represents the distance up or down.
To find the coordinates of the remaining vertices of square ABCD, we can use the information given about diagonal AC and the properties of a square. Since a square has equal side lengths and right angles, we know that the distance between opposite vertices on a diagonal must be equal to the side length of the square.
Given the coordinates of vertex A and C, we can use the distance formula to find the length of AC:
Let the equation be Distance [tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
substitute the values in the above equation, we get
AC = [tex]\sqrt{((2 - (-2))^2 + (4 - 1)^2)}[/tex]
simplifying the equation, we get
AC = √(4 + 9) = √(13)
We can utilize the knowledge of the square's side length to determine the locations of the remaining vertices. Vertex B is known to have the same y-coordinate as vertex A, while vertex C is two units to the left in terms of the x-coordinate. Therefore, the coordinates of vertex B exists (-2 + 2√(13), 1).
Similar to vertex A, vertex D is known to have an identical x-coordinate, but its y-coordinate is four units below vertex C. Therefore, the coordinates of vertex D exists (-2, 4√(13))
Therefore, the coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)) respectively.
The complete question is:
Square ABCD has a diagonal AC with vertices A(-2, 1) and C(2, 4). Find the coordinates of the remaining vertices. Express your answers as decimals, if necessary.
The coordinates are and D.
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What is the slope of the line?
Answer:
4/5
Step-by-step explanation:
rise over run
Davis has $5.40 in his bank account on his fourth birthday. If his parents add $0.40 to his bank account every week, when will he have enough to buy the new Smokin' Derby race car set which retails for $24.99
Answer:
49 weeks
Step-by-step explanation:
y = mx + b
y is the total amount saved
x is the number of weeks
24.99 = .4x + 5.40 Solve for the number of months Subtract 5.40 from both sides
24.99 - 5.40 = .4x + 5.40 -5.40
19.59 = .4x Divide both sides by .4
[tex]\frac{15.99}{.4}[/tex] = [tex]\frac{.4x}{.4}[/tex]
48.975 = x
We cannot have 48.975 week, so at 49 weeks Davis will have enough money.
Answer:
49
Step-by-step explanation:
differentiate with respect to z = (xy²z)². x²yz³ + (x²yz³)³.(xyz)²
In order to differentiate between objects, one must first recognise their distinctions.
What does the term "difference" mean?In order to differentiate between objects, one must first recognise their distinctions. The difference between the chocolate sauce and the spicy bean dip, for instance, could be difficult to see if the party lighting is low. It is possible to distinguish between various.
To distinguish between objects being compared, to demonstrate, or to discover: On the basis of colour, religion, or country of origin, we do not make distinctions amongst our personnel. The majority of customers can easily distinguish between the cereal from our brand and that of our main rival.
-(x²yz³)³.(xyz)²+z = (xy²z)². x²yz³ + (x²yz³)³.(xyz)².
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The derivative of the expression, x²yz³ + (x²yz³)³ with respect to z = (xy²z)² is:
d/dz (x²yz³ + (x²yz³)³) = d/dz (x²yz³) + d/dz ((x²yz³)³)
= 3x²y²z³ + 2x³yz⁴ + 3 * (x²yz³)² * (3x²y²z³ + 2x³yz⁴)
How to find derivative?The derivative of the first term, x²yz³, with respect to z = (xy²z)² can be found using the chain rule:
d/dz (x²yz³) = d/dy (x²yz³) * dy/dz + d/dx (x²yz³) * dx/dz
= 3x²yz² * yz + 2x¹yz³ * xy²z
= 3x²y²z³ + 2x³yz⁴
The derivative of the second term, (x²yz³)³, with respect to z = (xy²z)² can be found using the chain rule and the power rule:
d/dz ((x²yz³)³) = d/dy (x²yz³)³ * dy/dz + d/dx (x²yz³)³ * dx/dz
= 3 * (x²yz³)² * (3x²yz² * yz + 2x¹yz³ * xy²z)
= 3 * (x²yz³)² * (3x²y²z³ + 2x³yz⁴)
Finally, the derivative of the expression, x²yz³ + (x²yz³)³ with respect to z = (xy²z)² is:
d/dz (x²yz³ + (x²yz³)³) = d/dz (x²yz³) + d/dz ((x²yz³)³)
= 3x²y²z³ + 2x³yz⁴ + 3 * (x²yz³)² * (3x²y²z³ + 2x³yz⁴)
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PLS HELP ME
Select ALL!!!!!!! of the inequalities represented by the graph
The inequality that is represented on the given graph is;
y ≥ -2x + c
How to Interpret Inequality Graphs?The general formula for equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, in this question, the coordinate of the y-intercept is (c, 0) and as such, the y-intercept is c.
Ths slope is gotten from two coordinates (2, -3) and (4, -7)
Slope = (-7 - (-3))/(4 - 2)
Slope = -4/2
Slope = -2
Now, the Inequalities that use < or > symbols are plotted with a dashed line to indicate that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to indicate that the line is included in the region.
Also, when we shade above the line, it is greater than and in this case it will be greater than or equal to since the line is a solid line to give the equation; y ≥ -2x + c
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These polygons are congruent. That means all their corresponding parts are equal in measure. Solve for x.
The measures of x and y in the congruent polygons are:
x = 7
y = 8
What are Congruent Polygons?Congruent polygons are two or more polygons with the same number of sides and the same length for each side. In other words, they are polygons that have the same shape and size.
Two polygons are congruent if and only if it is possible to superimpose one polygon over the other by using a combination of translation, rotation and reflection. Congruent polygons have the same area and perimeter.
Therefore:
m<E = m<A
Substitute the values:
4y - 4 = 28
4y = 28 + 4
4y = 32
4y/4 = 32/4
y = 8
m<F = m<B
Substitute:
10x + 65 = 135
10x = 135 - 65
10x = 70
10x/10 = 70/10
x = 7
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Larry and Donna bought a sofa at the sale price of $1,152. The original price of the sofa was $1,920.
Find the amount of discount in dollars.
Answer:
$768 would be the discounted amount in dollars
Step-by-step explanation:
1920 - 1152= 768
Analyze the diagram below and complete the instructions that follow.
Find the unknown side length, x. Write your answer in simplest radical form.
A.24
B.4// 37
C.2 // 154
D.5 // 117 I posted the pictures below
The value of unknown side length x in simplest radical form is 4√37.
Option B is the correct answer.
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
Two right triangles.
Applying the Pythagorean theorem in the bigger triangle.
We get,
25² = 7² + Length²
25² = 49 + Length²
Length² = 625 - 49
Length² = 576
Length = √576
Length = 24
Now,
Applying the Pythagorean theorem in the smaller triangle.
We get,
x² = 4² + 24²
x² = 16 + 576
x² = 592
x² = 16 x 37
x = √(16 x 37)
x = √(4² x 37)
x = 4√37
Thus,
The value of x is 4√37.
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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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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.
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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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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graph y = 6/5x - 6/5
The ordered pairs are (1,0), (2,6/5),(3,12/5)
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: The equation as y = 6x/5 - 6/5
putting (1,0) in the equation we get 6×1/5-6/5=0
Similarly we can find the ordered pair as y = 6/5x - 6/5
Hence, The ordered pairs are (1,0), (2,6/5),(3,12/5)
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which graph best represents the function f(x)=1(1.5)^x
a boat traveled 90 miles each way downstream and back. the tip downstream took 5 hours. the trip back took 15 hours. find the speed of the boat in still water and the speed of the current.
The speed of the boat in still water is 12mikes per hour and the speed of the current is 6milesper hour
What is speed?Speed is defined as, the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
speed = distance /time
speed with downstream = 90/5 = 18miles per hour
speed against down stream = 90/15 = 6 miles per hour
represent the speed of the boat in still water by x and the speed of the downstream by y
therefore x+y = 18 equation 1
x-y = 6 equation 2
subtract equation 2 from 1
2y = 12
y = 12/2 = 6miles/hour
substitute 6 for x in equation 1
x + 6 = 18
x = 18-6 = 12 miles/hour
therefore the speed of the boat with in still water is 12miles per hour and the speed of the current is 6 miles per hour
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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.
How does an angle complementary to acuate angle A compare with an angle supplementary to angle A?
The angle complementary to an acute angle A is always acute and smaller than 90 degrees, while the angle supplementary to angle A is always larger than 90 degrees, they cannot be equal since they are adding up to 90 degrees and 180 degrees respectively.
What is Complementary AngleA complementary angle is a pair of angles that add up to 90 degrees. Two angles are said to be complementary if the sum of their measures is 90 degrees. The two angles are called complementary angles because they "complete" a right angle.
An angle is considered acute if it measures less than 90 degrees. A complementary angle is an angle that, when added to another angle, will sum up to 90 degrees. So, if angle A is acute, then its complement angle will also be acute.
On the other hand, an angle supplementary to angle A is an angle that, when added to angle A, will sum up to 180 degrees.
So, an angle complementary to an acute angle A is always acute and smaller than 90 degrees, while an angle supplementary to angle A will always be larger than 90 degrees. They can't be equal since they are adding up to 90 degrees and 180 degrees respectively.
For example, if angle A measures 60 degrees, its complementary angle will measure 30 degrees (90 - 60 = 30) and its supplementary angle will measure 120 degrees (180 - 60 = 120).
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Which of the numbers is divisible by 3, 4, 5, and 6?
A. 1,080
B. 588
C. 2,360
D. 375
bro just use a calculator, how hard is it to make some calculation for real..
anyway the answer is A. 1080
(2%)Find the solution set ofx^2+4x-21≤0.
Answer:
(-7,3)
Step-by-step explanation:
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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3 1/4 as an im propder fraction
[tex]3\dfrac{1}{4}[/tex] as an improper fraction.
To convert a mixed number into a fraction, you'll first have to multiply the whole number(3) by the denominator(4) and add that to the numerator(1).
The denominator will stay the same.
[tex]3\dfrac{1}{4}[/tex]
[tex]\dfrac{3\times4+1}{4}[/tex]
[tex]=\fbox{$\dfrac{13}{4} $}[/tex]
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.
Find an ordered pair (x, y) that is a solution to the equation.
4x-y=3
(x, y) = (_, _)
PLEASE HELP!!
Solve for y 4y+5/3=y-10/2
Answer:
y = -8
Step-by-step explanation:
the answer you chose is correct!!
Evaluate the following expression using the properties of logarithms.
log subscript 4 left parenthesis 4 right parenthesis plus log subscript 4 left parenthesis 16 right parenthesis plus log subscript 4 left parenthesis 64 right parenthesis
10
9
6
17
Answer:
6
Step-by-step explanation:
Given logarithmic expression:
[tex]\log_{4}\left(4\right)+\log_{4}\left(16\right)+\log_{4}\left(64\right)[/tex]
Rewrite 16 as 4² and 64 as 4³:
[tex]\implies \log_{4}\left(4\right)+\log_{4}\left(4\right)^2+\log_{4}\left(4\right)^3[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies \log_{4}\left(4\right)+2\log_{4}\left(4\right)+3\log_{4}\left(4\right)[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies 1+2(1)+3(1)[/tex]
Simplify:
[tex]\implies 1+2+3[/tex]
[tex]\implies 3 + 3[/tex]
[tex]\implies 6[/tex]
By what percentage does your current volume need to increase to meet your goal of 50% of the market share for Category A?
Answer: To determine this percentage, we would need to know the current market share for Category A and the desired market share goal of 50%. With this information, we could calculate the difference between the current market share and the desired market share and express that difference as a percentage of the current market share. Without this information, I am unable to provide an exact percentage.
Step-by-step explanation:
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?
You have two different saving accounts.for A, the interest earned after 18 months is 12.00. For account B, the interest earned after 27 months is 27.00 Which account earned you the most interest in the first year? Explain your answer
Account A earned the most interest in the first year, since it earned 12.00 in 18 months compared to the 27.00 earned by Account B in 27 months.
Which account earned you the most interest in the first year?This means that Account A earned 12.00 in 1 year, while Account B only earned 9.00 in the same time period.The account that earned you the most interest in the first year depends on the interest rate for each individual account.To find out which account earned you the most in the first year, we can use the equation A = P(1+r/n)^nt. In this equation, A stands for the amount of money in the account, P stands for the principal amount, r stands for the interest rate, n stands for the number of times the interest is compounded per year, and t stands for the number of years. For account A, plugging in the numbers given, we get A = P(1+12/18)^18. In this equation, P represents the principal amount in account A after the first year.For account B, plugging in the numbers given, we get A = P(1+27/27)^27. In this equation, P represents the principal amount in account B after the first year. By comparing the two equations, we can determine which account earned you the most interest in the first year.If we compare the two equations, we find that account B earned you more interest than account A in the first year because the interest rate for account B was higher than the interest rate for account A. Therefore, account B earned you the most interest in the first year.To learn more about earning interest at different rates refer to:
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Aaron is remodeling his patio. He will decrease the length of his patio, L, by 7 feet. Aaron will also changed the patio's width to be 3 times the original width, W. Which expression shows the ratio of the length to the width of the remodeled patio?
Answer: top right
Step-by-step explanation:
It says decrease by 7 which mean subtract (-) and times 3 mean multiply by 3 (x3)
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.
More about the transformation of the shape link is given below.
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Write the equation of the horizontal line passing through the given point (7,11)
Answer:
y = 11
Step-by-step explanation:
Answer:
77
Step-by-step explanation: