Answer:X=2.5
Step-by-step explanation:
Divide both sides by 3
3 over 3 cancels out and 7.5 over 3 equals 2.5
Answer:
x= 2.5
Step-by-step explanation:
divide both sides by 3
Unit Test Review
Active
Yellow light has a frequency of 5.2 x 1014 Hz and travels at a speed of 3.0 x 108 m/s. What is the wavelength of yellow light, in
meters?
5.8 x 10-7m
2.2 x 10-6m
1.7 106 m
8.2 * 1022 m
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the answer is 5.8 x 10-7m
your welcome
The required wavelength of the yellow light is [tex]5.8\times10^{-7}[/tex] m
The correct option is (A).
Wavelength:
The wavelength can be calculated when frequency and speed of the wave are given as
wavelength [tex]\lambda[/tex] = [tex]\frac{v}{f}[/tex]
where v is the velocity of the wave and f be the frequency of the wave.
How to calculate wavelength?Here we have given that
The frequency f = [tex]5.2 \times10^{14}[/tex] Hz
The speed v = [tex]3 \times10^{8}[/tex] m/s
Therefore substitute into above formula
Wavelength [tex]\lambda[/tex]= [tex]\frac{3\times10^{8}}{5.2\times10^{14}}}[/tex]
Wavelength [tex]\lambda[/tex] = [tex]\frac{3}{5.2}\times10^{8-14}[/tex]
Wavelength [tex]\lambda[/tex] = [tex]0.5769\times10^{-6}[/tex]
Wavelength [tex]\lambda[/tex] = [tex]0.5769\times10^{-6}[/tex]
Wavelength [tex]\lambda[/tex] = [tex]5.769\times10^{-7}[/tex]
Wavelength [tex]\lambda[/tex]= [tex]5.8\times10^{-7}}[/tex] m
Therefore the correct option is (A).
This is the conclusion to the answer
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Select the correct answer from each drop down
Answer:
The average rate of change on [1,3] is [tex]\frac{1}{2}[/tex] the average rate of change on [2,4]. The average rate of change on [1,3] is [tex]\frac{2}{5}[/tex] the average rate of change on [1,5]. So the function can not be linear.
Step-by-step explanation:
See the table attached.
The average rate of change on [1,3] is = [tex]\frac{32 - 8}{3 - 1} = 12[/tex]
The average rate of change on [2,4] is = [tex]\frac{64 - 16}{4 - 2} = 24[/tex]
Again, the average rate of change on [1,5] is = [tex]\frac{128 - 8}{5 - 1} = 30[/tex]
Therefore, the average rate of change on [1,3] is [tex]\frac{1}{2}[/tex] the average rate of change on [2,4]. The average rate of change on [1,3] is [tex]\frac{2}{5}[/tex] the average rate of change on [1,5]. So the function can not be linear. (Answer)
Jolie sends between 22 and 23 text messages per day. Each text message costs $0.89. Suppose Jolie's cellular bill spans a period of 6 weeks. Which is a reasonable amount that she would spend on text messages on one cellular bill? A. $135 B. $9,108 C. $945 D. $158
Answer:
C. $945
Step-by-step explanation:
Cost of 1 cellular bill = (number of text msgs per day) x (cost per text msg) x (number of days in billing period)
in this case, it is given that :
cost per text msg = $0.89
number of texts per day = 22 or 23
billing cycle = 6 weeks = 6 x 7 = 42 days
hence,
Cost of 1 cellular bill = (22 or 23) x $0.89 x 42 days
if she sends 22 messages,
Cost of 1 cellular bill = (22) x $0.89 x 42 days= $822.36
if she sends 23 messages,
Cost of 1 cellular bill = (2) x $0.89 x 42 days= $859.74
if we compare thse 2 numbers that we have calculated with the choices, the closest match would be C. $945. The rest are just too far away in comparison.
A rectangle has a height of 3b^2 and a width of 4b^4+2b-6.
Express the area of the entire rectangle.
Answer:
see the attach file
Step-by-step explanation:
if you have any question then reply me again
The area of the rectangle will be 12b⁶ + 6b³ – 18b².
What is the area of the rectangle?Let H be the height and W be the width of the rectangle. The area of the rectangle is the product of height and width.
Then the area of the rectangle will be
Area of the rectangle = H × W square units
A rectangle has a height of 3b² and a width of 4b⁴ + 2b – 6.
Then the area of the rectangle will be
Substitute H = 3b² and W = 4b⁴ + 2b – 6. Then the area of the rectangle will be
Area of the rectangle = 3b² x (4b⁴ + 2b – 6)
Simplify the equation, we have
Area of the rectangle = 3b² · 4b⁴ + 3b² · 2b – 3b² · 6
Area of the rectangle = 12b⁶ + 6b³ – 18b²
Thus, the area of the rectangle will be 12b⁶ + 6b³ – 18b².
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By what percent will a fraction decrease if its numerator is decreased by 50% and its denominator is decreased by 25%?
Answer:
33 2/3 % (33.33%)
Step-by-step explanation:
Fraction = x/y
After decrease: (x - .5) / (y-.25)
Simplify : .5x / .75y
= 2/3
1 - 2/3 = 1/3 = .33 = 33 1/3 %
Hope this helps
If Laura bought 2.1 pounds of apples is the price per pound of apples greater or less than $1
Answer:
The price per pound of apples is greater than $1.
Step-by-step explanation:
Please consider the complete question:
Three coworkers decided to buy fruit to share at lunch time. Antonii spent $1.47 on bananas.Laura spent $2.88 on apples. Suzanne spent $2.85 on oranges. If Laura bought 2.1 pounds of apples, is the price per pound of apples greater than or less than $1 ? how can you tell?
To find the price of apples per pound, we need to divide total amount paid by Laura ($2.88) with total pounds of apples (2.1 pounds) bought.
[tex]\text{Price of apples per pound}=\frac{\$2.88}{2.1}[/tex]
[tex]\text{Price of apples per pound}=\$1.37142857[/tex]
Since the price of apples per pound is $1.37, therefore, the price per pound of apples is greater than $1.
We can simply tell that the price per pound of apples is greater than $1 because 2.88 is greater than 2.1. So when we will divide 2.88 by 2.1, then we will get a number greater than 1.
To find the price per pound of apples, we divide the total cost of the apples by the weight of the apples.
Explanation:To determine whether the price per pound of apples is greater or less than $1, we need to divide the total cost of the apples by the weight of the apples. The question states that Laura bought 2.1 pounds of apples. To find the total cost, we can use the information given in the reference:
10 apples × 50 cents each = $5.00 spent on apples in 2001.
Dividing $5.00 by 2.1 pounds gives us the price per pound of apples Laura bought, which is approximately $2.38. Therefore, the price per pound of apples is greater than $1.
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a cafeteria worker is wondering how student lunch prices at a high school have changed over time. she researches lunch prices for the years 2000 through 2015 and plots the data in a scatter plot. the best-fit line for the data has the equation y=0.057 x + 1.150, where x is the number of years since 2000 and y is the student lunch price, in dollars.
determine whether each statement below is true ot false based on the question of the line best fit. select true or false for each question.
the student lunch price was generally increasing between 2000 and 2015.
the student lunch price was changed by approximately 5.7 cents a year.
the student price in 2015 was approximately $1.15.
Answer:
True false true
Step-by-step explanation:
TRUE, the student lunch price was generally increasing between 2000 and 2015 as the equation [tex]y=0.057x+1.150[/tex] is a linearly increasing function.
TRUE, the student lunch price was changed by approximately [tex]5.7\rm cents[/tex] a year.
FALSE, the student price in 2015 was approximately $1.15.
The best-fit line for the data has the equation [tex]y=0.057x+1.150[/tex] , where [tex]x[/tex] is the number of years since 2000 and [tex]y[/tex] is the student lunch price, in dollars.
So, it can be seen here from the best-fit line equation that it is a linearly increasing function so, the student lunch price was generally increasing between 2000 and 2015.
Now, differentiating the given best-fit line for the data has the equation [tex]y=0.057x+1.150[/tex] with respect to [tex]x[/tex] to determine the approximated change of the lunch price per year
[tex]\dfrac{dy}{dx}=\dfrac{d}{dx}(0.057x+1.150)\\\dfrac{dy}{dx}=\$0.057\\\dfrac{dy}{dx}=5.7\rm cents[/tex]
And, [tex]2015[/tex] is [tex]15[/tex] years from the year [tex]2000[/tex] so, substitute the value of the parameter [tex]x=15[/tex] in the best-fit line equation, we get
[tex]y=0.057\times 15 +1.150\\y=0.855+1.150\\y=2.005[/tex]
So, the lunch price in 2015 was approximately [tex]\$2.005[/tex].
Hence, the first two statements are TRUE while the last statement is FALSE.
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how many solutions does the system have? 4x-6y=-24 2x-3y=-6
Answer:
No Solution.
Step-by-step explanation:
4x-6y=-24
2x-3y=-6
-----------------
4x-6y=-24
-2(2x-3y)=-2(-6)
-------------------
4x-6y=-24
-4x+6y=12
----------------
0=-12
no solution
Answer:
I TRIED IT ON KHAN ITS NO SOULTIONS
Step-by-step explanation:
Mr. Emory bought 6 pizzas for the math team. The total cost of the order was $58.50. Each pizza cost the same amount. What is the unit cost per pizza of the order?
Answer:
58.50/6= $9.75 unit cost for each pizza
Write an equation in point-slope form for the line that is perpendicular to the given line and passes through the given point.
Y - 3 = 4 (x + 2) through the point ( -2,6
Answer:
y-6=-1/4(x+2)
Step-by-step explanation:
y-3=4(x+2)
y=4x+8+3
y=4x+11
-------------
Perpendicular means negative reciprocal of the slope.
y-6=-1/4(x-(-2))
y-6=-1/4(x+2)
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
x - 2y = -6
x - y = 12
Answer:
x = 30, y = 18
Step-by-step explanation:
Given the 2 equations
x - 2y = - 6 → (1)
x - y = 12 → (2)
Subtracting (2) from (1) term by term will eliminate the term in x
||(x - x) + (- 2y - (- y)) = (- 6 - 12), that is
- y = - 18 ( multiply both sides by - 1 )
y = 18
Substitute y = 18 into either of the 2 equations for value of x
Substituting in (2)
x - 18 = 12 ( add 18 to both sides )
x = 30
Answer: (30,18)
x - 2y = -6
x - y = 12
x - y = 12
- y = 12 - x
y = -12 + x
x - 2y = -6
x = -6 + 2*y
y = -12 + (-6+ 2*y)
y = -12 - 6 + 2*y
y - 2*y = -18
-y = -18
y = 18
y = -12 + x
18 = -12 + x
-x = -12 - 18
x = 12 + 18
x = 30
PLEASE HELP ANSWER THESE
Good evening ,
Answer:
1. t=44°
2. none is correct
3. V=12°
Step-by-step
look at the photo below for the details.
:)
Max is trying to prove to his friend that two reflections, one across the x-axis and another across the y-axis, will not result in a reflection across the line y = x for a pre-image in quadrant II. His friend Josiah is trying to prove that a reflection across the x-axis followed by a reflection across the y-axis will result in a reflection across the line y = x for a pre-image in quadrant II. Which student is correct, and which statements below will help him prove his conjecture? Check all that apply
Max is correct.
Josiah is correct.
If one reflects a figure across the x-axis from quadrant II, the image will end up in quadrant III.
If one reflects a figure across the y-axis from quadrant III, the image will end up in quadrant IV.
A figure that is reflected from quadrant II to quadrant IV will be reflected across the line y = x.
If one reflects a figure across the x-axis, the points of the image can be found using the pattern (x, y) (x, –y).
If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) (–x, y).
Taking the result from the first reflection (x, –y) and applying the second mapping rule will result in (–x, –y), not (y, x), which reflecting across the line should give.
Answer:
Max is correct
If one reflects a figure across the x-axis, the points of the image can be found using the pattern (x, y) ⇒ (x, –y).
If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) ⇒ (–x, y).
Taking the result from the first reflection (x, –y) and applying the second mapping rule will result in (–x, –y), not (y, x), which reflecting across the line should give.
Step-by-step explanation:
The answer above pretty well explains it.
The net result of the two reflections will be that any figure will retain its orientation (CW or CCW order of vertices). It is equivalent to a rotation by 180°. The single reflection across the line y=x will reverse the orientation (CW ⇔ CCW). They cannot be equivalent.
Max is correct in stating that two reflections, one across the x-axis and another across the y-axis, will not result in a reflection across the line y = x for a pre-image in quadrant II. Josiah's conjecture is incorrect. Statements that will help Max prove his conjecture include reflecting a figure across the x-axis and the y-axis, and how the coordinates of the image points change in each reflection.
Explanation:Max is correct. When a figure is reflected across the x-axis, the y-coordinate of each point is negated, resulting in an image in a different quadrant. Therefore, reflecting a figure across the x-axis from quadrant II will place the image in quadrant III. Similarly, when a figure is reflected across the y-axis, the x-coordinate of each point is negated, resulting in an image in a different quadrant. Reflecting a figure across the y-axis from quadrant III will place the image in quadrant IV.
A figure that is reflected from quadrant II to quadrant IV will be reflected across the line y = x. However, reflecting a figure across the x-axis followed by a reflection across the y-axis will result in an image that is reflected across the line y = -x, not y = x. Therefore, Josiah's conjecture is incorrect.
The following statements will help Max prove his conjecture:
If one reflects a figure across the x-axis from quadrant II, the image will end up in quadrant III.If one reflects a figure across the y-axis from quadrant III, the image will end up in quadrant IV.If one reflects a figure across the x-axis, the points of the image can be found using the pattern (x, y) → (x, -y).If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) → (-x, y).Therefore, Max's statements are correct and Josiah's conjecture is incorrect.
James is 46 years old. This is uncle John's age divided by 2, plus 14 years
Which of the following is the best definition of a circle?
A. The collection of all points in a plane that are the same distance
from a given point
B. A plane figure similar to a hexagon
C. The collection of all points in a plane that are the same distance
from a given line
D. A polygon with curved sides
Answer:
The answer is A
Step-by-step explanation:
The answer is A because a circle is a circle and it doesn't have any sides and it's a bunch of points that are the same distance from each other creating a circle like object.
Hope this helps :))
Option A is the correct answer that is a collection of all points in a plane that are the same distance from a given point.
What is a circle?The circle is defined as the locus of the point traces around a fixed point called the centre and is equidistant from the outer trace.
The circle is also defined as the collection of all points in a plane that are the same distance from a given point.
Therefore Option A is the correct answer that is a collection of all points in a plane that are the same distance from a given point.
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What is the equation of the line in slope-intercept form?
y=_ x +_
Answer:
y = 5/2x + 5
Step-by-step explanation:
Your b value is the place where the line crosses the y-axis. So, we can tell right away the b value in the equation is 5.
I'll use negative 2 as the point to find the slope. You go down 5, so we have -5, and go left 2, so -2. 2 negatives make a positive, so the slope is 5/2.
Final equation -
y = 5/2x + 5
William works at a nearby electronics store. He makes a commission of 6% percent on everything he sells. If he sells a computer for $764.00, how much money does William make in commission?
Commission earned by William is $ 45.84
Solution:Given that,
William makes a commission of 6% percent on everything he sells
He sells a computer for $764.00
To find: Commission amount of William
Given that he makes a commission of 6 % on everything he sells. So he has received a commission of 6 % of $ 764.00
Commission amount of William = 6 % of $ 764.00
a % of b can be written in fraction as [tex]\frac{a}{100} \times b[/tex]
[tex]6 \% \text { of } 764=\frac{6}{100} \times 764=0.06 \times 764=45.84[/tex]
Thus commission earned by William is $ 45.84
CAN SOMEONE HELP ME WITH REFLECTIONS??
Answer:
(5, 2 )
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y ), thus
P(5, - 2 ) → P'(5, - (- 2)) → P'(5, 2 )
A tennis ball bounces based on this equation y = x2 - x+2. A dog jumps based on this equation y=2x.
When will the dog receive the ball?
Answer: when the equations are equal, that is when x = 1 or x = 2
Step-by-step explanation:
The dog will receive the ball , when both equations intercept , that is , when both equations are equal. This implies :
[tex]x^{2}[/tex] - x + 2 = 2x
[tex]x^{2}[/tex] - x - 2x + 2 = 0
x(x-1) - 2 (x - 1 ) = 0
(x - 1 ) ( x - 2 ) =0
Therefore , x = 1 or x = 2
A school locker is foot wide, 13 feet deep, and 6 feet
tall. What is the volume of the locker?
Answer:
hi there!
the correct answer to this question is: 78 ft^3
Step-by-step explanation:
you use the volume formula: V= Base * height
base: 1 * 13
height: 6
so multiply 13 by 6 and you get 78
HELP I NEED IT TOMMOROW!! I WILL MARK YOU AS A BRAINLIEST!!!
Is profit negative or positive?
Is bill positive or negative?
Answer:
Profit is positive and bill is negative I believe. I hope this helped!
Answer:
Both ( if I had to choose one I would choose negative)
Step-by-step explanation:
The reason for my answer is because it could teach responsibility and time management. But it can also leave people without a home if not payed on time as well as hungry families.
You are choosing between two long-distance telephone plans. Plan A has a monthly fee of $40.00 with a charge of $0.05 per minute for all long-distance calls. Plan B has a monthly fee of $15.00 with a
charge of $0.10 per minute for all long-distance calls. Complete parts a and b.
a. For how many minutes of long-distance calls will the costs for the two plans be the same?
minutes
Answer:
The number of minutes of call for long distance is 500 minutes .
Step-by-step explanation:
Given as :
The two different long distance telephones plans are plan A and Plan B
Plan A
monthly fee = $40.00
The charge per minute = $0.05
Plan B
monthly fee = $15.00
The charge per minute = $0.10
now, for both plans
Let The number of minutes of call for long distance = n minutes
So, According to question
∵ The both plans to be same
Monthly fee for plan A + The charge per minute × number of minutes of call for long distance for A = Monthly fee for plan B + The charge per minute × number of minutes of call for long distance calls for B
i.e $40.00 + $0.05 × n = $15.00 + $0.10 × n
Or, $40.00 - $15.00 = $0.10 × n - $0.05 × n
Or, $25 = $0.05 × n
∴ n = [tex]\dfrac{25}{0.05}[/tex]
I.e n = 500 minutes
So, The number of calls minutes = n = 500 minutes
Hence, The number of minutes of call for long distance is 500 minutes . Answer
ork, and INTERPRET answers for word problems.
Chan Hee bought 3.4 pounds of cheese that
cost $6.95 per pound. How much did he spend
on cheese?'
Answer:
He spend on cheese is $23.63.
Step-by-step explanation:
Given:
Chan Hee bought 3.4 pounds of cheese that cost $6.95 per pound.
Now, to find the amount he spend on cheese.
As given the unit rate:
Cost of per pound of cheese = $6.95.
So, to get the amount Chan Hee spend on buying cheese we multiply the number of pounds of cheese to the cost of per pound of cheese.
[tex]Number\ of\ pounds\ of\ cheese\times cost\ of\ per\ pound\ of\ cheese.[/tex]
[tex]=3.4\ pounds\times \$6.95[/tex]
[tex]=\$23.63.[/tex]
Therefore, he spend on cheese is $23.63.
What is the weight in grams of a 6.2 pounds birds ?
Answer:
The weight of a 6.2 pounds bird is 2812.27 grams.
Step-by-step explanation:
Weight of a bird is 6.2 pounds.
Now, to find the weight in grams.
So, we have to convert the pounds into grams.
1 pound = 453.592 grams.
Thus, to get the weight in grams we multiply 6.2 pounds with 453.592 grams:
[tex]6.2\times 453.592 = 2812.27\ grams.[/tex]
Therefore, the weight of 6.2 pounds bird is 2812.27 grams.
Catalina works part-time at a bakery earning $7.50 an hour. In the last five days, her time
card shows that she worked 3.3, 2.9, 4.0, 3.5, and 2.1 hours.
What is her gross pay for the five days?
Answer:
Her gross pay is $118.50
Step-by-step explanation:
Firstly, find out how much she earn in each day :
Day 1 => 3.3hr × $7.50
= $24.75
Day 2 => 2.9hr × $7.50
= $21.75
Day 3 => 4.0hr × $7.50
= $30.00
Day 4 => 3.5hr × $7.50
= $26.25
Day 5 => 2.1hr × $7.50
= $15.75
Lastly, sum up altogether to calculate how much she earns in 5 days:
$24.75 + $21.75 + $30 + $26.25 + $15.75
= $118.50
Solve the quadratic equation by completing the square.
4x2 + 8x - 7 = 0
A) x =
2±
11
2
B) x =
2±
11
4
C) x = -
2±
11
2
D) x = -
2±
11
4
Answer:
x=(-2+sqrt(11))/2, (-2-sqrt(11))/2.
Step-by-step explanation:
Apply the quadratic formula with a=4, b=8 and c=-7.
Which statements accurately describe the function f(x) = 3(sqrt18)^x? Select three options.
Answer:
options 1, 3 and 5
=============================================
Step-by-step explanation:
The given function is [tex]f(x) = 3(\sqrt{18} )^x[/tex]
The given function is an exponential function and the graph of the function is as shown in the attached figure.
As shown in the figure:
The domain of the function is all the real numbers ⇒ R
The range of function ⇒ y > 0
The initial value will be at x = 0 ⇒ y =3
The base of the function = [tex]\sqrt{18} =\sqrt{9*2} =\sqrt{3^2 * 2} = 3\sqrt{2}[/tex]
So, the correct options will be options 1, 3 and 5
The width of the rectangle is 75% of its length
hat is the area of the rectangle?
19
b. The length of the rectangle is doubled. What percent of the length is the width now? Explain your reasoning.
Because the length is doubled the width of the rectangle is now half of
75% of its length.
And the square is 24 in
The area of the rectangle is 0.75 of the square of the length. When the length is doubled, the width is 37.5 % of the length.
Explanation:The area of a rectangle is calculated by multiplying its length and width. In this case, the width is 75% of the length. So if we denote the length as 'L', then the width would be 0.75 * L. Therefore, area would be L * 0.75L = 0.75 * L^2.
Now, if the length of the rectangle is doubled, the width remains the same, so it becomes 0.75 * 2L. So the width becomes a smaller fraction of the length. We can work out this out as follows: (0.75L / 2L) * 100 = 37.5%.
So, when the length of the rectangle is doubled, the width is 37.5 % of the length.
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1. The area of the rectangle is 0.75 times the square of the length.
2. The width is now 75% of the length.
Part 1:
What is the area of the rectangle?
If the width of the rectangle is 75% of its length, then we can express the width as 0.75 * length.
The area of a rectangle is calculated by multiplying the length and width, so the area of the rectangle in this case is:
Area = length * width = length * 0.75 * length = 0.75 * length^2
Therefore, the area of the rectangle is 0.75 times the square of the length.
Part 2:
The length of the rectangle is doubled. What percent of the length is the width now? Explain your reasoning.
If the length of the rectangle is doubled, then the width is now half of 75% of the new length.
To calculate this, we can use the following steps:
Calculate the new length of the rectangle: old_length * 2 = new_length
Calculate 75% of the new length: 0.75 * new_length
Divide the width by the new length to get the percentage: width / new_length
For example, if the old length of the rectangle was 10 cm, then the new length would be 20 cm. 75% of 20 cm is 15 cm. Therefore, the width is now 75% of the length.
Answer: The width is now 75% of the length.
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On a very cold morning,it was -7%f.As the day went on,the temperature rose 3 degrees each hour.Which equation shows the temperature over time?
Answer:
The equation that shows the temperature over time is t(x) = -7 + 3x
Step-by-step explanation:
Given:
Temperature at every morning = -7°F
Rise in Temperature per hour = 3 degrees
To Find:
Equation that shows the temperature over time
Solution:
Let x be the time (hours)
Now the temperature at time x (hours) is
=> [tex]-7 + (\text{Number of hours} \times \text {Increase in temperature per hour)}}[/tex]
=>-7 + 3x
Hence at time x hours the temperature will be
t(x) = -7 + 3x
A lake near the Arctic Circle is covered by a
22
2
2
-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After
33
3
3
weeks, the sheet is only
1.251.25
1.25
1, point, 25
meters thick.
Let
SS
S
S
represent the ice sheet's thickness (in meters) after
tt
t
t
weeks.
Answer:
S = 2 - 0.25W
Step-by-step explanation:
A lake near the Arctic Circle is covered by a 2 meters thick sheet of ice during the cold winter months.
At the warm air of spring gradually melts the ice thickness gradually.
Therefore, the equation that models the situation is S = 2 - bW ....... (1), where S is the remaining thickness of the ice sheet and W is the number of weeks passed and b is the rate of decrease of ice sheet thickness with respect to the number of weeks.
Now, putting W = 3 weeks and S = 1.25 meters in the equation (1) we get,
1.25 = 2 - 3b
⇒ 3b = 0.75
⇒ b = 0.25 meters per week.
Therefore, the equation (1) becomes S = 2 - 0.25W (Answer)