Answer:
-6 and 7.
Step-by-step explanation:
If we have a function called g, and we know that it has two factors: (x - 7) and (x + 6), then we can find the values of x that make g equal to zero. We call those values the "zeros" of the function g. To find the zeros, we just need to solve the equation (x - 7)(x + 6) = 0. The answer is that the zeros of g are -6 and 7.
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over x = −1.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−5, 5), M′(−2, 3), O′(−3, 7)
N′(3, 2), M′(0, 1), O′(1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)
The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).
To determine the vertices of the image N'M'O' after reflecting triangle NMO over the line x = -1, we need to apply the reflection transformation to each vertex.
For a reflection over the line x = -1, we can find the image of a point (x, y) by finding its reflection as (2(-1) - x, y).
Applying this transformation to each vertex of triangle NMO, we get:
N' = (2(-1) - (-5), 2) = (5, 2)
M' = (2(-1) - (-2), 1) = (2, 1)
O' = (2(-1) - (-3), 3) = (3, 3)
The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).
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7. At age 20, Heather began investing $3000 annually
into an account earning 7.5% interest compounded
annually. Lesley invested $6000 annually into a similar
account but began at age 40. They both stopped
contributing at age 65.
a) How much money did Heather and Lesley contribute
to their account?
b) What is the value of each of their investments when
they are 65 years old?
c) At age 65, when the investments mature, who has
more money and by how
much?
a) Heather contributed $135,000 and Lesley contributed $150,000 to their accounts.
b) Heather's investment is approximately $273,714.17, while Lesley's investment is approximately $191,048.18 when they are 65 years old.
c) Heather has more money by approximately $82,665.99 at age 65.
a) To find out how much money Heather and Lesley contributed to their accounts, we need to calculate the total contributions made by each of them.
Heather:
Heather started investing at age 20 and stopped at age 65, contributing $3000 annually. The number of years she contributed is (65 - 20) = 45 years.
Total contributions by Heather = $3000 × 45 = $135,000.
Lesley:
Lesley started investing at age 40 and stopped at age 65, contributing $6000 annually. The number of years she contributed is (65 - 40) = 25 years.
Total contributions by Lesley = $6000 × 25 = $150,000.
Therefore, Heather contributed $135,000 and Lesley contributed $150,000 to their respective accounts.
b) To calculate the value of their investments at age 65, we can use the formula for compound interest:
Future Value = Principal × (1 + interest rate)^number of years
Heather:
Principal (initial investment) = $3000
Interest rate = 7.5% = 0.075 (converted to decimal)
Number of years = 65 - 20 = 45
Future Value of Heather's investment = $3000 × (1 + 0.075)^45
Lesley:
Principal (initial investment) = $6000
Interest rate = 7.5% = 0.075 (converted to decimal)
Number of years = 65 - 40 = 25
Future Value of Lesley's investment = $6000 × (1 + 0.075)^25
Calculating these values:
Future Value of Heather's investment = $3000 × (1.075)^45 ≈ $273,714.17
Future Value of Lesley's investment = $6000 × (1.075)^25 ≈ $191,048.18
c) To determine who has more money at age 65 and by how much, we compare the future values of their investments.
Heather's investment value at age 65 = $273,714.17
Lesley's investment value at age 65 = $191,048.18
Therefore, Heather has more money at age 65, and the difference in their investments is approximately $273,714.17 - $191,048.18 = $82,665.99.
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Select all the statements that are true for the following systems of equations.
System A
2x-3y = 4
4x - y = 18
00
System B
3x - 4y = 5
y = 5x +3
All three systems have different solutions.
Systems B and C have the same solution.
System C simplifies to 2x-3y=4 and 4x-y=18 by dividing the second equation by three.
Systems A and B have different solutions.
Systems A and C have the same solution.
Reset
System C
2x-3y=4
12x-3y = 54
Next
The statements that are true about the system of equations are: Options C, D, and E.
How to Find the Solution to a Systems of Equations?Let's analyze each statement and determine whether it is true or false for the given systems of equations:
System A
2x - 3y = 4
4x - y = 18
System B
3x - 4y = 5
y = 5x + 3
System C
2x - 3y = 4
12x - 3y = 54
A. All three systems have different solutions.
To determine if the systems have different solutions, we need to solve them. Solving system A gives the solution x = 5 and y = -6. Solving system B gives the solution x = -1 and y = -2. Solving system C gives the solution x = 5 and y = -6. Therefore, this statement is false because systems A and C have the same solution.
B. Systems B and C have the same solution.
As mentioned above, solving system B gives the solution x = -1 and y = -2. Solving system C gives the solution x = 5 and y = -6. Therefore, this statement is false because systems B and C have different solutions.
C. System C simplifies to 2x-3y=4 and 4x-y=18 by dividing the second equation by three.
To simplify system C, we can divide the second equation by 3, resulting in:
2x - 3y = 4
4x - y = 18
This is exactly the same as system A. Therefore, this statement is true.
D. Systems A and B have different solutions.
As mentioned earlier, solving system A gives the solution x = 5 and y = -6. Solving system B gives the solution x = -1 and y = -2. Therefore, this statement is true.
E. Systems A and C have the same solution.
As mentioned earlier, solving system A gives the solution x = 5 and y = -6. Solving system C gives the solution x = 5 and y = -6. Therefore, this statement is true.
In summary:
A. False
B. False
C. True
D. True
E. True
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Complete Question:
Select all the statements that are true for the following systems of equations.
System A
2x - 3y = 4
4x - y = 18
System B
3x - 4y = 5
y = 5x +3
System C
2x - 3y = 4
12x - 3y = 54
A. All three systems have different solutions.
B. Systems B and C have the same solution.
C. System C simplifies to 2x-3y=4 and 4x-y=18 by dividing the second equation by three.
D. Systems A and B have different solutions.
E. Systems A and C have the same solution.
PLEASE HELP AS SOON AS POSSIBLE
Answer:
B
Step-by-step explanation:
Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.
A ____ is just another way of saying what we want to count by on our graph.
Answer:
A scale is just another way of saying what we want to count by on our graph.
Step-by-step explanation:
A "scale" is just another way of saying what we want to count by on our graph. The scale is the range of values that are shown on the axis of a graph. It helps to determine the size and spacing of the intervals or ticks on the axis. The scale can be in different units, such as time, distance, weight, or any other measurable quantity depending on the type of data being represented in the graph.
Find the slope and the y-intercept of the following linear equation. 5. 3x + 2y = 14
Answer:
slope = - [tex]\frac{3}{2}[/tex] , y- intercept = 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
3x + 2y = 14 ( subtract 3x from both sides )
2y = - 3x + 14 ( divide through by 2 )
y = - [tex]\frac{3}{2}[/tex] x + 7 ← in slope- intercept form
with slope m = - [tex]\frac{3}{2}[/tex] and y- intercept c = 7
Which linear equation shows a proportional relationship?
y equals negative one sixth times x
y equals one sixth times x minus 8
y = −6x + 1
y = 6
Answer:
y = (-1/6)x represents a proportional relationship.
Are the experimental probabilities after 300 trials closer to the theoretical probabilities?
After 300 trials, the experimental probabilities may not align perfectly with the theoretical probabilities. However, with more trials, the experimental probabilities tend to converge towards the theoretical probabilities for closer alignment.
To examine whether experimental probabilities after 300 trials align closely with theoretical probabilities, let's consider an example of flipping a fair coin.
Theoretical probability: When flipping a fair coin, the theoretical probability of obtaining heads or tails is 0.5 each. This assumes that the coin is unbiased and has an equal chance of landing on either side.
Experimental probability: After conducting 300 trials of flipping the coin, we record the outcomes and calculate the experimental probabilities. Let's assume that heads occurred 160 times and tails occurred 140 times.
Experimental probability of heads: 160/300 = 0.5333
Experimental probability of tails: 140/300 = 0.4667
Comparing the experimental probabilities to the theoretical probabilities, we can observe that the experimental probability of heads is slightly higher than the theoretical probability, while the experimental probability of tails is slightly lower.
In this particular example, the experimental probabilities after 300 trials do not align perfectly with the theoretical probabilities. However, it is important to note that these differences can be attributed to sampling variability, as the experimental outcomes are subject to random fluctuations.
To draw a more definitive conclusion about the alignment between experimental and theoretical probabilities, a larger number of trials would need to be conducted. As the number of trials increases, the experimental probabilities tend to converge towards the theoretical probabilities, providing a closer alignment between the two.
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The question probable may be:
Do experimental probabilities after 300 trials tend to align closely with theoretical probabilities? Consider an example scenario and calculate both the theoretical and experimental probabilities to determine if they are close.
Arc BC on circle A has a length of 115,
- inches. What is the radius of the circle?
115/6 pi
138°
The radius of the circle is 25 inches. The length of arc with a central angle of 138° is 115π/6 in
What is an equation?An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.
The length of an arc with a central angle Ф with circle radius (r) is given by:
Length of arc = (Ф/360) * 2πr
Given the length of arc as 115π/6 in and angle of 138°, hence:
Length of arc = (Ф/360) * 2πr
Substituting:
115π/6 = (138/360) * 2πr
r = 25 inches
The radius of the circle is 25 inches.
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A gaming system costs $600 and is on sale for 15% off. After the discount, there is a 5% tax. What is the final price of the gaming system?
Answer$535.50
Step-by-step explanation:
15% is equal to .15
So, multiply 600.00x .15=90
600.00 - 90.0=510.
510. 00x .05=25.50
510.00+25.50=535.50
Your answer is $535.5
Two cyclists, 54 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
Answer:
In summary, the faster cyclist cycles at a speed of 18 mi/h since they travel 36 of the 54 miles in 2 hours while cycling twice as fast as the slower cyclist.
Explanationn:
The two cyclists are 54 miles apart and heading toward each other.
One cyclist cycles 2 times as fast as the other. We will call the faster cyclist A and the slower cyclist B.
They meet 2 hours after starting. This means they travel a total distance of 54 miles in 2 hours.
Since cyclist, A cycles 2 times as fast as cyclist B, cyclist A travels 2/3 of the total distance, and cyclist B travels 1/3 of the total distance.
In two hours, cyclist A travels (2/3) * 54 miles = 36 miles.
We need to find the speed of cyclist A in miles per hour.
Speed = Distance / Time
So the speed of cyclist A is:
36 miles / 2 hours = 18 miles per hour
Therefore, the speed of the faster cyclist is 18 mi/h.
se logarithms to solve the problem.
The rule of 70 is a rule of thumb for estimating the doubling time of a quantity (e.g., investment, GDP, population) experiencing growth that is compounded continuously. The rule states that if the growth rate is r% per year, then the time it takes for the quantity to double is approximately 70/r years.
(a)
Use the rule of 70 to estimate the time it takes for an investment to double in value if it grows at the rate of 5% per year compounded continuously.
yr
(b)
What is the exact time it will take for the investment in part (a) to double in value? (Round your answer to two decimal places.)
yr
a. The investment to double in value take about 14 years for the funding to double in value.
b. The genuine time it will take for the funding to double in fee is about 13.86 years.
(a) To estimate the time it takes for an funding to double in cost the use of the rule of 70, we want to decide the increase rate. In this case, the increase price is given as 5% per 12 months compounded continuously.
Using the rule of 70, we can calculate the estimated doubling time:
Time to double ≈ 70 / boom rate
Time to double ≈ 70 / 5
Simplifying, we have:
Time to double ≈ 14 years
Therefore, it would take about 14 years for the funding to double in value.
(b) To decide the genuine time it will take for the funding to double in value, we can use the formulation for non-stop compounding:
Doubling time (exact) = ln(2) / (ln(1 + r))
where r is the increase fee as a decimal.
In this case, the increase charge is 5% per year, or 0.05 as a decimal.
Doubling time (exact) = ln(2) / (ln(1 + 0.05))
Doubling time (exact) ≈ 13.86 years (rounded to two decimal places)
Therefore, the genuine time it will take for the funding to double in fee is about 13.86 years.
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Toula owns the Pita Pan restaurant. She needs to order supplies for the upcoming weekend rush. She needs 150 bags of pita bread. The bread come in crates of 50, and each crate costs $15.00. She also needs 65 containers of hummus dip. There are 5 containers in a box, and each box costs $20.00 What expressions can Toula use to determine how much the pita bread and hummus dips will cost? What will the total be?
The total cost of the pita bread and hummus dips will be $305.00.
To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:
Cost of pita bread:
Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates
Cost of each crate = $15.00
Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00
Cost of hummus dips:
Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes
Cost of each box = $20.00
Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00
Therefore, the expressions Toula can use to determine the costs are:
Cost of pita bread = 3 crates × $15.00/crate
Cost of hummus dips = 13 boxes × $20.00/box
The total cost will be the sum of the costs of pita bread and hummus dips:
Total cost = Cost of pita bread + Cost of hummus dips
Total cost = $45.00 + $260.00
Total cost = $305.00
Therefore, the total cost of the pita bread and hummus dips will be $305.00.
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What is the volume of the triangular prism?
3 in.
15 in.
13 in.
0.059 and 0.01 which is greater?
Find the numbers with the following property three times the sum of four and a number is less than seven times the same number
Let's represent the number with the variable "x". According to the given property, we can write the following equation:
3(x + 4) < 7x
Now, let's solve this inequality to find the range of numbers that satisfy the property.
3x + 12 < 7x
Subtract 3x from both sides:
12 < 4x
Divide both sides by 4 (since the coefficient of x is 4):
3 < x
So, the range of numbers that satisfy the given property is x > 3.
Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:
Afish tank is 30 inches wide, 12 inches deep, and 18 inches tall Approximately how many gallons of water does it hold if there are 7 48 gallons per cubic foot of water?
39
28
19
Answer: 12
Step-by-step explanation:
The sum of three numbers is 71. The third number is 2 times the first. The second number is 5 less than the first. What are the numbers?
Answer:
19, 14, 38
Step-by-step explanation:
Let x, y, and z be each number respectively:
[tex]x+y+z=71\\z=2x\\y=x-5\\\\x+y+z=71\\x+(x-5)+2x=71\\2x-5+2x=71\\4x-5=71\\4x=76\\x=19\\\\y=x-5\\y=19-5\\y=14\\\\z=2x\\z=2(19)\\z=38[/tex]
Therefore, the three numbers are 19, 14, and 38.
(1.85)x + 2.55
Question 3
(3a) The equation that can be used to determine the cost, C is C = 2.55 + 1.85x.
(3b) The cost of 3 miles taxi ride is $8.1.
What is the solution of question 3?(3a) The equation that can be used to determine the cost, C is calculated by applying the following equation as follows;
C = f + nx
where
f is the fixed chargex is the number of milesn is the charge per milesC = 2.55 + 1.85x
(3b) The cost of 3 miles taxi ride is calculated as follows;
C = 2.55 + 1.85x
where;
x is the number of milesC = 2.55 + 1.85 (3)
C = $8.1
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Select the expression that is equivalent to (n²-25)
A. n² +10n - 25
B. n²-10-25
C. (n+5)(n-5)
D. (n-5) ²
Answer:
C. (n+5)(n-5)
Step-by-step explanation:
Select the expression that is equivalent to (n²-25)
Let's check each option. A and B are wrong, so we only check C & D.
C. (n + 5) (n - 5)
n² - 5n + 5n - 25
n² - 25
D. (n - 5)²
(n - 5) (n - 5)
n² - 5n - 5n + 25
n² - 10n + 25
So, the correct answer is C. (n+5)(n-5)
Which of the following steps indicates the addition property of equality while solving the equation –1 – 6x = x – 15?
A) x = 14∕2
B) –1 – 6x = x – 15
C) 23 – 6x – 24 = x – 15
D) –1 – 6x + 15 = x – 15 + 15
Answer:
-1 - 6x = x - 15
Add 15 to both sides using the addition property of equality.
14 - 6x = x
14 = 7x
2 = x
D) -1 - 6x + 15 = x - 15 + 15
Answer and Step-by-step explanation:
Please refer to the photo for the solution!
What is the solution to x – 5 + 2 < 20? –7 < x < 15 –13 < x < 23 x < –7 or x > 15 x < –13 or x > 23
Answer:
Therefore, the correct answer is: x < 23.
Step-by-step explanation:
To solve the inequality x - 5 + 2 < 20, we can simplify it step by step:
x - 5 + 2 < 20
Combine like terms:
x - 3 < 20
Add 3 to both sides of the inequality:
x - 3 + 3 < 20 + 3
Simplify:
x < 23
The solution to the inequality is x < 23.
Therefore, the correct answer is: x < 23.
Answer and Step-by-step explanation:
Please see the photo for the solution :)
Find the equation of the line in slope-intercept form, parallel to a line joining the points (1,-2) and (-4,3) and passing through (-4,-5).
I
The equation of the line parallel to a line joining points (1,-2) and (-4,3) and passing through (-4,-5) is
(Simplify your answer. Type your answer in slope-intercept form.)
The equation of the line parallel to the line passing through (1, -2) and (-4, 3) and passing through the point (-4, -5) is y = -x - 9 in slope-intercept form.
To find the equation of a line parallel to a given line, we need to determine the slope of the given line and then use it to construct the equation of the parallel line.
First, let's calculate the slope of the given line passing through points (1, -2) and (-4, 3). The slope, denoted as m, can be found using the slope formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates, we have:
m = (3 - (-2)) / (-4 - 1) = 5 / (-5) = -1
Now that we have the slope, we can use it to construct the equation of the parallel line.
We'll use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
where (x1, y1) represents the coordinates of a point on the line.
We'll use the point (-4, -5) on the parallel line:
y - (-5) = -1(x - (-4))
y + 5 = -1(x + 4)
Simplifying further:
y + 5 = -x - 4
y = -x - 9
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quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 62
minutes with a mean life of 606
minutes.
If the claim is true, in a sample of 99
batteries, what is the probability that the mean battery life would be greater than 619
minutes? Round your answer to four decimal places.
Answer:
Step-by-step explanation:
1,020.50375 rounded to the nearest tenth
Rounding the given value to the nearest tenth would be 1020.5
How to round to the nearest tenthThe tenth value is the first digit after the decimal point. Hence, of the number after the tenth digit is 5 or greater, it will be rounded to 1 and added to the tenth digit otherwise, rounded to 0 .
Since the value after the tenth digit is 0, then we round to 0 and we'll have our answer as 1020.5.
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Five clubs at Johnson School raised $2000. The incomplete circle graph shows what percent of the money was raised by each club. How much money did the Math Club raise?
$500
$600
$200
$400
$300
The Math Club raised $400.
To find out how much money the Math Club raised, we need to determine the percentage of the total amount raised that corresponds to the Math Club's portion.
Let's assume the Math Club raised "x" amount of money. The total amount raised by all five clubs is $2000.
According to the incomplete circle graph, the Math Club's percentage is missing, but we know the percentages for the other clubs: Computer Club raised 15%, Gardening Club raised 18%, Art Club raised 30%, and Spanish Club raised 17%.
To find the missing percentage for the Math Club, we subtract the percentages of the other clubs from 100%:
Missing percentage = 100% - (15% + 18% + 30% + 17%) = 100% - 80% = 20%
Now we can set up a proportion to determine the amount raised by the Math Club:
(x / $2000) = 20% / 100%
Cross-multiplying:
x = ($2000 * 20%) / 100%
Simplifying:
x = $400
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Enter the number that belongs in the green box
The angle C in the triangle is 34.05 degrees.
How to use cosine law to find angles in a triangle?
The sum of angles in a triangle is 180 degrees. The angle in a triangle can be found using cosine law as follows:
Therefore, let's find the unknown angle in the triangle as follows;
c² = a² + b² - 2ab cos C
Hence,
4² = 5² + 7² - 2 × 7 × 5 cos X
16 = 25 + 49 - 70 cos X
16 = 74 - 70 cos X
16 - 74 = -70 cos X
-58 = -70 cos X
cos X = 58 / 70
X = cos⁻¹ 0.82857142857
X = 34.0478785629
X = 34.05 degrees
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Q1. An industry analyst wants to compare the average salaries of two firms, both to each other and to the industry. Firm A's average salary is 93% of the industry average, Firm B's average salary is $58,000, and the industry average salary is 96% of Firm B's average salary. a. Determine the industry average salary. b. Determine Firm A's average salary. c. Express Firm B's average salary as a percentage of Firm A's average salary. Round the percentage to two decimals.
a.The Industry Average Salary is $55,680. b.The Firm A's Average Salary is $51,718.40 .c. Firm B's average salary is approximately 112.27% of Firm A's average salary.
a. To determine the industry average salary, we can use the information that the industry average salary is 96% of Firm B's average salary. Firm B's average salary is $58,000. Therefore, we can calculate the industry average salary as follows:
Industry Average Salary = 96% of Firm B's Average Salary
= 0.96 * $58,000
= $55,680
b. Firm A's average salary is stated as 93% of the industry average salary. To calculate Firm A's average salary, we can multiply the industry average salary by 93%:
Firm A's Average Salary = 93% of Industry Average Salary
= 0.93 * $55,680
= $51,718.40
c. To express Firm B's average salary as a percentage of Firm A's average salary, we can divide Firm B's average salary by Firm A's average salary and multiply by 100:
Percentage = (Firm B's Average Salary / Firm A's Average Salary) * 100
= ($58,000 / $51,718.40) * 100
≈ 112.27%
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Find y" by implicit differentiation.
cos(y) + sin(x) = 1
y" = cos(y) * dy/dx - sin(x) + sin(y) by implicit differentiation.
To find the second derivative (y") by implicit differentiation, we will differentiate the equation with respect to x twice.
Equation: cos(y) + sin(x) = 1
Differentiating once with respect to x using the chain rule:
-sin(y) * dy/dx + cos(x) = 0
Now, differentiating again with respect to x:
Differentiating the first term:
-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2
Differentiating the second term:
-d/dx(cos(x)) = -(-sin(x)) = sin(x)
The equation becomes:
-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2 + sin(x) = 0
Now, let's isolate the second derivative, d^2y/dx^2:
-d^2y/dx^2 = d/dx(sin(y)) * dy/dx - sin(x) + sin(y)
Substituting the previously obtained expression for d/dx(sin(y)) = cos(y):
-d^2y/dx^2 = cos(y) * dy/dx - sin(x) + sin(y)
Thus, the second derivative (y") by the equation:
y" = cos(y) * dy/dx - sin(x) + sin(y)
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In 1995, wolves were introduced into Yellowstone Park.
The function `w\left(x\right)=14\cdot1.08^{x}` models the number of wolves, `w`, in the years since 1995, `x`.
Determine the value of `w(25)`.
What does this value say about the wolf population?
Answer:
w(25) = 96
There are 96 wolves in the year 2020
Step-by-step explanation:
Given:
[tex]w(x)=14\cdot 1.08^{x}[/tex]
w(25) =
[tex]w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96[/tex]
Number of years : 1995 + 25 = 2020
In 2020, there are 96 wolves