if range of the function f(x) = 3x+2 is {5,8,11,14}, find the domain of the function
Answers
Answer:
{17,26,35,44}
Step-by-step explanation:
f(5) = 3(5)+2 = 17
f(8) = 3(8)+2 = 26
f(11) = 3(11)+2 = 35
f(14) = 3(14)+2 = 44
Related Questions
What is a quadratic equation.
Answers
Answer:
A quadratic equation is an equation of the second degree.
Step-by-step explanation:
Please help! (look at the image below!!)
Answers
The numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾. The third option is correct.
What is ordering of numbersThe ordering of numbers refers to arranging numbers in a specific sequence based on their magnitude or value. The ordering of numbers is determined by their relative values. Comparisons are made between numbers to determine their position in the order.
12⅝ = 101/8 = 12.645
12.62 = 12.62
√146 = 12.0830
12.39 = 12.39
12¾ = 51/4 = 12.75
Therefore, the numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾.
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Arrange the geometric series from least to greatest based on the value of their sums. 5 5 ΣΠ2) 4-1 Σ3-1 Σ 26-1 Σ2(3):-1! =1 < Λ
Answers
Determine the sum of each geometric series.
\(\begin{gathered} \sum ^5_{k\mathop=1}3(2)^{k-1}=3\cdot(2)^0+3\cdot(2)^1+3\cdot(2)^2+3\cdot(2)^3+3\cdot(2)^4 \\ =3+6+12+24+48 \\ =93 \end{gathered}\)\(\begin{gathered} \sum ^5_{k\mathop=1}3^{k-1}=3^0+3^1+3^2+3^3+3^4 \\ =1+3+9+27+81 \\ =121 \end{gathered}\)\(\begin{gathered} \sum ^7_{k\mathop=1}2^{k-1}=2^0+2^1+2^2+2^3+2^4+2^5+2^6 \\ =1+2+4+8+16+32+64 \\ =127 \end{gathered}\)\(\begin{gathered} \sum ^4_{k\mathop=1}2\cdot(3)^{k-1}=2\cdot(3)^0+2\cdot(3)^1+2\cdot(3)^2+2\cdot(3)^3 \\ =2+6+18+54 \\ =80 \end{gathered}\)Thus sums can be arranges from smallest to largest as,
\(undefined\)Question 20 The paraterized curve below is rotated abour the -axis. Find the area of the surface. x= cos^3(θ) y=sin^3(θ) for 0 <θ < π/2
Answers
The area of the surface generated by rotating the parametric curve about the x-axis is π/8.
To find the area of the surface generated by rotating the parametric curve about the x-axis, we can use the formula for the surface area of revolution:
\(A = \int\limits^a_b {2\pi y} \sqrt{(\frac{dx}{d\theta})^2+ (\frac{dy}{d\theta})^2} \, dx\)
In this case, the given parametric equations are:
\(x = cos^3\theta\\\\y = sin^3\theta\)
Let's calculate the derivatives of x and y with respect to θ:
\(\frac{dx}{d\theta} = -3cos^2\theta sin\theta\\\\\frac{dy}{d\theta} = 3sin^2\theta cos\theta\\\)
Now we can substitute these values into the surface area formula:
\(A = \int_{0}^{\pi /2} {2\pi sin^3\theta} \sqrt{(-3cos^2\theta sin\theta)^2+ (3sin^2\theta cos\theta)^2} \, d\theta\)
Simplifying the expression inside the square root:
\(A = \int_{0}^{\pi /2} {2\pi sin^3\theta} \sqrt{9cos^4\theta sin^2\theta+ 9sin^4\theta cos^2\theta} \, d\theta\)
\(A = \int_{0}^{\pi /2} {2\pi sin^3\theta} \sqrt{9cos^2\theta sin^2\theta(cos^2\theta +sin^2\theta)} \, d\theta\)
\(A = \int_{0}^{\pi /2} {2\pi sin^3\theta} \sqrt{9cos^2\theta sin^2\theta} \, d\theta\)
\(A = \int_{0}^{\pi /2} {2\pi sin^3\theta} \quad 3cos^2\theta sin^2\theta \, d\theta\)
\(A = 6\pi \int_{0}^{\pi /2} {sin^4\theta} \quad cos^2\theta d\theta\)
Now, we can use a trigonometric identity to simplify the integral. The identity is:
\(Sin^2\theta = \frac{1-cos2\theta}{2}\)
Using this identity, we can rewrite the integral as:
\(A = 6\pi \int_{0}^{\pi /2} {(\frac{1-cos2\theta}{2})^2 } \quad cos^2\theta d\theta\)
Simplifying further:
\(A = 6\pi \int_{0}^{\pi /2} {(\frac{1+cos^22\theta-2cos2\theta}{4}) } \quad cos^2\theta d\theta\)
\(A = 3\pi /2\int_{0}^{\pi /2} {cos\theta-2cos2\theta cos\theta+\frac{1}{4} cos^3\theta} d\theta\)
Evaluating the limits of integration:
\(A = 3\pi /2[\frac{1}{2} sin\theta-\frac{1}{3} cos^3\theta+\frac{1}{12} cos^32\theta]^{\pi /2}_0\)
Evaluating =
A = π/8
Therefore, the area of the surface generated by rotating the parametric curve about the x-axis is π/8.
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So, how many people does one cow (= steer or heifer) feed in a year? Actually, for our purposes, let’s say the average "cow" going to slaughter weighs 590 Kg. (1150 pounds) and after the "waste" is removed, yields about 570 pounds (258.1 Kg.) of prepared beef for market sales. This is roughly half the live weight. How many "cows" does it take to satisfy the beef appetite for the population of New York City? (Population of NYC is about 9,000,000 (rounded)
Answers
The number of cows needed to satisfy the beef appetite would be 5263
With an average yield of 570 pounds (258.1 Kg.) of prepared beef per cow, we need to determine how many people can be fed from this amount. The number of people fed per cow can vary depending on various factors such as portion sizes and individual dietary preferences. Assuming a reasonable estimate, let's consider that one pound (0.45 Kg.) of prepared beef can feed about three people.
To find the number of cows needed to satisfy the beef appetite for New York City's population of approximately 9,000,000 people, we divide the population by the number of people fed by one cow. Thus, the calculation becomes 9,000,000 / (570 pounds x 3 people/pound).
After simplifying the equation, we get 9,000,000 / 1710 people, which equals approximately 5,263 cows. However, it's important to note that this is a rough estimate and does not consider factors such as variations in consumption patterns, distribution logistics, or other sources of meat supply. Additionally, individual dietary choices and preferences may result in different consumption rates. Therefore, this estimate serves as a general indication of the number of cows needed to satisfy the beef appetite for New York City's population.
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105 +35x written in another way __ (__)
Answers
Answer
35 (3 + x)
Step-by-step explanation:
Please show work y’all thank you!
Answers
Lisa is seven times as old as her brother. She will be four times as old as her brother in three years. Represent the above situation in mathematical form.
Answers
Answer:
Let B = the brothers age now
Let L = Lisa's age now
Then today:
L = 7B
And three years from now, Lisa's current age plus 3 equals 4 times the brothers age plus 3 represented by the following formula
L+3 = 4(B+3)
Now we can substitute the value of L in the first formula for L in the second formula
7B + 3 = 4(B+3)
So the answer is C
Step-by-step explanation:
A polynomial function is shown below:
f(x) = x3 − 4x2 − x + 4
Which graph best represents the function? (5 points)
Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, 2, and 3. The graph intersects the y axis at a point between 10 and 15.
Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, 2, and 3. The graph intersects the y axis at a point between 15 and 20.
Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, 1, and 3. The graph intersects the y axis at a point between 5 and 10.
Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 1, 1, and 4. The graph intersects the y axis at a point between 0 and 5. pls help
Answers
Answer:
its the fourth graph (i took the test)
A gardener has two different strengths of weedkiller: a 6% solution and a 15% solution, some of each solution needs to be mixed together to make 30 litres of a 10% solution. How much of each kind of solution is required?
Answers
Answer:
Approximately 16.67 liters concentration of the 6% solution and approximately 13.33 liters of the 15% solution are required to make 30 liters of a 10% solution.
Step-by-step explanation:
Let's denote the amount of the 6% solution as x liters and the amount of the 15% solution as y liters. We need to find the values of x and y that satisfy the conditions.
Since we want to make 30 liters of a 10% solution, we can set up the following equations:
Equation 1: x + y = 30 (total volume equation)
Equation 2: (0.06x + 0.15y) / 30 = 0.10 (concentration equation)
From Equation 1, we have x = 30 - y. Substituting this into Equation 2, we get:
(0.06(30 - y) + 0.15y) / 30 = 0.10
Simplifying the equation gives:
(1.8 - 0.06y + 0.15y) / 30 = 0.10
1.8 + 0.09y = 3
0.09y = 1.2
y ≈ 13.33
Substituting y back into Equation 1, we find:
x + 13.33 = 30
x ≈ 16.67
Therefore, approximately 16.67 liters of the 6% solution and approximately 13.33 liters of the 15% solution are required to make 30 liters of a 10% solution.
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HELP NOW FOR MEGA POINTS
Which statement below about the graph of f(x)=-log(x+4)+2 is true?
1) f(x) has a y-intercept at (0,2)
2) −f(x) has a y-intercept at (0,2)
3) As x → ∞, f(x) → ∞.2)
4) x → −4, f(x) → ∞
SHOW WORK
Answers
Answer:
4 IS THE ANSWER MATE
Step-by-step explanation:
Absolutely, I can do that!
Let's take a look at each statement:
1) f(x) has a y-intercept at (0,2)
To find the y-intercept, we need to set x to 0 and solve for y. Plugging in x = 0 into the equation for f(x), we get:
f(0) = -log(0+4) + 2
f(0) = -log(4) + 2
f(0) = -0.602 + 2
f(0) = 1.398
Since the y-coordinate of the y-intercept is 1.398, not 2, this statement is false.
2) The function -f(x) has a y-intercept at (0,2)
Since the negative sign in front of f(x) reflects the graph of f(x) across the x-axis, we can determine the y-intercept of -f(x) by taking the opposite of the y-intercept of f(x). Since the y-intercept of f(x) is not 2, this statement is also false.
3) As x approaches positive infinity, the function f(x) approaches negative infinity.
The function f(x) is a logarithmic function with a negative coefficient, which means it approaches negative infinity as x approaches positive infinity. Therefore, this statement is true.
4) As x approaches -4 from the right, the function f(x) approaches negative infinity.
As x approaches -4 from the right, the value of f(x) becomes more and more negative without bound, which means that f(x) approaches negative infinity as x approaches -4 from the right. Therefore, this statement is also true.
In summary, statements (1) and (2) are false, while statements (3) and (4) are true.
the average of 8 girls is 15 and the average of 6 girls is 13 find the average of the other two girls with equal age
Answers
Answer:
21
Step-by-step explanation:
Since the girls have the same age, let their age be x.
Then, their average is
\(\frac{x+x}{2} = \frac{2x}{2} = x\)
Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)
Also, we have,
\(\frac{S_{8}}{8} =15 - eq(2)\)
\(\frac{S_{6}}{6} =13 - eq(3)\)
Then eq(2):
(from eq(1) and eq(3))
\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)
The average of the other two girls with equal age is 21
If adam’s credit card has an apr of 14.63%, what is adam’s balance at the end of june? a. $629.42 b. $629.66 c. $627.27 d. $628.40
Answers
The balance in Adam's account at the end of June which has the credit card with an apr of 14.63% is $627.27.
What is monthly payment?Monthly payment is the payment which has to paid against the loan amount or the borrowed money calculated with interest rate.
The Adam’s credit card has an Apr of 14.63%,The table below shows his use of that credit card over three months.
Date Amount ($) Transaction Remaining Balance ($) 4/1 626.45 Beginning balance 626.454/10 37.41 Purchase 663.864/12 44.50 Purchase 708.365/3 65.50 Payment 642.865/16 24.89 Purchase 667.755/20 104.77 Payment 562.986/6 23.60 Payment 539.386/10 15.00 Purchase 554.386/14 51.85 Purchase 606.23For the purchase add the previous balance and for payment subtract the previous balance. I have mentioned another column for remaining balance in the above table.
The total of this transaction when multiplied with number of days, we get the total balance, 56498.48.
Now the monthly average balance is,
\(m=\dfrac{56498.48}{90}\\m=627.76\)
Thus, the balance in Adam's account at the end of June which has the credit card with an Apr of 14.63% is near to $627.27.
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Adam’s balance at the end of June is $629.42.
What is the adjusted balance method?The adjusted balance method is an accounting method that bases finance charges on the amount(s) owed at the end of the current billing cycle after credits and payments post to the account.
Balance at the end of April = 626.45 + 37.41 + 44.50 = $708.36
Interest levied on $708.36= 708.36* (14.63/12) * 1/100
Interest levied on $708.36 = $8.64
So, balance on May 1st= 708.36+ 8.64 = $717
Balance at the end of May = 717-65.50+24.89-104.77 = $571.62
Interest levied on $571.62 = $571.62 * (14.63/12) * 1/100
Interest levied on $571.62=$6.97
So, balance on June 1st = $578.59
Balance at the end of June = 578.59-23.60 + 15+51.85 = $621.84
Interest levied on $621.84 = $621.84* (14.63/12) * 1/100
Interest levied on $621.84 =$ 7.58
So balance at the end of the june = 621.84 + 7.58 = $629.42
Therefore, Adam’s balance at the end of June is $629.42.
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Michele correctly solved a quadratic equation using the quadratic formula as shown below.
-(-5) ± √(-5)³-4(TX-2)
Which could be the equation Michele solved?
OA. 7z² - 5z -2=-1
B.
7z²
5z + 3 = 5
O c. 7z²
Ba ngô 8
O D. 7z² - 5z +5= 3
Answers
The solutions to the given quadratic equation are x=[5+13i]/14 or x=[5-13i]/14.
Given that, the quadratic formula is x= [-(-5)±√((-5)²-4×7×7)]/2×7.
Here, x= [5±√(25-196)]/14
x= [5±√(-171)]/14
x=[5±13i]/14
x=[5+13i]/14 or x=[5-13i]/14
Now, (x-(5+13i)/14) (x-(5-13i)/14)=0
Therefore, the solutions to the given quadratic equation are x=[5+13i]/14 or x=[5-13i]/14.
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chase ran 36 3/4 miles over 6 days he ran the same distance each day how many miles did he run each day
Answers
Therefore, Chase ran 49/8 miles each day.
To find out how many miles Chase ran each day, we need to divide the total distance he ran (36 3/4 miles) by the number of days (6 days).
First, let's convert the mixed number into an improper fraction. 36 3/4 is equal to (4 * 36 + 3)/4 = 147/4.
Now, we can divide 147/4 by 6 to find the distance he ran each day:
(147/4) / 6 = 147/4 * 1/6 = (147 * 1) / (4 * 6) = 147/24.
Therefore, Chase ran 147/24 miles each day.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 147 and 24 is 3.
So, dividing 147 and 24 by 3, we get:
147/3 / 24/3 = 49/8.
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Chase ran a total of 36 3/4 miles over six days. To find out how many miles he ran each day, simply divide the total distance (36.75 miles) by the number of days (6). The result is approximately 6.125 miles per day.
Explanation:To solve this problem, you simply need to divide the total number of miles Chase ran by the total number of days. In this case, Chase ran 36 3/4 miles over six days. To express 36 3/4 as a decimal, convert 3/4 to .75. So, 36 3/4 becomes 36.75 miles.
Now, we can divide the total distance by the total number of days:
36.75 miles ÷ 6 days = 6.125 miles per day. So, Chase ran about 6.125 miles each day.
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Who can help me please
Answers
Answer:
1) the first choice
2) the first choice
Step-by-step explanation:
1) "<" means less than, so if she wants to spend less than $300 that's your answer
2) "5x" means 5 times however many hours she chooses to have her carpet cleaned, so this is correct as well as the less than 300.
hope this helps <3
One side of a triangle is 3 inches and its area is 36 inches. The corresponding side of
a similar triangle is 7 feet. What is the area of the larger triangle?
Answers
its lonmg.answer
Step-by-step explanation:
Write and solve a system of equations for the problem. Label your answers.
4
Metropolitan High School sells student and adult tickets to athletic events. During the frist event, they sold 10
student tickets and 20 adult tickets for a total of $200. The school took in $280 during a second event by
selling 20 student tickets and 25 adult tickets. What is the price of one student ticket and one adult ticket?
Answers
Let's denote the price of a student ticket as "s" and the price of an adult ticket as "a".
From the information given, we can set up the following system of equations:
Equation 1: 10s + 20a = 200 (from the first event)
Equation 2: 20s + 25a = 280 (from the second event)
To solve this system of equations, we can use any method, such as substitution or elimination. In this case, let's use the elimination method.
Multiply Equation 1 by 2 to make the coefficients of "s" in both equations equal:
20s + 40a = 400
Now, subtract Equation 2 from this new equation:
(20s + 40a) - (20s + 25a) = 400 - 280
15a = 120
Divide both sides of the equation by 15:
a = 120/15
a = 8
Now, substitute the value of "a" back into Equation 1 to solve for "s":
10s + 20(8) = 200
10s + 160 = 200
10s = 200 - 160
10s = 40
s = 40/10
s = 4
Therefore, the price of one student ticket is $4, and the price of one adult ticket is $8.
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Salmon and Federico are choosing a number between 1 & 100, picking a color from ROY G BIV, and picking a letter out of "INDIANA". Either one will go first. State the probability of each situation as a percentage, fraction and decimal.
1. Salmon chooses a composite number, A cool color( G BIV) and an A.
2.Federico chooses a prime number, A color starting with a vowel, and a constanant.
3.Either chooses a number divisible by 7 or 8, any color, and a vowel.
4. Either chooses a number divisible by 5 or 4, blue or green, and L or N
Answers
To determine the probabilities, we need to consider the number of favorable outcomes for each situation divided by the total number of possible outcomes.
1.Probability: 228/700 = 0.3257 ≈ 32.57% ≈ 32.6% (rounded to one decimal place)
2. Probability: 200/3500 = 0.0571 ≈ 5.71% ≈ 5.7%
3. Probability: 504/2100 = 0.24 ≈ 24% (exact fraction)
4.Probability: 180/1400 = 0.1286 ≈ 12.86% ≈ 12.9% (rounded to one decimal place)
1. Salmon chooses a composite number, a cool color (G, B, I, or V), and an A:
a) Composite numbers between 1 and 100: There are 57 composite numbers in this range.
b) Cool colors (G, B, I, or V): There are 4 cool colors.
c) The letter A: There is 1 A in "INDIANA."
Total favorable outcomes: 57 (composite numbers) * 4 (cool colors) * 1 (A) = 228
Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 1 (possible letter) = 700
Probability: 228/700 = 0.3257 ≈ 32.57% ≈ 32.6% (rounded to one decimal place)
2. Federico chooses a prime number, a color starting with a vowel (E or I), and a consonant:
a) Prime numbers between 1 and 100: There are 25 prime numbers in this range.
b) Colors starting with a vowel (E or I): There are 2 colors starting with a vowel.
c) Consonants in "INDIANA": There are 4 consonants.
Total favorable outcomes: 25 (prime numbers) * 2 (vowel colors) * 4 (consonants) = 200
Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 5 (possible letters) = 3500
Probability: 200/3500 = 0.0571 ≈ 5.71% ≈ 5.7% (rounded to one decimal place)
3. Either chooses a number divisible by 7 or 8, any color, and a vowel:
a) Numbers divisible by 7 or 8: There are 24 numbers divisible by 7 or 8 in the range of 1 to 100.
b) Any color: There are 7 possible colors.
c) Vowels in "INDIANA": There are 3 vowels.
Total favorable outcomes: 24 (divisible numbers) * 7 (possible colors) * 3 (vowels) = 504
Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 3 (possible letters) = 2100
Probability: 504/2100 = 0.24 ≈ 24% (exact fraction)
4. Either chooses a number divisible by 5 or 4, blue or green, and L or N:
a) Numbers divisible by 5 or 4: There are 45 numbers divisible by 5 or 4 in the range of 1 to 100.
b) Blue or green colors: There are 2 possible colors (blue or green).
c) L or N in "INDIANA": There are 2 letters (L or N).
Total favorable outcomes: 45 (divisible numbers) * 2 (possible colors) * 2 (letters) = 180
Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 2 (possible letters) = 1400
Probability: 180/1400 = 0.1286 ≈ 12.86% ≈ 12.9% (rounded to one decimal place)
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Graph the absolute value equation that represents the given situation, d = |s 250 - 50.
Then mark the points that represent the horizontal distance from the left shore where the river bottom is
20 feet below the surface.
Answers
Answer:The answer is below
Step-by-step explanation:
The bottom of a river makes a V-shape that can be modeled with the absolute value function, d(h) = ⅕ ⎜h − 240⎟ − 48, where d is the depth of the river bottom (in feet) and h is the horizontal distance to the left-hand shore (in feet). A ship risks running aground if the bottom of its keel (its lowest point under the water) reaches down to the river bottom. Suppose you are the harbormaster and you want to place buoys where the river bottom is 20 feet below the surface. Complete the absolute value equation to find the horizontal distance from the left shore at which the buoys should be placed
Answer:
To solve the problem, the depth of the water would be equated to the position of the river bottom.
h is=380 or h=100
Step-by-step explanation:
Which of the ratios below has a unit rate of 5?
Answers
Answer:
Would you mind including the ratios in the comments?
You didn't post any material to solve.
In a game, one player throws two fair, six-sided die at the same time. If the player receives a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once
Answers
Answer:
probability that a player wins after playing the game once = 5/9
Step-by-step explanation:
To solve this, we will find the probability of the opposite event which in this case, it's probability of not winning and subtract it from 1.
Since, we are told that there are 2 fair six sided die thrown at the same time and that he receives a five or a one on either die ;
Probability of not winning, P(not win) = 4/6.
Thus;
P(winning) = 1 - ((4/6) × (4/6))
P(winning) = 1 - 4/9 = 5/9
Write an equation of a line through the point (6, 2) with slope 2/3.
Answers
Answer:
y=2/3x-2
Step-by-step explanation:
which graph of ordered pais shows a proportional relationship? i need help lol
Answers
how many numbers lie between square of 36 and 37
Answers
Answer:
73 numbers
Step-by-step explanation:
36²
=36 × 36
=1,296
37²
=37 × 37
=1,369
The total number that lies between 36² and 37² = 37² - 36²
=1,369 - 1,296
= 73 numbers
This is to say that, there are 73 numbers between 36² (1,296 ) and 37² ( 1,369)
The ratio of red marbles to blue marbles in a bag is 3:4 . if there are 42 marbles in the bag, how many are red ?
Answers
Answer:
hope it helped you
Step-by-step explanation:
in image
3+4=7
42/7=6
6 x 3 =18
There are 18 red marbles.
Elena deposits $1,500 in a savings account that earns 3.0% simple interest per year. If no deposits or withdrawals are made during the year, how much money will be in her account after one year?
Answers
Answer:
FV= $1,545
Step-by-step explanation:
Giving the following information:
Elena deposits $1,500 in a savings account that earns 3.0% simple interest per year.
To calculate the nominal value of the account after one year, we need to use the following formula:
FV= (P*r*t) + P
FV= future value
P= principal
r= interest rate
t= 1
FV= (1,500*0.03*1) + 1,500
FV= $1,545
Someone me help plz!!!
Answers
Answer:
(D) \(3 \pm i\sqrt{3}\)
Step-by-step explanation:
We can solve this using the quadratic formula, where a is 1, b is -6, and c is 12.
\(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\frac{-(-6)\pm\sqrt{6^2-4\cdot1\cdot12}}{2\cdot1}\\\\\frac{6\pm\sqrt{36-48}}{2}\\\\\frac{6\pm\sqrt{-12}}{2}\\\\\frac{6\pm i\sqrt{12}}{2}\\\\3\pm i\sqrt{3}\\\\\)
Hope this helped!
.THIS IS DIFFERENTIALS EQUATION SUBJECT.
THE TOPIC WAS ALL ABOUT APPLICATIONS ON 1ST ORDER OF DIFFERENTIALS EQUATIONS In an episode of How to Get Away with Murder, the intern lawyers were investigating a murder case. During investigation, the forensics informed them that the dead body was found within a closed room of a house where the temperature was 70 F. At the time of discovery the core temperature of the body was determined to be 85 F. One hour later a second measurement showed that the core temperature of the body was 80 F. Assume that the time of death corresponds to * = 0 and the core temperature at that time was 98.6 F. Determine how many hours elapsed before the body was found.Provide what is needed. Show your full solutions, no shorthand. Do notapproximate the value of k, do
approximation after you find your final answer
Answers
Approximately 0.456 hours (or about 27.36 minutes) elapsed before the body was found.
To solve this problem, we can use Newton's Law of Cooling, which states that the rate of change of temperature of an object is proportional to the difference between its temperature and the surrounding temperature.
Let's denote T(t) as the core temperature of the body at time t, and T_s as the surrounding temperature (which is 70 F in this case).
According to the problem, at time t = 0, the core temperature of the body is T(0) = 98.6 F. One hour later, at t = 1, the core temperature is T(1) = 80 F.
Using Newton's Law of Cooling, we can set up the differential equation:
dT/dt = k(T - T_s)
where k is the proportionality constant.
Substituting the given values at t = 0 and t = 1, we can find the specific value of k.
At t = 0: dT/dt = k(98.6 - 70)
At t = 1: dT/dt = k(80 - 70)
Integrating both sides of the equation, we get:
∫ dT/(T - T_s) = ∫ k dt
Applying the natural logarithm, we have:
ln|T - T_s| = kt + C
Simplifying the equation, we get:
T - T_s = Ce^(kt)
Substituting the values at t = 0, we have:
98.6 - 70 = Ce^(k * 0)
Solving for C, we get:
C = 28.6
Now we can rewrite the equation as:
T - 70 = 28.6e^(kt)
At t = 1, we have:
80 - 70 = 28.6e^(k * 1)
Simplifying the equation, we get:
10 = 28.6e^k
Dividing both sides by 28.6, we have:
e^k = 10/28.6
Taking the natural logarithm of both sides, we get:
k = ln(10/28.6)
Now, we can use this value of k to determine how many hours elapsed before the body was found.
We want to find the value of t when T(t) = 85. Substituting this value into our equation, we have:
85 - 70 = 28.6e^(ln(10/28.6) * t)
15 = 28.6(10/28.6)^t
Dividing both sides by 28.6, we get:
15/28.6 = (10/28.6)^t
Taking the natural logarithm of both sides, we have:
ln(15/28.6) = t * ln(10/28.6)
Dividing both sides by ln(10/28.6), we can solve for t:
t = ln(15/28.6) / ln(10/28.6)
Calculating this expression, we find:
t ≈ 0.456 hours
Therefore, approximately 0.456 hours (or about 27.36 minutes) elapsed before the body was found.
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perimeter of a quadrilateral is 590m its sides are in ratio 5 ratio 12 ratio 17 ratio 25 find the area of the quadrilateral
Answers
Answer:
255,000,000m^2
Step-by-step explanation:
Let 5:12:17:25 be 5x, 12x, 17 x, 25x respectively
So
Perimeter of quadrilateral=5x+12x+17x+25x
590m=59x
590m/59=x
10m=x
So now value
5x= 5*10 =50
12x= 12*10 =120
17x= 17*10 =170
25x= 25*10 =250
Now
Area of quadrilateral=50m*120m* 170m* 250m
=255,000,000m^2
Step-by-step explanation:
if I understand you correctly the sides are in a
5 : 12 : 17 : 25 ratio.
a ratio is basically a fraction. but instead of the denominator telling us the structure of the whole (e.g. 2/5 tells us that the whole is split into 5 equal parts), a ratio tells us this by the sum of its elements :
5 : 12 : 17 : 25
means that the whole perimeter of the quadrilateral has
5 + 12 + 17 + 25 = 59 equal parts.
since the perimeter is 590 m, we know with 59 equal parts, that one part is 590/59 = 10 m.
so, the sides are
50 m, 120 m, 170 m, 250 m
but for the area of the quadrilateral there is at least the information of one angle missing.
to have just the 4 side lengths is not enough. these sides can still have all kinds of angles between them, which creates different areas.