The Equation is biquadratic , the four solutions of the equation x⁴ - 5x² - 14 = 0 are x = +√7 , x = -√7 , x = +√2i and x = -√2i .
The Biquadratic equation is given as : x⁴ - 5x² - 14 = 0 ;
to change the given equation to a quadratic equation ,
we substitute x⁴ = y² and x² = y .....equation(1)
the quadratic equation becomes as : y² - 5y - 14 = 0;
Now, we observe that to factor this expression, we find the two number whose product is 14 and whose difference is 5, such numbers are 7 and 2.
that means ⇒ y² - 5y - 14 = (y - 7)(y + 2);
from equation(1) ,
we get ; ⇒ x⁴ - 5x² - 14 = (x² - 7)(x² + 2) = 0;
Solving the two factors ,
we get ;
⇒ x² - 7 = 0 ⇒ x² = 7 ⇒ x = +√7 and x = -√7 ; and
⇒ x² + 2 = 0 ⇒ x² = -2 ⇒ x = +√2i and x = -√2i .
Therefore , the given equation has two Real Solutions and two Complex Solutions .
The given question is incomplete , the complete question is
What are the solutions of the equation x⁴ - 5x² - 14 = 0 ?
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What is co-prime Class 10?.
A set of numbers is co-prime numbers if and only if these have only one common factor i.e., one.
Co-Prime Numbers are a set of numbers where the common factor between them is 1. This means that the HCF or highest common factor should be 1 for these numbers. Co-prime numbers are also referred to as "relatively prime numbers". This means that if we consider x and y to be the set of co-primes, then the only common factor between the two numbers is 1. The properties of co-primes are :
Every prime number is co-prime to each other.Any two consecutive numbers are always Co-prime.Consider a set of two numbers : 16 and 15 The factors of 16 are 1, 2, 8 and 16. The factors of 15 are 1, 3, 5 and 15. The common factor of 16 and 15 is only 1. So 16 and 15 are Co-prime numbers.
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Complete question:
What are co-prime numbers?.
*URGENT*
Also have been stuck on this for the past two days
Rounded to the nearest foot, the height of the tree is 31 feet.
What is height?Height is a measurement of distance from the ground to the top of an object, such as a person, animal, or building. It is typically measured in centimeters (cm) or feet and inches. Height is an important measurement for medical professionals, as it can provide insight into a person's overall health and wellbeing.
Using the tangent formula in trigonometry, the height of the tree can be calculated as follows:
tan(angle of elevation) = Opposite/Adjacent
tan(angle of elevation) = 47/h
h = 47/tan(angle of elevation)
Therefore, the height of the tree is h = 47/tan(angle of elevation) = 47/tan(47°) = 47/1.53 = 30.78 feet
Rounded to the nearest foot, the height of the tree is 31 feet.
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Complete Question:
From a point on the ground 47 feet from the foot of a tree, the angle of elevation of the top of the tree is : height of the tree to the nearest foot. The height of the tree is feet. Round your answer to the nearest foot. with explanation. (And photo in question)
Write a conjecture for: the relationhip between the volume of a phere with a radiu that equal to y and the volume of a phere with a radiu equal to 2y
The conjecture for the relationship between the volume of the two spheres is "the volume of a sphere with radius 2y is 8 times greater than the volume of a sphere with radius y."
A conjecture is an educated guess or a hypothesis about a mathematical statement that has not yet been proven. It can be based on patterns or observations and can lead to further exploration and eventually a proof or disproof.
The formula for the volume of a sphere is given by (4/3)πr³, where r is the radius of the sphere. To compare the volumes of two spheres with different radii, we can substitute their respective radii into the formula.
If we let the radius of one sphere be y, then the volume of that sphere can be represented as (4/3)πy³. If we let the radius of the other sphere be 2y, then the volume of that sphere can be represented as (4/3)π(2y)³. Dividing the latter by the former, we get (4/3)π(2y)³ / (4/3)πy³ = (2y)³ / y³ = 8.
Thus, the volume of a sphere with a radius equal to 2y is 8 times greater than the volume of a sphere with a radius equal to y.
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Without using a calculator, determine between which two integers the following surds lie (1) √5 (2)√1 (3)√107 (4)√3
Between these two integers the following surds lie
(1) √5 = 1-5
(2)√1 = 1-2
(3)√107 = 1-107
(4)√3 = 1-3
How to determine the two integers?There are two simple steps to surd simplification:
Split the number within the root into its prime factors. √50=√(5×5×2)
Based on the root write the prime factors, outside the root. In case of square root, write one factor outside the root, for every two similar factors within the root.
√18+√50.
Root of any whole number must always be greater than 1 as
√1 = 1
√2 = 1.41 > 1
Therefore, Between these two integers the following surds lie
(1) √5 = 1-5
(2)√1 = 1-2
(3)√107 = 1-107
(4)√3 = 1-3
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If
FH
and
IK
are parallel lines and mIJG = 125°, what is mKJG?
°
Applying the linear pair theorem, the measure of angle KJG is: 55°.
What is the Linear Pair Theorem?According to the linear pair theorem, if two angles lie on a straight line, they form a pair of angles whose sum is equal to 180 degrees.
In the image attached below, angles IJG and KLG are both angles on a straight line, and ate therefore equal to 180 degrees when added.
This:
Measure of angle IJG = 125°
m<KLG = 180 - m<IJG
m<KLG = 180 - 125
m<KLG = 55°
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How do you solve a 3 4 5 triangle?.
To solve the 3 4 5 triangle method to find the sides of the right-angle triangle we use the Pythagoras theory.
One type of triangle that has one right (90°) angle is a right triangle.
The Greek mathematician Pythagoras is credited with creating a mathematical formula for calculating the length of the third side of a right triangle given the lengths of the other two sides.
The triangle's right angle is formed by the sides of variables a and b. Either side may utilize either variable. The side that is left, or the side that leans away from the right angle, is represented by the variable c. The hypotenuse, or side c, is the longest side and is always present.
Thus, To solve the 3 4 5 triangle method to find the sides of the right-angle triangle we use the Pythagoras theory.
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What is the factored form of the following expression 9x² 30x 25?.
Yes, the trinomial 9z 30z + 25 is a perfect square. The square of the binomial equation can be used to construct a perfect square trinomial statement.
A trinomial of the form + bz + c is said to be a perfect square if and only if it satisfies the condition b = 4ac.In a perfect square trinomial, two of your words will be perfect squares. If two perfect square terms are absent, the trinomial is not a perfect square trinomial.
It is now necessary to calculate the square roots of each perfect square word, add the two square roots, and multiply the result by two. The square of this trinomial is perfect. Because both 922 = (3ae)° and 25 = 52 are perfect squares, the only thing left to decide is if the middle term matches when you square (3x-5).In order to at least produce a negative coefficient for the middle phrase, the minus sign was utilised.
Complete question:
What does the following equation, 9x2 30x 25, look like factored? . Is the trinomial 9x2 30x25 a perfect square?
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Use a table to find the break-even point.
C= 15x + 150
R = 45x
The break - even point is 5.
What is the break-even point?C=15x + 150
R=45x
Here, C = R
15x + 150 = 45x
30x = 150
x = 5
The break - even point is 5
The break-even point, or BEP, is typically the point where gains and losses are equal.The BEP is the point in a business where income and expenses are equal. There is currently no profit. Knowing and achieving the BEP is the first significant step for a firm in building a successful enterprise. At this stage, there is neither a profit nor a loss because the earnings are equal to the costs incurred to produce them. When revenue equals expenses and profit is equal to zero, this is the break-even point. The revenue left over after deducting the revenue from the variable costs incurred during unit production is known as the contribution margin. Here, The R = C = 45*5= 225
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What is the distance between the points (- 3 2 and 3 5?.
The distance between the two points (-3, 2) and (3, 5) is approximately 6.71 units.
The distance between two points in a plane can be found using the distance formula. The distance formula is given by:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
In this case, the points are (-3, 2) and (3, 5)
So, the distance between the two points is:
distance = √((3 - (-3))² + (5 - 2)²)
distance = √(6² + 3²)
distance = √(36 + 9)
distance = √(45)
distance = 6.7082039
So the distance between the points (-3,2) and (3,5) is approximately 6.71
It is worth mentioning that the distance formula is used to calculate the distance between two points in a 2D space, it is also called the Euclidean distance.
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40 women can do a piece of work in 60 days working 9 hours a day.how many more women should be added in order to do the same work in 48 days working 10 hours a day
Answer:
To complete the same work in 48 days working 10 hours a day, 40 additional women must be added. This is calculated by multiplying the number of days (60) by the number of hours worked per day (9) and dividing it by the number of days required (48) multiplied by the number of hours worked per day (10). This gives a total of 80 women.
give me brainiest
If the simple interest on $6,000 for 7 years is 2,100, then what is the interest rate?
Answer:
5%
Step-by-step explanation:
First, you do:
$2100/7 = $300
Then you do:
r x 6000 = $300
r = 300/6000 = 0.05
Finally, you do:
0.05 x 100 = 5%
So the interest rate is: 5%
Can someone please help me with this math problem? The math problem is in the picture, THANKS! ASAP.
Answer:
y = [tex]\frac{6}{4}[/tex] or [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Since we are given x=1, we can plug that into the equation given:
-4y + [tex]\sqrt[3]{1}[/tex] = -6(1) + [tex]1^{2}[/tex]
-4y + 1 = -6 + 1
-4y = -6
y = [tex]\frac{-6}{-4}[/tex]
y = [tex]\frac{6}{4}[/tex] or [tex]\frac{3}{2}[/tex]
Below are three side lengths. Classify the triangle as acute, right, or obtuse, if possible. (Recall, that the sum of the two smaller sides must be greater than the third side to form a triangle). 20, 21, 29
Answer: Right Triangle
Step-by-step explanation: You can use the Pythagorean Theorem. a^2+b^2=c^2
You test if the equation is true. 21^2 x 20^2 = 29^2 which is 841 = 841
Diego is solving the inequality 100 - 3x < -50.He first solves the equation and sees
that x = 50. Explain how Diego can use this information to find the solution to the inequality. Be sure to include the correct solution in your answer.
The solution of the inequality is x < -50.
And we can use the substitution method to find the solution of the inequality.
What is an inequality?
In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
An inequality 100 - 3x < -50.
Diego first solves the equation and sees that x = 50.
So, substituting the value of x to the inequality.
100 - 3(-50) < -50.
100 - 150 < -50
-50 < -50.
To find the solution of the inequality:
100 - 3x < -50.
-3x < -50 -100
x < - 50
Therefore, the solution of the inequality is x < -50.
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I need help I’ll give BRAINLIEST
The team Seahawk has a larger mean value of about 23 inches.
What are mean, median, and mode?The three main methods for identifying the average value of a set of integers are mean, median, and mode.
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean.
The middle value in a list that is arranged from smallest to greatest is called the median.
The value that appears the most frequently on the list is the mode.
We know the mean of a data set is [tex]\frac{1}{n}\sum_{i=1}^{n} x_i[/tex].
So, The mean of Pelicans is, [tex]\frac{1}{15}\sum_{i=1}^{n} x_i[/tex].
= (1/15)×[20 + 20 + 22 + 21 + 22 + 23 + 22.5 + 24 + 21.5 + 22 + 23.5 + 22 + 23.5 + 22 + 24.5].
= (1/15)×[333.5].
= 22.23.
The mean of Seahawks is,
= (1/15)[21 + 23.5 + 23.5 + 22.5 + 23 + 21 + 23.5 + 23.5 + 22.5 + 23 + 21 + 23.5 + 23.5 + 22.5 + 23].
= 22.7.
So, Seahawks have a larger value of about 23 inches.
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The grocery store has 1 1/4 times as many cashiers in late afternoon than in the morning. If there are 20 cashiers at 10:00 am, how many would there be at 4:00 pm?
Answer:
25 cashiers
Step-by-step explanation:
To solve this, you can multiply the number of cashiers at 10:00 am (20) by 1 1/4, which is the same as multiplying by 5/4.
20 x 5/4 = 25
So, there are 25 cashiers at 4:00 pm.
You can confirm this by dividing 25 by 5/4 to see if it equals 20:
25 * 4/5 = 20
Therefore, there are 25 cashiers at 4:00 pm.
Juliette planted a sunflower that was 18 inches tall. Each week it grows ½ inches. How long will it take the flower to reach a height of 26 inches?
Answer:
Step-by-step explanation:
okay bc the inches is 26 so the answer is 88
bc if u subtract this 26 with this 1 its will. be 25 so add 50 to 25 it will be 88
Miguel went for a drive in his new car. He drove at a speed of 53 miles per hour for 84.8 miles. For how many hours did he drive?
Miguel takes 1.6 hours to cover the distance of 84.8 miles with the given speed of 53 miles per hour.
What is speed?Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
here,
In the question, we are given a speed = 53 miles per hour and the distance traveled with the given speed is 84.8 miles, we have to determine the time for the same distance.
We know that,
Speed = distance/time
Speed = 84.8 / 53
Speed = 1.6 hours
Thus, the required time evaluated is 1.6 hours.
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Interior wall of a reidence conit of a 2 × 4 (31/2") with 1/2" heetrock on both ide. Exterior wall are 2 × 6 (51/2") contruction with 1/2" heetrock on the interior and 7/16" heeting with 35/8" brick on the exterior. Determine the outide dimenion of a houe if there are two interior room with an interior wall. One room dimenion i 11' 3", Room 2 dimenion i 15' 7". How do I olve thi?
The outside dimensions of the house are 11' 9" x 15' 11".
To determine the outside dimensions of the house, we need to take into account the thickness of the interior and exterior walls.First, we'll calculate the thickness of the interior walls. The interior walls are made of 2x4 (31/2") lumber with 1/2" drywall on both sides.
This means that each interior wall adds an additional 3 1/2" + 1/2" + 1/2" = 4 1/2" to the overall width and height of the house. Next, we'll calculate the thickness of the exterior walls. The exterior walls are made of 2x6 (51/2") lumber with 1/2" drywall on the interior and 7/16" siding with 35/8" brick on the exterior.
This means that each exterior wall adds an additional 5 1/2" + 1/2" + 7/16" + 3 5/8" = 8 11/16" to the overall width and height of the house. To calculate the outside dimension of the house, we will add the thickness of the interior and exterior walls to the dimensions of the interior rooms.
The outside dimension of the house will be:
Width = 11' 3" + 4 1/2" + 8 11/16" = 11' 9"
Height = 15' 7" + 4 1/2" + 8 11/16" = 15' 11"
So the outside dimensions of the house are 11' 9" x 15' 11".
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Question
The interior wall of a residence consists of a 2 × 4 (31/2") with 1/2" sheetrock on both sides. Exterior walls are 2 × 6 (51/2") construction with 1/2" sheetrock on the interior and 7/16" sheeting with 35/8" brick on the exterior. Determine the outside dimension of a house if there are two interior rooms with an interior wall. One room's dimensions I 11' 3", and Room 2 dimensions I 15' 7". How do I solve this?
At a fair, 500 pounds of mixed candy was sold for $192.50. If part of the candy mixture was candy corn and was worth $0.35 per pound and the other part of the candy was candy pumpkins worth $0.40 per pound, how many pounds of each were in the mixture?
Answer:
There are 150 pounds of Candy Corn and 350 pounds of Candy Pumpkins in the mixture.
Question content area top
Part 1
The owner of a small store buys coats for $55.00 each. Answer parts a and b.
Question content area bottom
Part 1
a. She sells the coats for $66.00 each. What percent of the purchase price is the sale price?
The sale price is 120120% of the purchase price.
Part 2
b. The owner increases the sale price by the same percent that you found in part a when she buys jackets for $45 and sells them. How many jackets must the owner buy for the total jacket sales to be at least $260? Explain your answer.
The owner must buy enter your response here jacket(s).
Part 1: The percentage of the purchase price to the sale price is 83.3%.
Part 2: The number of jackets the small store owner must sell to make $260 in total sales is 5.
What is the percentage?The percentage refers to the ratio of one value compared to another.
Percentages are computed as the quotients of a numerator divided by the denominator, multiplied by 100.
Purchase price of coats per unit = $55
Selling price per unit = $66
Markup = $11 ($66 - $55) or 20% ($11/$55 x 100)
Margin = 16.7% ($11/$66 x 100)
Percentage of the purchase price to the sales price = 83.3% ($55/$66 x 100) or (100 - 16.7)
b) Cost of jackets per unit = $45
Markup = 20%
Sale price per unit = $54 ($45 x 1.20)
The total expected jacket sales ≥ $260
The number of jackets to sell at $54 each = 5 ($260/54)
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Why does a chemical equation have to follow the law of conservation of mass?
The reason why a chemical equation have to follow the law of conservation of mass is that the mass of the products and the mass of the reactants must be equal.
What is the relationship between chemical equation and law of conservation of mass?Antoine Lavoisier discovered in 1789 that mass is neither created nor destroyed in chemical reactions, which led to the formulation of the Law of Conservation of Mass. To put it another way, the mass of any one element at the start of a reaction will be equal to that element's mass at the end of the reaction. . When the total mass of atoms on both sides of a chemical reaction is equal, the reaction is said to be balanced.
According to the rule of conservation of mass, mass is neither generated nor destroyed during a chemical process. The carbon atom in coal, for instance
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A mall box hold 60 hat. A large box hold 180% a many hat a the mall box. How many hat doe the large box hold
From probability of occurence of events the large box holds 180 hats.
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows
Let us check a simple application of probability to understand it better. Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.
The probability is classified into theoretical probability and experimental probability.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Here we have 60 hats in the mall box.
And a large box holds 180% as many hats as the mall box is given.
So, 180/100 ×60 = 180
Therefore, from probability of occurence of events the large box holds 180 hats.
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The following table shows the life expectancy for women in the United States for selected years in the period 1975-2000.
Year
1975
1980
1985
1990
1995
2000
Women
76.6
77.4
78.2
78.8
78.9
80.0
Which graph makes the increase in life expectancy from 1975-2000 appear to be relatively small?
a.
A graph titled Life Expectancy of Women has Years after 1975 on the x-axis, from 0 to 25, and life expectancy (years) on the y-axis, from 74 to 81 in increments of 0.7.
b.
A graph titled Life Expectancy of Women has Years after 1975 on the x-axis, from 0 to 25, and life expectancy (years) on the y-axis, from 0 to 100 in increments of 10.
c.
A graph titled Life Expectancy of Women has Years after 1975 on the x-axis, from 0 to 25, and life expectancy (years) on the y-axis, from 76 to 80, in increments of 0.4.
d.
A graph titled Life Expectancy of Women has Years after 1975 on the x-axis, from 0 to 25, and life expectancy (years) on the y-axis, from 70 to 85 in increments of 0.5.
The graph that makes the increase in life expectancy from 1975-2000 appear to be relatively small is given by the following option:
b. A graph titled Life Expectancy of Women has Years after 1975 on the x-axis, from 0 to 25, and life expectancy (years) on the y-axis, from 0 to 100 in increments of 10.
What is the graph that makes the increase appear relatively small?The total increase is given as follows:
80 - 76.6 = 3.4 years.
Hence the higher the difference between the bounds of y, the smaller the difference will appear, meaning that the graph is given by option b.
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After a long night of begging for candy, I ended up having a decent stash of Almond Joys and Kit Kals in the ratio of 5:3. If had 40 Almond Joys, how many Kit Kats did I have?
The 5:3 (5 to 3) ratio of the number of Almond Joys candy to Kit kats candy, and the 40 Almond Joys candies stashed, indicates that the number of Kit kandies also received are 24 Kit Kats candies.
What is a ratio?A ratio is an indication of the number of times one quantity is contained within another item.
The ratio of the Almond Joys to the Kit Kats = 5 : 3
The number of Almond Joys obtained = 40
The number of Kit Kats obtained can be found as follows;
The number of Almond Joys received for every 3 Kit Kats received = 5
Let x represent the total number of candies collected, we get;
[tex]\frac{5}{5+3} \times x = 40[/tex]
Therefore;
5·x = 40 × (5 + 3) = 320
x = 320 ÷ 5 = 64
The total number of candies collected = 64
The number of Kit Kats = The total number of candies collected - The number of Almonds Joys received
Therefore; The number of Kit Kats received = 64 - 40 = 24
The number of Kit Kats received = 24 Kit Kats
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You will have 24 Kit Kats based on the information given.
How to determine how many Kit Kats?A ratio is defined as the comparison of two or more quantities that indicates their sizes in relation to each other.
From the information, after a long night of begging for candy, the person ended up having a decent stash of Almond Joys and Kit Kals in the ratio of 5:3.
Since Almond Joys and Kit Kats are in the ratio of 5:3 and you had Almond Joys. Let K represent the number of Kit Kats. Then we have:
5 : 3 = 40 : K
5/3 = 40/K
5K = 3 × 40
5K = 120
K = 120/5
K = 24
Thus, you will have 24 Kit Kats
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STUV is a parallelogram. Solve for SV:
S
SV =
19
T
4x - 1
2x + 3
U
Answer:
SV = 13
Step-by-step explanation:
• the opposite sides of a parallelogram are congruent , so
UV = ST , that is
4x - 1 = 19 ( add 1 to both sides )
4x = 20 ( divide both sides by 4 )
x = 5
Then
TU = 2x + 3 = 2(5) + 3 = 10 + 3 = 13
SV = TU = 13
Which ordered pair lies on the graph of the exponential function f(x)=2^(x+4)−8?
(8,0)
(2, 12)
(-2,-4)
(1, 99)
The point that lies on the graph of the exponential function:
f(x) = 2^(x + 4) - 8
is (-2, -4)
Which of the ordered pairs lies on the exponential function?Here we have the exponential function:
f(x) = 2^(x + 4) - 8
And we want to see which one of the given points lies on the graph of the exponential function.
To check that, we just need to replace the variable x by the first value of the ordered point and see if the function is equal to the second value.
For example, for the second point^(2, 12) we will get:
x = 2
f(2) = 2^(2 + 4)- 8
f(2) = 2^6 - 8 = 56
So we have the point (2, 56)
Now for the point (-2, -4) we will get:
f(-2) = 2^(-2 + 4) - 8
f(-2) = 2^2 - 8 = -4
So we have the point (-2, -4), this is the correct option.
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Can sine law be used on a right triangle?.
No, the Sine law cannot be used directly on right triangles.
What is right triangle?
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). The angle that measures 90 degrees is formed by two sides of the triangle, called the legs, and the third side, called the hypotenuse, is the side opposite the right angle. The legs of the right triangle are perpendicular to each other, meaning they form a 90 degree angle.
What is law of sines?
The sine law, also known as the "law of sines," is a mathematical relationship that relates the lengths of the sides of a triangle to the sines of its angles. the law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
What is Pythagorean theorem ?
The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, can be used to solve for unknown side lengths in a right triangle. This theorem is particularly useful in trigonometry, geometry and navigation.
A right triangle is a special type of triangle that has one angle that measures exactly 90 degrees (a right angle). Since the sine law relates the lengths of the sides of a triangle to the angles, it can be used to solve for unknown side lengths or angles in a right triangle, as long as the other side lengths and angles are known.
However, it is important to note that the sine law is typically used to solve for unknowns in non-right triangles, where the angle measures are not known. In a right triangle, the Pythagorean theorem can be used instead, which relates the length of the hypotenuse to the lengths of the legs.
So, Sine law cannot be used directly on right triangles, but it can be used in solving triangles which includes right triangles as well.
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Answer:
Step-by-step explanation:
(c) On average, how fast is the liquid cooling in the first half-hour, in degrees per minute? On average, how fast is it cooling in the second half-hour, in degrees per minute? Round both answers to the nearest hundredth
The evaluation of the average rate of change of the function for the cooling rate of the liquid can be presented as follows;
(c) The rate at which the liquid is cooling in the first half-hour is about 4.15 °F/min
The cooling rate in the second half-hour is about 0.11 °F/min
What is the average rate of change of a function?The average rate of change of a function f(x) between the values, x = a, and x = b, can be found as follows;
Average rate of change = [tex]\frac{f(b) - f(a)}{b - a}[/tex]
(c) The function for the temperature obtained from a similar question posted online is presented as follows;
[tex]T(m) = 128\cdot e^{-0.12\cdot m}+ 74[/tex]
The time duration of the cooling in minutes = m
Therefore, the initial temperature is the temperature at 0 minutes, which indicates that we get;
m = 0, [tex]T(0) = 128\cdot e^{-0.12\times 0}+ 74[/tex] = 202
The initial temperature of the liquid is 202 °FThe temperature of the liquid after 30 minutes, can be found as follows;
[tex]T(30) = 128\cdot e^{-0.12\times 30}+ 74[/tex] ≈ 77.50
The temperature after 30 minutes is about 77.50 °FThe rate at which the liquid is cooling on average in the first half hour therefore, is; Cooling rate = (202 - 77.50)/(30) = 4.15
The liquid cools at a rate of 4.15°F/min in the first half hourThe average cooling rate in the second half hour is found as follows;
After the second half hour, the duration of cooling = 60 minutes
Therefore, we get;
[tex]T(60) = 128\cdot e^{-0.12\times 60}+ 74[/tex] ≈ 74.1
The average cooling rate in the second half-hour is therefore;
(77.50 - 74.1)/(60 -30) ≈ 0.11
The cooling rate in the second half-hour is about 0.11 °F/minLearn more about average rate of change of a function here: https://brainly.com/question/29431817
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