Considering the definition of mole fraction, the mole fraction of O₂ in the mixture is 0.434.
Definition of mole fractionThe molar fraction is a way of measuring the concentration that expresses the proportion in which a substance is found with respect to the total moles of the solution.
In other words, the mole fraction expresses the concentration of solute in a solution as the ratio of moles of substance to total moles of solution:
[tex]mole fraction=\frac{moles of substance}{moles of solution}[/tex]
Mole fraction of O₂ in this mixtureIn this case, you know a gas mixture used for anesthesia contains 4.60 mol oxygen (O₂) and 6.00 mol nitrous oxide (N₂O).
So, the total moles of the solution can be calculated as:
Total moles = moles of oxygen (O₂) + moles of nitrous oxide (N₂O)
Then:
Total moles= 4.60 moles + 6 moles
Total moles= 10.60 moles
Finally, the more fraction of O₂ can be calculated as follow:
[tex]Mole fraction of O_{2} =\frac{moles of O_{2}}{total moles}[/tex]
[tex]Mole fraction of O_{2} =\frac{4.60 moles}{10.6o moles}[/tex]
Solving:
Mole fraction O₂ = 0.434
Finally, the mole fraction of O₂ in the mixture is 0.434.
Learn more about mole fraction:
brainly.com/question/14434096
brainly.com/question/10095502
#SPJ1
Determine the mass of CO2 produced when 51.2 g of CaO is reacted with 50.0 g of C according to the unbalanced chemical equation:
CaO (s) + C (s) ---> CaC2 (s) + CO2 (g)
Hint: You will need to balance the equation first.
The mass of CO2 produced will be 8.01 grams
Stoichiometric problemThe balanced equation of the reaction is written as:
[tex]2CaO (s) + 5C (s) --- > 2CaC_2 (s) + CO_2 (g)[/tex]
The mole ratio of CaO and C is 2:5 from the balanced equation.
Mole of 51.2 g CaO = mass/molar mass = 51.2/56 = 0.91 moles
Mole of 50.0 g C = 50/12 = 4.17 moles
From the mole ratio, 0.91 mole CaO will require 5/2 x 0.91 = 2.28 moles C.
This means 4.17 moles carbon is excessive. In other words, C is the limiting reagent.
The mole ratio of C and CO2 is 5:1. Thus, the equivalent mole of CO2 that will be produced from 0.91 moles C will be:
0.91/5 = 0.182 moles.
Mass of 0.182 moles CO2 = mole x molar mass = 0.182 x 44 = 8.01 grams
More on stoichiometric problems can be found here: https://brainly.com/question/14465605
#SPJ1
What classifies a substance as an element?
What classifies a substance as a compound?
Actually, answer what the question is asking and give a short answer. No copying and pasting.
The difference between an element and a compound is that an element is a substance made of same type of atoms, whereas a compound is made of different elements in definite proportions.Examples of elements include iron, copper, hydrogen and oxygen. Examples of compounds include water (H2O) and salt (Sodium Chloride - NaCl).
what is the mass of 9.3 x 10^ 24 molecules of glucose, C6H12O6 (C6,H12,O6; 180.18 g/mol
Molecular mass of 9.3 x 10^ 24 molecules of glucose = 1675.6 x 10^ 24
It is given that the mass of glucose is 180.18 g/mol
so if we have to calculate the mass of 9.3x 10^ 24 molecules of glucose
we will apply a simple unitary method i.e,
9.3 x 10^ 24 * 180.18 g/mol = 1675.67 x 10^ 24
To calculate the molecular mass of a molecule, multiply the subscript (number of atoms) by the atomic mass of each element in the molecule and add those masses together.
Remember that - To determine the compound's molecular mass in grams per mole, use the molecular formula.
Divide the supplied mass by the molar mass of the chemical to convert it to moles.
By dividing the number of moles by Avogadro's number, you may convert from moles to molecules.
To learn more about molecular mass please visit -
https://brainly.com/question/18446366
#SPJ1
which element is trigonal pyramidal molecular shape ? a) NF3. b) BCL3 c) COCL2 d) CLO3- e) BRF3
Answer:
A.) NF₃
D.) ClO₃⁻
Explanation:
To determine the molecular shape of the molecules, you need to:
1.) Calculate the total valence electrons in the molecule
-----> The sum of the element's valence electrons
2.) Draw the Lewis structure
A weather balloon calibrated at 0.00 °C to
have a volume of 20.0 L has what volume at
-36.2 °C assuming pressure is held
constant? Answer is in L
Answer:
17.3 L
Explanation:
With all other variables held constant, you can find the missing volume using the Charles' Law equation:
V₁ / T₁ = V₂ / T₂
In this equation, "V₁" and "T₁" represent the initial volume and temperature. "V₂" and "T₂" represent the final volume and temperature. Before we can solve, we need to convert Celsius to Kelvin (because we don't want negative numbers or temp. of 0).
V₁ = 20.0 L V₂ = ? L
T₁ = 0.00 °C + 273.15 = 273.15 K T₂ = -36.2 °C + 273.15 = 236.95 K
V₁ / T₁ = V₂ / T₂ <----- Charles' Law equation
20.0 L / 273.15 K = V₂ / 236.95 K <----- Insert values
0.0732 = V₂ / 236.95 K <----- Simplify left side
17.3 L = V₂ <----- Multiply both sides by 236.95
Which of the following aqueous solutions are good buffer systems?
(Select all that apply.)
a. 0.28 M hydrobromic acid + 0.24 M sodium bromide
b. 0.29 M ammonia + 0.38 M ammonium bromide
c. 0.22 M hypochlorous acid + 0.18 M hydroiodic acid
d. 0.37 M sodium chloride + 0.25 M barium chloride
e. 0.13 M sodium hydroxide + 0.28 M sodium bromide
0.29 M ammonia + 0.38 M ammonium bromide and 0.22 M hypochlorous acid + 0.18 M hydroiodic acids of aqueous solutions are good buffer systems.
Buffer Systems:A solution that resists pH change when acids or bases are added to it is referred to as a buffer system. Either a weak acid and its salt, or a weak base and its salt, make up buffer systems. The ratio of HX/X- does not considerably alter when an acid or a base is introduced to a buffer.
Solutions known as buffers withstand pH changes when an acid or base is added. A weak base (A) and its conjugate weak acid (HA) are both present in buffers. When a reactive system is in equilibrium, adding a strong electrolyte with one common ion will cause the equilibrium to shift, lowering the concentration of the common ion. Buffers differ from one another in terms of pH range and buffer capacity.
Learn more about buffers here:
https://brainly.com/question/1385846
#SPJ1
How many grams of calcium are in 2.25 molar of calcium
Answer:
40 g
Explanation:b
Count the significant digits in 95700 kg
What do the letters “P.P.E” stand for in chemical
Answer:
Personal Protective Equipment
Explanation:
Some examples of PPE are safety glasses, lab coats, steel-toed shoes, etc.
The purpose of PPE is to keep the user from getting injured when using dangerous equipment or chemicals.
PLEASE ANSWER THIS FAST... tysm
●what will happen to the texture off egg shell if you place it in.
1. Coca cola
2. orange juice
3. grape juice
4. normal water
5. a dark coloured sugary drink like sting
Answer all these correctly please
thanks
Answer:
4. the egg shell you place in normal water
what is the type of chemical reaction that vinegar, baking soda, and dish soap have?
Reaction 1: Two reactions are occurring:
sodium bicarbonate + acetic acid sodium acetate + carbonic acid
carbonic acid carbon dioxide + water
Add a teaspoon of dish soap to a cup of vinegar and mix well. Add a table spoon of baking soda to the vinegar soap mixture.
What are the two reactions that occur? I only noticed one and that was when I added baking soda.
what is the type of chemical reaction that vinegar, baking soda, and dish soap have (Combustion, decomposition, etc.) and what is the balanced chemical equation of this reaction?
Answer:
Explanation:
The reaction between baking soda (sodium bicarbonate) and vinegar (dilute acetic acid) generates carbon dioxide gas, which is used in chemical volcanoes and other projects.
A gas that has a volume of 13 liters, a temperature of 25 0C, and an unknown pressure has its volume increased to 27 liters and its temperature decreased to 15 0C. If I measure the pressure after the change to be 1.3 atm, what was the original pressure of the gas?
This is an exercise in the general or combined gas law.
To start solving this exercise, we obtain the data:
Data:V₁ = 13 LtT₁ = 25 °C + 273 = 298 kV₂ = 27 LtT₂ = 15 °C + 273 = 288 kP₁ = 1.3 atmP₂ = ¿?We use the following formula:
P₁V₁T₂ = P₂V₂T₁ ⇒ General FormulaWhere
P₁ = Initial pressureV₁ = Initial volumeT₂ = Initial temperatureP₂ = Final pressureV₂ = Final volumeT₁ = Initial temperatureWe clear the general formula for the final pressure.
[tex]\large\displaystyle\text{$\begin{gathered}\sf P_{2}=\frac{P_{1}V_{1}T_{2} }{V_{2}T_{1}} \ \to \ Clear \ formula \end{gathered}$}[/tex]
We substitute our data into the formula to solve:
[tex]\large\displaystyle\text{$\begin{gathered}\sf P_{2}=\frac{(1.3 \ atm)(13\not{l})(288\not{k} )}{(27 \not{l})(298 \not{K})} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf P_{2}=\frac{4867.2}{8046} \ atm \end{gathered}$}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf P_{2}=0.604 \ atm \end{gathered}$}}[/tex]
If I measure the pressure after the change by 1.3 atm, the original pressure of the gas will be 0.604 atm.
3 Br2 + 6 OH1- → 5 Br1- + BrO31- + 3 H2O
If 8.5 moles of Br2 are reacted with an unlimited supply of OH1-, how many moles of BrO31- can be formed?
Answer:
2.8 moles BrO₃⁻
Explanation:
To find the amount of moles, you need to convert moles Br₂ to moles BrO₃⁻ using the mole-to-mole ratio. This ratio is made up of the balanced equation coefficients in front of the relevant molecules.
3 Br₂ + 6 OH⁻ -----> 5 Br⁻ + 1 BrO₃⁻ + 3 H₂O
8.5 moles Br₂ 1 mole BrO₃⁻
----------------------- x ---------------------- = 2.8 moles BrO₃⁻
3 moles Br₂
Calculate the amount of heat deposited on the skin of a person burned by 1.00g of steam at 100.0C. Skin temperature is 37C. ΔHvap= 40.7kJ/mol.
The amount of heat deposited on the skin is 2.26 kJ.
What is the amount of heat given off by 1.0 g of steam?The amount of heat given off by steam is determined using the formula below:
Quantity of heat = mass * latent heat of vaporization.
Moles of steam = 1.0/18
Heat = 1.0/18 * 40.7
Heat deposited = 2.26 kJ
In conclusion, the quantity of heat is determined from the latent heat of vaporization and the moles of steam.
Learn more about heat of vaporization at: https://brainly.com/question/26306578
#SPJ1
To answer this question, you may need access to the periodic table of elements.
Which of these would likely be the best conductor of electricity?
a.) H₂
b.) NO₂
c.) CaCl₂
d.) H₂O
Answer:
A
Explanation:
Beacuse the hydrogen is best
The best conductor of electricity here is calcium chloride because, metals are good conductors by the presence of free electrons. The CaCl₂ solution ionizes to Ca²⁺ ions and Cl- ions make it a good electrolyte.
What is conductivity?Conductivity is a physical property which describes the ability of a substance to pass electricity through it. The substance which shows good conductivity at normal temperatures are called conductors and those only conducts at higher temperatures are semiconductors.
Substance which does not conduct in any condition are called insulators. Metals are electron rich and the metal crystal lattice is composed of a sea of mobile electrons and a pool of positive ions. The delocalization of electrons make it easy to pass current through it.
When a metallic solution is ionized, it gives free ions and electrons and make the solution conducting. CaCl₂ is a good conductor since it contains the metal ions Ca²⁺ . Hence, option c is correct.
To find more on conductivity, refer here:
https://brainly.com/question/15085692
#SPJ2
what is the cation of Al2(SO4)3
Answer:
Al has a 3+ charge, and SO4 has a 2- charge. So, it takes 3 of the SO4 anions to balance 2 of the Al cations. So, you get Al2(SO4)3
What state of matter is Polaris, the north star?
A. Plasma
B. Liquid
C. Light
D. Gas
The state of matter of Polaris, the north star is gas.
What are stars made of?Stars are made up of a mixture of hot gases.
The mixture consists of helium and hydrogen. Hydrogen burns into helium to give starts a shining appearance when observed from a far distance.
Thus, the state of matter of all stars, including the north star, is gas.
More on stars can be found here: https://brainly.com/question/21521087
#SPJ1
A drop of water with a mass of 0.48 g is vaporized at 100 ∘C and condenses on the surface of a 55- g block of aluminum that is initially at 25 ∘C . If the heat released during condensation goes only toward heating the metal, what is the final temperature in Celsius of the metal block? (The specific heat capacity of aluminum is 0.903 J/(g⋅∘C ).)
Express the temperature in Celsius to two significant figures.
The final temperature in Celsius of the metal block is 49°C.
How to find the number of moles ?Moles water = [tex]\frac{\text{Given mass}}{\text{Molar Mass}}[/tex]
= [tex]\frac{0.48\ g}{18\ \text{g/mol}}[/tex]
= 0.0266 moles
Heat lost by water = 0.0266 mol x 44.0 kJ/mol
= 1.17 kJ
= 1170 J [1 kJ = 1000 J]
Heat lost = Heat gained
Heat gained by aluminum = 1170 J
1170 = 55 x 0.903 (T - 25) = 49.7 T - 1242
1170 + 1242 = 49.7 T
T = 48.5°C (49°C at two significant figures)
Thus from the above conclusion we can say that The final temperature in Celsius of the metal block is 49°C.
Learn more about the Moles here: https://brainly.com/question/15356425
#SPJ1
grams of hydrogen contains the same number of atoms as 9.79 grams of nitrogen?
Answer:
1.44 g
Explanation:
1. get number of nitrogen atoms in 9.79 grams of nitrogen
1 mole of Nitrogen is 6.022 x 10^23 atoms N which is = 14.01g N
2.
if 6.022 x 10^23 atoms of Nitrogen is 14
then x atoms of Nitrogen is 9.79
3.
6.022 x 10^23/ x = 14/9.79 ->
x = 8.431 x 10^24 / 9.79 =
8.61799714478 x 10^23
4.
8.61799714478 x 10^23 atoms of N
6.022 x 1023 atoms of H have a mass of 1.008g, so
8.61799714478 x 10^23 atoms of H have a mass of (1.008/6.022 x 1023) x 8.61799714478 x 10^23) = 1.44250051072175g
1.44 g
yeahchemistrycom
5. Which of the following personal protective equipment is selected based on a
chemical's IDLH value?
O A. Respirator
O B. Eyewear
O C. Body suit
O D. Gloves
Respirator - It is chosen based on a chemical's IDLH value, ensuring protection against immediate life-threatening respiratory hazards.
Option (A) is correct.
The correct personal protective equipment (PPE) selected based on a chemical's IDLH (Immediately Dangerous to Life or Health) value is a respirator. IDLH value is a critical safety parameter that represents the maximum concentration of a chemical in the air above which an individual could suffer immediate or long-term health effects, such as life-threatening respiratory issues.
When a chemical's IDLH value is exceeded, it becomes essential to use appropriate respiratory protection. A respirator helps filter and remove harmful contaminants from the air, preventing inhalation and protecting the wearer's respiratory system.
Different types of respirators are available, ranging from simple dust masks to full-face air-purifying respirators or supplied-air respirators, based on the specific hazard and IDLH value of the chemical involved.
Eyewear, body suits, and gloves are essential PPE, but they are not specifically selected based on the chemical's IDLH value.
To learn more about IDLH value here
https://brainly.com/question/31842241
#SPJ2
what’s the amino acid for this?
Determine the moles of solute in a 350g solution that is 2.5 molal.
Answer:
0.875 moles solute
Explanation:
You can find the moles of the solute using the molality ratio:
Molality = moles solute / mass (kg) solution
After converting the mass to kilograms, you can plug the values into the ratio and simplify to find the moles.
1,000 g = 1 kg
350 g 1 kg
-------------- x --------------- = 0.35 kg solution
1,000 g
Molality = moles solute / mass solution
2.5 m = moles solute / 0.35 kg
0.875 = moles solute
The molar heat of fusion of gold is 12.550 kJ mol–1. At its melting point, how much mass of melted gold must solidify to release 235.0 kJ of energy?
The mass of melted gold to release the energy would be 3, 688. 8 Kg
How to determine the massWe have quantity of energy is;
Q = n × HF
n = number of moles
HF = heat of fusion
Let's find number of moles
235.0 = n × 12.550
number of moles = [tex]\frac{235}{12. 550}[/tex] = 18. 725 moles
Note that molar mass of Gold is 197g/ mol
Number of moles = mass/ molar mass
Mass = number of moles × molar mass
Mass = 18. 725 × 197
Mass = 3, 688. 8 Kg
Thus, the mass of melted gold to release the energy would be 3, 688. 8 Kg
Learn more about molar heat of fusion here:
https://brainly.com/question/15634085
#SPJ1
1.______ language is the ability to understand what’s said.
2. When babies handle objects, they learn that they can
make something happen. This helps them begin to
understand and _______.
3. Caregivers can encourage language development by _____
to the baby.
4.______ is the ability of an infant to understand when
an object is present even if he or she can't see it.
5. Language development and thinking ability are _______.
6. Toddlers gain self-confidence when they _______.
Caregivers should expect toddlers to _______.
7.Caregivers should help children select television programs to watch and _______ the time they spend in this activity.
8. Superhero and fantasy play should be tempered with discussing the differences between _______ and reality.
The 1 month old baby sees up to 30 cm away, following objects and people that move around him and fixing his gaze on bright and flashy objects. To say that he wants something or that something is bothering him, the baby usually expresses himself through crying.
What is baby development?1.Clear language is the ability to understand what’s said.
2. When babies handle objects, they learn that they can
make something happen. This helps them begin to
understand and do.
3. Caregivers can encourage language development by sign
to the baby.
4.imagine is the ability of an infant to understand when
an object is present even if he or she can't see it.
5. Language development and thinking ability are indispensable.
6. Toddlers gain self-confidence when they make mistakes.
Caregivers should expect toddlers to mistakes.
7.Caregivers should help children select television programs to watch and monitor the time they spend in this activity.
8. Superhero and fantasy play should be tempered with discussing the differences between fantasy and reality.
With this information, we can conclude that If your baby does not respond to stimuli and even as the months go by, simple steps of the baby's development are not happening, such as smiling, turning around, crawling, the pediatrician will follow up and refer the competent specialist to carry out evaluation tests to investigate a possible delay. psychomotor.
Learn more aboute baby development in brainly.com/question/9622335
#SPJ1
What classifies a substance as an element?
What classifies a substance as a compound?
Actually, answer what the question is asking and give a short answer. No copying and pasting.
Elements cannot be broken down into simpler substances by any or series of chemical reactions.
A compound can be broken done by chemical reactions
Element and compoundAn element can be defined as species of atoms having a certain number of protons in their nuclei and pure substance of that species.
Elements cannot be broken down into simpler substances by any or series of chemical reactions.
A compound can be defined as a chemical substance that is composed of numerous identical molecules containing atoms from more than one element and held together by chemical bonds.
A compound can be broken done by chemical reactions
Learn more about chemical properties here:
https://brainly.in/question/78631
#SPJ1
Boyels law lab report
Boyle's law is a model used in chemistry and physics to estimate the pressure behavior of gases in a closed system.
What is Boyle's law?Boyle's law is a model used to calculate pressure and volume relationships among gases in a thermodynamically closed system.
This law states that the pressure of a given gas represents an inversely proportional measurement of its volume in steady conditions.
In conclusion, Boyle's law is a model used in chemistry and physics to estimate the pressure behavior of gases in a closed system.
Learn more about Boyle's law here:
https://brainly.com/question/26040104
#SPJ1
if 14.0 g of aluminium reacts with excess sulfuric acid to produce 75.26 g of aluminium sulfate, what is the percent yield?
Taking into account definition of percent yield, the percent yield for the reaction is 84.88%.
Reaction stoichiometryIn first place, the balanced reaction is:
2 Al + 3 H₂SO₄ → Al₂(SO₄)₃ + 3 H₂
By reaction stoichiometry (that is, the relationship between the amount of reagents and products in a chemical reaction), the following amounts of moles of each compound participate in the reaction:
Al: 2 moles H₂SO₄: 3 molesAl₂(SO₄)₃. 1 moleH₂: 3 molesThe molar mass of the compounds is:
Al: 27 g/moleH₂SO₄: 98 g/moleAl₂(SO₄)₃: 342 g/moleH₂: 2 g/moleThen, by reaction stoichiometry, the following mass quantities of each compound participate in the reaction:
Al: 2 moles ×27 g/mole= 54 gramsH₂SO₄: 3 moles ×98 g/mole= 294 gramsAl₂(SO₄)₃: 1 mole ×342 g/mole= 342 gramsH₂: 3 moles ×2 g/mole= 6 gramsMass of aluminium sulfate formedThe following rule of three can be applied: if by reaction stoichiometry 54 grams of aluminium form 342 grams of aluminium sulfate, 14 grams of aluminium form how much mass of aluminium sulfate?
[tex]mass of aluminium sulfate=\frac{14 grams of aluminium x342 grams of aluminium sulfate}{54 grams of aluminium}[/tex]
mass of aluminium sulfate= 88.67 grams
Then, 88.67 grams of aluminium sulfate can be produced if 14.0 g of aluminium reacts with excess sulfuric acid.
Percent yieldThe percent yield is the ratio of the actual return to the theoretical return expressed as a percentage.
The percent yield is calculated as the experimental yield divided by the theoretical yield multiplied by 100%:
[tex]percent yield=\frac{actual yield}{theorical yield} x100[/tex]
where the theoretical yield is the amount of product acquired through the complete conversion of all reagents in the final product, that is, it is the maximum amount of product that could be formed from the given amounts of reagents.
Percent yield for the reaction in this caseIn this case, you know:
actual yield= 75.26 gramstheorical yield= 88.67 gramsReplacing in the definition of percent yields:
[tex]percent yield=\frac{75.26 grams}{88.67 grams} x100[/tex]
Solving:
percent yield= 84.88%
Finally, the percent yield for the reaction is 84.88%.
Learn more about
the reaction stoichiometry:
brainly.com/question/24741074
brainly.com/question/24653699
percent yield:
brainly.com/question/14408642
#SPJ1
a 3.211 g sample of gypsum a hydrated salt of magnesuim sulfate, MgSO4.XH2OIS HEATED IN A CRUCIBLE UNTIL A CONSTANT MASS IS REACHED . THE MASS OF THE ANHYDROUS MgSO4 IS 2.539g
a) calculate the percentage by the mass of water in the hydrated MgSO4.xH2O
b) calculate the moles , the amount of H2O released during heating and the amount (in moles) of the anhydrates MgSO4 remaining after heating
c) calculate the value of x in MgSO4.xH2O/ This is the empirical formula of the hydrated magnesium sulfate
From the calculation, the compound is MgSO4.2H2O.
What is a hydrated salt?A hydrated salt is a salt that contains molecules of the water of crystallization.
a) Percentage of the water of crystallization = 3.211 g - 2.539g/ 3.211 g * 100/1 = 21%
b) Number of moles of water of crystallization = 3.211 g - 2.539g/ 18 g/mol =
0.037 moles
c) Number of moles of anhydrous salt = 2.539g/120 g/mol = 0.021 moles
Number of moles of hydrated salt = 3.211 g/120 + 18x
Hence;
0.021 = 3.211 /120 + 18x
0.021(120 + 18x) = 3.211
2.52 + 0.378x = 3.211
0.378x = 3.211 - 2.52
x = 3.211 - 2.52/ 0.378
x = 2
Hence the compound is MgSO4.2H2O
Learn more about hydrated salt:https://brainly.com/question/5586505
#SPJ1
State the oxidation number of the following: M n
The oxidation number of Mn is 0. Details about oxidation number can be found below.
What is oxidation number?Oxidation number is the hypothetical charge of an atom within a molecule.
However, when an atom exists independently as an element, the oxidation number of such element is 0.
The oxidation number is assigned to an atom in a element/compound. It can either be +, -, or 0 and it tells us if electrons are lost or gained.
Therefore, according to this question, the oxidation number of Mn is 0.
Learn more about oxidation number at: https://brainly.com/question/15167411
#SPJ1
I need help with my work
By the mean value theorem, the function y = sin x² on the interval [0, π/4] has this guaranteed number: x ≈ 0.460.
How to find a number that guarantees the mean value theorem
According to the mean value theorem, a function that is differentiable at an interval [a, b] has a number c within the interval such that:
f'(c) = [f(b) - f(a)]/(b - a) (1)
The first derivative of the function is f'(x) = 2 · x · cos x² and by the mean value theorem we know that:
2 · c · cos c² = [sin (π/4)²- sin 0²]/(π/4 - 0)
2 · c · cos c² = [- √2 / 2]/(π /4)
2 · c · cos c² ≈ 0.900
This equation cannot be solved analytically. By the resource of a graphing tool we found the following solution within the interval: c ≈ 0.460.
To learn more on mean value theorem: https://brainly.com/question/1581272
#SPJ1