Answer:
NaCl, Na⁺,Cl⁻.
MgCl₂, Mg²⁺, Cl⁻.
CaO, Ca²⁺, O²⁻.
Li₃P, Li⁺, P³⁻.
Al₂S₃, Al³⁺, S²⁻.
Ca₃N₂, Ca²⁺, N³⁻.
FeCl₃, Fe³⁺, Cl⁻.
FeO, Fe²⁺, O²⁻.
Cu₂S, Cu⁺, S²⁻.
Cu₃N₂, Cu²⁺, N³⁻.
ZnO, Zn²⁺, O²⁻.
Ag₂S, Ag⁺, S²⁻.
K₂CO₃, K⁺, CO₃²⁻.
NaNO₃, Na⁺, NO₃⁻.
Ca(HCO₃)₂, Ca²⁺, HCO₃⁻.
Al(OH)₃, Al³⁺,OH⁻.
Li₃PO₄, Li⁺, PO₄³⁻.
K₂SO₄, K⁺, SO₄²⁻.
Explanation:
Sodium chloride. NaCl, formed by the cation Na⁺ and the anion Cl⁻.
Magnesium chloride. MgCl₂, formed by the cation Mg²⁺ and the anion Cl⁻.
Calcium oxide. CaO, formed by the cation Ca²⁺ and the anion O²⁻.
Lithium phosphide. Li₃P, formed by the cation Li⁺ and the anion P³⁻.
Aluminum sulfide. Al₂S₃, formed by the cation Al³⁺ and the anion S²⁻.
Calcium nitride. Ca₃N₂, formed by the cation Ca²⁺ and the anion N³⁻.
Iron(III)chloride. FeCl₃, formed by the cation Fe³⁺ and the anion Cl⁻.
Iron(II)oxide. FeO, formed by the cation Fe²⁺ and the anion O²⁻.
Copper(I)sulfide. Cu₂S, formed by the cation Cu⁺ and the anion S²⁻.
Copper(II)nitride. Cu₃N₂, formed by the cation Cu²⁺ and the anion N³⁻.
Zinc oxide. ZnO, formed by the cation Zn²⁺ and the anion O²⁻.
Silver sulfide. Ag₂S, formed by the cation Ag⁺ and the anion S²⁻.
Potassium carbonate. K₂CO₃, formed by the cation K⁺ and the anion CO₃²⁻.
Sodium nitrate. NaNO₃, formed by the cation Na⁺ and the anion NO₃⁻.
Calcium bicarbonate. Ca(HCO₃)₂, formed by the cation Ca²⁺ and the anion HCO₃⁻.
Aluminum hydroxide. Al(OH)₃, formed by the cation Al³⁺ and the anion OH⁻.
Lithium phosphate. Li₃PO₄, formed by the cation Li⁺ and the anion PO₄³⁻.
Potassium sulfate. K₂SO₄, formed by the cation K⁺ and the anion SO₄²⁻.
The surface of silver metal, Ag(s), became tarnished when it was exposed to oxygen, producing Ag2O. In Ag2O, the oxidation state of silver is 1. According to this information, silver metal was _____. Please choose the correct answer from the following choices, and then select the submit answer button. Answer choices reduced
Answer: The silver metal was OXIDIZED.
Explanation:
OXIDATION is defined as loss of electrons and increase in oxidation number of an atom.
Oxidation number is the charge on an ion in an ionic compound or the charge that an atom in a covalent compound would have it it were ionic. There are basic rules governing oxidation number, they include:
--> the oxidation number of elements in their free states is ZERO. Example O2, Cl2,Na, Al, Ag.
-->The oxidation number for an ion is the same as the size and sign of the charge on the ion. For example the oxidation number of Zn2+ is +2.
--> the sum of all the oxidation numbers of the elements in a compound is zero.
--> oxidation numbers are always written with either a positive or a negative sign.
On the other hand, reduction is the opposite of oxidation. As oxidation is taking place, reduction is also taking place. Reduction involves:
--> Gain of electron and
--> decrease in oxidation number
From the question, the silver metal had ZERO as it's oxidation number because it's in free state. After being exposed to oxygen to form silver oxide, the oxidation number became +1.
Since there is an increase in the oxidation number, the silver metal was OXIDIZED
why Ethyl amine is more basic than aniline?
Answer:
Because a Lone pair of electrons on nitrogen is involved in delocalization.
Hope this helps you ( ◕ᴗ◕✿)
If it doesn't i'm sorry(◞ ‸ ◟)
Explanation:
In ethylamine ethyl is electron donating group. So more electrons are available aroudn nitrogen for donation. But in aniline phenyl group is electron attracting group.
Hello, I am a bit stuck on this. Could someone help?
A sample of oxygen gas at a pressure of 1.19 atm and a temperature of 24.4 °C, occupies a volume of 18.7 liters. If the gas is allowed to expand at constant temperature to a volume of 29.4 liters, the pressure of the gas sample will be ______ atm.
Answer:
[tex]\boxed {\boxed {\sf 0.757 \ atm}}[/tex]
Explanation:
We are asked to find the pressure of a gas given a change in volume. Since the temperature remains constant, we are only concerned with volume and pressure. We will use Boyle's Law, which states the volume is inversely proportional to the pressure. The formula for this law is:
[tex]P_1V_1= P_2V_2[/tex]
Initially, the oxygen gas occupies a volume of 18.7 liters at a pressure of 1.19 atmospheres.
[tex]1.19 \ atm * 18.7 \ L = P_2V_2[/tex]
The gas expands to a volume of 29.4 liters, but the pressure is unknown.
[tex]1.19 \ atm * 18.7 \ L = P_2 * 29.4 \ L[/tex]
We are solving for the new pressure, so we must isolate the variable [tex]P_2[/tex]. It is being multiplied by 29.4 liters. The inverse operation of multiplication is division. Divide both sides of the equation by 29.4 L.
[tex]\frac {1.19 \ atm * 18.7 \ L}{29.4 \ L} =\frac{ P_2 * 29.4 \ L}{29.4 \ L}[/tex]
[tex]\frac {1.19 \ atm * 18.7 \ L}{29.4 \ L} =P_2[/tex]
The units of liters cancel.
[tex]\frac {1.19 \ atm * 18.7 }{29.4 } =P_2[/tex]
[tex]\frac {22.253}{29.4 } \ atm = P_2[/tex]
[tex]0.7569047619 \ atm =P_2[/tex]
The original measurements all have 3 significant figures, so our answer must have the same. For the number we calculated, that is the thousandth place. The 9 in the ten-thousandth place to the right of this place tells us to round the 6 up to a 7.
[tex]0.757 \ atm \approx P_2[/tex]
The pressure of the gas sample is approximately 0.757 atmospheres.
According to Boyle's law, for a given mass of ideal gas, pressure of gas is inversely proportional to the volume of gas, Provided the Temprature remains constant.
P₁ = 1.19 atmP₂ = ?V₁ = 18.7 LV₂ = 29.4 LT = constant = 24.4° C = Isothermal process[tex]\implies \sf P_1 V_1 = P_2 V_2 \\ [/tex]
[tex]\implies \sf 1.19 \times 18. 7= P_2 \times 29.4 \\[/tex]
[tex]\implies \sf 22.253= P_2 \times 29.4 \\[/tex]
[tex]\implies \sf P_2 = \dfrac{22.253}{29.4} \\[/tex]
[tex]\implies \underline{ \red{\boxed{ \bf P_2 \approx0.756 \: atm }}} \\[/tex]
A student isolated an unknown organic compound through extraction. The student measures the melting point and fins it to be 115-122 C. The student looks through the list of possible strucures and decides the comound is most likely 2-napthol. Do you believe this choice is correct?
Which one of the following compounds will NOT be soluble in water?
A) LiNO3
B) PbS
C) NaOH
D) MgCl2
E) K2SO4
The element Co exists in two oxidation states, Co(II) and Co(III), and the ions form many complexes. The rate at which one of the complexes of Co(III) was reduced by Fe(II) in water was measured. Determine the activation energy of the reaction from the following data:
T(K) K(s^-1)
293 0.054
298 0.100
We measured the Fe(II) reduction of one of the Co(III) complexes by water at a rate of about 0.545 kJ/mol (to three significant figures).
How is activation energy determined?Calculating a Reaction's Activation Energy A reaction's rate is influenced by the temperature at which it is carried out. The molecules travel more quickly and clash more frequently as the temperature rises. Moreover, the molecules contain greater kinetic energy.
We can use the Arrhenius equation to calculate the reaction's activation energy:
k = A × exp(-Ea/RT)
When the activation energy Ea, the rate constant k, the gas constant R, and the temperature T in Kelvin are all present.
Finding the natural logarithm of the equation's two sides results in:
ln(k) = ln(A) - (Ea/RT)
This equation can be rearranged to take a linear form:
ln(k) = (-Ea/R) × (1/T) + ln(A)
y = mx + b, where (1/T) is x, (-Ea/R) is the slope, and ln(A) is the y-intercept, has the form of a linear equation.
We can get the slope of the line using the given data:
slope = (-Ea/R) = (ln(k2/k1)) / (1/T2 - 1/T1)
where the rate constants for temperatures T1 and T2, respectively, are k1 and k2.
substituting the specified values:
k1 = 0.054s⁻¹ at 293 K
k2 = 0.100s⁻¹ at 298 K
T1 = 293 K
T2 = 298 K
slope = (-Ea/R)
= (ln(0.100/0.054)) / (1/298 - 1/293)
= 65.5 kJ/mol
Therefore, the activation energy of the reaction is:
Ea = slope * R = 65.5 kJ/mol × 8.314 J/mol-K = 545 J/mol
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The standard redox potentials of isolated components of an electron transport chain in a cyanobacterium are found to be as follows:
Complex A: standard redox potential: -100 mV
Complex B: standard redox potential: -780 mV
Complex C: standard redox potential: +510 mV
Complex D: standard redox potential: +310 mV
Plastocyanin: standard redox potential: +360 mV
Which complex will likely have a binding site with high affinity for reduced plastocyanin?
A. Complex A.
B. Complex B.
C. Complex C.
D. Complex D.
Answer:
B. Complex B.
Explanation:
Complex B will have binding site with high affinity for reduced plastocyanin due to greater redox potential. The high number of redox potential will will transport electron chain in cyanobacteria.
Redox potential is the measure of the electron gain or loss to the electrode. For reduced plastocyanin complex B will have the highest affinity.
What is electron affinity?Electron affinity is the energy released when the atom gets attached to the atom or other molecule. The high number of redox potential increases the electron transport in the cell.
The greater the redox potential more will be its tendency to show electron affinity. To bond with reduced species, the oxidized species must have greater redox potential.
Therefore, option B. complex b will have the highest affinity.
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Which method separates components of a mixture according to how quickly the particles travel through a medium?
A. distillation
B. evaporation
C. filtration
D. chromatography
Taking into account its definition, the correct answer is option D) Chromatography.
Chromatography is a method that allows the separation, identification and determination of chemical components in complex mixtures. By means of a chromatography it is possible to separate analytes that are very similar to each other in terms of their physico-chemical properties.
For the separation to occur, the principle of selective retention is used, which consists of the different behavior of the components of a mixture on a specific support (such as paper, a gas, a liquid) and a flowing liquid or gaseous phase. through the bracket.
In other words, there is a stationary phase immobilized on a support and a mobile phase that will drag the sample through the stationary phase. During this process, each component of the sample will move according to its own physicochemical characteristics. The general concept will be that those components that prefer the stationary phase are more retained, while those that prefer the mobile phase will move faster.
In summary, the components of the sample are distributed between two phases of different nature, as a consequence of the speed variation that is established when being dragged by a mobile, liquid or gaseous phase, through a stationary, solid or liquid phase.
Finally, the correct answer is option D) Chromatography.
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Why is bromine more electronegative than iodine?
Answer
Accordingly the order of electronegativity of the given elements would be: Fluorine > Chlorine > Bromine > Iodine. ( Fluorine has the highest electronegativity.)
An outdoor gear company develops a new type of fabric that works with electricity to warm the body without interfering with motion like heavy jackets do. Research biologists, studying life in extremely cold conditions on the polar ice caps, begin wearing the new fabric because it helps them work more comfortably, and they find it increases their productivity.
What best describes how the processes of scientific investigation and technological design are involved in this situation?
The clothing company conducted a scientific investigation to communicate results to researchers, who then used the knowledge in a technological design.
The clothing company conducted a scientific investigation to produce a product that researchers could then test while designing new technology.
The clothing company used technological design to create a product that helped aid researchers conducting a scientific investigation.
The clothing company designed a new technology that provided information researchers needed in order to continue with their scientific investigation.
Answer:
C: The clothing company used technological design to create a product that helped aid researchers conducting a scientific investigation.
Explanation:
I just did the assignment on EDGE2020 and it's 200% correct!
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How to distinguish between ethanol and 2 -methyl-2-propanol
Answer:
There are many reagents.
1. Use acidified potassium permanganate solution
2. Use acidified potassium dichromate solution
3. Fehling solution.
4. Silver/ oxygen at 500°C
5. Copper/ oxygen at 300°C
6. Lucas reagent ( anhydrous zinc and conc. hydrochloric acid)
Explanation:
Observations:
[with acidified potassium permanganate solution]
» Ethanol : The purple solution turns colourless.
» 2-methyl-2-propanol : no observable change.
[with acidified potassium dichromate solution]
» Ethanol : orange solution turns green
» 2-methyl-2-propanol : no observable change.
[Fehling solution]
» Ethanol : a white precipitate is formed
» 2-methyl-2-propanol : no observable change
Which of the following represents a physical change?
Answer:
» Water evaporating to gas.
» Solid subliming to gas.
» Water freezing to solid.
» Solid melting to liquid.
Explanation:
[tex]{ \underline{ \blue{ \sf{christ \:† \: alone }}}}[/tex]
313.9 liters of a gas has a pressure of 390.89 kPa at 76.6°C. If the pressure increases to 718.3 kPa and the temperature to 154.2°C, what would be the new volume of the gas?
A.) 210
B.) 353
C.) 470
D.) 209.92
Explanation:
P1V1/T1 = P2V2/T2
=((390.89×313.9)/76.6)×((718.3×V2)/154.2)
= (122700.371/76.7) × ((718.3×V2)/154.2)
make V2 the subject of the formula...
V2 =(122700.371×154.2)/(76.6×718.3)
V2 =18920397.21/55021.78
V2 = 343.87
Write the balanced equation for the hydration of CuSO4CuSO4. Indicate the physical states using the abbreviations (ss), (ll), or (gg) for solid, liquid, or gas, respectively. Use (aqaq) to indicate the aqueous phase. Indicate appropriate charges on negative and positive ions if they are formed.
Answer:
CuSO4(s) + 5H2O(l) ----> CuSO4.5H2O(s)
Explanation:
Hydration is the process by which anhydrous CuSO4 acquires molecules of water of crystalization to form the pentahydrate.
The water of crystalization becomes attached go the crystals of the CuSO4 to form the hydrated salt.
Beginning with solid anhydrous CuSO4 we have;
CuSO4(s) + 5H2O(l) ----> CuSO4.5H2O(s)
oxidation number of Ni in Ni(CO)4 is
Answer:
0
Explanation:
answer from gauth math
Alex drips hydrochloric acid onto a 5.9 g piece of magnesium in a single displacement reaction. How many molecules of HCl are required? 2HCl(aq) + Mg(s) → MgCl2(aq) + H2(g)
how do you do this?
2.96 × 10²³ molecules is required if Alex drips hydrochloric acid onto a 5.9 g piece of magnesium in a single displacement reaction
According to this question, hydrochloric acid (HCl) reacts with magnesium metal (Mg) to produce magnesium chloride and hydrogen has as follows:
2HCl(aq) + Mg(s) → MgCl2(aq) + H2(g)
Based on the balanced chemical equation above; 2 moles of HCl reacts with 1 mole of Mg. Next, we convert 5.9g of Mg to moles by using the formula; mole = mass/molar massWhere; Mg = 24g/mol
mole = 5.9/24
mole = 0.246mol of Mg
If 2 moles of HCl reacts with 1 mole of Mg. 0.246 mol of Mg will react with (0.246 × 2) = 0.492mol of HClTo convert mole to number of molecules, we multiply number of moles by 6.02 × 10²³ (Avogadro's no.)
Hence, number of molecules of HCl required is 0.492mol × 6.02 × 10²³
= 2.96 × 10²³ molecules of HClHCl
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Draw the structure of the organic product(s) of the Grignard reaction between methyl benzoate and excess phenylmagnesium bromide, followed by aqueous workup. You do not have to consider stereochemistry. If a compound is formed more than once, add another sketcher and draw it again. Alternatively, you may use the square brackets tool to add stoichiometries greater than one. Draw one structure per sketcher. Add additional sketchers using the drop-down menu in the bottom right corner. Separate multiple products using the sign from the drop-down menu.
Answer:
See explanation and image attached
Explanation:
The product of the Grignard reaction between methyl benzoate and excess phenylmagnesium bromide is triphenyl methanol.
The reaction proceeds by nucleophillic reaction as the carbonyl moiety is attacked. A tetrahedral intermediate is formed. Loss of the -OMe group is accompanied by the attack of the first molecule of PhMgBr.
Attack by a second PhMgBr molecule yields trimethyl phenoxide. Protonation of this specie yields the final product which is obtained by aqueous workup.
Which of the following is an example of an optional deduction ? " a ) Medicare Ob ) Social Security c ) Retirement plan d ) State tax
Medicare
United states program for people who are older than 60
Consider a hypothetical metal that has a density of 10.6 g/cm3, an atomic weight of 176.8 g/mol, and an atomic radius of 0.130 nm. Compute the atomic packing factor if the unit cell has tetragonal symmetry, values for the a and c lattice parameters are 0.570 and 0.341, respectively.
Answer:
0.3323
Explanation:
GIven that:
Density of the metal = 10.6 g/cm^3
atomic weight = 176.8 g/mol
atmic radius = 0.130 nm
values of a and c = 0.570 nm and 0.341 nm respectively
For us to determine the atomic packing factor, we need to first determine the volume of all spheres (Vs) and the volume of unit cell (Vc).
However, the number of atoms in the unit cell (n) can be computed as:
[tex]n = \dfrac{\rho * V_c *N_A}{A} \\ \\ n = \dfrac{(10.6) * (5.7)^2 (3.41)*(10^{-24}) *(6.022*10^{23})}{176.8}[/tex]
n = 4.0
Thus, the number of atoms in the unit cell is 4
∴
The atomic paking factor (APF) is calculated by using the formula:
[tex]\dfrac{Vs}{Vc} = \dfrac{4 * \dfrac{4}{3}\pi *R^3 }{a^2 *c} \\ \\ \\ \dfrac{Vs}{Vc} = \dfrac{4 * \dfrac{4}{3}\pi *(1.30*10^{-8})^3 }{(5.70*10^{-8})^2 *(3.41*10^{-8})}[/tex]
= 0.3323
10. At 573K, NO2(g) decomposes forming NO and O2. The decomposition reaction is second order in NO2 with a rate constant of 1.1 M-1s-1. If the initial concentration of NO2 is 0.056 M, how long will it take for 75% of the NO2 to decompose
Answer:
48.67 seconds
Explanation:
From;
1/[A] = kt + 1/[A]o
[A] = concentration at time t
t= time taken
k= rate constant
[A]o = initial concentration
Since [A] =[A]o - 0.75[A]o
[A] = 0.056 M - 0.042 M
[A] = 0.014 M
1/0.014 = (1.1t) + 1/0.056
71.4 - 17.86 = 1.1t
53.54 = 1.1t
t= 53.54/1.1
t= 48.67 seconds
Hence,it takes 48.67 seconds to decompose.
potassium and chlorine react to form potassium chloride. a.it is a redox reaction,explain why. b.see if u can write a balanced equation for it.
Answer:
K+ClKCl
Explanation:
because the reaction is between metal Potassium and Non-metal Chlorine
Answer:
Explanation:
a) It is a redox reaction because KCl is an ionic compounds with K having a + charge and Cl having a - charge. Originally, both have an oxidation state of 0 and not K has 1+ and Cl has 1-. Therefore, one species was oxidized and one was reduced which is indicative of a redox reactions.
b)
2K + Cl2 => 2KCl
When naming organic compounds, there are strict rules regarding punctuation.
1. A comma is used to separate two numbers.
2. A hyphen is used to separate a number from a letter.
Rewrite the name of this compound using hyphens and commas as appropriate.
The question is incomplete, the complete question is shown in the image attached to this answer
Answer:
2,3,3-trimethylhexane
Explanation:
IUPAC nomenclature provides a universally acceptable method of naming organic compounds from its structure.
According to this system of nomenclature;
A comma is used to separate two numbers.
A hyphen is used to separate a number from a letter.
Applying these rules, the name of the compound shown in the question should be written as 2,3,3-trimethylhexane.
Which one of these statements is/are true: I. All redox reactions with positive emfs are spontaneous. II. If a redox reaction is spontaneous, it must be fast. III. A spontaneous redox reaction will have a cathode reaction that has a more negative reduction potential than the anode. III only. I and III are true. I only. II only. All of I, II, and III are true.
Answer:
yea all the answers are true
Redox reaction is the transfer of the electron from one species to another. All of the three statements are true about the redox reaction.
What is a redox reaction?A redox reaction is a type of chemical reaction in which the electrons are gained and lost by a species. The positive EMF of the cell results in spontaneous and will move the reaction in the forward direction.
In a redox reaction, the cathode reaction is comparatively more negative than the reduction potential present at the anode.
Therefore, option E. All I, II, and III are true.
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A person uses 400.8 kcal of energy to run a race. Convert the energy used for the race to the following energy units:
(provide an answer in 4 significant figures)
Calories
calories
Food Calories
Joules
Kilojoules
Hint: 1kcal=4.184kJ
Calories, we know that fat burn is calories.
What does the third quantum number (m) describe?
A. Which energy level the electron is in
B. What type of orbital the electron is in
C. What direction the electron is spinning
D. The specific orbital within a sublevel
The third quantum number (m) describes the specific orbital within a sublevel. The correct answer is option D.
Quantum numbers are a set of four numbers that describe the properties of an electron in an atom. They specify the energy, position, and orientation of an electron in an atom.
The third quantum number (m) is also called the magnetic quantum number. It describes the orientation of the orbital in space. Each orbital within a sublevel has a different orientation in space, and the magnetic quantum number tells us which orbital we are talking about.
The value of m can range from -l to +l, where l is the second quantum number (the angular momentum quantum number). The value of l determines the number of orbitals in a sublevel, and the value of m determines the specific orbital within that sublevel.
In conclusion, the third quantum number (m) describes the specific orbital within a sublevel. It tells us how the orbital is oriented in space, and it can have values ranging from[tex]\rm -l \ to +l[/tex], where l is the second quantum number.
Option D is the correct answer.
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How many moles of HNO3 are needed to prepare 5.7 liters of a 1.64 M solution of HNO3
We are given:
Volume of Solution: 5.7 Liters
Concentration: 1.64 Molar
Number of moles required:
We know that the formula for concentration (in molar) is:
M = N / V
where M is the concentration, N is the number of moles, and V is the volume of solution (in L)
plugging the given values in the equation:
1.64 = N / 5.7
N = 1.64 * 5.7
N = 9.35 moles
A piece of metal has a volume of 30.0cm3 and a mass of 252g. What is its density? what metal do you think this is?
Answer:
Explanation:
get density = D = m / V = 0.252 / 0.00003 = 8400 metal will be Cu => bronzeHow many grams of sodium chloride are contained in 250.0 g of a 15% NaCl solution?
Please explain and show work.
Given concentration of NaCl=15%
Means ,
In every 100g of Solution 15g of NaCl is present .
Now
Given mass=250gSo ,
[tex]\\ \Large\sf\longmapsto 250\times 15\%[/tex]
[tex]\\ \Large\sf\longmapsto 250\times \dfrac{15}{100}[/tex]
[tex]\\ \Large\sf\longmapsto 37.5g[/tex]
37.5g of NaCl present in 250g of solution.
Answer:
Given concentration of NaCl=15%
Means ,
In every 100g of Solution 15g of NaCl is present .
Now
Given mass=250g
So ,
➡250 × 15%
➡250×15/100
➡37.5g
37.5g of NaCl present in 250g of solution.
If position vector r=bt²i + ct³j, where c are positive constants, when does the velocity vector make an angle of 45° with the x and y axes?
We want to find the value of t such that the velocity vector makes an angle of 45° with both axes.
We found that:
t = (2/3)*(b/c)
The velocity vector makes an angle of 45° with the x and y axes.
We know that the position vector is:
r = r=b*t²i + c*t³j
Remember that the versor "i" corresponds to the x-component, and the versor "j" corresponds to the y-component, then:
r = r=b*t²i + c*t³j = (b*t², c*t³)
The velocity vector is the vector that we get when we differentiate the position one, remember that if:
f(x) = a*x^n
then
f'(x) = n*a*x^(n - 1)
Using this, we can find that the velocity vector is:
v = (2*b*t, 3*c*t²)
Now we want to know, when does the velocity vector make an angle of 45° with the x and y axes.
Let's think of the vector as the hypotenuse of a triangle rectangle, where the x-component is the adjacent cathetus, and the y-component is the opposite cathetus. (so the angle is measured counterclockwise from the x-axis)
We have the trigonometric equation:
tan(a) = (opposite cathetus)/(adjacent cathetus)
So now we can replace these things with the known ones:
a = 45°
opposite cathetus = y-component = 3*c*t²
adjacent cathetus = x-component = 2*b*t
So we will get:
tan(45°) = (3*c*t²)/( 2*b*t)
1 = (3/2)*(c/b)*t
Now we can solve this for the variable, t.
1*(2/3)*(b/c) = t
t = (2/3)*(b/c)
We can conclude that at the time:
t = (2/3)*(b/c)
The velocity vector makes an angle of 45° with the x and y axes.
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