How is an ellipse described numerically?
An ellipse is described numerically by its mathematical equation, which includes the center, major and minor axes, and values of a and b. The foci of ellipse can also be calculated from its equation.
How is an ellipse described numerically?An ellipse is a geometric shape that is defined by two points called foci and a constant sum of distances from any point on the ellipse to the two foci. This constant sum is called the major axis or the length of the ellipse, while the distance between the center of ellipse and the foci is called the minor axis or width of the ellipse.
To describe an ellipse numerically, we use its mathematical equation, which is in the form of: ((x-h)² / a²) + ((y-k)² / b²) = 1
(h, k) is center of ellipse
a is length of major axis divided by 2; b is length of minor axis divided by 2
The values of a and b determine the shape of ellipse. If a = b, the ellipse is a circle. If a > b, ellipse is stretched horizontally and is called an oblong ellipse. If a < b, ellipse is stretched vertically and is called a flat ellipse.
Two foci of ellipse can also be calculated using: c = √(a² - b²)
c is distance from the center of the ellipse to either of the foci.
To know more about ellipse, refer
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16. How many molecules are present in 3.0 X 102 grams of calcium
carbonate? [Calcium - 40 g/m;Carbon - 12g/m. Oxygen - 16 g/m]
A) 6.02 X 1023
B 81.1 X 1023.
C) 1.81 X 1024
To solve this problem, we need to use the concept of Avogadro's number and molecular weight.
The molecular weight of calcium carbonate (CaCO3) can be calculated as follows:
Calcium (Ca) atomic weight = 40 g/molCarbon (C) atomic weight = 12 g/molOxygen (O) atomic weight = 16 g/molMolecular weight of CaCO3 = (1 x 40) + (1 x 12) + (3 x 16) = 100 g/molNow, we can calculate the number of molecules in 3.0 x 10^2 grams of CaCO3 as follows:
Convert the mass of CaCO3 to moles using the formula:moles = mass / molecular weight
moles = 3.0 x 10^2 g / 100 g/mol
moles = 3.0 x 10^0 mol
Use Avogadro's number to calculate the number of molecules:number of molecules = moles x Avogadro's number
number of molecules = 3.0 x 10^0 mol x 6.02 x 10^23 molecules/mol
number of molecules = 1.806 x 10^24
Therefore, the answer is C) 1.81 x 10^24.
The term used to describe the non-living parts of an eco system
Answer:
Abiotic Factor
Explanation:
Is a non-living part of an ecosystem that shapes its enviroment.
Suppose that the microwave radiation has a wavelength of 12.4 cm. How many photons are required to heat 205 mL of coffee from 25.0 ∘C to 62.0 ∘C ? Assume that the coffee has the same density, 0.997 g/mL, and specific heat capacity, 4.184 J/(g⋅K), as water over this temperature range.
Answer:
To calculate the number of photons required to heat the coffee, we can follow these steps:
Calculate the mass of the coffee using its volume and density:
mass = volume x density = 205 mL x 0.997 g/mL = 204.185 g
Calculate the amount of heat required to raise the temperature of the coffee using its mass, specific heat capacity, and temperature change:
q = m x c x ΔT = 204.185 g x 4.184 J/(g⋅K) x (62.0 - 25.0) °C = 32289.6 J
Calculate the energy of each photon using the formula E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength of the microwave radiation:
E = (6.626 x 10^-34 J⋅s) x (3.00 x 10^8 m/s) / (0.124 m) = 5.067 x 10^-23 J
Calculate the number of photons required to deliver the amount of energy needed to heat the coffee:
number of photons = q / E = 32289.6 J / 5.067 x 10^-23 J = 6.368 x 10^25 photons
Therefore, approximately 6.368 x 10^25 photons are required to heat 205 mL of coffee from 25.0 ∘C to 62.0 ∘C using microwave radiation with a wavelength of 12.4 cm.
A sample of gas has an initial pressure of 740 mmHg and an initial volume of 32.0 L. If the volume is changed to 21.8 L, what is the new pressure? Assume temperature and amount remain constant
Answer:
1086.2 mmHg
Explanation:
P1×V1=P2×V2
740mmHg×32.0L=P2×21.8L
23680L mmHg= P2×21.8L
divide both sides by 21.8L
1086.2mmHg=P2
A 1.0 L of a 6.0 M solution of HCl acid is titrated with a 0.2 M basic solution. How much base is needed to reach its titration endpoint?
(I only have four more questions to ask lol)
Answer:
No worries, happy to help! To find out how much base is needed to reach the titration endpoint, we need to use the balanced chemical equation for the reaction between HCl and the basic solution, and the stoichiometry of the reaction. The balanced chemical equation is: HCl + NaOH → NaCl + H2O From the equation, we can see that 1 mole of HCl reacts with 1 mole of NaOH. We also know that the initial volume of HCl solution is 1.0 L, and the initial concentration is 6.0 M. This means we have: moles of HCl = volume x concentration = 1.0 L x 6.0 mol/L = 6.0 mol To reach the titration endpoint, we need to add enough NaOH solution to completely neutralize all