The volume V of an ideal gas varies directly with the temperature T and inversely with thepressure P. A cylinder contains oxygen at a temperature of 320 degrees Kelvin and a pressure of
25 atmospheres in a volume of 120 liters. Find the pressure if the volume is decreased to 110
liters and the temperature is increased to 335 degrees Kelvin.
Hint: Look at the equation V = k* Then use the initial values to solve for k. Then plug in the
values you know for the second set of values and solve for your unknown.
Answers
Answer:
Pressure=22.55 atmospheres
Step-by-step explanation:
Let
V=volume of the ideal gas
P=pressure
T=temperature
Volume varies directly with temperature and inversely with pressure
V=kT/P
t=320°K
P=25 atmospheres
V=120 liters
V=kT/P
120=k*320/25
120=320k/25
120×25=320k
3000=320k
k=300/320
=9.375
k=9.375
V=110 liters
p=?
t=335°K
V=kT/P
110=9.375*335/p
110=3,140.625/p
110p=3,140.625
P=3,140.625/110
=28.55
P=22.55 atmospheres
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Answers
Final answer:
Cos(88°) can be estimated using the 3rd degree Taylor polynomial for cos(x) centered at a = π/2. The degrees need to be converted to radians, and by substituting into the polynomial, the cosine value to five decimal places is approximately 0.03490.
Explanation:
To estimate cos(88°) using the 3rd degree Taylor polynomial for cos(x) centered at a = π/2, we first need to convert 88 degrees to radians as cos(x) expects x in radians. 88 degrees is roughly 1.53589 radians. Now, substituting x = 1.53589 into the Taylor polynomial yields the estimate.
The given Taylor polynomial is represented as cos(x) = - (x - π/2) + 1/6 * (x - π/2)³. Substituting x with 1.53589, we get:
cos(1.53589) = - (1.53589 - π/2) + 1/6 * (1.53589 - π/2)³
To get the estimate correct to five decimal places, you calculate the above expression to get roughly 0.03490. Therefore, cos(88°) is approximately 0.03490.
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Final answer:
First, we convert the given angle 88° into radians, since standard trigonometrical functions take angles in radians. We then substitute this into the Taylor series given, keeping in mind the importance of the remainder term.
Explanation:
This problem deals with the concept of Taylor series approximation, which is a widely used method in mathematics to estimate the value of functions. The given Taylor polynomial approximates the cosine function. To estimate cos(88°), we first need to convert the angle from degrees to radians, because the standard trigonometric functions in mathematics take input in radians. Remember that 180° equals π radians. So 88° can be represented as (88/180)π radians.
Substitute this into the provided series − x − π/2 + 1/6 * (x − π/2)³ + R3(x). Be wary of the remainder term R3(x). This term ensures the correctness of the approximation on the interval of convergence. The closer x is to the center, the more accurate the approximation. In practical computations, you might need to take more terms into account to ensure sufficient accuracy to five decimal places in this case.
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Answers
Answer:A
Step-by-step explanation:
The dot means less than or equal to 2
Open dot means greater than 2
many inches of ribbon will she need?
24 inches
36 inches
A 156 inches B 120 inches
C90 inches
D 60 inches
Answers
The amount of ribbon needed is 120 inches
what is perimeter?
The perimeter formula for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width.
Given:
length = 24 inches
width = 36 inches
So, amount of ribbon needed
=2(36+ 24)
=2(60)
=120 inches
Hence, the amount of ribbon needed is 120 inches
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Answer:
option B
Step-by-step explanation:
a. 15
b. 5
c. 25
d. 1
2. Suppose y varies inversely with x, and y = a when x = a^2. What inverse variation equation related x and y?
a. y = a^2/x
b. y = a^3/x
c. y= a^3x
d. y = ax
3. Suppose y varies inversely with x, and y = 3 when x = 1/3. What is the inverse variation equation that relates x and y?
a. y = 1/x
b. y =x
c. y = 3x
d. y = 3/x
Answers
Answer:
1. D. 1
2. B. y=a³/x
3. A. y=1/x
Step-by-step explanation:
too long to give te explanations but they're there in the attachments
x1 = 172 x2 = 654
Answers
Answer:
The calculated value Z = 3.775 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
The Two Population proportion are not equal
Step-by-step explanation:
Given first sample size n₁ = 677
First sample proportion
Given second sample size n₂ = 3377
second sample proportion
Null Hypothesis : H₀ : p₁ = p₂.
Alternative Hypothesis : H₁ : p₁ ≠ p₂.
Test statistic
where
P = 0.2036
Q = 1 - P = 1 - 0.2036 = 0.7964
Z = 3.775
Critical value ∝=0.05
Z- value = 1.96
The calculated value Z = 3.775 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
The Two Population proportion are not equal
Answers
When the shadow is 51.96 meters long, the angle of the sun is arctan(30/51.96) = 30°