Sphere A has a radius of 24 centimeters, and sphere B has a diameter of 42 centimeters. The radius of sphere A is multiplied by
2 answers:
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Answer:
a) 42°F < x < 176°F
b) The inequality graph is attached.
c) No, This is because at 20° F benzene would not be in liquid form but in solid form.
Step-by-step explanation:
According to the Question,
a) For the benzene to remain in liquid form, the temperature of benzene must be less than the boiling point and greater than the boiling point. Let x be the temperature of benzene, For benzene to remain as liquid, its temperature must be between:
42°F < x < 176°F
b) The inequality graph is attached. The graph shows that the temperature of benzene must be between 42°F and 176°F so that it would be a liquid. The Closed circles represent that it is greater than 2.
c) No, This is because at 20° F benzene would not be in liquid form but in solid form. Because the temperature cannot go below 42 before it freezes, she would not have been able to conduct her research .
Answer:
a)
b)
Step-by-step explanation:
a) The first part requires that we use line integral to evaluate directly.
The line integral is
where C is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 2)
The boundary of integration is shown in the attachment.
Our first line integral is
The equation of this line is y=0, x varies from 0 to 1.
When we substitute y=0 every becomes zero.
Our second line integral is
The equation of this line is:
y varies from 1 to 2.
We substitute the boundary and the values to get:
The 3rd line integral is:
The equation of this line is
x varies from 0 to 1.
We substitute to get:
The value of the line integral is
b) The second part requires the use of Green's Theorem to evaluate:
Since C is a closed curve with counterclockwise orientation, we can apply the Green's Theorem.
This is given by:
We choose our region of integration parallel to the y-axis.
