First note the intersections of each pair of lines.
x = 3 ⇒ y = 2•3 + 1 = 7 ⇒ (3, 7)
y = -3 ⇒ -3 = 2x + 1 ⇒ x = -2 ⇒ (-2, -3)
y = -3 and x = 3 ⇒ (3, -3)
Using the disk method, we consider disks with thickness ∆y and radius equal to the horizontal distance between the line y = 2x + 1 (or x = (y - 1)/2) and the axis of revolution, x = 3. Each disk will then contribute a volume of
∆V = π (radius)² (thickness) = π/4 (y - 1)² ∆y
As we let ∆y go to zero and let the number of disks go to infinity, the total volume of the resulting cone will be given by the integral
Answer:
x ≤ -3 or 1 < x
Step-by-step explanation:
Solve an inequality the same way you would solve an equation, with one exception. If you multiply or divide by a negative number, the inequality symbol is reversed.
... x + 7 ≤ 4 . . . . . left inequality
... x ≤ -3 . . . . . . . subtract 7 to get the x-term by itself
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... 5 - 3x < 2 . . . . right inequality
... -3x < -3 . . . . . . subtract 5 to get the x-term by itself
... x > 1 . . . . . . . . . divide by -3. Since -3 is negative, we reverse the inequality symbol
The problem statement says the solution is the OR of these, so ...
... x ≤ -3 . . or . . 1 < x
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These are graphed on a number line with a solid dot at -3, and an arrow to the left from there; and an open dot at +1, and an arrow to the right from there. (The dot at 1 is open because x=1 is not in the solution set.)
The molar mass of N2O5 (Dinitrogen pentoxide) is 108.01 g/mol.
Answer:
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Step-by-step explanation:
Answer:
Step-by-step explanation: If Professor Lam grades 4 papers per hour, in 11 hours he will graded 44 papers. (11 x 4= 44). He had previously graded 6 papers giving him a total of 50 papers graded. His assistant can grade 5 papers per hour, thus it would take him 10 hours to grade the same amount of papers as Professor Lam. (10 x 5= 50) Thus: 11 hours Professor Lam 50 papers graded; 10 hours his assistant 50 papers graded.
