8. A banker's loan officer rates applications for credit. The rates are normally distributed with a mean of 200 and a standard d
1 answer:
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Answer:
<em>The last is the correct option</em>
<em>"all real values except x not-equals 7 and the x for which f (x) not-equals negative 3"</em>
Step-by-step explanation:
<u>Domain and Range of Functions</u>
Given the function f(x), the domain of f is the set of all the values that x can take such f(x) exists. The range of f is the set of all the values that f takes.
We have a problem where we have to find the domain of a composite function. Let's recall that being f and g real functions, then
is the composite function of f and g.
We know the domain of f is the set of all real values except 7, and the domain of g is the set of all real values except –3.
Since f is the innermost function, the domain of the composite function is directly restricted by the domain of f. So, x cannot be 7.
Now, g takes f as its independent variable, and we know the domain of g excludes -3. It can be found that f(x) cannot be -3 because it will cause g not to exist.
Thus, the domain of is
All real numbers except x=7 and those where f(x)=-3
The last is the correct option
Answer:
Width = 10 inches
Step-by-step explanation:
Given the perimeter of a rectangle of 68 inches, and a length that is 14 inches longer than its width.
We can establish the following values to help us solve for the width of a rectangle:
Perimeter (P) = 68 inches
Length (L) = 14 + W inches
Width (W) = unknown
<h3 /><h3><u>Solve for the Width (W)</u></h3>P = 2(L + W) ⇒ This is the same as P = 2L + 2W, except that 2 is factored out from the right-hand side.
Divide both sides by 2:
Substitute the value of the Perimeter and the length (L) into the formula:
Combine like terms on the right-hand side, and simplify the left-hand side of the equation:
Subtract 14 from both sides:
34 - 14 = 14 - 14 + 2W
20 = 2W
Divide both sides by 2 to solve for the width (W):
W = 10 inches
Therefore, the width of the rectangle is 10 inches.
<h3 /><h3><u>Double-check:</u></h3>Verify whether the derived value for the width is correct:
P = 2L + 2W
68 = 2(14 + 10) + 2(10)
68 = 2(34) + 20
68 = 48 + 20
68 = 68 (True statement).
Thus, the length of the rectangle is 34 inches, and the width is 10 inches.
Answer:
Same angular velocity
Same angular acceleration
Point 1 has greater tangential speed
Point 1 has greater tangential acceleration
Point 1 has greater centripetal acceleration
Step-by-step explanation:
Since both points are located on the rigid wheel, their angular velocity and acceleration must be the same for all point located on the wheel.
The tangential quantities, however, would depend on how far they are from the axis of rotation:
where are the angular velocity and acceleration, respectively, which is the same for 2 points. R is the radius of rotation. In this case point 1 has a larger radius since it lies on the rim and point 2 is only half way between.
Therefore, tangential speed, acceleration and centripetal acceleration of point 1 is larger than point 2.