Part A. You have the correct first and second derivative.
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Part B. You'll need to be more specific. What I would do is show how the quantity (-2x+1)^4 is always nonnegative. This is because x^4 = (x^2)^2 is always nonnegative. So (-2x+1)^4 >= 0. The coefficient -10a is either positive or negative depending on the value of 'a'. If a > 0, then -10a is negative. Making h ' (x) negative. So in this case, h(x) is monotonically decreasing always. On the flip side, if a < 0, then h ' (x) is monotonically increasing as h ' (x) is positive.
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Part C. What this is saying is basically "if we change 'a' and/or 'b', then the extrema will NOT change". So is that the case? Let's find out
To find the relative extrema, aka local extrema, we plug in h ' (x) = 0
h ' (x) = -10a(-2x+1)^4
0 = -10a(-2x+1)^4
so either
-10a = 0 or (-2x+1)^4 = 0
The first part is all we care about. Solving for 'a' gets us a = 0.
But there's a problem. It's clearly stated that 'a' is nonzero. So in any other case, the value of 'a' doesn't lead to altering the path in terms of finding the extrema. We'll focus on solving (-2x+1)^4 = 0 for x. Also, the parameter b is nowhere to be found in h ' (x) so that's out as well.
Answer:
$25.65
Step-by-step explanation:
Since we are applying a discount to a price tag, we will be <u>decreasing</u> the amount of that price tag.
In this case, we will be taking 5% off of $27. This means that our new price tag will be 95% of what it originally was. To find the answer, we must first change 95% into a decimal.
95% -> 
-> 0.95
Next, we multiple $27 by 0.95 as shown below:
Our answer will be:
$25.65
Answer:
264 in²
Step-by-step explanation:
Parameters given:
Base, b = 24 inches
Height, h = 12 inches
Top side length, a = 20 inches
We are told that the front face of the basket is in the shape of a trapezoid.
The area of a trapezoid is:
A = ½ * (a + b) * h
The area of the front face of the basket is:
A = ½ * (20 + 24) * 12
A = ½ * 44 * 12
A = 264 in²
The area of the front face of the basket is 264 in².
The Pythagorean theorem can tell you the length of "b".
c² = a² + b²
b² = 19² -3² = 360
b = 6√10 ≈ 18.8
Sin = Opposite/Hypotenuse
sin(A) = a/c = 3/19
A = arcsin(3/19) ≈ 9.1°
B = 90° - A = 80.9°
The remaining sides and angles are ...
b = 18.8
A = 9.1°
B = 80.9°
The solution of the system of equations is (-3 , -2)
Step-by-step explanation:
Steps for Using Linear Combinations Method)
- Arrange the equations with like terms in columns
- Analyze the coefficients of x or y
- Add the equations and solve for the remaining variable
- Substitute the value into either equation and solve
∵ 3 x - 8 y = 7 ⇒ (1)
∵ x + 2 y = -7 ⇒ (2)
- Multiply equation (2) by 4 to make the coefficients of y are equal in
magnitude and different in sign
∴ 4 x + 8 y = -28 ⇒ (3)
Add equations (1) and (3)
∵ 3 x - 8 y = 7 ⇒ (1)
∵ 4 x + 8 y = -28 ⇒ (3)
∴ 7 x = -21
- Divide both sides by 7
∴ x = -3
Substitute the value of x in equation (2) to find y
∵ x + 2 y = -7 ⇒ (2)
∵ x = -3
∴ -3 + 2 y = -7
- Add 3 to both sides
∴ 2 y = -4
- Divide both sides by 2
∴ y = -2
The solution of the system of equations is (-3 , -2)
Learn more:
You can learn more about the system of the linear equations in brainly.com/question/13168205
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