Question 8

What is the quotient StartFraction 15 p Superscript negative 4 Baseline q Superscript negative 6 Baseline Over negative 20 p Sup

zhannawk [14.2K]

Answer:

$- \frac{3}{4} \times \frac{p^{8} }{q^{3} }$

Step-by-step explanation:

We have to find the quotient of the following division, $\frac{15p^{-4}q^{-6} }{- 20p^{-12} q^{-3}}$ .

Now, $\frac{15p^{-4}q^{-6} }{- 20p^{-12} q^{-3}}$

= $- \frac{3}{4} p^{[- 4 - (- 12)]} q^{[-6 - (- 3)]}$ {Since all the terms in the expression are in product form, so we can treat them separately}

{Since we know the property of exponent as $\frac{a^{b} }{a^{c} } = a^{(b - c)}$ }

= $- \frac{3}{4} p^{8} q^{-3}$

= $- \frac{3}{4} \times \frac{p^{8} }{q^{3} }$ (Answer)

{Since we know, $a^{-b} = \frac{1}{a^{b} }$ }

3 0

2 years ago

Read 2 more answers

Which angles are supplementary to each other?

Rus_ich [418]

Answer:

Angle 4 and Angle 1 are supplementary to each other.

Step-by-step explanation:

A line is 180°. Because angle 4 and angle 1 and right next to each other and they share a straight line, both of their angles should add up to 180°, making these two angles supplementary.

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6 0

2 years ago

F(x) = x2 − x − ln(x) (a) find the interval on which f is increasing. (enter your answer using interval notation.) find the inte

Mekhanik [1.2K]

Answer:

(a) Decreasing on (0, 1) and increasing on (1, ∞)

(b) Local minimum at (1, 0)

(c) No inflection point; concave up on (0, ∞)

Step-by-step explanation:

ƒ(x) = x² - x – lnx

(a) Intervals in which ƒ(x) is increasing and decreasing.

Step 1. Find the zeros of the first derivative of the function

ƒ'(x) = 2x – 1 - 1/x = 0

2x² - x -1 = 0

( x - 1) (2x + 1) = 0

x = 1 or x = -½

We reject the negative root, because the argument of lnx cannot be negative.

There is one zero at (1, 0). This is your critical point.

Step 2. Apply the first derivative test.

Test all intervals to the left and to the right of the critical value to determine if the derivative is positive or negative.

(1) x = ½

ƒ'(½) = 2(½) - 1 - 1/(½) = 1 - 1 - 2 = -1

ƒ'(x) < 0 so the function is decreasing on (0, 1).

(2) x = 2

ƒ'(0) = 2(2) -1 – 1/2 = 4 - 1 – ½ = ⁵/₂

ƒ'(x) > 0 so the function is increasing on (1, ∞).

(b) Local extremum

ƒ(x) is decreasing when x < 1 and increasing when x >1.

Thus, (1, 0) is a local minimum, and ƒ(x) = 0 when x = 1.

(c) Inflection point

(1) Set the second derivative equal to zero

ƒ''(x) = 2 + 2/x² = 0

x² + 2 = 0

x² = -2

There is no inflection point.

(2). Concavity

Apply the second derivative test on either side of the extremum.

$\begin{array}{lccc}\text{Test} & x < 1 & x = 1 & x > 1\\\text{Sign of f''} & + & 0 & +\\\text{Concavity} & \text{up} & &\text{up}\\\end{array}$

The function is concave up on (0, ∞).

6 0

3 years ago

When the Defense Department ordered 132 new airplanes, the cost per plane was estimated to be $580 million. A cut in the order t

aliina [53]

Answer:

C. The loss of economies of scale

By definition represent "the cost advantages that enterprises obtain due to their scale of operation, with cost per unit of output decreasing with increasing scale" and thats the corrct option since if we increase the order we have a lower price.

Step-by-step explanation:

Assuming the following options we analyze one by one to select the correct one

A. A move to minimum efficient scale

By definition the minimum efficient scale (MES) or efficient scale of production is "the lowest point where the plant can produce such that its long run average costs are minimized" but thats not the case since the department order new planes and the costs are not minimized .

B. The law of diminishing returns

The law of diminishing marginal returns says that "at some point, adding an additional factor of production results in smaller increases in output" but that's not the case since we don't have smaller increases in output.

C. The loss of economies of scale

By definition represent "the cost advantages that enterprises obtain due to their scale of operation, with cost per unit of output decreasing with increasing scale" and thats the corrct option since if we increase the order we have a lower price.

D. An increase in fixed cost

That's False since on this case we don't have a fixed cost, the cost on this case depend on the size of the order.

4 0

2 years ago

Graph the ordered pairs. 25 y 20 15 Total Time (min) 10 5 X 0 1 2 2 3 4 5 Number of Pages 2. Describe the pattern in the graph.

Genrish500 [490]

Answer:

When the Supreme Court rules on a constitutional issue, that judgment is virtually final; its decisions can be altered only by the rarely used procedure of constitutional amendment or by a new ruling of the Court. However, when the Court interprets a statute, new legislative action can be taken.

6 0

2 years ago