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zavuch27 [327]
2 years ago
5

84 pounds is how many pounds on the moon

Mathematics
2 answers:
Vladimir79 [104]2 years ago
8 0
84 pounds on Earth is 13.89 pounds on the moon.
ddd [48]2 years ago
7 0
84 pounds on earth is about 14 pounds on the moon but to be exact it is 13.89 pounds.
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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
A cone and a cylinder both have a diameter of four feet and a height of six feet. Determine if the statement is true by selectin
Anettt [7]

Answer:

yes, no, yes, no

Step-by-step explanation:

4 0
3 years ago
ANSWER QUICKLY! Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2
Dafna1 [17]

Answer:

y= -2/3x+490

slope: -2/3

y-intercept: 490

Step-by-step explanation:

Y-intercept form is y=mx+b, so you would first subtract 2x from both sides to get 3y= -2x+1,470. Then you divide both sides by 3, to get y= -2/3x+490. -2/3 is in the place of m, so it is the slope, and 490 is in the place of b, so it is the y-int.

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3 years ago
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The interior angles of a triangle have measures 90°, 48°, and xº.<br> What is the value of x?
Ahat [919]

Answer:

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Step-by-step explanation:

The interior angles of a triangle always add to 180 degrees.

90+48+x=180

x=180-90-48

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x is 42°

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2 years ago
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DedPeter [7]

Answer:

  • (2, 0)

Step-by-step explanation:

<u>Given system:</u>

  • x - 2y = 1
  • 2x - y = 2

In order to solve it graphically, graph both lines and find the point of their intersection.

Graphing easy if you plot the x- and y- intercepts and connect them with a line.

<em>See attached.</em>

Both lines have same x-intercept, which is also the solution: (2, 0)

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