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lbvjy [14]
2 years ago
11

Jordan volunteered for the same amount of time each day for 7 days. If he volunteered for 329 minutes altogether, how many minut

es did he volunteer for each day?
Mathematics
1 answer:
AVprozaik [17]2 years ago
3 0

Answer:

47

Step-by-step explanation:

Just divide 329 by 7

That gives you 47

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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
Jack is mixing red paint with blue paint to make purple paint. he adds 2/5 of a fluid ounce of red to 11/15 of a fluid ounce of
Sedaia [141]

Answer:

Step-by-step explanation:

Change 2/5 to a decimal

2/5 = 0.4

Change 1 2/15 of a fluid ounce to a decimal.

1.133333

Set up your proportion.

0.4 / 1.133333 = x / 5               Cross multiply

0.4*5 = 1.133333*x

2 = 1.133333 x                         Divide by 1.1333333

2/1.33333 = x

x = 1.5 ounces.

He needs 1.5 ounces of red to make 5 ounces of purple.

8 0
2 years ago
Find the volume of this figure:<br> cm<br> 7<br> 3 cm<br> Cin<br> 3
Vladimir79 [104]

Answer:

4 i guess i dont rlly know

6 0
2 years ago
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Johan sold 9 of his video games online. The next day, he sold 27 Video games. He collected a total of $900 if Johann charged the
Setler79 [48]

Answer:

$25

Step-by-step explanation:

First you would add 27 and 9 to find the total number of games he sold, next you would divide 900 by 36 to get 25, then you would do 25 times 36 to check your answer.

6 0
3 years ago
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Estimate two and three fiths minus one and three eighths
frosja888 [35]
2.6  - 1.3 <span>≈ 1.3 .
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