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jasenka [17]
2 years ago
5

The is thinking of a number which he calls n. He finds 1/3 of the number and subtracts 5

Mathematics
1 answer:
Alona [7]2 years ago
5 0

Answer:

I just did it its 1/3n - 5

Step-by-step explanation:

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timama [110]
I think the mean of variable a is 4
4 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
PLEASE HELP ME!!!!<br><br> (if you don’t know don’t answer)
Sergio039 [100]

Answer:

Here are my answers

hope this helps

Step-by-step explanation:

1. isosceles triangle

2.   3x + 15 = 90       x = 25

     x + 25 = 90        x = 65

     x + 55 = 90        x = 35

3. The size for DAB is 84

My reasoning is I went from one angle to another by subtracting 180 from my answers. For example angle 132 is supplementary to the missing angle next to it. I subtract 180 from 132 and get 48. That already solves the 2 equivalent angles in the triangle so I have 48+48+x = 180 because a full triangle equals 180. I get x = 84 then I do the same thing I did with angle 132. Angle 84 is supplementary to the missing angle next to it. I subtract 84 from 180 and get 96 then go diagonal from angle C (which is 96) to angle A. Those are supplementary so I subtract 96 from 180 and get 84.

3 0
2 years ago
Please help me with this question
Bezzdna [24]

Answer:

1.03

Step-by-step explanation:

To find the volume of a prism, find the area of the base and multiply it by the height.

The base is an octagon. The area is found A = 2(1+\sqrt{2})a^2. Substitute a = 0.5.

A = 2(1+\sqrt{2})(0.5^2)\\A = 4.828...(0.25)\\A = 1.21

The volume is 1.21*2.5 = 3.025.

However, there are three holes drilled out half way which each have volume 0.06.

The volume is found as V = πr²h. Substitute r = 0.125 which is half the diameter of 0.25. Since they go half way, the height is h = 1.25.

V = π(0.125)²(1.25) = 0.06.

Since there are 3, they equal 3*0.06 = 0.18.

Subtract this from the volume.

1.21 - 0.18 = 1.03

4 0
3 years ago
Square RSTU is translated to form R'S'T'U', which has vertices R'(–8, 1), S'(–4, 1), T'(–4, –3), and U'(–8, –3). If point S has
Zarrin [17]

Answer:

C. (-1, -6)

Step-by-step explanation:

Hope this helps :)

7 0
2 years ago
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