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a_sh-v [17]
2 years ago
13

Here is a list of numbers.

Mathematics
1 answer:
nirvana33 [79]2 years ago
7 0

Answer:

A=20 B=23 C=17,19,23

Step-by-step explanation:

A=20

B=23

C=17,19,23

You might be interested in
Find the average value of the function on the given interval.<br> f(x)=2 ln x; [1,e]
JulijaS [17]

Answer:

f_{avg}=\frac{1}{e-1}

Step-by-step explanation:

We are given that a function

f(x)=2lnx

We have to find the average value of function on the given interval [1,e]

Average value of function on interval [a,b] is given by

\frac{1}{b-a}\int_{a}^{b}f(x)dx

Using the formula

f_{avg}=\frac{1}{e-1}\int_{1}^{e}lnx dx

By Parts integration formula

\int(uv)dx=u\int vdx-\int(\frac{du}{dx}\int vdx)dx

u=ln x and v=dx

Apply by parts integration

f_{avg}=\frac{1}{e-1}([xlnx]^{e}_{1}-\int_{1}^{e}(\frac{1}{x}\times xdx))

f_{avg}=\frac{1}{e-1}(elne-ln1-[x]^{e}_{1})

f_{avg}=\frac{1}{e-1}(e-0-e+1)=\frac{1}{e-1}

By using property lne=1,ln 1=0

f_{avg}=\frac{1}{e-1}

8 0
2 years ago
1.    An AP has a common difference of 3.  Given that the nth term is 32, and the sum of the first n terms is 185, calculate the
netineya [11]

Answer:

The value of n is 10

Step-by-step explanation:

The formula of the nth term of the arithmetic progression is a_{n} = a + (n - 1)d

  • a is the first term
  • d is the common difference between each 2 consecutive terms
  • n is the position of the term

The formula of the sum of nth terms is S_{n} = \frac{n}{2} [2a + (n - 1)d]

∵ An AP has a common difference of 3

∴ d = 3

∵ The nth term is 32

∴ a_{n} = 32

→ Substitute them in the 1st rule above

∵ 32 = a + (n - 1)3

∴ 32 = a + 3(n) - 3(1)

∴ 32 = a + 3n - 3

→ Add 3 to both sides

∴ 35 = a + 3n

→ Switch the two sides

∴ a + 3n = 35

→ Subtract 3n from both sides

∴ a = 35 - 3n ⇒ (1)

∵ The sum of the first n terms is 185

∴ S_{n} = 185

→ Substitute the value of S_{n} and d in the 2nd rule above

∵ 185 = \frac{n}{2} [ 2a + (n - 1)3]

∴ 185 = \frac{n}{2} [2a + 3(n) - 3(1)]

∴ 185 = \frac{n}{2} [2a + 3n - 3]

→ Multiply both sides by 2

∴ 370 = n(2a + 3n - 3)

∴ 370 = 2an + 3n² - 3n

→ Substitute a by equation (1)

∴ 370 = 2n(35 - 3n) + 3n² - 3n

∴ 370 = 70n - 6n²+ 3n² - 3n

→ Add the like terms in the right side

∵ 370 = -3n² + 67n

→ Add 3n² to both sides

∴ 3n² + 370 = 67n

→ Subtract 67 from both sides

∴ 3n² - 67n + 370 = 0

→ Use your calculator to find n

∴ n = 10 and n = 37/3

∵ n must be a positive integer ⇒ 37/3 neglecting

∴ n = 10

∴ The value of n is 10

4 0
2 years ago
Determine the Y intercept PLEASE HELP!!<br> X Y<br> -3 -3<br> 0 -1<br> 3 1
BartSMP [9]
You are adding two each time
4 0
3 years ago
12 pts? Harris and Annabelle are 200 feet apart, and they are standing on opposite sides of a tree. The angles of elevation from
Sergio [31]
If we are to connect the root of the tree to a person to the top of the tree, we form two right triangles. If we let x and and 200 - x be the distance of Harris and Annabelle from the tree, respectively and h be the height, we form the trigonometric functions,
                                       tan 30° = h/x
                                       tan 35° = h/(200 - x)
The values of h and x in the equations are 63.28 ft and 109.62 ft, respectively. Thus, the answer to this item is approximately 63.28 ft. 
5 0
3 years ago
Is 2/3 greater than 9/10??????? ANSWER NOW
jarptica [38.1K]
No it is not , it is less than 9/10.
7 0
3 years ago
Read 2 more answers
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