lim x ->0 ln(1+5x)/2x

Answer:

y = 1/3x + 14/3

Step-by-step explanation:

y = mx + b

we know the slope, so the equation would be --> y = 1/3x + b

Now we plug in the coordinates of the given point (4, 6) the line goes through, and solve for b:

y = 1/3x + b

6 = 1/3(4) + b

6 = 4/3 + b

-4/3   -4/3

----------------

14/3 = b

Answer:

(6, 6)

Step-by-step explanation:

T (-1, 2) = move down 1, right 2

(1, 4) turns into (3, 3)

Dilation scale factor = 2

Multiply x and y value by 2

(3, 3) = (6, 6)

Answer:

[tex]radius \: of \: first \: circle \: = \frac{3}{2} = 1.5cm \\ radius \: of \: \: second = \frac{4}{2} = 2cm \\ radius \: of \: third = \frac{6}{2} = 3cm \\ then \: ab \: length \\ = radius \: of \: first + diameter \: of \: second \: +r adius \: of \: third \\ = 1.5 + 4 + 3 \\ = 1.5 + 7 \\ = 8.5 cm\\ thank \: you[/tex]

Answer:

[tex]f(1)=70[/tex]

[tex]f(n)=f(n-1)+6[/tex]

Step-by-step explanation:

One is given the following function:

[tex]f(n)=64+6n[/tex]

One is asked to evaluate the function for [tex](f(1))[/tex], substitute [tex](1)[/tex] in place of [tex](n)[/tex], and simplify to evaluate:

[tex]f(1)=64+6(1)[/tex]

[tex]f(1)=64+6[/tex]

[tex]f(1)=70[/tex]

A recursive formula is another method used to represent the formula of a sequence such that each term is expressed as a function of the last term in the sequence. In this case, one is asked to find the recursive formula of an arithmetic sequence: that is, a sequence of numbers where the difference between any two consecutive terms is constant. The following general formula is used to represent the recursive formula of an arithmetic sequence:

[tex]a_n=a_(_n_-_1_)+d[/tex]

Where ([tex]a_n[/tex]) is the evaluator term ([tex]a_(_n_-_1_)[/tex]) represents the term before the evaluator term, and (d) represents the common difference (the result attained from subtracting two consecutive terms). In this case (and in the case for most arithmetic sequences), the common difference can be found in the standard formula of the function. It is the coefficient of the variable (n) or the input variable. Substitute this into the recursive formula, then rewrite the recursive formula such that it suits the needs of the given problem,

[tex]a_n=a_(_n_-_1_)+d[/tex]

[tex]a_n=a_(_n_-_1_)+6[/tex]

[tex]f(n)=f(n-1)+6[/tex]

Answer:

1/4

Step-by-step explanation:

1/6 + 1/12 = 1/4

Answer:

3/3

Step-by-step explanation:

1/6= to 2/12 and 1 /12 = 2 /6

Answer:

[tex]\displaystyle f(x) = -\frac{11}{4}(x + 1) + 2[/tex]

Step-by-step explanation:

We want to find the linear function given that:

[tex]f^{-1}(2) = -1\text{ and } f^{-1} (-9) = 3[/tex]

Recall that by the definition of inverse functions:

[tex]\displaystyle \text{If } f(a) = b\text{ then } f^{-1}(b) = a[/tex]

In other words, f(-1) = 2 and f(3) = -9.

This yields two points: (-1, 2) and (3, -9).

Find the slope of the linear function:

[tex]\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(-9) - (2)}{(3) -(-1)} = -\frac{11}{4}[/tex]

From point-slope form:

[tex]\displaystyle y - (2) = -\frac{11}{4}( x- (-1))[/tex]

Hence:

[tex]\displaystyle f(x) = -\frac{11}{4}(x + 1) + 2[/tex]

We can simplify if desired:

[tex]\displaystyle f(x) = -\frac{11}{4}x -\frac{3}{4}[/tex]

The range of a function is the set of possible values that can be obtained from the dependent variable. The range of the function is: [tex]R: (500, \infty)[/tex]

Given that:

[tex]Phone = \$500[/tex]

[tex]Monthly\ Plan = \$60[/tex]

Let the number of months be t. So, the function C(t) is calculated as follows:

[tex]C(t) = Phone + Monthly\ Plan \times t[/tex]

[tex]C(t) = 500 + 60 \times t[/tex]

[tex]C(t) = 500 + 60t[/tex]

The range is calculated as follows:

The smallest possible value of t is 0 i.e. when no monthly subscription is done.

So, we have:

[tex]C(0) = 500 + 60\times 0= 500 + 0 = 500[/tex]

And the highest is [tex]\infty[/tex] i.e. for a large value of t

So, we have:

[tex]C(\infty) = 500 + 60\times \infty= 500 + \infty = \infty[/tex]

Hence, the range of the function is:

[tex]R: (500, \infty)[/tex]

Read more about range of functions at:

https://brainly.com/question/13824428

Answer:

12500 - 10190 = 2310 ft.

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

6*7-3^2*9+4^3

Exponents first

6*7-9*9+64

Multiply and divide from left to right

42 -9*9+64

42 - 81 +64

Add and subtract from left to right

-39 +64

25

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{\mathsf{6\times7-3^2\times9+4^3 }}\\\huge\boxed{\mathsf{= 42 - (9)(9) + 4^3}}\\\huge\boxed{\mathsf{= 42 - 81 + 64}}\\\huge\boxed{\mathsf{= -39 + 64}}\\\huge\boxed{\mathsf{= 25}}}}\\\huge\boxed{\mathsf{Therefore, your\ answer\ is: 25}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

100,000>56,313 56, 56,313<100,000

Answer:

The statement in the question is wrong. The series actually diverges.

Step-by-step explanation:

We compute

[tex]\lim_{n\to\infty}\frac{n^2}{(n+1)^2}=\lim_{n\to\infty}\left(\frac{n^2}{n^2+2n+1}\cdot\frac{1/n^2}{1/n^2}\right)=\lim_{n\to\infty}\frac1{1+2/n+1/n^2}=\frac1{1+0+0}=1\ne0[/tex]

Therefore, by the series divergence test, the series [tex]\sum_{n=1}^\infty\frac{n^2}{(n+1)^2}[/tex] diverges.

EDIT: To VectorFundament120, if [tex](x_n)_{n\in\mathbb N}[/tex] is a sequence, both [tex]\lim x_n[/tex] and [tex]\lim_{n\to\infty}x_n[/tex] are common notation for its limit. The former is not wrong but I have switched to the latter if that helps.

Answer:

[tex]\displaystyle \sum^{\infty}_{n = 1} \frac{n^2}{(n + 1)^2} = \text{div}[/tex]

General Formulas and Concepts:

Calculus

Limits

Series Convergence Tests

Step-by-step explanation:

*Note:

Always apply the nth Term Test as the first test to use for convergence.

Rules:

Step 1: Define

Identify

[tex]\displaystyle \sum^{\infty}_{n = 1} \frac{n^2}{(n + 1)^2}[/tex]

Step 2: Find Convergence

∴ by the nth Term Test, the series diverges.

Topic: AP Calculus BC (Calculus I + II)

Unit: Convergence Tests

Step-by-step explanation: Answer is

(i). 19% or 14/75

(ii) 28% or 7/25

We are asked to find multiple probabilities.

We got to find the number of combinations posible,

Use the combinations formula

[tex]c {}^{n} _r{?} = \frac{(r + n - 1) \: fractorial).}{r \: fractorial(n - 1)fractorial} [/tex]

For math this is read as,

if n choose r,( r+n-1)!/r!(n-1)!.

Where r is how many things we need from and n is the number of things we choose from.

We need 2 things and we have 24 objects to pick from.

So r=2 N equal=24

Which equal

25!/2!(23)!

Which equals

[tex]300[/tex]

So there are 300 possible combinations.

Using

For the 1st question, Since we are given two independent events, we can just multiply the number of good articles by major.

[tex]14 \times 4 = 56[/tex]

So this means the probability is

[tex] \frac{56}{300} = \frac{14}{75} [/tex]

Which is 19%

For the 2nd question, the can multiply the number of minor articles by major articles.

[tex]6 \times 4 = 24[/tex]

So the probability

is

[tex] \frac{24}{300} = \frac{8}{100} = \frac{2}{25} [/tex]

Which is equal to 8%

Answer:

(a) A

(b) x = 7

Step-by-step explanation:

(a) Given : -3 + 2x = 4

Step 1: Isolate the x to one side. To do so, we get rid of -3 by adding 3 to both sides. (-3 + 3 =0)

2x = 4 + 3

(b) -3 + x = 4

     x = 4 + 3

        = 7

Answer:

b = -3

Step-by-step explanation:

-4b + 3(6 - 7b) = 93

-4b + 18 - 21b = 93

-4b - 21b = 93 - 18

-25b = 75

[tex]\sf{b = \frac{75}{ - 25} }[/tex]

b = -3

b = - 3

Step-by-step explanation:

-4b + 3(6-7b) = 93

-4b + 18 - 21b = 93

-25b + 18 = 93

-25b = 93 - 18

-25b = 75

b = 75 : - 25

b = - 3

At centroid medians bisect each other in the ratio 2:1

[tex]\\ \sf\longmapsto OC=2(OD)[/tex]

[tex]\\ \sf\longmapsto 2(3x-2)=5x[/tex]

[tex]\\ \sf\longmapsto 6x-4=5x[/tex]

[tex]\\ \sf\longmapsto 6x-5x=4[/tex]

[tex]\\ \sf\longmapsto x=4[/tex]

The value of x is 4, when we are given O is the centroid of the triangle ABC, OD = 3x - 2, and OC = 5x.

The center of the thing is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians connect. The junction of all three medians is another definition for it. The median is a line that connects the middle of a side to the triangle's opposite vertex. The median is divided by the centroid of the triangle in a ratio of 2:1.

In the question, we are given that O is the centroid of triangle ABC, and are asked to find the value of x, for which OD = 3x - 2, and OC = 5x.

We know that the median is divided by the centroid of the triangle in a ratio of 2:1.

Thus, the median CD is divided by the ratio of 2:1 as,

2/1 = OC/OD,

or, 2/1 = (5x)/(3x - 2),

or, 2(3x - 2) = 1(5x) {Cross-multiplying},

or, 6x - 4 = 5x,

or, 6x - 5x = 4,

or, x = 4.

Thus, the value of x is 4, when we are given O is the centroid of the triangle ABC, OD = 3x - 2, and OC = 5x.

Learn more about the centroid of a triangle at

https://brainly.com/question/8059821

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Answer:

» ◻ Add and divide to isolate x²

[tex]2 {x}^{2} - 7 = 9 \\ 2 {x}^{2} = 9 + 7 \\ 2 {x}^{2} = 16 \\ {x}^{2} = \frac{16}{2} \\ \\ {x}^{2} = 8[/tex]

» ◻ use the square root property of equality

[tex] {x}^{2} = 8 \\ x = \sqrt{8} [/tex]

Answer:

length*breadth*height

Answer:

Solution=96°+x+35°

=x+96°+35°

=x=96°-35°

=x=61°

Answer: depends how much you type

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Step-by-step explanation:

As x increases. f(x) increases so their is a positive linear association.

Answer:

(x-27)(x+4) = 0

Step-by-step explanation:

I think you have a typo, and meant

x^2 -23x-108

what are two factors of 108 that differ by 23?

x^2 -24x-108 does not factor with rational coefficients.

Answer:

Step-by-step explanation:

2y = 3-2x

y = -x + 3/2

Slope of line = coefficient of x = -1

Answer:

hey

here is the attachment of your question

Answer:

[tex]thank \: you[/tex]

Step-by-step explanation:

First convert the amount of dough into an improper fraction:

[tex]3\frac{3}{4}\:\text{lbs} = \dfrac{15}{4}\:\text{lbs}[/tex]

Each roll is 1/8 lb so divide the amount of dough by this amount:

[tex]\dfrac{\left(\dfrac{15}{4}\:\text{lbs}\right)}{\left(\frac{1}{8}\:\text{lb/roll}\right)} = \left(\dfrac{15}{4}\:\text{lbs}\right)\cdot \left(8\:\dfrac{\text{roll}}{\text{lb}}\right) = 30\:\text{rolls}[/tex]

Answer:

{x : x Σ N, x<15}

Step-by-step explanation:

Set of all natural number less than 14 = {x : x Σ N, x<15}