What is the recursive formula for this
geometric sequence?
-3, -21, -147, -1029, ...

9514 1404 393

Answer:

Step-by-step explanation:

The expression written is interpreted according to the order of operations as ...

  sin(x) -(1/x) -1

As x approaches 0 from the left, this approaches +∞. As x approaches 0 from the right, this approaches -∞. These values are different, so the limit does not exist.

__

Maybe you intend ...

  sin(x -1)/(x -1)

This can be evaluated directly at x=0 to give sin(-1)/-1 = sin(1). The argument is interpreted to be radians, so sin(1) ≈ 0.84147098...

The limit is about 0.841 at x=0.

Answer:

-[tex]x^{2} + 3x -8 = 0[/tex]

Step-by-step explanation:

Answer:

b=14 cm

Step-by-step explanation:

Use pythagorean equation

A^2+b^2=c^2

1^2+b^2=14^2

1+b^2=196

b^2=195

b=13.964

Answer:

356 streams

Step-by-step explanation:

From the graph, you will see that the line cross the x-axis at x = 8.8

Substitute into the expression y = 40x + 4

y = 40(8.8)+4

y = 352 + 4

y = 356

Hence the distributor charges will be paid for after 356 streams

Answer:

..............................what this

9514 1404 393

Answer:

  d/15 = y/20

Step-by-step explanation:

At a given rate, distance is proportional to time. The distance d that Jack can drive in 15 minutes will be ...

 d/15 = y/20 . . . . the equation

  d = (3/4)y . . . . . the solution (multiply the above equation by 15, reduce)

Answer:

14 and 21 and 28

Step-by-step explanation:

2:3:4.

The shortest side is 14

14/2 = 7

Multiply each side by 7

2*7:3*7:4*7

14 : 21 : 28

Answer:

Step-by-step explanation:

Answer:

3 : 15 : 2

Step-by-step explanation:

Let cranberry juice = x,

3/4 + 1/10 + x = 1

x = 3/20

Ratio = cranberry : apple : orange

= 3/20 : 3/4 : 1/10

= 3 : 15 : 2 (Times everything with 20)

Answer:

Step-by-step explanation:

If the 2s are exponents, you need to indicate this with "^":  

x^2 = 144^2 means x² = 144²

x = ±√144² = ±144

Answer:

Step-by-step explanation:

f the 2s are exponents, you need to indicate this with "^":  

x^2 = 144^2 means x² = 144²

x = ±√144² = ±144

First integrate the indefinite integral,

[tex]\int(1-x^2)^{3/2}dx[/tex]

Let [tex]x=\sin(u)[/tex] which will make [tex]dx=\cos(u)du[/tex].

Then

[tex](1-x^2)^{3/2}=(1-\sin^2(u))^{3/2}=\cos^3(u)[/tex] which makes [tex]u=\arcsin(x)[/tex] and our integral is reshaped,

[tex]\int\cos^4(u)du[/tex]

Use reduction formula,

[tex]\int\cos^m(u)du=\frac{1}{m}\sin(u)\cos^{m-1}(u)+\frac{m-1}{m}\int\cos^{m-2}(u)du[/tex]

to get,

[tex]\int\cos^4(u)du=\frac{1}{4}\sin(u)\cos^3(u)+\frac{3}{4}\int\cos^2(u)du[/tex]

Notice that,

[tex]\cos^2(u)=\frac{1}{2}(\cos(2u)+1)[/tex]

Then integrate the obtained sum,

[tex]\frac{1}{4}\sin(u)\cos^3(u)+\frac{3}{8}\int\cos(2u)du+\frac{3}{8}\int1du[/tex]

Now introduce [tex]s=2u\implies ds=2du[/tex] and substitute and integrate to get,

[tex]\frac{3\sin(s)}{16}+\frac{1}{4}\sin(u)\cos^3(u)+\frac{3}{8}\int1du[/tex]

[tex]\frac{3\sin(s)}{16}+\frac{3u}{4}+\frac{1}{4}\sin(u)\cos^3(u)+C[/tex]

Substitute 2u back for s,

[tex]\frac{3u}{8}+\frac{1}{4}\sin(u)\cos^3(u)+\frac{3}{8}\sin(u)\cos(u)+C[/tex]

Substitute [tex]\sin^{-1}[/tex] for u and simplify with [tex]\cos(\arcsin(x))=\sqrt{1-x^2}[/tex] to get the result,

[tex]\boxed{\frac{1}{8}(x\sqrt{1-x^2}(5-2x^2)+3\arcsin(x))+C}[/tex]

Let [tex]F(x)=\frac{1}{8}(x\sqrt{1-x^2}(5-2x^2)+3\arcsin(x))+C[/tex]

Apply definite integral evaluation from b to a, [tex]F(x)\Big|_b^a[/tex],

[tex]F(x)\Big|_b^a=F(a)-F(b)=\boxed{\frac{1}{8}(a\sqrt{1-a^2}(5-2a^2)+3\arcsin(a))-\frac{1}{8}(b\sqrt{1-b^2}(5-2b^2)+3\arcsin(b))}[/tex]

Hope this helps :)

Answer:[tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{3arcsin(a) + 2a(1 - a^2)^\Big{\frac{3}{2}} + 3a\sqrt{1 - a^2}}{8} - \frac{3arcsin(b) + 2b(1 - b^2)^\Big{\frac{3}{2}} + 3b\sqrt{1 - b^2}}{8}[/tex]General Formulas and Concepts:

Pre-Calculus

Calculus

Differentiation

Integration

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                    [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

U-Substitution

Reduction Formula:                                                                                               [tex]\displaystyle \int {cos^n(x)} \, dx = \frac{n - 1}{n}\int {cos^{n - 2}(x)} \, dx + \frac{cos^{n - 1}(x)sin(x)}{n}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx[/tex]

Step 2: Integrate Pt. 1

Identify variables for u-substitution (trigonometric substitution).

Step 3: Integrate Pt. 2

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Answer:

16 and 3

Step-by-step explanation:

Let x and y represent the positive integers. We know that

[tex]x + y = 19[/tex]

[tex]xy = 48[/tex]

Isolate the top equation for the x variable.

[tex]x = 19 - y[/tex]

Substitute into the second equation.

[tex](19 - y)y = 48[/tex]

[tex]19y - {y}^{2} = 48[/tex]

[tex] - {y}^{2} + 19y = 48[/tex]

[tex] - {y}^{2} + 19y - 48[/tex]

[tex](y - 16)(y - 3)[/tex]

So our values are

16 and 3.

Answer: Hello your question is poorly written attached below is the complete question

answer:

[tex]y = \left[\begin{array}{ccc}-4\\-11\\5\end{array}\right][/tex]

[tex]x = \left[\begin{array}{ccc}16\\12\\-40\end{array}\right][/tex]

Step-by-step explanation:

[tex]y = \left[\begin{array}{ccc}-4\\-11\\5\end{array}\right][/tex]

[tex]x = \left[\begin{array}{ccc}16\\12\\-40\end{array}\right][/tex]

attached below is the detailed solution using LU factorization

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Answer:

Since [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the normal distribution can be used to approximate the binomial distribution.

The mean is 13.3 and the standard deviation is 3.28.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex], if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex].

The probability than an adult never had the flu is 19%.

This means that [tex]p = 0.19[/tex]

You randomly select 70 adults and ask if he or she ever had the flu.

This means that [tex]n = 70[/tex]

Decide whether you can use the normal distribution to approximate the binomial distribution

[tex]np = 70*0.19 = 13.3 \geq 10[/tex]

[tex]n(1-p) = 70*0.81 = 56.7 \geq 10[/tex]

Since [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the normal distribution can be used to approximate the binomial distribution.

Mean:

[tex]\mu = E(X) = np = 70*0.19 = 13.3[/tex]

Standard deviation:

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{70*0.19*0.81} = 3.28[/tex]

The mean is 13.3 and the standard deviation is 3.28.

Answer:

let length be x

b = x - 3

perimeter = 2( l + b)

54 = 2(x+x-3)

27 = 2x - 3

30 = 2x

x = 15

l = 15

b = 15 - 3

b = 12

Answer:

[tex]c =\frac{8}{3}[/tex]

Step-by-step explanation:

Given

[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}[/tex]

Required

Shorten

We have:

[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}[/tex]

Rationalize

[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7} * \frac{4 + \sqrt 7}{4 + \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}*\frac{4 - \sqrt 7}{4 - \sqrt 7}}[/tex]

Expand

[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{4^2 - (\sqrt 7)^2}} + \sqrt{\frac{(4 - \sqrt 7)^2}{4^2 - (\sqrt 7)^2}[/tex]

[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{16 - 7}} + \sqrt{\frac{(4 - \sqrt 7)^2}{16 - 7}[/tex]

[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{9}} + \sqrt{\frac{(4 - \sqrt 7)^2}{9}[/tex]

Take positive square roots

[tex]c =\frac{4 + \sqrt 7}{3} + \frac{4 - \sqrt 7}{3}[/tex]

Take LCM

[tex]c =\frac{4 + \sqrt 7 + 4 - \sqrt 7}{3}[/tex]

Collect like terms

[tex]c =\frac{4 + 4+ \sqrt 7 - \sqrt 7}{3}[/tex]

[tex]c =\frac{8}{3}[/tex]

Step-by-step explanation:

the answer is in picture

Answer:

0 senior tickets were sold

5 more adult tickets were sold than chil tickets

Step-by-step explanation:

You need to see the frequency of each bar

Answer by Gauthmath

(3a^4b/2b^3)^3

cube all the terms:

3^3 = 27

b^3

(a^4)^3 = a^(4*3) = a^12

2^3 = 8

(b^3)^3 = b^3*3 = b^9

27a^12b^3 / 8b^9

Divide the b terms to get the final answer:

27a^12 / 8b^6

Answer:

3:5 = 6:10

3x2 : 5x2

= 6:10

Answer:

Step-by-step explanation:

Draw 3:5 balls shaded, and draw 6:10 balls shaded. Then, divide the 10 balls into two, with three shaded balls and 5 total balls on one side.

Answer:

The answer is "[tex]\bold{\frac{22}{171}}[/tex]"

Step-by-step explanation:

There are 22 million males that have completed four years of undergraduate, according to the data below: (or more). This is predicated on a population of 171 million.

The chances we're searching about [tex]\frac{(22\ million)}{(171\ million)} = \frac{22}{171}[/tex]

however

This proportion could be further reduced because 22 and 171 have no common features (other than 1).

Answer:

35 full bags

Step-by-step explanation:

$305-$35.75=$269.25

$269.25 divided by $7.50=35.9 bags (round off to lowest for number of full                                            bags)

Answer:

0

Step-by-step explanation:

it says the answer is zero

9514 1404 393

Answer:

  3. 151°

  4. 42°

Step-by-step explanation:

3. The measure of the supplement is found by subtracting the angle from 180°.

  supplement of 29° = 180° -29° = 151°

__

4. The total of angles in a triangle is 180°, so the third one can be found by subtracting the other two from 180°.

  third angle = 180° -128° -10° = 42°

Answer:

the domain is ALL reals numbers except ZERO

- ∞ < x < 0    ∪   0 <  x < ∞

Step-by-step explanation:

Answer:

(-∞,0) ∪ (0,∞), {x|x≠0}

Step-by-step explanation:

I think this is it. Im not completely sure though

Answer:

Step-by-step explanation:

Segment EF is mid-segment of ABCD ⇒ ( 2x - 4 ) + ( x - 5 ) = 2x

x - 9 = 0

x = 9

AD = 4

EF = 9

BC = 14

The length of segments AD, EF, and BC in the trapezoid are 4, 9 and 14 respectively

A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.

We have to find the lengths of AD, EF, and BC in the trapezoid

Segment EF is mid-segment of ABCD

So ( 2x - 4 ) + ( x - 5 ) = 2x

Now let us solve for x

2x-4+x-5=2x

Combine the like terms

x-9=0

x=9

So AD =x-5

=9-5= 4

EF = 9

BC = 2x-4

=18-4

=14

Hence, the length of segments AD, EF, and BC in the trapezoid are 4, 9 and 14 respectively

To learn more on Coordinate Geometry click:

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