Mathematics College

Find the common ratio of the sequence
-125,-25,-5,-1.....

1/5

5

-100

100

Answers

Answer 1

common ratio = -25/-125 = 1/5 answer

Answer 2

Answer:

Step-by-step explanation:

common ratio of a Geometric series can be found by dividing the second term by first term of the series .

we are given that first term a1= -125 and second term a2 =-25

so the common ratio must be

[tex]r=\frac{a2}{a1}[/tex]

[tex]r=\frac{-25}{-125}[/tex]

[tex]r= \frac{1}{5}[/tex]

Hence the common ratio is 1/5.

Related Questions

Kelly is having a party. She wants to make punch. The recipe for punch uses 3 pints of pineapple juice, 5 cups or orange juice, 1/4 gallon of lemonade, and 1 quart of apricot nectar. Kelly says her recipe will make 20 cups of punch. Is Kelly correct? Explain your answer. How does one arrive at the answer? Are all the ingredients added? Is anything multiplied?

Answers

First convert all the ingredients into cups.
3 pints = 6 cups
5 cups = 5 cups
1/4 gallon = 4 cups
1 quart = 4 cups

Add all the ingredients.
6 + 5 + 4 + 4 = 19 cups

Therefore, Kelly does not make 20 cups of punch because her recipe is enough for only 19 cups of punch. All the ingredients are added and noting is multiplied.

Solve for C. See photo

Answers

[tex]F = \frac{9}{5} C+32 \\ F - 32 = \frac{9}{5} C \\ \frac{5}{9} (F -32)=C[/tex]

Please try this, I forget absolutely everything about rhombuses. Thanks for all the help, shouldn't be too hard

Answers

so, check the picture below. It has four sections.

the volume of a pyramid is, 1/3 ( base area)(height).

well, we know the base is a rhombus, and rhombuses diagonals meet at right-angles, therefore the center O has 4 right-angles where they meet.

since we know the angle at A, 50°, and since rhombuses are quadrilaterals with all equal sides, we know all the sides are 6 long, and the angle at C is 50° as well, and the remaining angles are 130°, as shown there.

now, if we tease out one of those triangles from the rhombus, as shown on the 1st section in the picture, we can say use the angle of 65° to get "x" and "y" lengths

[tex]\bf cos(65^o)=\cfrac{x}{6}\implies 6cos(65^o)=x \\\\\\ sin(65^o)=\cfrac{y}{6}\implies 6sin(65^o)=y[/tex]

now, we'll use those to get the area of the rhombic base.

and then onto the second section

is a right-triangle with a perpendicular line through it, which creates 3 similar triangles, by using the "geometric mean" of "w" there.

anyhow, we used the medium-sized and large-sized triangles there, to draw proportions and get what the "w" distance is, and you can see there what "w" is.

and onto the 3rd section

now that we know how long "w" is, we can use the triangle containing the 40° angle, in order to get the pyramid's height of "h", by using the tangent function, as you see there.

and we also use the same triangle, to get the "z" distance, which is namely the slant-height of the pyramid, however, is also the "altitude" of the triangular faces.

and onto the 4 and last section in the picture

that's a triangular face by herself, it has a base of 6, and an altitude of "z".

now, all that said, let's plug those values to get the volume, and then the surface area, keeping in mind the surface area is just the area of the rhombus plus the area of all four triangles.

[tex]\bf V=\cfrac{1}{3}\left[ \stackrel{\textit{area of the rhombic base}}{4\left( \frac{1}{2}xy \right)} \right](h) \\\\\\ SA=\left[ \stackrel{\textit{area of the rhombic base}}{4\left( \frac{1}{2}xy \right)} \right]~~+~~\left[ \stackrel{\textit{area of the four triangles}}{4\left[ \frac{1}{2}(6)(z) \right]} \right][/tex]

x ≈ 2.54 y ≈ 5.44 w ≈ 2.298 h ≈ 1.93 z = 3

V ≈ 17.7265 SA ≈ 63.58

For which k will the graph of f(x)=x^2−kx+k^2 cross the x-axis twice?

Answers

for the graph to cross the x axis twice, b²-4ac needs to be larger than 0
b=-k, a=1, c=k²
b²-4ac=k²-4k²=-3k²
-3k² will never be larger than 0.

Treys online music club charges a monthly rate of $20 plus $0.80 per song download. Debs online music club charges a monthly rate of $21 plus $0.60 per song download. For what number of songs will the monthly charge be the same for both clubs? How much will it cost?

Answers

For this case, the first thing we must do is define variables.
We have then:
x: number of songs.
y: total charge
For Treys online music club:
[tex]y = 0.80x + 20 [/tex]
For Debs online music club:
[tex]y = 0.60x + 21 [/tex]
Equaling both equations we have:
[tex]0.80x + 20 = 0.60x + 21 [/tex]
Clearing x we have:
[tex]0.80x - 0.60x = 21 - 20 0.20x = 1 x = 1 / 0.20 x = 5 songs[/tex]
Substituting the value of x for any of the equations we have:
[tex]y = 0.60 (5) + 21 y = 3 + 21 y = 24 $[/tex]
Answer:
The monthly charge will be the same for 5 songs in both clubs.
the cost will be $ 24

Answer:

For 5 songs the monthly charge be the same for both clubs.

It will cost $ 24.

Step-by-step explanation:

Let, for x songs, the monthly charges are same for both clubs,

Given,

For Treys online music club,

Monthly rate = $ 20,

Additional Charges for a song = $ 0.80,

⇒ Additional Charges for x song = $ 0.80x,

Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song

= 20 + 0.80x

Now, for Debs online music club,

Monthly rate = $ 21,

Additional Charges for a song = $ 0.60,

⇒ Additional Charges for x song = $ 0.60x,

Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song

= 21 + 0.60x

Hence, we can write,

[tex]20 + 0.80x = 21 + 0.60x[/tex]

[tex]0.80x - 0.60x = 21 - 20[/tex]

[tex]0.20x = 1[/tex]

[tex]\implies x = \frac{1}{0.20}=5[/tex]

Hence, for 5 songs the monthly charge be the same for both clubs.

Also, the cost for 5 songs = 20 + 0.80 × 5 = 20 + 4 = $ 24

A sphere with a radius of 3 cm has the same volume as a cone with a radius of 6 cm. What is the height of the cone?
A) 2 cm
B) 3 cm
C) 4 cm
D) 5 cm

Answers

Try this option:

[tex]if \ the \ volume \ of \ the \ sphere \ is \ the \ same \ one \ as \ a \ cone, \ then \ V_s=V_c; \ <=> \ \frac{4 \pi}{3}*3^3=\frac{1}{3} \pi*6^2*h_c; \ => \ h_c=3(cm)[/tex]

answer: B

B) 3 cm

Vsphere = [tex]\frac{4}{3}\pi r^{3} = \frac{4}{3}\pi(3)^{3} = 36\pi[/tex]

Vcone =

πr2h

36π =

π(6)2h

36π = 12πh

h = 3

Thus, the height is 3 cm.

Alternatively, the two equations could be set equal to each other and solved for the unknown height of the cone.

How many triangles are with two sides each 6 inches long and one angle measure of 90°.

Answers

A Right triangle is a type of triangle is the only type of triangle that should contain a right angle. If there are 2 equal sides it must be an isosceles triangle.
So the triangle is a Right Isosceles triangle

The description relates to an isosceles right triangle.

An isosceles right triangle can be described as the triangle that has two sides that are both equal while it also has an angle that will be 90° which is the right angle.

In this case, the two equal sides are given as 6 inches while it also has an angle of 90°. Therefore, it's an isosceles right triangle.

Read related link on:

https://brainly.com/question/8790412

Select two rations that are equivalent to 3: 12.

Answers

1 over 4 and 2 over 8. I just multiplied both sides of the ration to get this answer.

226Ra has a half-life of 1599 years. How much is left after 1000 years if the initial amount was 10 g?

Answers

[tex]\bf \textit{Amount for Exponential Decay using Half-Life}\\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &10\\ t=\textit{elapsed time}\to &1000\\ h=\textit{half-life}\to &1599 \end{cases} \\\\\\ A=10\left( \frac{1}{2} \right)^{\frac{1000}{1599}}[/tex]

tickets for a football match are sold at $30 for adults and $15 for children a company bought 28 tickets if x of these tickets were for adults, write in terms of x a. the number of tickets for children b. the amount spent on tickets for adults c. the amount spent on tickets ...

Answers

Final answer:

The number of tickets for children is represented by '28-x' and the amount spent on tickets for adults is '$30x'. The amount spent on tickets for children is '$15*(28-x)'.

Explanation:

We will use the concept of algebraic expressions to solve this question. If we represent the number of adult tickets as x, we know that the total number of tickets is 28. Hence, the number of children tickets can be represented as 28-x. The cost of a ticket for adults is $30, so the amount spent on adult tickets can be represented as $30x. Similarly, as the cost of a ticket for children is $15, the amount spent on children tickets can be represented as $15*(28-x).

Learn more about Algebraic Expressions here:

https://brainly.com/question/953809

#SPJ12

Final answer:

The number of ticket for children is (28 - x), the amount spent on tickets for adults would be $30x, and the total amount spent on tickets would be $30x + $15(28 - x).

Explanation:

If a company bought 28 tickets and x of these tickets were for adults, then:

a. The number of tickets for children would be 28 - x. This is because from the total number of tickets purchased, we subtract the number of adult tickets to find the number of children's tickets.

b. The amount spent on tickets for adults would be $30x. This is because each adult ticket costs $30 and there are x number of adults.

c. To find out the total amount spent by the company, we will multiply the number of adult tickets by the price of an adult ticket ($30x) and add this to the product of the number of children tickets (28 - x) and the price of a child's ticket ($15). Therefore, the total spent would be $30x + $15(28 - x).

Learn more about Algebraic Expressions here:

https://brainly.com/question/953809

#SPJ12

Look at the figure. How can you prove ∆ABD and ∆ACD are congruent?

A. ∆ABD ≅ ∆ACD by the SAS Postulate.

B. It is not possible to determine if the triangles are congruent.

C. ∆ABD ≅ ∆ACD by the SSS Postulate.

Answers

I think its A. what does everybody else think?

Answer: The correct option is (B). It is not possible to determine if the triangles are congruent.

Step-by-step explanation: We are given to select the correct option by which we can prove that ∆ABD and ∆ACD are congruent.

As shown in the figure,

In ∆ABD and ∆ACD, we have

∠ADB = ∠ADC = 90°,

AD is the common side.

So, one angle and the adjacent side of one triangle are congruent to the corresponding angle and the adjacent side of the other triangle.

That is, to prove that the two triangles are congruent, we need one of the following two conditions:

(i) BD = CD

(ii) ∠BAD = ∠CAD.

Since none of these two are given, so we cannot determine the congruence of the two triangles.

Therefore, it is not possible to determine if the triangles are congruent.

Thus, option (B) is correct.

J is 25 more than 3 help???

Answers

j would equal 28!!!!!!!!!!!!!!!!!!!

I think the answer would be 28

Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.2, 0.4, and 0.4, respectively. what is the expected number of books a customer will purchase? the standard deviation of the customer's book purchases is

Answers

Porobability distribution of X
x P(x)
0 0.2
1 0.4
2 0.4
Total .1.0
i] Expectation
Mean=Σxp
Variance=x²p-(∑xp)²
thus:
Mean=(0*0.2)+(1*0.4)+(2*0.4)
=0+0.4+0.8
=1.2

ii] Variance
Variance=[(0²*0.2)+(1²*0.4)+(2²*0.4)]-(1.2)²
=[0+0.4+1.6]-1.44
=0.56
hence:
standard deviation=sqrt(0.56)=0.74833

The expected number of books a customer will purchase is 1.2 books, and the standard deviation of their book purchases is approximately 0.78 books.

To find the expected number of books a customer will purchase,

use the formula for the expected value (also known as the mean) of a random variable:

Expected Value (μ) = Σ (x × P(x))

Where:

μ is the expected value.

x represents the possible values of the random variable (in this case, 0, 1, and 2).

P(x) is the probability associated with each value of x.

Probability of purchasing 0 books (P(0)) = 0.2

Probability of purchasing 1 book (P(1)) = 0.4

Probability of purchasing 2 books (P(2)) = 0.4

Now, calculate the expected value:

μ = (0 × 0.2) + (1 ×0.4) + (2 × 0.4)

μ = 0 + 0.4 + 0.8

μ = 1.2

To find the standard deviation (σ) of the customer's book purchases,

use the formula for the standard deviation of a discrete random variable:

Standard Deviation (σ) = √[Σ((x - μ)² × P(x))]

Where:

σ is the standard deviation.

x represents the possible values of the random variable.

μ is the expected value.

P(x) is the probability associated with each value of x.

In this case, you already calculated μ as 1.2, and you have the probabilities P(0), P(1), and P(2).

Now, calculate the standard deviation:

σ = √[((0 - 1.2)² × 0.2) + ((1 - 1.2)² × 0.4) + ((2 - 1.2)² × 0.4)]

σ = √[(1.44 ×0.2) + (0.16 × 0.4) + (0.64 × 0.4)]

σ = √[0.288 + 0.064 + 0.256]

σ = √0.608

σ ≈ 0.78

Therefore, the expected number and the standard deviation of books a customer will purchase is 1.2 books and approximately 0.78 books respectively.

Learn more about expected number here

brainly.com/question/29073636

#SPJ3

Find the points on the curve y = 2x3 + 3x2 − 12x + 9 where the tangent line is horizontal.

Answers

y = 2x^3 + 3x^2 − 12x + 9
y' = 6x^2 + 6x − 12

tangent line is horizontal y'=0
6x^2 + 6x − 12=0
x^2+x-2=0
(x+2)(x-1)=0
x=-2 or x=1
when x=-2, y=2x^3 + 3x^2 − 12x + 9 = -16 + 12 + 24 + 9 =29
when x=1, y=2x^3 + 3x^2 − 12x + 9 = 2 +3 -12 +9 =2
two points (-2,29),(1,2)

2). y = 2x^3 + 3x^2 − 12x + 9

slope of horizontal-tangent-line, y' = 6x^2+6x-12 = 0
SO,
6(x+2)(x-1) = 0,
x=1, and x=-2,
SO, for, x= 1, y= 2+3-12+9 = 2,
Hence,
the 1st. point is : Answer (1, 2)

and, for, x=-2,
y = 2(-2)^3 +3(-2)^2 -12(-2) +9 = -16+12+24+9 = 29
Hence,
the 2nd-point is : Answer (-2, 29)

the points on the curve [tex]y = 2x^3 + 3x^2 - 12x + 9 are (-2,29) \; and \; (1,2)[/tex]where the tangent line is horizontal.

Given :

The equation of the curve is [tex]y=2x^3\:+\:3x^2\:-\:12x\:+\:9[/tex]

Given tangent line is horizontal . Tangent line is horizontal when slope =0

Slope is nothing but the derivative.

So we find out x values where derivative =0

Lets take derivative for the given curve y

[tex]y=2x^3+3x^2-12x+9\\y'=2(3x^2)+3(2x)-12\\y'=6x^2+6x-12[/tex]

Now we set the derivative =0 and solve for

[tex]6x^2+6x-12=0\\Divide\; whole \; equation \; by \; 6\\x^2+x-2=0\\(x+2)(x-1)=0\\x+2=0, x=-2\\\\x-1=0, x=1[/tex]

So , the slope =0 when x=1 and x=-2

Now we find out the points . Use the original function

[tex]y=2x^3\:+\:3x^2\:-\:12x\:+\:9\\x=-2\\2\left(-2\right)^3+3\left(-2\right)^2-12\left(-2\right)+9=29\\(-2,29)\\\\x=1\\2\left(1\right)^3+3\left(1\right)^2-12\left(1\right)+9=2\\(1,2)[/tex]

the points on the curve [tex]y = 2x^3 + 3x^2 - 12x + 9 are (-2,29) \; and \; (1,2)[/tex]where the tangent line is horizontal.

Learn more : brainly.com/question/22392334

Milli plans to rent a room for her birthday party for $40. The catering charge is $12 per person but there is no charge for Milli's meal since she is the guest of honor. If Milli has $100 to spend on her birthday party, what is the maximum number of friends Milli can invite?

Answers

The answer is (5 guest) hope it helps and have a good one!

5 is the maximum number of friends that Milli can invite because she has a budget of $100. 100-40 (the required cost to rent the room) =60. 60/12 (the catering charge per person, excluding Milli) =5. Hope this helps

The cylinder shown has a volume of π in3. Find the volume of a cone with the same base and height as the cylinder.

Answers

The volume of a cylinder is 3 times larger than a cylinder. So find your answer for the cylinder and multiply it by 1/3 to get your answer. Hope this helps! Study on!

Answer:

Step-by-step explanation:

Alright, lets get started.

Suppose the height of cylinder is h and radius of base is r.

The volume of cylinder will be : [tex]\pi r^2h[/tex]

The cone is of same height means h and same base means radius will be r.

The formula of volume of cone is : [tex]\frac{1}{3} \pi r^2h[/tex]

It means the volume of cone is one third of the volume of cylinder.

The volume of cylinder is given as π.

So, the volume of cone will be : [tex]\frac{\pi }{3}[/tex] : Answer

Hope it will help :)

Find the inverse of this 3x3 matrix. [1 5 2]
[ 1 1 7]
[0 -3 7]

Answers

Lets say the 3x3 Matrix is

M = [1 5 2 ]
[1 1 7 ]
[0 -3 7 ]

We apply the Gauss-Jordan elimination method (Procedure and result shown in the image below)

Answer:

Step-by-step explanation:

⎡−25 26 −33⎤

⎥ 4 −4 5 ⎥

⎥ 3 −3 4 ⎦

PLEASE HELPS NEED THIS DONE BEFORE 3 O CLOCK

1)Jerome noticed the following house numbers on his street:

305, 318, 331, 344

The house numbers follow a pattern. Which expression can be used to determine the nthnth house number on his street?

A) 292 +13n

B) 292n

C) 292n + 13

D) 13(n + 292)

2) A polynomial expression is shown below.

(mx+8)(2x−4)

The expression is simplified to:

−6x2+28x−32-6x2+28x-32

What is the value of m?

A) 3

B) 4

C) -3

D) -4

3) What is the domain of the function shown below? (PICTURE AT BOTTOM)

A) 2
B) −8 ≤ x <3and 4 ≤ x <8

C) −8 ≤ x < 8

D) −7 ≤ x ≤ 7

Answers

1) Put n=2 in each of the offered expressions and see which one gives you 318 (the second house number).
A) 292 + 13*2 = 318 . . . . a good candidate
B) 292*2 = 584 (nope)
C) 292*2 + 13 = 597 (nope)
D) 13(2 + 292) = 3822 (nope)
The appropriate choice is ...
A) 292 +13n

2)The squared term in the product is 2mx^2. The squared term in the given expression is -6x^2. Comparing the coefficients, we have
2m = -6
m = -3
The appropriate choice for the value of m is ...
C) -3

3) The end point of one segment matches up with the beginning of the next except in the region 3 ≤ x < 4.
The appropriate choice is ...
B) -8 ≤ x < 3 and 4 ≤ x < 8

Answer:

Jerome noticed the following house numbers on his street:

Answer 292 +13n

A polynomial expression is shown below. What is the value of m?

Answer -3

What is the domain of the function shown below

Answer −8 ≤ x <3and 4 ≤ x <8

ONLY ANSWER IF YOU KNOW THE ANSWER Which shows a correct order to solve this story problem? The Johnson Chair Factory used 165.6 pounds of nails in 6 weeks. The Martinez Table Factory used 154.2 pounds of nails in 6 weeks. How many pounds of nails did the two factories use altogether in one week? A. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Add the two amounts. B. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Add the two amounts. Step 4: Multiply the sum by 2. C. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Divide the two amounts by 6. D. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Multiply the two amounts by 6.

Answers

A, you need to figure out what the companies use per week. A does that. Good luck with further math

Answer:

A if you look close at the story you will learn alot! hope this helps!

how many rootes are in f(x)=(x^2-3x+1)^2
2
5
6
9

Answers

Since there is an x^2 inside the parenthesis, there will be only 2 roots. so A

Write the explicit formula for the geometric sequence.

64, 32, 16, 8, ...
A) an = 8 · 4n-1
B) an = 8 · 2n-1
C) an = 32 · 0.5n-1
D) an = 64 · 0.5n-1

Answers

Answer:

D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]

Step-by-step explanation:

The answer is D because it is the only answer that has an=64 and a decimal, 64 is your first term and the sequence is getting smaller

AND OR

Answer:

D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]

Step-by-step explanation:

Explicit Formula: an = a1 · dn-1

a1 = 64, d = 0.5

an = 64 · 0.5n-1

The formula for the volume of a cube is V(s) = s3 where s is the side length of the cube. In which quadrant(s) is the graph of the function V(s)?

Answers

For this case what you should know is that we are in the presence of a cubic function that could take both positive and negative values.
However, when talking about the volume of a figure, a cube specifically, so that there is a physical sense, it must be fulfilled:
s> 0
Thus:
V (s)> 0
Thus, the function V (s) = s3 belongs to the first quadrant.
Answer:
the graph of the function V (s) is in the first quadrant.

Answer:

The answer is A: Quadrant 1

Step-by-step explanation:

On Edge :)

Evaluate the integral. (use c for the constant of integration.) 7 ln(x)/ x sqrt(5 + (ln(x))^2) dx

Answers

Okay, so we have

[tex] \int\limits { \dfrac{7ln(x)}{x \sqrt{5+ln(x)^2}}} \, dx [/tex].

Substitute [tex]u=ln(x)^2+5[/tex] and differentiate.
[tex]dx= \dfrac{x}{2ln(x)}du[/tex]
[tex] \dfrac{7}{2} \int\limits { \dfrac{1}{ \sqrt{u}}} \, du [/tex]

[tex]\int\limits { \dfrac{1}{ \sqrt{u}}} \, du = 2 \sqrt{u} [/tex]

[tex] \dfrac{7}{2} \int\limits { \dfrac{1}{ \sqrt{u}} } \, du = 7 \sqrt{ln(x)^2+5}+C [/tex]

The expression for the integral [tex]\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex] after the evaluation is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].

Given an integral expression:

[tex]\text{I}=\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]

This can be written as:

[tex]\text{I}=7\int\frac{ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]

It is required to find the integral value.

Let u = 5 + (ln (x))²

Differentiate.

[tex]du=2ln(x)*\frac{1}{x} dx[/tex]

Or [tex]\frac{du}{2} =\frac{lnx}{x} dx[/tex]

Substitute the values.

[tex]\text{I}=7\int\frac{1}{\sqrt{u} } \frac{du}{2}[/tex]

[tex]\text{I}=\frac{7}{2} \int\frac{1}{\sqrt{u} }du[/tex]

[tex]\text{I}=\frac{7}{2} (2\sqrt{u} )+C[/tex]

Substitute back the value of u.

[tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex]

Hence the value of the integral is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].

Learn more about Integration here :

https://brainly.com/question/33615518

#SPJ4

A cable hangs between two poles of equal height and 30 feet apart. set up a coordinate system where the poles are placed at x=−15 and x=15, where x is measured in feet. the height (in feet) of the cable at position x i

Answers

The length of the cable is the number of units on it.

The cable is 35.26 feet long

How to determine the cable length

The function is given as:

[tex]h(x) = 15\cos(x/15)[/tex]

For all the lengths, we have the following differential equation

[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + (\frac{dy}{dx})^2} \, dx[/tex]

So, we have:

[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + (15 * \frac{1}{15} * \tanh^2(\frac{x}{15}))} \, dx[/tex]

Evaluate

[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + \tanh^2(\frac{x}{15})} \, dx[/tex]

This gives

[tex]Length = \int\limits^{15}_{-15} {\sqrt{cosh^2(\frac{x}{15})} \, dx[/tex]

Evaluate the exponents

[tex]Length = \int\limits^{15}_{-15} {cosh(\frac{x}{15}) \, dx[/tex]

The above function is an even function.

So, we have:

[tex]Length = 2\int\limits^{15}_{0} {cosh(\frac{x}{15}) \, dx[/tex]

Integrate

[tex]Length = 2 * [\frac{sinh(\frac{x}{15})}{1/15}]|\limits^{15}_{0}[/tex]

Simplify

[tex]Length = 30 * [\sinh(\frac{x}{15})]|\limits^{15}_{0}[/tex]

Expand

[tex]Length = 30 * [\sinh(\frac{15}{15}) - \sinh(\frac{0}{15})][/tex]

Solve

[tex]Length = 35.26[/tex]

Hence, the length of the cable is 35.26 feet

Answers

Solve for x over the real numbers:
x^2 = 49

Take the square root of both sides:
Answer: x = 7 or x = -7

While the equation x² = 49 suggests that x = 7, it also has a negative solution, x = -7. Both solutions can be verified by substitution into the original equation, proving they are correct through resulting identities.

The equation x² = 49 has two solutions in the realm of real numbers, not just x = 7. To find the values of x that satisfy the equation, we take the square root of both sides. Since the square root of a number has both a positive and a negative value, the solutions are x = 7 and x = -7. To verify these solutions, we can substitute them back into the original equation to confirm that they work, demonstrating identities such as 7² = 49 and (-7)² = 49.

given right triangle XYZ what is the value of tan 60°

Answers

I have attached the image associated with this question

Answer:
tan (60) = √3

Explanation:
The given triangle is right-angled triangle, therefore, we will use Pythagorean theorem to get the length of the third side.
third side = sqrt [(hypotenuse)^2 + (second side)^2]
third side = 21√3 units

Since the given triangle is a right-angled triangle, we can apply the special trigonometric identities.
Therefore:
tan θ = opposite / adjacent
In the given triangle:
θ = 60°
The opposite side = 21√3
The adjacent side = 21

Substitute in the above equation to get tan 60 as follows:
tan (60) = (21√3) / (21) = √3

Hope this helps :)

Answer:

√3

Step-by-step explanation:

got 100%

Gas prices in Cook county are at $3.30 per gallon. If a market scientist predicts a 20% increase in the price of gas in the coming month, what will the price of gas be?

Answers

3.30*1.2=3.96
$3.96 will be the new price of gas

The price of the gas is $3.96.

What is a percentage?

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Gas prices in Cook-County are at $3.30 per gallon.

If a market scientist predicts a 20% increase in the price of gas in the coming month,

that means,

100 + 20% = 120% increase = 1.2 in decimals.

The price of gas,

= 3.30 + 3.30 x 1.2

= 3.96

Therefore, the new price is $3.96.

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ2

How much would $500 invested at 7% interest compounded annually be worth after 5 years?

Answers

interest compound= p(r+1)^t A=interest compound

7%= 7/100=0.07
A=500(0.07+1)^5
A=701.28

Quadrilateral ABCD is inscribed in a circle. What is the measure of angle A? Enter your answer in the box. m∠A= ° A quadrilateral inscribed in a circle. The vertices of the quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle A is labeled as left parenthesis 3 x plus 6 right parenthesis degrees. The angle C is labeled as left parenthesis x plus 2 right parenthesis degrees.

Answers

Since the quadrilateral is inscribed in the circle, the two angles add to a 180 degrees angle.
We deduce the following equation:
[tex](3x+6)+(x+2)=180[/tex]
Solve for x like this:
[tex](3x+x)+(6+2)=180\\4x=180-8\\4x=172\\x=43.[/tex]

Now we deduce the measure of A:
[tex]A=3x+6=3\times(43)+6=135[/tex]

Final answer:

The measure of angle A in a cyclic quadrilateral ABCD, where the measure of angle A is (3x + 6) degrees and the measure of angle C is (x + 2) degrees, is determined to be 135 degrees.

Explanation:

Given that quadrilateral ABCD is inscribed in a circle, it follows from the properties of cyclic quadrilaterals that the sum of the opposite angles of such a quadrilateral is always 180 degrees. Therefore, if the measure of angle A is represented by the expression (3x + 6) degrees and the measure of angle C is represented by the expression (x + 2) degrees, then we can set up an equation that (3x + 6) + (x + 2) = 180. Solving this equation gives x = 43. Using x = 43, substitute it into 3x + 6 to get the value of angle A, which is equal to 135 degrees.

Learn more about Cyclic Quadrilateral here:

https://brainly.com/question/34351391

#SPJ2

2x - y + 3z = -9
x + 3y - z = 10
3x + y - z = 8

find the ordered triple

Answers

Try the suggested option, note, that the used method is Gauss' method.

Other Questions

A(n) _____________ is a pattern of dark bands on photographic film that is made when DNA fragments are separated by gel electrophoresis and tagged. The photograph produced is often used to determine whether or not suspects were involved in a crime. The nurse is preparing discharge teaching for a client with a history of recurrent pneumonia. what deep breathing techniques will the nurse plan to teach? 12 is 36 less than 4 times a number. What is the number? What hardships were faced by immigrants entering America in the early 1900s? A)They became enslaved if they moved to the south. B)They were separated from their families because they could not afford to live together. C)They received low wages, labored in hazardous working conditions, and lived in overcrowded areas. D)They were unable to find other people from their homelands because of the small number of immigrants. Brayden is simplifying the expression 4n (n 3)2. He begins by distributing the negative to the terms inside the parentheses. What should he have done instead? combine like terms square the binomial cube the binomial rewrite the expression as a fraction Manne lives, shops, and socializes with many other immigrants from the same part of the world who live nearby. this information suggests that an important social group for him is _. what tools were vital for king leopold and others imperalists in Africa What made the Battle of Antietam the single bloodiest day in American history?A) Union troops outnumbering Confederate troops 2 to 1B) Confederate troops unexpectedly using guerilla tacticsC) marching troops forward in close order against newer, more accurate weaponD) amassing the largest armies ever in one place Match the sentence to its correct label. MatchTermDefinition She played video games all day long without stopping.A) Immature Writing Without ceasing, she gripped her controller in her hands and dominated her video games all day long.B) Mature Writing For what had the quality of time interminable, she toiled merrily at her digital amusement.C) Overuse of Thesaurus money in a bank account earning compound interest at an annual percentage rate 3% is an example of exponential growth Help Please Homework Due tomorrow:4. 3 + [5 - 2 ( 8 + 4)] + 6 A fish tank has 16 gallons, the length is 7 feet and the width is 2 feet.Find the hypotenuse length using the Pythagorean theorem .please help fast Solve the triangle.A = 48, a = 32, b = 27I am completely blanking on how to do this, so if you could please do a step by step process, that would be greatly appreciated :) Ppose you have two coins, one biased, one fair, but you don't know which coin is which. coin 1 is biased. it comes up heads with probability 2/3, while coin 2 comes up heads with probability 1/2. suppose you pick a coin at random and flip it. let ci denote the event that coin i is picked. let h and t denote the possible outcomes of the flip. given that the outcome of the flip is a head, what is p[c1|h], the probability that the biased coin is picked? I have trouble converting Which is not true of the weak nuclear force?A. It is a repellent force.B. It acts over a shorter range than the strong nuclear force.C. It is an attractive force.D. It is weaker than the strong nuclear force. There are 84 students in the glee club there are 12 more boys than girls what is the ratio of the number of girls to the number of boys Which transformation gives the same result as a reflection over the y-axis followed by a reflection over the x-axis?a.A rotation of 180 around the originb.A rotation of 270 around the originc.A translation to the left and then downd.A rotation of 90 around the origin How do consumers feelings about the economy help contribute to growth? Positive consumer attitudes influence spending habits. Positive consumer attitudes increase job prospects. Positive consumer attitudes inspire increased production. Positive consumer attitudes can end a depression. Mail merge allows for the sending of an email to multiple recipients. True False

Find the common ratio of the sequence -125,-25,-5,-1..... 1/5 5 -100 100

Answers

Related Questions

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Find the common ratio of the sequence
-125,-25,-5,-1.....

1/5

5

-100

100