dimensions of a cuboid are consecutive terms of a geometric sequence. the volume of the cuboid is 216 cm^3 and the surface of the cuboid is 312 cm^3 . determine the dimensions of the cuboid

Answer:

x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 = 7(x + 1)

Step-by-step explanation:

Equations

The situation can be written as an algebraic equation by setting the variables as follows:

x = first integer

x + 1 = second integer

x + 2 = third integer

x + 3 = fourth integer

x + 4 = fifth integer

x + 5 = sixth (and last) integer

The sum of all six numbers must be equal to 7 times the second number, thus:

x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 = 7(x + 1)

Answer:

72 : 24 = 15 : 5

Answer: (P+S) + 5

Step-by-step explanation:

5= price + sock

Answer:

Step-by-step explanation:

If you were really careful, you should say there is no solution. You have to know that x and 8 are parallel.

The side showing 6 and 6 are sides of a large and small triangle

The large triangle is 6 + 6 = 12

The small triangle is 6

So 8 and x are going to be in the same proportion.

x/6 = 8/12      Cross multiply

12x =48

x = 48/12

x = 4

Answer:

inverse

Step-by-step explanation:

If one variable increases in value and the other variable decreases in value, the variables have a(n) inverse relationship. Option B is correct.

Given that,

A statement " If one variable increases in value and the other variable decreases in value, the variables have a(n) ________ relationship." is given blank space to fill in the state from the option given.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense that are they directly proportional or inversely proportional to each other.

Here, when two variable are proportional to each other,

Case 1
The value of one variable increases as the value of another variable variable are directly proportional to each other

Case 2
The value of one variable decreases as the value of another variable increase implies variables are inversely proportional to each other.

Thus, If one variable increases in value and the other variable decreases in value, the variables have a(n) inverse relationship. Option B is correct.

Learn more about proportionality here:
https://brainly.com/question/22620356

#SPJ2

Answer:

[tex]v=\frac{80}{3}\pi \frac{m}{min}[/tex]

Step-by-step explanation:

In order to start solving this problem, we can begin by drawing a diagram of what the problem looks like (see attached picture).

From that diagram, we can see that we have a triangle we can analyze. We'll call the angle between the vertical line and the slant line [tex]\theta[/tex]. And we'll call the distance between W and the point we are interested in l.

Now, there are different things we need to calculate before working on the triangle. For example, we can start by calculating the angle [tex]\theta[/tex].

From the diagram, we can see that:

[tex]tan \theta = \frac{l}{3}[/tex]

when solving for [tex]\theta[/tex] we will get:

[tex]\theta = tan^{-1} (\frac{l}{3})[/tex]

we could use our calculator to figure this out, but for us to get an exact answer in the end, we will leave it like that.

Next, we can calculate the angular velocity of the beam. (This is how fast the beam is rotating).

We can use the following formula:

[tex]\omega = \frac{2\pi}{T}[/tex]

where T is the period of the rotation. This is how long it takes the beam to rotate once. So the angular velocity will be:

[tex]\omega = \frac{2\pi}{3} \frac{rad}{s}[/tex]

Next, we can take the relation we previously got and solve for l, so we get:

[tex]tan \theta = \frac{l}{3}[/tex]

[tex]l = 3 tan \theta[/tex]

Now we can take its derivative, so we get:

[tex]dl = 3 sec^{2} \theta d\theta[/tex]

and we can divide both sides of the equation into dt so we get:

[tex]\frac{dl}{dt} = 3 sec^{2} \theta \frac{d\theta}{dt}[/tex]

in this case [tex]\frac{dl}{dt}[/tex] represents the velocity of the beam on the wall and [tex]\frac{d\theta}{dt}[/tex] represents the angular velocity of the beam, so we get:

[tex]\frac{dl}{dt} = 3 sec^{2} (tan^{-1} (\frac{l}{3})) (\frac{2\pi}{15})[/tex]

we can simplify this so we get:

[tex]\frac{dl}{dt} = (\frac{2\pi}{5})sec^{2} (tan^{-1} (\frac{l}{3}))[/tex]

we can use the Pythagorean identities to rewrite the problem like this:

[tex]\frac{dl}{dt} = (\frac{2\pi}{5})(1+tan^{2} (tan^{-1} (\frac{l}{3})))[/tex]

and simplify the tan with the [tex]tan^{-1}[/tex] so we get:

[tex]\frac{dl}{dt} = (\frac{2\pi}{5})(1+(\frac{l}{3})^{2})[/tex]

which simplifies to:

[tex]\frac{dl}{dt} = (\frac{2\pi}{5})(1+(\frac{l^{2}}{9}))[/tex]

In this case, since l=1, we can substitute it so we get:

[tex]\frac{dl}{dt} = (\frac{2\pi}{5})(1+(\frac{1}{9}))[/tex]

and solve the expression:

[tex]\frac{dl}{dt} = (\frac{2\pi}{5})(\frac{10}{9})[/tex]

[tex]\frac{dl}{dt} = \frac{20}{45}\pi[/tex]

[tex]\frac{dl}{dt} = \frac{4}{9}\pi \frac{m}{s}[/tex]

now, the problem wants us to write our answer in meters per minute, so we need to do the conversion:

[tex] \frac{dl}{dt} = \frac{4}{9}\pi \frac{m}{s} * \frac{60s}{1min} [/tex]

[tex]velocity = \frac{80}{3} \pi \frac{m}{min}[/tex]

Answer: umm the  first one put $6

and the total price is around $6.50

Step-by-step explanation:

Answer:

$2337.54

Step-by-step explanation:

100%+6.3%=106.3%

106.3%=1.063

1.063×2199=2337.537

So when you round it the answer will be $2337.54.

Answer:

Si, en tanto los kilómetros siguen un patrón decimal, al igual que los números enteros.

Step-by-step explanation:

La pregunta refiere a si el .1 implica un mismo valor en 20.1 km que en 5.1, es decir, en un numero sin unidad de medición.

Y la respuesta es positiva, en tanto los kilómetros, al igual que los números enteros, se rigen por un patrón decimal, es decir, donde los números pueden descomponerse en unidades divisibles por diez. Así, el .1 implica que, tanto en el kilómetro como en el numero entero, se trata del 10% del valor de la unidad en cuestión.

Answer:

B. David's sprinkler uses less water per minute.

Step-by-step explanation:

David's sprinkler uses 10 gallons every 5 minutes, which is 2 gallons a minute.

George's sprinkler uses 6 gallons a minute, which means it uses more.

David's sprinkler uses less and it uses exactly 2 gallons a minute.

Answer:

1 3/20

Step-by-step explanation:

2/5 = 8/20

3/4 = 15/20

8/20+15/20 = 13/20

Answer:

23/20

Step-by-step explanation:

To add the fractions we have to make the denominators match so 20 is the least common denominator.

8+15/20

Then add the numerators together and you'll get

23/20

Pls vote me brainliest <3

C, 4r^4 - 2r^2 - 3r + 13 simplify the expression

Answer:

325

Step-by-step explanation:

Notice you are adding 7 everytime.

So the sequence would be:

a(n) = 10 + 7n

n=0 gives a(0)=10, which is the first term.

so the 46th term has n=45.

a(45)=10 + 7*45=325

Answer:

325

Step-by-step explanation:

since the series have the same common difference(d) is known as arithmetic progression so 46th is obtained by 46th=1term+45d but d is obtainned by taking difference between 1st and 2nd term or 2nd and 3rd term and 1st term=10

Answer:

y=5x-12

Step-by-step explanation:

y=5x+3, and just replace the x and y to get the b. The slope is the same.

1) 3=5(3)+b

2)3=15+b

3)-12=b

4) y=5x-12

Answer:

The minimum number of assignment statements needed is 5

Step-by-step explanation:

To write the algorithm, we apply the strategy of interchanging the values of variables in the assignment statements.

Assume "tmp" is the new variable, let assign tmp to w

The algorithm is:

Procedure exchange (w,x,y,z: integers)

 tmp := w

    w := x

     x := y

     y := z

     z := tmp

    return (w,x,y,z)

end

From the algorithm, it is obvious that there will be a minimum of 5 assignment statements needed.

Answer:

When you read a sentence, you may first look for the subject or what the sentence is about. The subject usually appears at the beginning of a sentence as a noun or a pronoun. A noun is a word that identifies a person, place, thing, or idea. A pronoun is a word that replaces a noun. Common pronouns are I, he, she, it, you, they, and we. In the following sentences, the subject is underlined once.

Step-by-step explanation:

You will often read a sentence that has more than one noun or pronoun in it. You may encounter a group of words that includes a preposition with a noun or a pronoun. Prepositions connect a noun, pronoun, or verb to another word that describes or modifies that noun, pronoun, or verb. Common prepositions include in, on, under, near, by, with, and about. A group of words that begin with a preposition is called a prepositional phrase. A prepositional phrase begins with a preposition and modifies or describes a word. It cannot act as the subject of a sentence. The following circled phrases are examples of prepositional phrases.

Answer:

this is a rotation. you can tell because point Z is (-5,2) and Z' is (2,5)

Point X was (-5,7) and X' is (7,5) and Point Y was (-2, 2) and Y' is (2,2).

by looking at the picture it was rotated 90 degrees counterclockwise

Step-by-step explanation:

Answer:

(x3 - 3x2 - 6x - 3) • (2x - 1)

 ——————————————

               x2              

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:

4.2735

you can use calculator to verify

Answer:

87-13 = 74

Step-by-step explanation:

Answer:

1/2 or 0.5

Step-by-step explanation:

Answer:

45 cups of flour

Step-by-step explanation:

80/8=10

4 1/2 x 10 = 45

Answer:

3

Step-by-step explanation:

y=mx+b

the m here is 3

Answer:

Step-by-step explanation:

Rule for the dilation of a point by a scale factor 'k' about the origin is,

(x, y) → (kx, ky)

If the scale factor for the dilation is [tex]k=\frac{6}{5}[/tex],

Rule for the dilation,

A(x, y) → A'[tex](\frac{6}{5}x,\frac{6}{5}y)[/tex]

If the coordinates of point A' (Image) is given and we have to find the coordinates of point A (Preimage),

Rule for the dilation,

A'(x, y) → [tex]A(\frac{5}{6}x,\frac{5}{6}y)[/tex]

             Quadrilateral CART                   Quadrilateral C'A'R'T'

                          (x, y)                                           [tex](\frac{6}{5}x,\frac{6}{5}y)[/tex]

                       C(-5, 15)                                       C'(-6, 18)

                       A(10, 5)                                         A'(12, 6)

                       R(-20, -10)                                    R'(-24, -12)                          

                       T(-25, 0)                                       T'(-30, 0)

Answer: y-intercept is 0,4

Step-by-step explanation:

Answer:

I believe its C

Step-by-step explanation:

The x intercept is (5,0) and the y intercept is (0,4)

Here's a video for more help:

ht tps://w ww.you tube .com/w atch? v=hG yK6i v0 Lg8

Please erase the spaces

hope i helped! GL!!

Answer:

B. must undergo a logarithmic transformation before undergoing logistic regression.

Step-by-step explanation:

A logistic regression model allows us to establish a relationship between a binary outcome variable and a group of predictor variables. It models the logit-transformed probability as a linear relationship with the predictor variables.