Complete the equation with values that will result in infinitely many solutions. 7x+2(x+5)=

By using the concept of rate of change, it is obtained that

Water level is falling at the rate of \(\frac{2}{9\pi}\) m per minute

What is rate of change?

Suppose there is a function and there are two quantities. If one quantity of a function changes, the rate at which other quantity of the function changes is called rate of change of a function.

Here the concept of rate of change has been used

Let the radius of cone at any point be r m and height be h m

Volume of cone = \(\frac{1}{3}\pi\times r^2\times h\)

Now,

By the concept of similarity,

\(\frac{r}{h} = \frac{4}{16}\\\\\frac{r}{h} = \frac{1}{4}\\\\r = \frac{1}{4}h\)

Volume of cone (V) =

\(\frac{1}{3}\times \pi \times (\frac{1}{4} h)^2\timesh\\\\\frac{1}{48}\times \pi \times h^3\\\)

\(\frac{dV}{dt} = \frac{1}{48} \times \pi \times 3h^2\times \frac{dh}{dt}\\\\\frac{dV}{dt} = \frac{1}{16} \times \pi \times h^2\times \frac{dh}{dt}\\\\\)

Now,

\(\frac{dV}{dt} = -2,\ h = 12\)

So,

\(-2 = \frac{1}{16}\times \pi \times (12)^2 \times \frac{dh}{dt}\\\\\frac{dh}{dt} = -\frac{2 \times 16}{\pi \times 12 \times 12}\\\\\frac{dh}{dt} =- \frac{2}{9\pi}\)

So water level is falling at the rate of \(\frac{2}{9\pi}\) m per minute

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Answer:

125/6

Step-by-step explanation:

So if these two have the same volume it is just the sense of plugging number in. Let’s first find the whole volume of cube a

Cube A : L x W x H

             18 x 15 x 25

             270 x 25

             6750 inches cubed

now let’s find what we know of cube b

Cube B: L x W x H

             18 x 18 x h

             324 x h

Now we know that in order for the volumes to be the same, we have to find a number that when multiplied by 324 would give us 6750. We can do this by dividing the two numbers

6750 / 324

125/6

when we multiply

18 x 18 x (125 / 6)

We get a volume of 6750

lmk if this helps

The height of safe B is 20 inches.

The volume of a rectangular prism is the product of all its dimensions.

∴ The volume of a rectangular prism = height*width*length

We are given dimensions of two safes A and B, in the shape rectangular prism.

Denoting safe A with subscript 1, and the safe B with subscript, we get:

l₁ = 18 inches, w₁ = 15 inches, h₁ = 24 inches.

l₂ = 18 inches, w₂ = 18 inches, h₂ = h inches.

We are told that the volumes of the safe A and B are equal, so

The volume of safe A = The volume of safe B

or, 18*15*24 = 18*18*h

or, h = (18*15*24)/(18*18) = 20

∴ The height of safe B is 20 inches.

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Answer:

3.2 x 4.1= 13.12

Step-by-step explanation:

3.2

4.1

____

3.2

+ 12.0=. 13.12

Answer:

Hey there! I hope this helps you. If you have any questions or concerns feel free to leave them in the comments so I can answer. Thank you!

A rhombus would be a flat shape that has 4 equal straight sides. People also refer to it as a parallelogram.

-All sides are equal

-Opposite sides parallel

~I hope I helped you! :)~

Joe can afford a car loan of approximately $12,944.

To determine the loan amount Joe can afford, we need to calculate the present value of the continuous monthly payments he can make. Joe can pay $360 per month for 4 years, which amounts to a total of 4 * 12 = 48 payments.

The formula to calculate the present value of continuous payments is given by:

PV = (PMT / r) * (1 - e^(-rt))

Where:

PV is the present value of the continuous payments,

PMT is the monthly payment amount,

r is the annual interest rate, and

t is the loan term in years.

Substituting the given values, we have:

PMT = $360,

r = 0.125 (12.5% expressed as a decimal),

t = 4.

Plugging in these values, we can calculate the present value:

PV = (360 / 0.125) * (1 - e^(-0.125 * 4))

Using a calculator or spreadsheet, we find that the present value is approximately $12,944. Therefore, Joe can afford a car loan of approximately $12,944 and still make monthly payments of $360 for 4 years.

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To find the work required to stretch the spring from 10.0 cm to 17.0 cm, we need to calculate the area under the force vs. displacement curve.

The force required to keep the spring stretched to a length of 24.0 cm is 25.0 N.

First, let's calculate the work required to stretch the spring from 10.0 cm to 24.0 cm. Since the force is constant, the work is given by the formula:\(\( W = \text{{force}} \times \text{{displacement}} \).\)

Substituting the values, we have:

\(\[ W = 25.0 \, \text{{N}} \times (24.0 \, \text{{cm}} - 10.0 \, \text{{cm}}) = 350.0 \, \text{{N-cm}} \]\)

Now, let's calculate the work required to stretch the spring from 10.0 cm to 17.0 cm. We can subtract the work required to stretch the spring from 10.0 cm to 24.0 cm from the work required to stretch the spring from 10.0 cm to 17.0 cm.

\(\[ W = 350.0 \, \text{{N-cm}} - 25.0 \, \text{{N}} \times (24.0 \, \text{{cm}} - 17.0 \, \text{{cm}}) = 250.0 \, \text{{N-cm}} \]\)

Therefore, the work required to stretch the spring from 10.0 cm to 17.0 cm is 250.0 N-cm.

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Answer:6.1 ounces

Step-by-step explanation:

Answer:

your right it is a rational number

Answer:

Slope:  1/4

y - int: (0,-6)

Step-by-step explanation:

-x+4y=-24

4y = -24+x

y=1/4 * x - 6

Answer:

$11.84

Step-by-step explanation:

2.96*4= 11.84

The general solution to the phase plane differential equation is: (1/3) y^3 + C1 = (1/10) x^10 + ln|y| + C2

To solve the phase plane differential equation for the given system, let's assume that x = x(t) and y = y(t).

The differential equation is given as:

dx/dt = x^9 - y^(-2)

To solve this equation, we need to find the relationships between x and y. We can rewrite the equation as follows:

dx/dt = x^9 - 1/y^2

Now, let's consider y as a function of x. We can rewrite it as y = y(x).

Taking the derivative of y with respect to x using the chain rule, we have:

dy/dx = (dy/dt) / (dx/dt)

Substituting the given differential equation into the above expression, we get:

dy/dx = (1/y^2) / (x^9 - 1/y^2)

Rearranging the equation, we have:

y^2 dy = (x^9 - 1/y^2) dx

Now, we can integrate both sides of the equation with respect to x:

∫ y^2 dy = ∫ (x^9 - 1/y^2) dx

Integrating the left side, we get (1/3) y^3 + C1, where C1 is the constant of integration.

Integrating the right side, we get (1/10) x^10 + ln|y| + C2, where C2 is the constant of integration.

Therefore, The general solution to the phase plane differential equation is: (1/3) y^3 + C1 = (1/10) x^10 + ln|y| + C2

This equation represents the solution curve in the phase plane for the given system.

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Answer: i feel like its C but im not sure

Step-by-step explanation:

Answer:

they're equal

Step-by-step explanation:

Trick question. They're equal. 80/100 can be simplified to 8/10 by dividing by 10. if you type them both in a calculator, they both equal .80

The slower cyclist travels at a speed of 16 miles per hour, while the faster cyclist travels at twice the speed, which is 32 miles per hour.

Let's assume that the slower cyclist's speed is x mi/h, then the faster cyclist's speed is 2x mi/h.

Since they are riding towards each other, their relative speed is the sum of their speeds, which is 3x mi/h.

They travel a total distance of 48 mi in 1 hour, so we can use the formula:

distance = rate x time

48 = 3x x 1

Solving for x, we get:

x = 16

Therefore, the slower cyclist's speed is 16 mi/h and the faster cyclist's speed is 32 mi/h.

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Answer:

The 1) and 2) lines are parallel.

Step-by-step explanation:

Answer:

The answers C if you plug in the answer and re-write it 11.3.04 is correct.

Step-by-step explanation:

Answer:

Undefined

Step-by-step explanation:

For a unit circle, which has a radius as 1, we can derive the tangent values of all the degrees. With the help of a unit circle drawn on the XY plane, we can find out all the trigonometric ratios and values.

Answer:

C)Undefined

Not defined

Step-by-step explanation:

According to research ,

Tangent function denotes that for a given right-angled triangle, the tan of angleθ is equal to the ratio of the opposite side to the angle and adjacent side or base.

Tan θ = Opposite Side/Adjacent Side

We can also represent the tangent function as the ratio of the sine function and cosine function.

∴ Tan θ =Sin θ /Cos θ

So, tan 90 degrees in terms of ratio is,

Tan 90°=Sin 900 / Cos90°

From the trigonometric table, we know,

Sin 90° = 1

And,

Cos90° = 0

∴ Tan 90°= 1/0 = Undefined

That means, we cannot define Tan 900 value.

My source : The internet .

Answer:

92

Step-by-step explanation:

Answer:

The correct option is;

Exponential function 2ˣ + 2

x = 0, 2, 4, 6, 8

f(x) = 3, 6, 18, 66, 258

Step-by-step explanation:

The given functions are;

f(x) = 2x + 2

x = 0, 2, 4, 6, 8

f(x) = 2, 6, 10, 14, 18

f(x) = 2ˣ + 2

x = 0, 2, 4, 6, 8

f(x) = 3, 6, 18, 66, 258

f(x) = 2·x² + 2

x = 0, 2, 4, 6, 8

f(x) = 2, 10, 34, 74, 130

f(x) = 3·x + 2

x = 0, 2, 4, 6, 8

f(x) = 2, 8, 14, 20, 26

By comparison, the function that increases at the fastest rate between x = 0 and x = 8 is Exponential function 2ˣ + 2

Answer: The answer is B on edg

Step-by-step explanation:

Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).

Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.

At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

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The area of the portion of the sphere of radius 10 that is in the cone `z > sqrt(x² + y²)` is `50π√2`.

The radius of the sphere as 10, that is `r = 10`.

The equation of the cone is given by `z > √(x²+y²)` which represents the top half of the cone.

The cone is centered at the origin, which means the vertex is at the origin.

Here, the equation of the sphere is `x² + y² + z² = 10²`

`We need to find the area of the portion of the sphere of radius 10 that is in the cone `z > sqrt(x² + y²)`Since the cone is symmetric about the xy-plane and centered at the origin, we can work in the upper half of the cone and multiply by 2 at the end.

Let the projection of the point P on the xy-plane be Q. This means that `z = PQ = sqrt(x² + y²)`.The equation of the sphere is `x² + y² + z² = 10²`

Substituting `z = sqrt(x² + y²)` to get `x² + y² + (sqrt(x² + y²))² = 10²`Simplifying and rearranging to get

`z = sqrt(100 - x² - y²)`

This is the equation of the sphere in the first octant. The portion of the sphere in the cone `z > sqrt(x² + y²)` is the part of the sphere that is above the cone, i.e., `z > sqrt(100 - x² - y²) > sqrt(x² + y²)`

Since the sphere is centered at the origin, we can integrate in cylindrical coordinates.Let `r` be the distance from the origin, and let `θ` be the angle made with the positive x-axis.

Then `x = r cos θ` and `y = r sin θ`.Since we are working in the first octant, `0 ≤ θ ≤ π/2`.The limits of integration for `r` can be found by considering the intersection of the two surfaces.`z = sqrt(100 - x² - y²)` and `z = sqrt(x² + y²)` gives `sqrt(100 - x² - y²) = sqrt(x² + y²)` or `100 - x² - y² = x² + y²`.

This simplifies to `x² + y² = 50`.Thus the limits of integration for `r` are `0 ≤ r ≤ sqrt(50)`

Substitute `z = sqrt(100 - x² - y²)` into the inequality `

z > sqrt(x² + y²)` to get `sqrt(100 - x² - y²) > sqrt(x² + y²)`.

This simplifies to `100 - x² - y² > x² + y²`. This simplifies to `2y² + 2x² < 100`.

Thus the limits of integration for `θ` are `0 ≤ θ ≤ π/2`.

The area of the portion of the sphere of radius 10 that is in the cone `z > sqrt(x² + y²)` is given by the integral:

`A = 2 ∫₀^(π/2) ∫₀^sqrt(50 - r²) sqrt(100 - r²) r dr dθ`

To evaluate this integral lets make the substitution `u = 100 - r²`.

Then `du/dx = -2x` and `du = -2x dr`. Thus, `x dr = -1/2 du`.

Substituting to get:

`A = 2 ∫₀^(π/2) ∫₀^sqrt(50) √u * (-1/2) du dθ`

This simplifies to:`

A = -∫₀^(π/2) u^(3/2) |₀^100/√2 dθ`

Evaluating

:`A = 2 ∫₀^(π/2) 100^(3/2)/2 - 0 dθ`

Simplifying:`

A = ∫₀^(π/2) 100√2 dθ`Evaluating:`

A = 100√2 * π/2`

Simplifing:`A = 50π√2`

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The equation (x - 9)^2/36 + (y - 7)^2/9 = 1 models the elliptical platform with a center at (9, 7), a major axis of 12 ft parallel to the front edge of the stage, and extending to within 3 ft of the edge.

To model the elliptical platform, we can use the equation of an ellipse.

An ellipse is defined by the distances from its center to any point on its perimeter, called the semi-major axis (a) and semi-minor axis (b). The center of the ellipse is given as (h, k), where (h, k) is (9, 7) in this case.

Given that the major axis is 12 ft and parallel to the front edge of the stage, the semi-major axis (a) is half of the major axis, which is 12/2 = 6 ft.

The platform extends to within 3 ft of the edge, so the semi-minor axis (b) is the semi-major axis (6 ft) minus 3 ft, which is 6 - 3 = 3 ft.

Using these values, we can write the equation of the ellipse:

(x - h)^2/a^2 + (y - k)^2/b^2 = 1

Plugging in the values we have:

(x - 9)^2/6^2 + (y - 7)^2/3^2 = 1

Simplifying the equation:

(x - 9)^2/36 + (y - 7)^2/9 = 1

To model the platform, we use the equation of an ellipse, which takes the form (x - h)^2/a^2 + (y - k)^2/b^2 = 1. We are given the center of the platform as (9, 7) and the major axis as 12 ft.

From this, we determine that the semi-major axis (a) is 6 ft and the semi-minor axis (b) is 3 ft.

We plug these values into the equation, simplifying it to (x - 9)^2/36 + (y - 7)^2/9 = 1.

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The total cost paid by Matt if he joins for 6 months is found as 320.

For the stated query:

The joining cost of gym = 200

The month cost = 20.

Let the number of month be 'x'.

Let the total cost be 'c'.

Then , linear equation forms be.

c = 200 + 20x

For 6 months, put x = 6.

c = 200 + 20*6

c = 200 + 120

c = 320

Thus, the total cost paid by Matt if he joins for 6 months is found as 320.

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The complete question is-

Matt joins a gym the cost includes a one time fee of 200 plus a monthly fee of 20. Find the total cost paid by Matt if he joins for 6 months.

Answer:

135 is the maximum number of cubes that can be obtained

The points jada score is 159.25.

Given that james scored 182 points while playing a video game and he scored 7 times as many points as jada scored.

Let x be the points scored by james and y be the points scored by jada.

The total points scored by james and jada is 182 points.

x+y=182    .....(1)

James scored 7 times many points as jada scored.

y=7x         .....(2)

So, there are two equations and two unkowns.

Firstly, we will substitute equation (2) in equation (1), we get

x+7x=182

8x=182

Divide both sides by 8, we get

8x/8=182/8

x=22.75

Further, we will substitute the value of x in equation (2), we get

y=7×22.75

y=159.25

Hence, the jada score 159.25 when james scored 182 points while playing a video game and ahe scored 7 times as many points as jada scored.

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The wavelength of an atom is 3.28× 10−11 m when it is travelling at its root-mean-square speed at 20 °C. Decide on the atom. Consequently, M = 2 and the gas's molar mass is 2 kgmol−1 .

Radio waves, light waves, and infrared (heat) waves are examples of electromagnetic radiation that flow through space in distinct patterns. Every wave is a specific size and shape.

calculation

urms=  \(\sqrt{\frac{3RT}{M} }\)

and

λ=h/murms

⟹urms=h/mλ⟹

 \(\sqrt{\frac{3RT}{M} }\)=h/mλ

72.2 = 148.17 / M

M = 148.17/72 ≈ 2

Consequently, M = 2 and the gas's molar mass is 2  kgmol−1. A gas with a molecular mass of 2 kgmol-1, however, does not exist.

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The general solution of the ordinary differential equation y'' - 3x^2y = 2x^2 is y(x) = C1x^(-1) + C2x^2, where C1 and C2 are arbitrary constants.  The equation is a second-order linear homogeneous differential equation with variable coefficients.

First, let's find the complementary solution, which represents the solution of the homogeneous equation y'' - 3x^2y = 0. The complementary solution can be written as y_c(x) = C1y1(x) + C2y2(x), where C1 and C2 are arbitrary constants, and y1(x) and y2(x) are linearly independent solutions.

To find the complementary solution, we assume a solution of the form y(x) = x^m. Plugging this into the homogeneous equation, we get the characteristic equation:

m(m - 1) - 3x^2 = 0

Solving this quadratic equation, we find two roots: m1 = -1 and m2 = 2.

Therefore, the complementary solution is y_c(x) = C1x^(-1) + C2x^2.

Now, to find the particular solution for the non-homogeneous equation y'' - 3x^2y = 2x^2, we assume a particular solution of the form y_p(x) = Ax^4, where A is a constant to be determined.

Substituting this into the differential equation, we get:

24Ax^2 - 3x^2(Ax^4) = 2x^2

Simplifying, we have:

24Ax^2 - 3Ax^6 = 2x^2

Comparing the coefficients of like powers of x, we get:

-3A = 2      (coefficients of x^6)

24A = 0       (coefficients of x^2)

From the second equation, we find A = 0, and from the first equation, we find A = -2/3. Since these values contradict each other, there is no particular solution of the form Ax^4.

Therefore, the general solution of the given differential equation is:

y(x) = y_c(x) + y_p(x)

     = C1x^(-1) + C2x^2          (complementary solution)

     + 0                           (no particular solution)

In conclusion, the general solution of the ordinary differential equation y'' - 3x^2y = 2x^2 is y(x) = C1x^(-1) + C2x^2, where C1 and C2 are arbitrary constants.

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By working with the given mixed numbers, we will get that for the project they need (4 + 1/4) yards of metal.

At this point, we have two pieces that measures (1 + 1/6) yd and (3/12) yd, adding that length we get a total length:

L = (1 + 1/6) yd + (3/12) yd = (1 + 2/12) yd + 3/12yd = (1 + 5/12) yd

Now we know that we need 3 times that amount of metal for the project, then the total amount of metal that we need is:

3*L = 3*(1 + 5/12) yd = (3 + 15/12) yd

We can write this as a mixed number as:

(3 + 12/12yd + 3/12yd) = (4 + 3/12)yd = (4 + 1/4) yd

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The best description of the probability of drawing a king from the deck is 1 out of 13, or 1/13.

The probability of drawing a king from a standard deck of 52 playing cards can be determined by dividing the number of favorable outcomes (number of kings) by the total number of possible outcomes (total number of cards in the deck).

In a standard deck, there are 4 kings (one king for each suit: hearts, diamonds, clubs, and spades). Therefore, the number of favorable outcomes is 4.

The total number of possible outcomes is 52 (the total number of cards in the deck).

So, the probability of drawing a king is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 4 / 52

Simplifying the fraction gives us:

Probability = 1 / 13

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