parallel to the line y =-3x + 5; passes through (-4,5)

The radius is increasing at rate of [tex]\frac{10}{36\pi } \\[/tex]

What is volume ?

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

As we know Volume of sphere V=

[tex]V=\frac{4}{3} \pi r^3\\dv/dt=6\\Given\\radius=3cm\\[/tex]

so, we need to find dr/dt

Since there is no t in our equation. So differentiate using chain rule

[tex]\frac{dv}{dt} =\frac{dv}{dr} *\frac{dr}{dt} \\[/tex]

Since, in question it is given dv/dt=6

[tex]6=\frac{dv}{dr} .\frac{dr}{dt} \\[/tex]

To find dv/dr differentiate

 [tex]4/3\pi r^3\\dv/dr(\frac{4}{3} \pi r^3)=4\pi r^2\\6=4\pi r^2\frac{dr}{dt} \\[/tex]

Dividing

[tex]\frac{10}{4\pi (3)^2} =dr/dt\\dr/dt=\frac{10}{36\pi } \\[/tex]

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The radius is increasing at rate of 10/36π

What is volume ?

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

As we know Volume of sphere V= 4/3 πr³

dv/dt =6

Given  r = 3 cm.

so, we need to find dr/dt

Since there is not in our equation. So differentiate using chain rule

dv/dt =dv/dr * dr/dt

Since, in question it is given dv/dt=6

6 =dv/dr * dr/dt

To find dv/dr differentiate

dv/dr (4/3πr³) = 4πr²

6 = 4πr² dr/dt

Finally,

dv/dt = 10/36π

Hence, The radius is increasing at rate of 10/36π

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The equation for the plane through P₀ (-1, -7, 2) perpendicular to the following line. x = -1+t , y= -7-5t , z= -2t is x - 5y - 2z = 30

The plane is passing through point P₀(-1, -7, 2)

And the parametric equation of the line is:

x = -1+t , y= -7-5t , z= -2t

L: (-1, -7, -2) + t(1, -5, -2)

The required plane passes through P₀ and perpendicular to line L.

The direction vector of L is V = <1, -5, -2>.

The equation of a plane with normal vector <1, -5, -2> passing through a given point P(x₁, y₁, z₁) is

1(x - x₁) - 5(y - y₁) - 2(z - z₁) = 0

The equation of plane P passing through point P₀ (-1, -7, 2) is:

1(x - (-1)) - 5(y - (-7)) - 2(z - 2) = 0

(x + 1) - 5(y + 7) - 2(z - 2) = 0

x - 5y-2z + 1 - 35 + 4 = 0

x - 5y - 2z = 30 is the required equation of the plane

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The complete question is:

Find the equation for the plane through P₀ (-1, -7, 2) perpendicular to the following line. x = -1+t , y= -7-5t , z= -2t

The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50 .

The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50.

1. Calculate the price of a Deluxe room for check-in on Sunday until Thursday:

$223 / 1.70 = $131.18

2. Calculate the price of a Deluxe room for check-in on Friday and Saturday:

$131.18 x 1.25 = $163.98

3. Calculate the price of a Suite room for check-in on Friday and Saturday:

$163.98 x 1.70 = $278.50

The price per night for a Suite room for check-in on Friday and Saturday would be $278.50.

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The height of the mountain is 10000ft.

Now, According to the question:

A mountain has a snow line at an elevation of 9000 feet which runs parallel to its base.

The snow covers 1,200,000 square feet of part of the mountain.

We know that:

Area of triangle = 1/2 × base × height

Area of a triangle = 1/2 × 2.4 h × h

1200000 = 2.4[tex]h^2[/tex]/2

cross multiply

1200000 × 2 = 2.4[tex]h^2[/tex]

2400000  = 2.4[tex]h^2[/tex]

Divide both sides by 2.4

[tex]h^2[/tex] = 2400000/2.4

[tex]h^2[/tex] = 1000000

h = √1000000

h = 1000  ft.

The height of the mountain = 1000 ft. + 9000 ft. = 10000 ft.

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The decrease in Kaitlin's investment account is 7%, which is calculated by multiplying the initial $5200 by 0.07.

This gives a decrease of $364. The amount in her account at the end of the year is the initial $5200 minus the decrease of $364, which equals $4836.

This can be expressed algebraically as:

Let x = amount in Kaitlin's account at the end of the year

Initial Amount (x) = 5200

Decrease (%) = 0.07

Decrease in Dollars = x * 0.07

Decrease in Dollars = 5200 * 0.07

Decrease in Dollars = 364

Amount in Account at the End of the Year = 5200 - 364

Amount in Account at the End of the Year = 4836

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Answer:

The answer is 685 km hopefully I understood your question and helped you ☻

Step-by-step explanation:

710 km - 25 = 685

Answer:

B) Horizontal Asymptote

A horizontal asymptote is a horizontal line that the graph of a function approaches as the input values get larger or smaller. The end behavior of a rational function is determined by the degree of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the function will approach a horizontal asymptote as the x-values get larger or smaller. If the degree of the numerator is greater than the degree of the denominator, the function will not have a horizontal asymptote.

By using linear equations, The winning team scored 3 less 3s than the losing team.

What are linear equations?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

For winning team

let x=no. of 2s and y=no. of 3s

Therefore, these linear equations will be formed

x+y=50

2x+3y=114

After solving these we get x=36 and y=14

For losing team

let a=no. of 2s and b=no. of 3s

Therefore, these linear equations will be formed

a+b= 48

2a+3b=113

After solving these we get a=31 and b=17

Difference between 3s scored=17-14

Difference between 3s scored=3

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The row percentage of A is 0% , B is 83.3% and of C is 15.4%.

Percentage describes the relative value of a number. Its shows the 100th part of the number with respect to a number whose value is provided in the problem.

Here various data is given about A, B and C in the format of two tables and this shows the relationship between the two.

Now, the row  percentage of A is

[tex]\frac{0}{5} * 100=0%[/tex]%

Then, the row percentage of B is

[tex]\frac{10}{12}*100 = 83.3%[/tex]%

Now, we have to find the row percentage of C

[tex]\frac{2}{13}*100 = 15.4%[/tex].%

Hence, The row percentage of A is 0, the row percentage of B is 83.3% and the row percentage of C is 15.5%.

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The value of x and y is -10 and 5 respectively in the given equations.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The first linear equation is - x + 3y = 5

The second linear equation is - -3x - 2y = 20

On evaluating individually the equation obtained is -

-3x - 2y + x + 3y = 20 + 5

-2x + y = 25

Multiply equation (1) with 3 -

3(x + 3y) = 5 × 3

3x + 9y = 15.....(3)

Adding equation (3) and (2) -

-3x - 2y + (3x + 9y) = 20 + 15

-3x - 2y + 3x + 9y = 35

-2y + 9y = 35

7y = 35

y = 35/7

y = 5

Substituting the value of y in equation (1) -

x + 3y = 5

x + 3(5) = 5

x + 15 = 5

x = 5 - 15

x = -10

Therefore, the value of x and y is -10 and 5 respectively.

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Taylan sold 3 wooden frames and 5 plastic frames. the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation

Given: Taylan sold 7 total frames, with the number of plastic frames being less than twice the number of wooden frames

Let x = number of wooden frames

Since the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation to represent this:

x + (x * 2) < 7

2x < 7

x < 7/2

x = 3

Therefore, Taylan sold 3 wooden frames and 5 plastic frames.

Taylan sold 3 wooden frames and 5 plastic frames. the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation

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A ring with a idempotent not equal to 0 or 1 is 3 and 4.

Make (R,+) a domain that is integral.

As a commutative ring with two elements, R, ab = 0 when either an or b are equal to zero.

If a ∈ R is an idempotent element, then a ≠ 0,a ≠ 1 will result.

[tex]a^{2}[/tex] = a

We can take multiple of 1 because the same number return if we multiply 1 to any number.

[tex]a^{2}[/tex] = a·1

Subtract a·1 on both side, we get

[tex]a^{2}[/tex] - a·1 = 0

Taking a common

a(a -1) = 0

(a -1) = 0 or a =0

R has no zero divisors.

So, a = 1 or a = 0

As a result, the only idempotent elements in the integral domain R are 0 and 1.

A ring that is not equal to 0 or 1 and is idempotent.

A ring with respect to addition and multiplication is the set R = 0 through 5.

Let 3 ∈ R,

[tex]3^{2}[/tex] = 6+3 = 0+3 = 3

Let 4 ∈ R.

[tex]4^{2}[/tex] = 16 = 12+4 = 2

Hence, 3 and 4 are idempotent elements other than 0 and 1

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The complete question is:

An element x in a ring is called an idempotent if [tex]x^2[/tex] = x. Prove that the only idempotents in an integral domain are 0 and 1. Find a ring with an idempotent x not equal to 0 or 1.

It is not possible to conclude a causal relationship from this study alone. This is because the study only shows a correlation between eating large amounts of bananas and being bitten by mosquitoes, it does not demonstrate that one causes the other. There could be other factors that are not controlled for in the study that could be the true cause of the relationship, such as people who eat more bananas also spend more time outdoors. To establish a causal relationship, further research would be needed such as a randomized control trial.

To determine a causal relationship between eating bananas and being bitten by mosquitoes, a randomized controlled trial could be conducted. This type of study would involve randomly assigning participants to two groups: one group would eat a large amount of bananas, while the other group would eat a smaller amount of bananas. The number of mosquito bites each participant receives would be recorded and compared between the two groups.

If the group that ate a large amount of bananas had a significantly higher rate of mosquito bites than the group that ate a smaller amount of bananas, it would suggest that eating bananas may cause an increase in the number of mosquito bites.

Additionally, other variables that could influence the result should be controlled or measured, such as time spent outdoors, skin type, or use of mosquito repellent.

It's important to note that even if the study shows a correlation between eating bananas and being bitten by mosquitoes, it doesn't mean that the banana causes the bites, there could be other factors that are not controlled for in the study that could be the true cause of the relationship.

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The y-intercept of function f is 1.

f(x) = -3x -2 , -∞ < x < -2 = -x + 1, -2 ≤ x < 3  = 2x + 5, 3 ≤ x < ∞

For y-intercept, x =0, f(x) = -x + 1                   [∵ -2 < 0 < 3]

f(0) = -0 + 1 = 1

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet.

This relationship is commonly symbolized as y = f(x)—which is said “f of x”—and y and x are related such that for every x, there is a unique value of y. That is, f(x) can not have more than one value for the same x. To use the language of set theory, a function relates an element x to an element f(x) in another set.

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The answer is that the earthquake in Alaska was 1.5 times or 1000 times more intense than the one in Japan.

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The graph of the function is added as an attachment and the function values are y = 4 for all x values

From the question, we have the following parameters that can be used in our computation:

y=1-3sin(3/2)Theta

Express properly

So, we have the following representation

y = 1 - 3sin(3/2π)

Next, we create a plot of the graph (see attachment)

From the graph, we can see that the function is a horizontal line at y = 4

This means that for all x values, the y value is constant at 4

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The zeros of this polynomial are (1, 0), (2, 0), and (0, 4).

The zeros of the polynomial can be determined by setting the equation equal to zero and solving for the roots.

For example, if the polynomial is given as [tex]ax^{2}[/tex] + bx + c, then the zeros can be determined by solving the equation [tex]ax^{2}[/tex] + bx + c=0.

Step 1: To determine the zeros of the polynomial, set the polynomial equal to 0 and solve for x.

f(x) = [tex]x^{3}[/tex] - [tex]3x^{2}[/tex] + 4 = 0

Step 2: Factor the polynomial to solve for x.

[tex]x^{3}[/tex] - [tex]3x^{2}[/tex] + 4 = 0

x([tex]x^{2}[/tex] - 3x + 4) = 0

Step 3: Factor the quadratic equation.

x(x - 1)(x - 2) = 0

Step 4: Set each factor equal to 0 and solve for x.

x = 0, x = 1, x = 2

Step 5: Plug each x-value into the original equation to determine the corresponding y-value for each zero.

When x = 0, y = 4

When x = 1, y = 0

When x = 2, y = 0

Step 6: The coordinate points of the zeros are (1, 0), (2, 0), and (0, 4).

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Triangle ABC is similar to triangle FGH.

And the value of the x is  22.5 centimeters.

Those triangles that looks the same but different in sizes.

And in the similar triangle,

the corresponding sides in proportion to each other and corresponding angles are equal to each other.

Given:

Triangle ABC is similar to triangle FGH.

That means, the corresponding sides of the triangles are in proportion to each other.

That means,

13.5/9 = 18/12 = x/15

Now,

18/12 = x/15

x = 270/12

x =22.5 centimeters

Therefore, the value of the x is 22.5 centimeters.

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Considering the figure the side length x is solved to be 6.6

Information given from the question is interpreted as

√11 = adjacent

x = hypotenuse

The side x  is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The side x is calculated using cos, CAH

cos 60 = Adjacent / hypotenuse

cos 60 = √11  / x

x =  √11  / cos 60

x = 6.633

x = 6.6 to the nearest tenth

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Answer:

13.99 + 5.75 + 3.29 + 7.35 = 30.38

30.38 - .65 - 3.00 = 26.73

Step-by-step explanation:

Hope this helps! =D

Answer:

$26.73

Step-by-step explanation:

razor = $13.99 - $3.00(rebate) = $10.99

refill pack of razor blades = $5.75

shaving cream = $3.29 - $0.65(coupon) = $2.64

lotion = $7.35

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 7900\\ r=rate\to 2.3\%\to \frac{2.3}{100}\dotfill &0.023\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 7900\left(1+\frac{0.023}{1}\right)^{1\cdot 5} \implies A=7900(1.023)^5\implies A \approx 8851.26[/tex]

Mr. and Mrs. Zeta want to make sure that their baby's monogram, which consists of the first, middle, and last initials, is in alphabetical order with no letters repeated. We may utilize the idea of permutations to determine the number of possible monograms.

A permutation is a way to arrange a group of things in a particular sequence. In this instance, we are examining the alphabet's set of letters (from A to Z), and we are trying to determine how many different ways there are to arrange them so that the monogram is composed entirely of unique letters.

The breakdown of the computation is as follows:

There are 26 different alternatives for the first initial (A to Z).

Since the monogram must be in alphabetical sequence, the letter for the second initial must appear after the first initial. There are so 25 possibilities left (the letters that come after the first initial in the alphabet).

There are 24 possibilities left for the final initial (the remaining letters that come after the second initial in the alphabet).

By multiplying the alternatives for each initial, we can calculate the total number of possible monograms using the basic counting principle:

26 x 25 x 24 = 15,600

Because they must be in alphabetical order and contain no repeating letters, there are 15,600 number of monograms are possible .

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The end behavior of the radical function represented by this graph is option C. As x decreases in value, f ⁡ ( x ) increases in value. As x increases in value, f ⁡ ( x ) decreases in value.

A radical function is a type of mathematical function that includes a radical symbol, such as a square root sign (√) or cube root sign (3√), in its equation.

The graph of a radical function is a curve that may open upward or downward, depending on the specific function. For example, the graph of the square root function, y = √x, starts at the point (0,0) and extends upward and to the right, creating a "V" shape. As the input (x) increases, the output (y) also increases, but at a decreasing rate.

Therefore, the correct answer is as given above

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Hey Mate,

Answer is (4,3),

Thank you .

The polynomial function that has the zeros 3 and 4 - 5i is P(x) = (x - 3)((x - 4)^2 + 25)

From the question, we have the following parameters that can be used in our computation:

zeros 3 and 4 - 5i

The polynomial is represented as

P(x) = (x - zeros)

So, we have

P(x) = (x - 3)(x - (4 - 5i))(x - (4 + 5i))

Expand

So, we have

P(x) = (x - 3)((x - 4)^2 + 25)

Hence, the polynomial is P(x) = (x - 3)((x - 4)^2 + 25)

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Answer:

30/20 = 6/4 = 2/3 (I hope this makes sense)

Step-by-step explanation:

U are dividing by LCM

The number of centimetres in the 1 yard will be 9.144 cm.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Given that:-

Metric System Units

1 inch = 2.54 centimetres

1 foot = 0.3048 meters

1 mile = 1.61 kilometres

1 yard = 3 feet

1 yard = 36 inches

First, we will calculate 1 yard to feet.

1 yard = 3 feet

1 feet = 0.3048 meters

1 feet = 3.048 centimeters

1 yard = 3 x 3.048 centimeters

1 yard = 9.144 centimeters

Hence, the length of 1 yard in cm is 9.144 cm.

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Dupes's age is 14 year and Olu's age is 11 year now.

What is linear algebraic equations?

Unknown quantities can often be determined using linear algebra. Among linear algebra's practical uses are the following: to calculate time, distance, or speed. used by linear maps to translate a three-dimensional image into a two-dimensional plane.

Mathematical structures that can be closed under addition and scalar multiplication are the focus of this area of study, which also encompasses the theory of linear equation systems, matrices, determinants, vector spaces, and linear transformations.

Assume that Dupe is x years old and Olu is y. We may create two linear algebraic equations using the given data:

x + y = 25

(x - 8) = 2(y - 8)

This system of linear equations can be transformed into the following by using a little algebraic trickery:

x + y = 25

x - 2y = -8

To obtain x = 14 and y = 11, construct an augmented matrix and use either Gaussian elimination or Gauss-Jordan elimination.

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