the change in the x-coordinates of any two points on a line in the xy-plane is the

The speed of the particle in rpm is 43170.32 rpm.

Given:

The distance of particle (radius) from the axis is [tex]r=6\rm \: cm=0.06\; m[/tex].

The acceleration (centripetal) experienced by the particle is,

[tex]a=125000\rm \; g's\\a=125000\times 9.81 \rm \; m/s^2\\a=1226250\rm \; m/s^2[/tex]

Let ω be the angular velocity of the particle and N be the speed in rpm.

So, ω will be  [tex]\omega=\dfrac{2\pi N}{60}[/tex]

Now, the acceleration of the particle can be written as,

[tex]a=\omega^2r\\a=\left(\dfrac{2\pi N}{60}\right)^2\times 0.06[/tex]

So, the speed of the particle in rpm will be,

[tex]a=\left(\dfrac{2\pi N}{60}\right)^2\times 0.06\\12262550=0.01095N^2\times 0.06\\N=43170.32\rm \; rpm[/tex]

Therefore, the speed of the particle in rpm is 43170.32 rpm.

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Answer:

The solution set for the provided inequity is {x | x > 2}.

Step-by-step explanation:

Consider the provided inequity.

[tex]5x+7>17[/tex]

Subtract both the side by 7.

[tex]5x+7-7>17-7[/tex]

[tex]5x>10[/tex]

Now divide both the side by 5.

[tex]\frac{5x}{5}>\frac{10}{5}[/tex]

[tex]x>2[/tex]

Hence, the solution set for the provided inequity is {x | x > 2}.

Answer:

The y-intercept of f(x) is 3 units below the y-intercept of g(x).

Step-by-step explanation:

We are given,

The functions [tex]f(x)=x-1[/tex] and [tex]g(x)=x+2[/tex].

Now, y-intercept is the point where the graph of the function crosses y-axis.

Substituting x= 0 in the functions, we get,

[tex]f(0)=0-1\\f(0)=-1[/tex] and [tex]g(0)=0+2\\g(0)=2[/tex].

Thus, we get that,

The y-intercept of the the function f(x) is -1.

The y-intercept of the function g(x) is at 2.

Thus, the y-intercept of f(x) is 2-(-1)= 3 units below the y-intercept of g(x) as seen below.

Answer:

This is FALSE.

Step-by-step explanation:

Writing a check on an account with insufficient funds is never allowed by any bank. This will only lead to check bounce and sometimes can land you up in legal trouble. When a check bounces, you will have to pay your bank the bounce fee also. Hence, we should be careful while writing any check.

The value of n is 4. This means that it took 4 years for the investment to grow to £5469.78.

We can use the compound interest formula to solve this problem:

A = P(1 + r/n)nt

where:

A is the future value of the investment

P is the principal amount invested

r is the annual interest rate

n is the number of times per year the interest is compounded

t is the number of years

In this problem, we have the following information:

A = 5469.78

P = 4500

r = 0.05 (5%)

n = ?

t = n

We can plug these values into the formula and solve for n:

5469.78 = 4500(1 + 0.05/n)n

1.2155066 = (1.05)n

n = 4

Therefore, the value of n is 4. This means that it took 4 years for the investment to grow to £5469.78.

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Answer: just copy and paste


We want to find the relationship between the opposites of a and b, given that both are positive and a < b.

That relation is:

-a > -b.

Remeber that the opposite of a real number is just -1 times that number.

The opposite of a is: -a

The opposite of b is: -b

Remember that for negative numbers, the closer the number is to zero, the larger is the number.

Because we know that a and b are positive, and a < b, then we know that a is closer to zero.

So for -a and -b, we know that -a is also closer to zero (then -a is larger than -b), so the relationship between these two is:

-a > -b.

When a < b and both a and b are positive numbers, the opposites of these numbers will have opposite signs.

In mathematical terms, when two positive numbers add, the answer has a positive sign. Similarly, when two negative numbers add, the answer has a negative sign. However, when a negative number is added to a positive number, the answer will depend on the magnitudes of the numbers:

So, in the given scenario where a < b, if both a and b are positive numbers, the opposites of these numbers will have opposite signs.

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The answer is interval or ratio. In interval level of measurement, the distances between have attributes does have a meaning. The best example to be used here is temperature. The distance from 40-50 is like the distance from 70-80. While in ratio level of measurement, there is constantly an absolute zero that is significant. Meaning, that you can build a meaningful fraction (or ratio) with a ratio variable. 

To convert grams per cubic centimeter to pounds-mass per cubic foot, you can use the conversion factors. By applying the conversion factors of 1 lb = 454 g and 1 ft³ = (30.5 cm)³, you can calculate that 40 grams per cubic centimeter is equal to 500 pounds-mass per cubic foot.

To convert grams per cubic centimeter to pounds-mass per cubic foot, we need to use conversion factors. Firstly, we need to convert grams to pounds by using the conversion factor 1 lb = 454 g. Then, we convert cubic centimeters to cubic feet by using the conversion factor 1 ft³ = (30.5 cm)³. Finally, we combine the two conversion factors to find the desired unit: pounds-mass per cubic foot.

Given:

Conversion factor:

Calculation:

Simplifying the calculation gives:

Therefore, 40 grams per cubic centimeter is equal to 500 pounds-mass per cubic foot.

The volume of 10 drops of liquid is approximately 0.0001 fluid ounces.

To find the volume of 10 drops of liquid, we can use the given information that the volume of 10000 drops is 10 fluid ounces. Let's set up a proportion to solve for the volume of 10 drops.

Let V be the volume of 10 drops in fluid ounces.

We know that the volume of 10000 drops is 10 fluid ounces, so we can write:

10,000 drops / V = 10 fluid ounces / 10 drops

Now, cross-multiply and solve for V:

10,000 drops * 10 drops = 10 fluid ounces * V

100,000 drops² = 10 fluid ounces * V

Now, divide both sides by 100,000 drops^2 to solve for V:

V = 10 fluid ounces / 100,000 drops^2

V ≈ 0.0001 fluid ounces

Therefore, the volume of 10 drops of liquid is approximately 0.0001 fluid ounces.

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Eight and one-half years ago the age of Steven was 7 years, then the present age of Steven is 15.5 years.

Mathematical equations with two algebraic symbols on either side of the equal (=) sign are called equation. This connection is illustrated by the left and right expression being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

Assume the current age of Steven is x years.

From the given information in the question,

8.5 years ago from now,

x - 8.5 = 7 years

x = 15.5 years.

So, the current age is 15.5 years.

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Answer:

P=1.2

Step-by-step explanation:

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Answer:

option C

[tex]20\°[/tex]

Step-by-step explanation:

we know that

An isosceles triangle has two equal angles and two equal sides. The two equal angles are the base angles and the third angle is the vertex angle

In this problem the base angles are angle B and angle C

so

m∠B=m∠C

substitute

[tex](5x+5)\°=(7x-25)\°[/tex]

[tex](7x-5x)\°=(5+25)\°[/tex]

[tex]2x=30\°[/tex]

[tex]x=15\°[/tex]

m∠B=[tex](5x+5)\°=5*15+5=80\°[/tex]

Remember that the sum of the internal angles of the triangle is equal to [tex]180\°[/tex]

Find m∠A

m∠A=[tex]180\°-2*80\°=20\°[/tex]

The maximum value of [tex]\(f(x, y)\)[/tex]  is given by:

[tex]\(f\left(\frac{b}{a+b}, \frac{a}{a+b}\right) = \left(\frac{b}{a+b}\right)^a \left(\frac{a}{a+b}\right)^b\)[/tex]

To find the maximum value of the function [tex]\(f(x, y) = x^a y^b\)[/tex] subject to the constraint (x + y = 1, use the method of Lagrange multipliers.

Let's set up the Lagrangian function:

[tex]\(L(x, y, \lambda) = x^a y^b + \lambda(x + y - 1)\)[/tex]

Taking the partial derivatives and setting them to zero:

Equation 1: [tex]\(\frac{\partial L}{\partial x} = a x^{a-1} y^b + \lambda = 0\)[/tex]  

Equation 2: [tex]\(\frac{\partial L}{\partial y} = b x^a y^{b-1} + \lambda = 0\)[/tex]

Equation 3: [tex]\(\frac{\partial L}{\partial \lambda} = x + y - 1 = 0\)[/tex]  

From equations (1) and (2) it can be written as

Equation 4: [tex]\(a x^{a-1} y^b = -\lambda\)[/tex]  ... (4)

Equation 5: [tex]\(b x^a y^{b-1} = -\lambda\)[/tex] ... (5)

Dividing equation (4) by equation (5) gives

[tex]\(\frac{a}{b} \frac{x^{a-1}}{x^a} \frac{y^b}{y^{b-1}} = 1\)[/tex]

[tex]\(\frac{a}{b} \frac{y}{x} = 1\)[/tex]

From equation (3) [tex]\(y = 1 - x\)[/tex].

Substituting [tex]\(y = 1 - x\)[/tex] into the equation [tex]\(\frac{a}{b} \frac{y}{x} = 1\)[/tex]

[tex]\(\frac{a}{b} \frac{1-x}{x} = 1\)[/tex]

[tex]\(a x = b (1-x)\)[/tex]

[tex]\((a + b) x = b\)[/tex]

[tex]\(x = \frac{b}{a+b}\)[/tex]

Substituting [tex]\(x = \frac{b}{a+b}\)[/tex] into the constraint equation (3):

[tex]\(y = 1 - x[/tex]

  [tex]= 1 - \frac{b}{a+b} = \frac{a}{a+b}\)[/tex]

Therefore, the critical point (x, y) that satisfies the constraint equation is:

[tex]\(x = \frac{b}{a+b}\) and \(y = \frac{a}{a+b}\)[/tex]

Therefore, the critical point gives the maximum value of the function [tex]\(f(x, y) = x^a y^b\)[/tex] subject to the constraint x + y = 1.

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i just took a test.