A cylindrical cup measures 12cm in height. When filled to the very top, it holds 780 cubic centimeters of water. What is the radius of the cup, rounded to the nearest tenth? Explain or show your reasoning.

Answer: B = B ∈ {70° + n*360° I n ∈ Z  } where Z is the set of the integer numbers.

Step-by-step explanation:

If we have an angle A, the other angles that have the same terminal arm than A can be written as:

B = A + n*360°

Here B is a "coterminal" angle to A. (they have the same terminal side)

where n can be any integer number (if n = 0 we have A = B, which is trivial, this means that any angle can be coterminal with itself.)

So we can write the set as:

B = B ∈ {70° + n*360° I n ∈ Z  }

The set of angles that has the same terminal arm as 70 degrees is B = B ∈ {70° + n*360°, n ∈ Z}.

We have to determine, which set of angles has the same terminal arm as 70 degrees.

According to the question,

Let, The angle A and other angle B that have the same terminal arm as A can be written as,

B  = A + n × 360°

Where the value of angle A is 70 degrees.

B is the coterminal angle, and they have the same terminal,

And n is the number of integers.

Substitute the value of A in the equation,

B  = 70 + n × 360°

Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.

Since the value of n is equal to 0 then A = B,

Therefore, The angles coterminal with itself is called trivial.

Hence, The set of angles that has the same terminal arm as 70 degrees is B = B ∈ {70° + n*360°, n ∈ Z}.

To know more about Terminal Arm click the link given below.

https://brainly.com/question/20333574

Correlational statistics quantify the strength of a relationship between variables but do not provide information about causality because they cannot assess the temporal sequence of variables.

Correlational statistics, such as correlation coefficients, measure the degree of association between variables.

They indicate the strength and direction of the relationship but do not establish a cause-and-effect relationship. This limitation arises because correlational analysis does not allow for determining the temporal sequence of variables, which refers to the order in which the variables occur or change.

Without knowledge of the temporal sequence, we cannot ascertain whether one variable causes the other or if they are both influenced by an external factor. To establish causality, additional research methods such as experimental designs or longitudinal studies are necessary, where variables can be manipulated or observed over time, respectively.

Thus, correlational statistics serve as valuable tools for understanding associations but do not provide insights into causation.

Learn more about Correlation statistics click here :brainly.com/question/13786078

#SPJ11

Answer:

y= -1/10x + 77 /10.........

Step-by-step explanation:

\( - 2 - - 5 \\ \)

\( \div - 3 - - 3\)

Answer:

An elevator can hold up to about 2000 pounds of weight.The combined weight of everyone currently in the elevator is 1980 pounds. Write an inequality showing the possible amount of weight that can be added to the elevator. S can be your variable hope this helps.

Answer:

\(x=\frac{-8+y}{6}\)

Step-by-step explanation:

Let us evaluate this problem.

First, add Y to both sides

\(-6x-y+y=-8+y\)

Always remember to simplify.

\(-6x=-8+y\)

Divide both sides by -6

\(\frac{-6x}{6} =\frac{8}{-6} +\frac{y}{-6}\)

Simplify one more time.

\(x=\frac{-8+y}{6}\)

Your final answer is:
\(x=\frac{-8+y}{6}\)

Answer:

Step-by-step explanation:

Let the distance between docks be d.

This is the opposite side to 45° angle of triangle with other sides 400 ft and 500 ft.

Use the law of cosines to find the value of d:

Answer:

Step-by-step explanation:

Acid present in the solution = 10 L

Required volume concentration of acid = 8/100

Let x amount of water be added to achieve the required %.

In the new solution, proportion of acid= 10/(50+x)

Therefore,

10/(50+x) = 8/100

x=75

Ans: 75 L of water must be added to the solution

I can't see pictures T^T.

To find the are of a triangle, you multiply the dimensions as you would a rectangle, but divide the product by 2.

Example:

The dimensions of triangle B are 4 and 9.

4x9=36

Now divide.

36/2=18

So the area of triangle B is 18.

---

hope it helps

Answer:

container A

Step-by-step explanation:

In Container A, we can plot the points (0,60) adn (2, 35)

The slope is :

\(m_A = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{35-60}{2-0} \\\\= \frac{-25}{2}\\ \\m_A = -12.5\\\)

For container B, the slope is:

\(m_B = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{32-54}{3-1} \\\\= \frac{-22}{2}\\ \\m_B = -11\\\)

The negative sign of the slope indicates the direction of the slope

\(|m_A| = 12.5\\\\|m_B| = 11\)

12.5 > 11

The slope of container A is steeper than container B

Therefore, the water is draining out of container A at a faster rate than container B

The given differential equation is:

2x²y"+2xy'-2x²y-y/2=0

To solve the Bessel differential equation given below for y(2.4) under the boundary conditions given by

y(1) = 2 and y(pi)=0,

we can follow the steps given below:

Step 1: First, we can write the given differential equation in the standard form by dividing both sides of the equation by x²:

2y"+y'/x-y/2=0

Step 2: Now, we can substitute

y(x) = v(x)*x², and simplify the differential equation using product and chain rules of differentiation:

2v''(x)+2xv'(x)+xv''(x)+2v'(x)-v(x)/2 = 0

2v''(x)+(2x+v'(x))v'(x)+(x/2-v(x)/2) = 0

Step 3: Now, we can substitute v(x) = u(x)*exp(-x²/4), and simplify the differential equation using product, quotient, and chain rules of differentiation:

2u'(x)exp(-x²/4)+(2x-v(x))u(x)exp(-x²/4)+(x/2-v(x)/2)exp(-x²/4) = 0

u'(x)exp(-x²/4) + (2-x/2)u(x)exp(-x²/4) = 0

u'(x) + (2/x - 1/2)u(x) = 0

Step 4: Now, we can solve the above differential equation using the integrating factor method.

We can first find the integrating factor by integrating the coefficient of u(x) with respect to x:

IF = exp[∫ (2/x - 1/2)dx]

= exp[2ln|x| - x/2]

= x²e^(-x/2)

We can now multiply the above integrating factor to both sides of the differential equation to get:

u'(x)x²e^(-x/2) + (2/x - 1/2)u(x)x²e^(-x/2) = 0

This can be rewritten as:

d(u(x)x²e^(-x/2))/dx = 0

Integrating both sides with respect to x, we get:

u(x)x²e^(-x/2) = C1,

where C1 is an arbitrary constantSubstituting the value of u(x), we get:

v(x) = u(x)exp(x²/4)

= C1x^-2*exp(x²/4)

Substituting the value of v(x) and y(x) in the original equation, we get:

Bessel's equation:

x²v''(x) + xv'(x) + (x² - p²)v(x) = 0,

where p = 0 is the order of the Bessel equation.

Substituting v(x) = C1x^-2*exp(x²/4), we get:

2x²*[-2x²*exp(x²/4) + 4x*exp(x²/4) + 2exp(x²/4)] + 2x*[-4x*exp(x²/4) + 2exp(x²/4)] - 2x²*exp(x²/4) - C1x²*exp(x²/4)/2 = 0

Simplifying the above equation, we get:

4x²C1*exp(x²/4) = 0

Therefore, C1 = 0

Therefore, v(x) = 0

Therefore, y(x) = v(x)*x² = 0

Therefore, y(2.4) = 0

Hence, the correct answer is 0.

To know more about integrating visit:

https://brainly.com/question/30900582

#SPJ11

Answer:

B,C

Step-by-step explanation:

The sum of B is 1

The sum of C is -1/2

Let's try each option.

Option A:

-3 + 5 + (-1) = 2 + (-1) = 1

FALSE

Option B:

5 + (-8) + 4 = -3 + 4 = 1

TRUE

Option C:

-19/2 + 9 = -9.5 + 9 = -0.5

TRUE

Option D:

-17 + 36/2 = -17 + 18 = -1

FALSE

So, the correct answers are B and C

Best of Luck!

The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

To learn more about Accelation , refer:

https://brainly.com/question/10307723

#SPJ4

Answer:

13,440 is the area of this irregular object....

The conjecture "A square number is either measurable by 4 or will be after the removal of a unit" is true. If a number is a perfect square, it can be expressed as either 4k or 4k+1 for some integer k.

However, if 4 is replaced by 3 in the conjecture, it is no longer valid. Counterexamples can be found where square numbers are not necessarily divisible by 3.

To prove the conjecture that a square number is either divisible by 4 or will be after subtracting 1, we can consider two cases:

Case 1: Let's assume the square number is of the form 4k. In this case, the number is divisible by 4.

Case 2: Let's assume the square number is of the form 4k+1. In this case, if we subtract 1, we get 4k, which is divisible by 4.

Therefore, in both cases, the conjecture holds true.

However, if we replace 4 with 3 in the conjecture, it is no longer valid. Counterexamples can be found where square numbers are not necessarily divisible by 3. For example, consider the square of 5, which is 25. This number is not divisible by 3. Similarly, the square of 2 is 4, which is also not divisible by 3. Hence, the conjecture does not hold when 4 is replaced by 3.

Learn more about conjecture here : brainly.com/question/29381242

#SPJ11

Answer:

Solution here,

1 US dollar=NRS 120.74

Therefore Rs 180000= 180000/120.74

=$1490.99

Answer:

she can conclude that 20 percent of the students in the sample use the streaming service.

Orthogonal matrix A that satisfies the given conditions is:

[3 3 0 ]

[1/√(2) -1/√(2) √(2/9)]

[-√(2)/2 √(2)/2 √(2)/2]

Let's call the first row of matrix A as r1, which is a multiple of (3, 3, 0). Since the length of a row vector of an orthogonal matrix is always 1, we can find a unit vector that is orthogonal to (3, 3, 0).

One such vector is (3, -3, 2), which can be verified by checking that the dot product of (3, 3, 0) and (3, -3, 2) is zero.

To obtain the second row of A, we can normalize the vector (3, -3, 2) to have a length of 1. This gives us:

(3, -3, 2)/√(18) = (1/√(2), -1/√(2), √(2/9))

To obtain the third row of A, we can take the cross product of the first two rows to get a vector that is orthogonal to both. This gives us:

(3, 3, 0) x (1/√(2), -1/√(2), √(2/9)) = (-2√(2)/3, 2√(2)/3, 2√(2)/3)

We can then normalize this vector to obtain the third row of A:

(-2√(2)/3, 2√(2)/3, 2√(2)/3)/√(8/9) = (-√(2)/2, √(2)/2, √(2)/2)

Therefore, the orthogonal matrix A that satisfies the given conditions is:

[3 3 0 ]

[1/√(2) -1/√(2) √(2/9)]

[-√(2)/2 √(2)/2 √(2)/2]

Learn more about Orthogonal matrix.

brainly.com/question/31426997

#SPJ11

The equation, as the problem requests will be 16 - 0.2h.

The mean is an appropriate measure of central tendency to use for this data, since there are no extreme outliers apparent upon inspection of the data.

Hence, the mean is

(0.5+0.6+0.5+0.7+0.7+0.5+0.5+0.6)/8 = 0.575

The average burning candle from this factory, then, loses 0.575 ÷ 3 ounces per hour (the table showed the weight lost by each of the eight candles after three hours of burning, so we need to divide that by 3 to get an hourly rate).

In conclusion, the equation, as the problem requests will be 16 - 0.2h.

Learn more about equations on

https://brainly.com/question/2972832

#SPJ1

x = 4 is the point of inflection on the curve.

The second derivative of f(x) = 1/2 x^4 - 4x^3 is f''(x) = 6x^2 - 24x.

To find the critical points, we set f''(x) = 0, which gives us the equation 6x(x - 4) = 0.

Solving for x, we find x = 0 and x = 4 as the critical points.

We evaluate the second derivative of f(x) at different intervals to determine the sign of the second derivative. Evaluating f''(-1), f''(1), f''(5), and f''(9), we find that the sign of the second derivative changes when x passes through 4.

Therefore, The point of inflection on the curve is x = 4.

Learn more about inflection

https://brainly.com/question/30760634

#SPJ11

Multiply the time spent on the bus the the total length of the bus trip:

57 x 2/3 = 114/3 = 38 minutes

Now add the amount of time they walk:

38 + 10 + 10 = 58 minutes total.

Answer: C. 58 minutes

The two purple ones are the parallelograms

Hope this helps! ^^

Answer:

All of them are parallelograms because.....

Step-by-step explanation:

parallelograms have for sides and all of them have for sides

NVM sorry this is wrong i got the wrong word

The value of the iterated integral 5∫_(-5)^(5) ∫_0^(π/2) (y + y^2 cos x) dx dy is 5π^2/4 + (π^3/12) sin 5.

To calculate the iterated integral ∬_S (y + y^2 cos x) dA over the given region S, where S is the rectangle defined by -5 ≤ x ≤ 5 and 0 ≤ y ≤ π/2, we will evaluate the integral in two steps: first integrating with respect to x and then integrating with respect to y.

Let's start by integrating with respect to x:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) ∫_(-5)^5 (y + y^2 cos x) dx dy

To integrate with respect to x, we treat y as a constant and integrate the expression (y + y^2 cos x) with respect to x over the range -5 to 5:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) [(y * x + y^2 sin x)]|_(-5)^(5) dy

Now we have an expression in terms of y only. We substitute the limits of integration for x, which are -5 and 5, into the expression (y * x + y^2 sin x) and evaluate it:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) [5y + y^2 sin 5 - (-5y - y^2 sin(-5))] dy

Simplifying further:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) [10y + 2y^2 sin 5] dy

Now we integrate the expression [10y + 2y^2 sin 5] with respect to y over the range 0 to π/2:

∫_S (y + y^2 cos x) dA = [5y^2 + (2/3)y^3 sin 5] |_0^(π/2)

Evaluating the expression at the limits:

∫_S (y + y^2 cos x) dA = [5(π/2)^2 + (2/3)(π/2)^3 sin 5] - [5(0)^2 + (2/3)(0)^3 sin 5]

Simplifying:

∫_S (y + y^2 cos x) dA = [5(π^2/4) + (2/3)(π^3/8) sin 5] - [0]

Finally, we simplify the expression:

∫_S (y + y^2 cos x) dA = 5π^2/4 + (π^3/12) sin 5

Therefore, the value of the iterated integral 5∫_(-5)^(5) ∫_0^(π/2) (y + y^2 cos x) dx dy is 5π^2/4 + (π^3/12) sin 5.

Learn more about iterated integral here

https://brainly.com/question/30216057

#SPJ11

Answer:

25  triangles

Step-by-step explanation:

100/4

By applying unitary method it can be obtained that Ryan drank 2 liters of water in one hour.

What is Unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here, Unitary method is used In \(\frac{3}{4}\) of an hour, Ryan drinks \(1\frac{1}{2}\) liters of water at a constant rate.
In 1 hour, Ryan drinks \(1\frac{1}{2} \div \frac{3}{4}\) liters of water at a constant rate.
In 1 hour, Ryan drinks \(\frac{3}{2} \div \frac{3}{4}\) liters of water at a constant rate.
In 1 hour, Ryan drinks \(\frac{3}{2} \times \frac{4}{3}\) liters of water at a constant rate.
In 1 hour, Ryan drinks \(2\) liters of water at a constant rate.

To learn more about unitary method, refer to the link - https://brainly.com/question/24587372
#SPJ13

The rational root of the fourth degree equation f(x) = 0, with leading coefficient 1 and constant term 23, is 3. By the rational root theorem, only certain rational numbers can be roots, and testing the possibilities shows that only 3 is a root.

By the rational root theorem, any rational root of f(x) must have the form p/q, where p is a factor of 23 and q is a factor of 1. The factors of 23 are ±1 and ±23, and the factors of 1 are ±1, so the possible rational roots of f(x) are ±1, ±23, ±1/1, and ±23/1.

Since the problem states that there is a rational root greater than 1, we can eliminate the negative roots and the root -1. We are left with the possibilities 1, 23, 23/1, and 3. We can test each of these roots using synthetic division or long division to see if any of them are roots of f(x).

Let's start with x = 1:

   1 | 1  0  0  0  23

     |___ ___ ___ ___

       1  1  1  1  24

Since the remainder is not zero, 1 is not a root of f(x).

Next, let's try x = 23:

  23 | 1  0  0  0  23

     |___ ___ ___ ___

       1 23 529 12167 279614

Again, the remainder is not zero, so 23 is not a root of f(x).

Now, let's try x = 23/1 = 23:

This is the same as the previous calculation, so 23/1 = 23 is not a root of f(x).

Finally, let's try x = 3:

   3 | 1  0  0  0  23

     |___ ___ ___ ___

       1  3  9  27  98

The remainder is zero, so 3 is a root of f(x). To find the other roots, we can divide f(x) by (x-3) using polynomial long division or synthetic division.

To know more about rational root theorem, visit:
brainly.com/question/31805524
#SPJ11

Answer: The lowest price you can pay for 15kg of apples is $10.77

Step-by-step explanation:

3.59*3= 10.77 = 15kg

2.49*5= 12.45 = 15kg