2. A common formula in physics is shown below. my2 FE a) Solve for m in terms of F, v, and r. b) Solve for v in terms of F, m, and r.

The definition of the cosecant function is

Therefore,

To find sin(-pi/2), use the diagram below.

Consider that the circumference has a radius equal to 1. Then, the coordinates of the orange point are (0,-1). Furthermore, the points on the circumference are given as (cos(theta), sin(theta)); therefore,

Thus, the answer is csc(-pi/2)=-1

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-1)}) \implies {\large \begin{array}{llll} y -5= -(x +1) \end{array}}[/tex]

Given:

Length of a rectangle is a+1

width of a rectangle is a

Given:

Number of sophomores attended jazz band concert = 35

Total number of students = 137

Required: Probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert.

Explanation:

The formula to find probability is

Probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert

Option D is correct.

Final Answer: Probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert is 0.26.

Step 1

Given;

Required; To solve by completing the square method.

Step 2

Subtract 15 from both sides of the equation.

Find half of the coefficient of x (i.e 6) and square it

Add it to both sides

Answer;

We need to find how much will be left after 6 half-lives of a radioactive isotope starting with 130g.

One way to write the amount N of radioactive isotope left after a time t, with an initial amount N₀ and a half-life τ is:

Notice that when t = τ, we have:

In this problem, we have:

Then, we obtain:

Therefore, rounding to the nearest gram, the answer is 2 grams.

From the double number line, we can see that the corresponding number of Green and Purple beads needed in each case are stated.

Therefore, for 20 Green beads she will need to use 25 Purple Beads.

Solution

Explanation:

Given:

(b) Equation of the axis of symmetry

where

The formula for the axis of symmetry and the x value of the vertex

Plug in the value

(d) To find the y value of the vertex, substitute 1 for x in the equation.

The vertex is (-2 , -42) Since a > 0 the vertex is the minimum point and the parabola opens upward.

Hence the vertex = (-2 , -42)

Since this is a right triangle we can use trig functions

First we can find the length of the hypotenuse using the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

28^2 + 45^2 = c^2

784+2025 = c^2

2809 = c^2

Taking the square root of each side

sqrt(2809) = sqrt(c^2)

53 = c

The hypotenuse, DR = 53

Then we can find the measurements of the angles

sin F = opp/ hyp

sin F = 28/53

Taking the inverse sin of each side

sin D = opp/ hyp

sin D = 45/53

Taking the inverse sin of each side

By definition, an equation of a Combined Variation has the following form:

Where "k" is the Constant of Variation.

In this case, you know that the resistance "R" of a wire varies directly as its length and inversely as the square of its diameter.

Then, let be "R" the resistance of the wire (in ohms), "l" its length of the wire (in feet), and "d" its diameter (in inches).

Therefore, you can set up that the equation has this form:

According to the information given in the exercise, when:

The resistance is:

Then, you can substitute values into the equation and solve for "k":

Therefore, you can set up the following equation that represents this situation (using the value of "k"):

Hence, if:

You can substitute these values into the equation and then evaluate, in order to find the corresponding resistance. This is:

Therefore, the answer is:

I think this is a physics problem.

I'll read it

a) A rectangular prism and a cylinder

b) Volume of the log = pi*r^2 x h

Volume of the log = 3.14*5^2* 30

Volume of the log = 2355 in^3

density = weight / volume

density = 4263 / 2355

density = 1.81 lb/in^3 This is the result

When a function is compose by its inverse, the result is its original input. Therefore,

The rule of the compounded interest is

A is the new amount

P is the initial amount

r is the rate in decimal

n is the number of periods per year

t is the time in years

Since the principal is $1000, then

P = 1000

Since the yearly interest rate is 6%, then change it to decimal by dividing it by 100

r = 6/100 = 0.06

Since the interest is compounded yearly, then

n = 1

Since the time is 10 years, then

t = 10

Substitute them in the rule above

The amount of money in the account after 10 years is $1790.847697

Recall that :

1) A function

translated n-units to the left is

2) A function

translated m-units up is:

3) A function g(x) reflected over the x-axis is:

The parent function is:

The function of the graph of the above function translated horizontally 3 units to the left is:

The function of the graph of the above function translated vertically 4 units up is:

The function of the graph of the above function reflected over the x-axis is:

Finally, the function of the graph of the above function stretched vertically by a scale factor of 2 is:

Answer:

The graph of the function has a horizontal translation Left 3 and vertical translation Up 4. The graph has been reflected over the x-axis and has been Vertically stretched.

Answer

4.5

Step-by-step explanation

Given the equation:

Dividing at both sides by 4.5, we get:

Answer:

Divide each side by 4.5

Step-by-step explanation:

(4.5)x = 264.5456

We want to isolate x

Divide each side by 4.5

(4.5)x / 4.5 = 264.5456/ 4.5

x =58.78791

we have the following:

therefore, the answer is 2x

Solution:

Experimental probability is a probability that is determined on the basis of a series of experiments. A random experiment is done and is repeated many times to determine their likelihood, and each repetition is known as a trial.

If 219 of the first 264 customers have not received a star on the receipt, then a customer that would win a free gallon of milk would be among (264 - 219) customers. Thus;

The experimental probability of winning a free gallon of milk is;

CORRECT OPTION:

Choosing two points: A(0, 3) and B(3, -9)

• Sope (m):

• Find b: choosing point A

y = mx + b

• Education:

Answer: A. y= -4x + 3

Given:

The roller-coster is moving in the trajectory of this curve

Step by step solution:

To solve this complete problem we need to draw the estimated graph of this function, so that we can answer this question easily.

First of all, we need to find the roots of the given equation,to plot the curve:

let us put the random numbers that may satisfy the equation:

Let us put x = 1:

From here we can say that 1 is the root of the equation.

We will now divide this function from (x-1), so that we can get the cubic equation:

We will use long division method for division, the result we get after the division is:

We will now try to factorize the cubic equations, by putting the random numbers that may satisfy the equation:

let us put x = 2:

From here we can say that f(2) is also the root of this cubic

We will now divide the cubic equation with (x-2), so we can break the cubic into quadratic:

Upon division the cubic equation break into following factors:

From here we have found out four roots of the initial function that are:

x = 1,2,6,-3

Now we can easily plot the curve:

This is estimated curve, there are no sharp edges.

On the basis of this curve, we can easily answer all the questions related to this curve.

To find the x intercept of the line we have to replace y for 0 and solve for x:

To find the y intercept of the line we have to replace x for o and solve for y:

It means that the x intercept is 0.79 and the y intercept is -0.59.

What would happen if X doesn't lie on OM? If it is true that X lies on OM, if we suppose the opposite then we should have a contradiction, so the only way the contradiction doesn't happen is that it is true

1. We know that BX:XA = 1:2

2. We know that M is the middle point between B and P

We need to prove that X lies on OM

Let's suppose X doesn't lie on OM

By 2, we know that 2BM = BP

If X doesn't lie on OM then the intersection between OM and BA is not X

Let's say the line that goes from O to the line BP and intersects BA on X is OX', where X'≠M

and solve x

the number is -6.5

Given:

The radius of the quarter circle is given 3 mm.

To find:

The perimeter of the quarter circle.

Solution:

It is known that the perimeter of the quarter circle is given by:

So, the perimeter of the quarter circle:

Thus, the perimeter of the quarter circle is 10.71 mm.

Answer:

(B)

Explanation:

The base of a right rectangular pyramid is a rectangle, so if we cut the pyramid with a plane that is parallel to the base, we will get a cross-section with a rectangular form or (A)

We can also cut the pyramid with a plane that is perpendicular to the base, In this case, we will get a cross-section with a triangular form (C)

Finally, we can cut the pyramid with a transversal plane and get a cross-section with the form of a trapezoid (D)

Therefore, the answer is (B) because a square is not a cross-section for the right rectangular pyramid.

If y varies directly as x, we have that

Then

The relationship between x and y is given as

Therefore when x= 12, y=?

Hence, the value of y when x = 12 is 168

Final answer: y = 168

Answer

ADB= 8145.16

Problem Statement

The question tells us to calculate the Average Daily Balance (ADB) for a period of December 1 - December 31 using the balances given in the table.

Method

To find the Average Daily Balance (ADB), we apply the formula given below:

The question has given us the Balance after Day 1 - Day 10 (10 days) to be 11,000. We are also given that the Balance from Day 11 to Day 20 (10 days) is 8000, from Day 21 to 30 (10 days), the Balance is 5500 while Day 31 (1 day) with a balance of 7500.

The total number of days in the billing cycle is from Day 1 to Day 31, which is 31 days altogether.

Thus we can use the above formula to find the Average Daily Balance (ADB).

Implementation

Final Answer

The Answer is:

ADB= 8145.16

The distance travelled by the two boats forms a right triangle. Thus, applying the Pythagorean Theorem we find out that the two boats are 65 kilometers apart from each other after travelling 39 kilometers north and 52 kilometers east. Thus, 1st option is correct.

It is given to us that -

There are two boats

One boat heads north while the other heads east

The boat travelling north has traveled 39 kilometers

The boat travelling south has traveled 52 kilometers

We have to find out the distance between the two boats after they have travelled the respective distances.

It is known to us that one boat heads north while the other heads east. We can see that the trajectory formed between the two boats resembles a right triangle as they start from the same point.

One leg of the right triangle formed equals to the distance travelled by the boat travelling north.

Let us say the distance travelled by the boat travelling north be "a".

=> a = 39 kilometers ----- (1)

Other leg of the right triangle formed equals to the distance travelled by the boat travelling east.

Let us say the distance travelled by the boat travelling east be "b".

=> b = 52 kilometers ------ (2)

Now, the distance between the two boats after they have travelled the respective distances is equal to the value of the hypotenuse of the right triangle formed.

Let us say the hypotenuse of the right triangle formed be "h".

According to the Pythagorean Theorem for a right triangle,

[tex]a^{2} +b^{2} =h^{2}[/tex] ---- (3)

where, a, b = legs of the right triangle

and, h = hypotenuse of the right triangle

Substituting the values of a and b from equations (1) and (2) respectively in equation (3), we have

[tex]a^{2} +b^{2} =h^{2}\\= > 39^{2} +52^{2} =h^{2}\\= > h^{2}=1521+2704\\= > h^{2}=4225\\= > h=65[/tex]

So, the value of the hypotenuse of the right triangle formed is 65 kilometers.

Thus, applying the Pythagorean Theorem we find out that the two boats are 65 kilometers apart from each other after travelling 39 kilometers north and 52 kilometers east. Thus, 1st option is correct.

To learn more about Pythagorean Theorem visit https://brainly.com/question/28361847

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Given

perimeter = 42 inches

length of a rectangle is 5 inches more than the width.

Find

width, length

Explanation

Let width of rectangle = x inches

length = 5 + x

Perimeter of rectangle = 2 (l + b) = 2(5+x+x) = 42

width = 8 inches

Length = 5 + 8 = 13 inches

Final Answer

The width of the rectangle is 8 inches.

The length of the rectangle is 13 inches.

Not, the left graph is discontinuous in x=2, the kind of discontinuity is removable discontinuity. It is not continuous because in x=2 there us a abrupt change in the function value.

To determine if the function is left or right continuous you identify if the function in a jump discontionuity has the defined point on the left or on the right.

The function given in number 11 has a jump discontinuity at x=3, as the defined point is on the part of the graph on the left, you say the function is left continuous at x=3.

Given: Ted Borrowed $1200 for two years and made monthly payments. The total finance charge is $175.92

Required: To determine the Annual Percentage Rate.

Explanation: The formula for APR is as follows-

where n is the total number of days in the loan term.

Here, the total finance charge is $175.92, and the Principal amount is $1200.

Also, n=2 years or 730 days. Substituting these values into the formula as-

Further solving as-

Final Answer: The Annual Percentage Rate is 7.29%