you are standing at the point x = 300 m, y = 400 m in a reference frame with synchronized clocks.

Answers

Answer 1

The time on clock shows at the instant you see the clock at the origin showing 3.80 μs is 5.47 × [tex]10^{-6[/tex] s.

As per the given data the values of x and y are as follows:

x = 300 m

y = 400 m

Here you are standing at the point (300, 400) in a reference frame with synchronized clocks.

Here we have to determine the time on clock shows at the instant you see the clock at the origin showing 3.80 μs.

The point where you're standing (300, 400) is 500 m from the origin.

Therefore my distance from the origin is 500 m

Speed of light , c = 3 × [tex]10^8[/tex] m/s

The clock at the origin showing, [tex]T_0[/tex] = 3.80 μs

[tex]T_0 = 3.8 \times 10^{-6}[/tex] s

Time shown by my clock , T = distance ÷ c + [tex]T_0[/tex]

T = [tex]\frac{500}{(3 \times 10^8)} + 3.8 \times 10^{-6[/tex]

T = 5.47 × [tex]10^{-6[/tex] s

Therefore the time shown by my clock is 5.47 × [tex]10^{-6[/tex] s.

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Related Questions

find the value of x in the figure?

Answers

Answer:

x = 11

Step-by-step explanation:

the sum of the 3 angles in the triangle = 180°

sum the 3 angles and equate to 180

80 + 60 + 3x + 7 = 180

147 + 3x = 180 ( subtract 147 from both sides )

3x = 33 ( divide both sides by 3 )

x = 11

Answer:

x = 11

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

60 + 80 + 3x+7 = 180

Combine like terms

3x+147=180

Subtract 147 from each side

3x+147-147=180-147

3x = 33

Divide each side by 3

3x/3 = 33/3

x = 11

[very easy] [100 pt and brainliest]
The table shows the weights of apples at a grocery store. There is a proportional relationship between the number of apples and their weight. What is the weight of TWO apples?

TYPE ONLY THE NUMBER

Answers

Answer:

2 apples = 0.24 kg

12 apples = 1.44 kg

Step-by-step explanation:

Find the weight of one apple.

If 5 apples weigh 0.60 kg, then 1 apple weighs:

[tex]\implies \sf 1\;apple=\dfrac{0.60}{5}=0.12\; kg[/tex]

Therefore:

2 applies = 2 × 0.12 - 0.24 kg12 apples = 12 × 0.12 = 1.44 kg

3-quart carton of milk costs $4.92. What is the price per cup?

Answers

Answer:

The price per cup would be 0.41 cents.

Step-by step explaination:

Answer:

$0.41

Step-by-step explanation:

To find the price per cup of milk, we first need to know how many cups are in a 3-quart carton.

1 quart is equivalent to 4 cups, so a 3-quart carton contains:

[tex]\sf 3\;quarts=3 \times 4 \;cups= 12\;cups[/tex]

Now, we can calculate the price per cup by dividing the total price by the number of cups:

[tex]\begin{aligned}\textsf{Price per cup} &= \dfrac{\textsf{Total price}}{\textsf{Number of cups}} \\\\&=\sf \dfrac{\$4.92}{12}\\\\&=\sf \$0.41\end{aligned}[/tex]

Therefore, the price per cup of milk is $0.41.

Mai is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Mai has been adding money. Suppose that x and y are related by the equation y= 550 + 40x.
Answer the questions below.
Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What is the change per week in the amount of money in the account?
What was the starting amount of money in the account?

Answers

The change per week in the amount of money in the account is 40

The starting amount of money in the account is 550.

How to illustrate the equation?

The statement that exemplifies the provided variables is called an equation. In this instance, the scenario is described by taking into account two or more factors. The definition of an equation as a mathematical statement that consists of two expressions joined by an equal sign must be understood.

In this instance, x and y are connected by the formula y=550 + 40x. In light of this, the weekly change in the account's balance is 40 dollars, while the initial balance was 550.

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Which of the following is an example of an arithmetic sequence?
a.1/2, 1/4, 1/6, 1/8, ...
b. 3, 5, 7, 9, 11, ...
c.2, 6, 18, 54, ...
d.64,32,16, 8, ...​

Answers

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a fixed number, called the common difference, to the previous term. For example, the sequence 1, 2, 3, 4, … is an arithmetic sequence because each term is obtained by adding 1 to the previous term, which is the common difference.

Out of the four given options, only the sequence 1/2, 1/4, 1/6, 1/8, … is an arithmetic sequence. The common difference of this sequence is 1/4-1/2 = -1/4, so each term is obtained by subtracting 1/4 from the previous term. The other three sequences, 3, 5, 7, 9, 11, …, 2, 6, 18, 54, …, and 64, 32, 16, 8, … are not arithmetic sequences because the difference between each consecutive pair of terms is not constant. Therefore, the correct answer is a.

20. Keith is offered an interest rate of 8.27% for a
loan with continuous compounding. Calculate
his equivalent rate with simple compounding.
[A] 0.0795 or 7.95%
[B] 0.0998 or 9.98%
[C] 0.0106 or 1.06%
[D] 0.0863 or 8.63%
[E] 0.1108 or 11.08%

Answers

To calculate Keith's equivalent rate with simple compounding, we need to use the following formula:

r = (e^(i/n) - 1) * n

where r is the equivalent rate with simple compounding, i is the interest rate with continuous compounding, and n is the number of compounding periods per year.

In this case, we are given that i = 8.27% and we can assume that the number of compounding periods per year is 12, since many loans are compounded monthly. Plugging these values into the formula, we get:

r = (e^(0.0827/12) - 1) * 12

= (1.0082 - 1) * 12

= 0.0082 * 12

= 0.0984 or 9.84%

Therefore, Keith's equivalent rate with simple compounding is [B] 0.0998 or 9.98%.

Find the value of the variable

A. 180 degree
B. 25 degree
C. 55 degree
D. 125 degree

Help!!!!!

Answers

Answer:

120°

Step-by-step explanation:

125° + ( y + 5 )° + y = 360°

or, 125° + y + 5° + y = 360°

or, 2y + 130° = 360°

or, 2y = 360° - 130°

or, 2y = 230

or, y = 230/ 2

. y = 115°

. .

. ( y + 5 )°

. . ( 115 + 5 )°

.

. . 120°

Option are wrong.

Tommy i buying ued book the price of the book are 180. He ue the 30% off tudent dicount and there i a 4 % ale tax. What i the total price

Answers

Using percentages we know that the total price of the book that Tommy will pay is $131.04.

What is the percentage?

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.

Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.

A% is a number that has neither dimensions nor a defined unit of measurement.

For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).

So, we know that the price of the book is 180.

Sales tax is 4%. So, the total price:

180/100 * 4 = 7.2$ ⇒ $187.2

Now, there is a 30% discount:

187.2/100 * 30 = $56.16

⇒ 187.2 - 56.16 = $131.04

Therefore, using percentages we know that the total price of the book that Tommy will pay is $131.04.

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Complete the square-
x^2-1/2x=8/16

thank you :)))

Answers

Answer: (x- 1/4)^2=9/16

Step-by-step explanation:

x^2 -1/2x =8/16

(x^2-1/2x +1/16)^2= 8/16+1/16)

(x- 1/4)^2=9/16

find an equation of the tangent line to the given curve at the specified point. y = e^x / x , (1, e)

Answers

y = e is the equation of the tangent line to the given curve at the specified point , y = [tex]e^{x}[/tex] / x , (1, e)

Through the coordinate geometry formal of point-slope form, the equation of tangent and normal can be calculated.

The tangent has the equation (y - y1) = m(x - x1), and a normal travelling through this point and perpendicular to the tangent has the equation (y - y1) = -1/m (x - x1).

thus , y' =  [tex]\frac{e^{x}-xe^{x} }{x^{2} }[/tex]

y'(1) = 0 = m

Our slope is indicated by the horizontal line.

y−[tex]y_{1}[/tex]=m(x−[tex]x_{1}[/tex])

Our line will simply be our y-coordinate because our slope(m) is 0:

e

Therefore:

The tangent line's equation is y=e.

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In the entence, the author want to ue alliteration. Which choice provide the bet example of thi?
Ted abolutely aced hi teaching exam

Answers

The choice that provides the best example of alliteration for the given sentence is tested terrifically on teaching. (Option C)

Alliteration is a literary device in which there is a noticeable repetition of initial consonant sounds in consecutive or nearby words in a phrase. It refers to the occurrence of the same sound or letter at the beginning of adjacent or closely connected words. Alliteration is created by repeated sound at the start of the words and not the repeated letter. For example, the phrase “kids’ coats” is alliterative, and the phrase “phony people” is not alliterative. In the given sentence, author can create alliteration by using tested terrifically in place was absolutely aced.

Note: The question is incomplete. The complete question probably is: In the sentence, the author wants to use alliteration. Which choice provides the best example of this? Ted absolutely aced his teaching exam. A) NO CHANGE B) was astounded at how well he did on C) tested terrifically on teaching.

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Resolver:
|3x − 4| = 9 - 5x

Answers

Answer:

Step-by-step explanation:

find the area of the region bounded by the given curves. y = sin2(x), y = sin3(x), 0 ≤ x ≤ π

Answers

The area of the region bounded by the given curves is 0.7123 square units

In this question we have been given two curves y = sin^2(x), y = sin^3(x), 0 ≤ x ≤ π

We need to find the area of the region bounded by the given curves.

We know that the formula for the area between two curves f and g :

A = |∫_[a to b] [f(x) - g(x)] dx|

here, a = 0, b = π, f(x) = sin^2(x) and g(x) = sin^3(x)

So, A = |∫_[0 to π] [sin^2(x) - sin^3(x)] dx|

A = |∫_[0 to π] sin^2(x) dx - ∫_[0 to π] sin^3(x) dx|

consider ∫_[0 to π] sin^2(x) dx

= ∫_[0 to π] (1 - cos(2x) / 2) dx

= π/2

Now consider ∫_[0 to π] sin^3(x) dx

= ∫_[0 to π] (1 - cos^2(x)) sin(x)  dx

= 4/3

So A = |π/2 - 4/3|

        = 3π - 8/2

        = 0.7123

Therefore, the required area: 0.7123 square units

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Given: AB = CD
Prove: AC = BD
What reason can be used to justify statement 4 in the proof above?
the reflexive property the symmetric property the transitive property the segment addition property

Answers

Step-by-step explanation:

To prove that AC = BD, we can use the symmetric property. The symmetric property states that if two quantities are equal, then their opposites are also equal.

In this case, we are given that AB = CD. Since AB and CD are opposite quantities (they are the lengths of the diagonals of a rectangle), we can use the symmetric property to conclude that AC = BD.

Therefore, the reason that can be used to justify statement 4 in the proof is the symmetric property.

question 4 while verifying cleaned data, a data analyst encounters a misspelled name. which function can they use to determine if the error is repeated throughout the dataset? 1 point case counta check count

Answers

To determine if a misspelled name is repeated throughout a dataset, a data analyst can use the COUNT function. This function counts the number of occurrences of a value in a range of cells.

Alternatively, the data analyst could use the COUNTA function, which counts the number of cells in a range that contain data (including text and numbers, but not empty or blank cells). The COUNTA function would also count the number of occurrences of the misspelled name in the dataset.

What is a dataset, using an example?

A collection of numbers or values pertaining to one subject constitutes a data set. An example of a data set might be each student's test scores for a certain class. The amount of fish that each dolphin eats in an aquarium is a data set.

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proof: fill in the reasons for the proof

Answers

∠1≅∠2 if RECT is the rectangle and M is the midpoint of EC.

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

RECT is the rectangle and M is the midpoint of EC.

we need to prove angle one is congruent to angle two.

By given,RECT is the rectangle and M is the midpoint of EC.

∠E≅∠C

In the rectangle all the angles are 90 degrees.

∠EM≅∠MC.

As M is midpoint, it has equidistant from E and C.

ER≅CT both sides are congruent.

ΔERM≅ΔCTM both are similar triangles.

RM≅TM both sides are congruent.

∠1≅∠2 by SAS postulate.

Hence, RECT is the rectangle and M is the midpoint of EC then ∠1≅∠2

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discuss the continuity of the function. f(x, y) = sin(xy) xy , xy ≠ 0 1, xy = 0

Answers

The function f(x,y) is at origin [tex]\left|\frac{\sin x y}{x y}-1\right| < \varepsilon[/tex].

We can treat this function as h=xy and then it will looks like sin h/h because if we choose any path passing through original it will always continuous so above f(x,y) is continuous

[tex]$$f(x, y)= \begin{cases}\frac{\sin x y}{x y,} & \text { if } x y \neq 0 \\ 1, & \text { if } x y=0\end{cases}$$[/tex]

Choose y=mx path y→0, x→0

[tex]$$\begin{aligned}\lim _{\substack{x \rightarrow 0 \\y=\infty}} f(x, x) & =\lim _{x \rightarrow 0} \frac{\sin m x^2}{m x^2} \\& =\lim _{x \rightarrow 0} \frac{\cos m x^2 \cdot 2 m x}{2 m x}=1\end{aligned}$$[/tex]

Now consider,

[tex]$|f(n, y)-L 1=| \frac{\sin x-1}{n y}-1 \mid < \varepsilon$[/tex]

[tex]$$$\forall \varepsilon > 0$, and $|n| < \delta,|y| < d$$$=\left|\frac{\sin x y}{x y}-1\right| < \varepsilon$$[/tex]

Hence f(x,y) is continues at origin.

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Discuss the continuity of the function:

[tex]$$f(x, y)= \begin{cases}\frac{\sin x y}{x y,} & \text { if } x y \neq 0 \\ 1, & \text { if } x y=0\end{cases}$$[/tex]

x + 2y = 5; P = (2,-5)

Answers

Answer:

....................

find the exact length of the curve. x = et − t, y = 4et/2, 0 ≤ t ≤ 4

Answers

The exact length of the curve is [tex]& \mathbf{L}=\mathbf{e}^5+\mathbf{4}[/tex].

Let the given equation is [tex]x=e^t-t, y=4 e^{\frac{t}{2}}, 0 \leq t \leq 5[/tex].

Length of Parametric Curve: A parametric curve is a function expressed in components form, such that x=f(t),y=g(t). The length of a parametric curve on the interval a ≤ t ≤ b is given by the definite integral [tex]$L=\int_a^b \sqrt{\left(\frac{d x}{d t}\right)^2+\left(\frac{d y}{d t}\right)^2} d t$[/tex]

Let’s begin by getting the first derivative of the components of the function with respect to the variable t.

[tex]$$\begin{aligned}x & =e^t-t, y=4 e^{\frac{t}{2}} \\\frac{d x}{d t} & =\frac{d}{d t}\left(e^t-t\right)=\frac{d}{d t}\left(e^t\right)-\frac{d}{d t}(t)=e^t-1 \\\frac{d y}{d t} & =\frac{d}{d t}\left(4 e^{\frac{t}{2}}\right)=\left(4 e^{\frac{t}{2}}\right) \frac{d}{d t}\left(\frac{t}{2}\right)=\left(4 e^{\frac{t}{2}}\right)\left(\frac{1}{2}\right)=2 e^{\frac{t}{2}}\end{aligned}$$[/tex]

Substitute the derivatives into the following definite integral which computes the length of the parametric curve on the interval [a,b]=[0,5].

[tex]$$\begin{aligned}L & =\int_a^b \sqrt{\left(\frac{d x}{d t}\right)^2+\left(\frac{d y}{d t}\right)^2} d t \\& =\int_0^5 \sqrt{\left(e^t-1\right)^2+\left(2 e^{\frac{t}{2}}\right)^2} d t \\& =\int_0^5 \sqrt{\left(e^{2 t}-2 e^t+1\right)+\left(4 e^t\right)} d t \\& =\int_0^5 \sqrt{\left(e^{2 t}+2 e^t+1\right)} d t \\& =\int_0^5 \sqrt{\left(e^t+1\right)^2} d t \\& =\int_0^5\left(e^t+1\right) d t\end{aligned}$$[/tex]

We need to find the value of the definite integral to get the exact length of the curve.

Take out the limits of integration and evaluate the resulting indefinite integral to solve.

[tex]$$\begin{aligned}L & =\left.\left[\int\left(e^t+1\right) d t\right]\right|_0 ^5 \\& =\left.\left[\int e^t d t+\int 1 d t\right]\right|_0 ^5 \\& =\left.\left[e^t+t\right]\right|_0 ^5\end{aligned}$$[/tex]

Evaluate the solution at the limits of integration to get the length.

[tex]$$\begin{aligned}& L=\left[e^{(5)}+(5)\right]-\left[e^{(0)}+(0)\right] \\& L=\left(e^5+5\right)-\left(e^0+0\right) \\& L=e^5+5-(1+0) \\& L=e^5+5-1 \\& \mathbf{L}=\mathbf{e}^5+\mathbf{4}\end{aligned}$$[/tex]

Therefore, the exact length of the curve is [tex]& \mathbf{L}=\mathbf{e}^5+\mathbf{4}[/tex].

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Annual salary at r rupees per month along with a Christmas bonus of Rs2000. Find the total annual salary with a festive bonus.

Answers

The total annual salary with a festive bonus is Rs (12r+2000)

What is multiplication?

In maths, multiply means the repeated addition of groups of equal sizes.

Given that, there is an annual salary at r rupees per month along with a Christmas bonus of, Rs 2000.

Here, a person is getting monthly salary  = Rs r

Therefore, his annual salary = Rs r × 12

= Rs 12r

He is also getting a bonus for Christmas = Rs 2000

So, in total, he will get =  Rs (12r+2000)

Hence, The total annual salary with a festive bonus is Rs (12r+2000)

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Suppose n represents a power of 10.
What is the value of n when 3562 is rounded to the nearest power of 10?

Answers

Answer:

We get the approximate value of [n] as 5.

What is logarithm? What is a mathematical equation and expression?

A quantity representing the power to which a fixed number (the base) must be raised to produce a given number. We can write -

$$$\log_{b}({b^x})=x$$

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions.

A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have 31,100 is rounded to the nearest power of 10 and [N] represents a power of 10.

We can write -

We can write -10ⁿ = 31100

We can write -10ⁿ = 3110010ⁿ = 311 x 10²

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5n = 4.5

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5n = 4.5n = 5 (approx.)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5n = 4.5n = 5 (approx.)Therefore, we get the approximate value of [n] as 5.

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Wanda sews small and large gloves. It takes her 45 minutes to sew a small pair of gloves and 120 minutes to sew a large pair of gloves. The costs of producing the gloves are $2 for a small pair and $4 for a large pair. Wanda has 16 hours available to sew gloves. The materials to make the gloves must cost at most $40. The system of linear inequalities represents this situation. {45x+120y≤9602x+4y≤40 What does the solution (16, 2) represent?

Answers

All you have to do is follow the attachment I have linked

a

b

c
whuch is the answer look at the picture

d

Answers

Answer:

Step-by-step explanation:

[tex]evaluate 2^{-1}(\alpha +\beta)^{2} if \alpha and \beta are the roots of the quadratic equaton x^{2}-4x+1=0[/tex]

Answers

The value of α + β  is 4. Then the value of the expression 2⁻¹ x (α + β)² will be 8.

What are the sum and product of the roots?

Let the equation be ax² + bx + c = 0 and the roots are α and β.

Then the sum of the roots will be

α + β = - b / a

And the product of the roots will be

α · β = c / a

The quadratic equation is given below.

x² - 4x + 1 = 0

The sum of the roots of the equation is given as,

α + β = - (-4) / 1

α + β = 4

Then the value of the expression will be given as,

⇒ 2⁻¹ x (α + β)²

⇒ 2⁻¹ x (4)²

⇒ 16 / 2

⇒ 8

The value of the expression 2⁻¹ x (α + β)² will be 8.

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two arithmetic sequences $a$ and $b$ both begin with $30$ and have common differences of absolute value $10$, with sequence $a$ increasing and sequence $b$ decreasing. what is the absolute value of the difference between the $51$st term of sequence $a$ and the $51$st term of sequence $b$?

Answers

The difference between  51th term of a and 51th term of b is 1000.

nth term of an arithmetic series is given by [tex]a_n = a_0 +( n-1)* d[/tex]

where [tex]a_0[/tex] is first term of arithmetic series , [tex]a_n[/tex] is nth term of the series and d is the common difference

given [tex]a_0 = b_0 = 30[/tex]

and given that both series have common difference have absolute value of 10.

common difference of series a is 10 as this series is increasing

similary common difference of series b is -10 as it is decreasing

putting the values in the above equation we get:

[tex]a_5_1[/tex]  = [tex]a_0[/tex] +(n-1)*d

=> 30 + (51-1)*10

=> 30 + 500

so [tex]a_5_1[/tex] = 530

[tex]b_5_1[/tex]  = [tex]b_0[/tex] +(n-1)*d

=> 30 + (51-1)*-10

=> 30 -500

so [tex]b_5_1[/tex] = -470

so we have to find value of [tex]a_5_1 - b_5_1[/tex] which is 530 - (-470) =530 +470 =1000

so the differnce of 51th term of a and b is 1000

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delivered.
a. What is the constant rate of​ change? What does it​ represent?
b. What is the initial​ value? What might that​ represent?

Answers

The constant rate of change and initial value for the given graph are 40 and 20 respectively. the initial value might represent the fixed cost of the soil.

What is the slope of straight line?

The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference. The negative slope indicates the rate of decrease while the positive shows the rate of increase.

The given problem can be solved as follows,

(a) The graph given is a straight line that passes through (0, 40) and (10, 240).

The constant rate of change is equivalent to the the slope of the line given as,

⇒ (240 - 40)/(10 - 0) = 20

(b) The initial value of the graph is given as the y-intercept of the line.

Which is given as 40.

It might represent the fixed cost.

Hence, the constant rate of change is given as 40 and the initial value is 20 which might represent the fixed cost.

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The missing graph is attached here.

question and ente your response in the box provided. Use the
Factor the following expression: x² + x - 6

Answers

Answer:

-3

Step-by-step explanation:

x² + x = 3

3 - 6 = -3

find the exact length of the curve. y = 4 + 6x3/2, 0 ≤ x ≤ 1

Answers

[tex]\frac{2}{243} (82^\frac{3}{2} -1)[/tex] is the required length of the curve y = 4 + 6[tex]x^\frac{3}{2}[/tex]

Given equation of curve:

y = 4 + 6[tex]x^\frac{3}{2}[/tex]

length of the curve is given by L= [tex]\int\limits^a_b {\sqrt{1+(y^')^2} } \, dx[/tex]

where [tex]y^'[/tex] is derivative of y with respect to x

so [tex]y^'[/tex] = 6*(3/2) * [tex]\sqrt{x}[/tex]

=> 9 [tex]\sqrt{x}[/tex]

given a=1 and b=0

so L= [tex]\int\limits^1_0 {\sqrt{1+(9\sqrt{x})^2 } } \, dx[/tex]

L=  [tex]\int\limits^1_0 {\sqrt{1+81x } } \, dx[/tex]

let 1+81x be t

81dx = dt

as the value of x changes after the substitution of the value.

so now the L changes as:

L= 1/81 [tex]\int\limits{\sqrt{t } } \, dt[/tex]

L=1/81* [tex]\left \{ {{t=82} \atop {t=1}} \right.[/tex]  [tex]\frac{t^\frac{3}{2} }{\frac{3}{2} }[/tex]

the min value of t=1 and max value of t=82

L=[tex]\frac{2}{243} (82^\frac{3}{2} -1)[/tex]

so the exact length of the curve is given by L=[tex]\frac{2}{243} (82^\frac{3}{2} -1)[/tex]

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5x2 to the power of 5

Answers

5x2 to the power of 5 is 160.

The perimeter of a regular pentagon is 100 centimeters. how long is each side?
a. 100 cm
b. 40 cm
c. 20 cm
d. 80 cm

Answers

The correct option c. 20 cm, is the length of each sides of the regular pentagon.

Explain the term regular pentagon?Every side of a regular pentagon has the same length, and its five angles are all the same size. A pentagon is said to as irregular if its side length as well as angle measurement are not equal.

A quadrilateral with five equal sides is known as a regular Pentagon.

Regular pentagon perimeter equals 5*side

Since we already know that a normal pentagon's perimeter is 100 cm.

Hence, 100 = 5*side

Side = 20 cm

Each side is 20 cm long.

As a result, the side of a regular pentagon is 20 cm long.

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