Write the linear equation that gives the rule for this table. x f(x) 1 22 2 23 3 24 4 25 Write your answer as an equation with f(x) first, followed by an equals sign.

Temperature change for water due to sheer drop is approximately 0.7 °C when Multnomah Falls in the Columbia River has a sheer drop of 543 ft.

Given that,

Multnomah Falls in the Columbia River Gorge has a sheer drop of 543 feet.

We have to find estimate the water temperature change in °F caused by this drop using the steady flow energy equation.

We know that,

Sheer drop is z₁ - z₂ = 543 feet

We required to calculate temperature change that is ∆T caused by this drop using steady flow energy equation says SFEE.

Assuming

Adiabatic flow i.e. Q =0

No work done, i.e. W=0

Neglecting kinetic energies.

Steady flow energy equation is a mathematical expression that states that for a steady flow the net energy at the inlet of control volume is equal to the net energy at the exit of of the control volume.

SFEE is given as,

h₁ + \(\frac{(v_1)^2}{2}\) + gz₁ + Q = h₂ + \(\frac{(v_2)^2}{2}\) + gz₂ + Q -------> equation(1)

Where, h₁ and h₂ enthalpies at inlet and exit of control volume,

v₁ and v₂ are velocities at inlet and exit of control volume (kinetic energies),

z₁ and z₂ are elevation at inlet and exit of control volume (potential energies),  

Q is energy flow into the control volume and

W is work done by control volume.

Neglecting change in kinetic energies ; Q=0; W=0

Then equation (1) will be,

h₁ - h₂ = g(z₂ - z₁)

Cp(ΔT) =  g(z₂ - z₁)

ΔT = \(\frac{g(z_2-z_1)}{Cp}\)

Here,

Value of g is 32.2 feet per second square and value of Cp for water is 25100 feet

Substituting all values we get,

ΔT = \(\frac{32.2(543)}{25000}\)

ΔT = 0.69°C

ΔT = 0.7°C (approximately)

Therefore, Temperature change for water due to sheer drop is approximately 0.7 °C.

To know more about temperature visit:

https://brainly.com/question/32983996

#SPJ4

Answer:

x = 300 minutes

Step-by-step explanation:

20 + .15x = 35 + .10x

.05x = 15

Answer: 5, | 4 |, | -1 |, -2

Answer:

0, l-1l, l-2l, l4l, 5

Step-by-step explanation:

The absolute value bars l l, turn any negative number positive and any positive number remains positive.

The correct option is C. 0.541, The constant of integration K can be found by setting x = 0 and g(x) = 0. This gives us K = 0.

We can use the following steps to solve this problem:

Here is a more detailed explanation of each step:

We can then use the following steps to solve the integral:

We can now solve this integral using integration by parts. Let u = u and v' = e^-u cos(u). Then du = du and v = -e^-u sin(u).

This gives us g(x) = C [-e^-u sin(u)] + ∫ e^-u sin(u) du.

The integral ∫ e^-u sin(u) du can be solved using integration by parts again. Let u = sin(u) and v' = e^-u. Then du = cos(u) du and v = -e^-u.

This gives us g(x) = C [-e^-u sin(u)] - e^-u cos(u) + ∫ e^-u cos(u) du.

The integral ∫ e^-u cos(u) du can be solved using integration by parts again. Let u = cos(u) and v' = e^-u. Then du = -sin(u) du and v = -e^-u sin(u).

This gives us g(x) = C [-e^-u sin(u)] - e^-u cos(u) + e^-u sin(u) + K.

The constant of integration K can be found by setting x = 0 and g(x) = 0. This gives us K = 0.

This gives us the final solution for g(x): g(x) = -e^-u sin(u) - e^-u cos(u).

Evaluating g(4). We know that g(4) = 0.325. We can use this value to find the constant of integration in the solution to the differential equation.

To do this, we can set x = 4 and g(x) = 0.325 in the solution to the differential equation. This gives us -e^-4 sin(4/100) - e^-4 cos(4/100) = 0.325.

We can solve this equation for the constant of integration K. This gives us K = 0.325 + e^-4 sin(4/100) + e^-4 cos(4/100).

Evaluating g(1). We can now evaluate g(1) using the value of the constant of integration and the solution to the differential equation.

To do this, we can set x = 1 and g(x) = 0.541 in the solution to the differential.

To know more about variable click here

brainly.com/question/2466865

#SPJ11

Answer:

Natural

Step-by-step explanation:

To use long division in polynomials, we follow steps similar to normal long division, but we look for the terms from higher degree to lower.

We are dividing:

By:

We want to multiply the divisor by some expression that will make the higher term equal to the higher term of the dividend. The higher term of the dividend is 4x³, to get to that, we can multiply the divisor by 2x²:

Now we have the same term, so we just substract what we have got from the dividend:

Notice that we don't have a third degree term anymore.

So, until now we have done:

- Multiplied the divisor by 2x²

- Got a remainder of -5x² + 3

Now, we just repeat with the remainder.

We want to multiply 2x - 1 so that the higher term is -5x², so we can multiply by -5x/2:

And we do the substraction:

So, now we have got:

- Multiplied the divisor by 2x² and then by -5x/2

- Got a remainder of -5x/2 + 3

Now, we repeat once more:

To get -5x/2, we multiply the divisor by -5/4:

And we substract from the remainder:

So, we have done:

- Multiplied the divisor by 2x² then -5x/2 then -5/4

- Got a remainder of 7/4

This means that th result of the division is:

And the remainder is:

But, the answer wants us to write what the dividend is equal to.

Let's write first in the division form:

Notice that we result is the quotient plus the remainder divided by the divisor.

If we multiply both sides by the divisor, we will get:

That is the answer.

Answer:

LM = 8 cm

Step-by-step explanation:

LM = KN = x + 7

NM = KL = x + 7 + NQ = x + 7 + 2 = x + 9

KN×NM = 80

(x+7)(x+9) = 80

x² + 7x + 9x + 63 = 80

x² + 16x + 63 = 80

x² + 16x - 17 = 0

solution of a quadratic equation

x = (-b ± sqrt(b² - 4ac))/(2a)

a=1

b=16

c=-17

(-16 ± sqrt(256 + 4×17))/2 = (-16 ± sqrt(256+68))/2 =

= (-16 ± sqrt(324))/2 = (-16 ± 18)/2

x1 = (-16 + 18)/2 = 2/2 = 1

x2 = (-16 - 18)/2 = -34/2 = -17

x2 as negative value is no valid solution for a side length.

so, only x1 remand as solution.

=> x=1, LM = KN = 1+7 = 8, NM = KL = 1+9 = 10

The answer is 231 inches.

To understand how we arrive at this answer, let's break down the given measurement step by step. We have 6 yards, 3 feet, and 7 inches.

Starting with yards, we know that 1 yard is equal to 3 feet, so 6 yards would be equivalent to 6 * 3 = 18 feet. Adding the 3 feet given, we have a total of 18 + 3 = 21 feet.

Moving on to inches, we know that 1 foot is equal to 12 inches. So, the 21 feet we calculated earlier would be equal to 21 * 12 = 252 inches. Finally, adding the 7 inches given, we get a total of 252 + 7 = 259 inches.

Therefore, 6 yards 3 feet 7 inches is equal to 259 inches.

To learn more about measurement click here:

brainly.com/question/2107310

#SPJ11

Answer:

1.5 hours

Step-by-step explanation:

Answer:

answer is D

The difference of the two means is not significant, so the null hypothesis must be accepted.

Answer:

.

Step-by-step explanation:

the interval of time between when a vector takes an infectious meal, and when it begins to transmit the pathogen, is referred to as the extrinsic incubation period.

The incubation period refers to the duration of time between the invasion by an infectious pathogen and the start (first appearance) of symptoms of the disease in question. The host enters the symptomatic phase after the incubation period is over. Additionally, after infection, the host develops the ability to spread infections to other people, or they become infectious or communicable. The host person may or may not be contagious throughout the incubation phase, depending on the disease. The dynamics of disease transmission depend on the incubation period since it establishes the timing of case detection in relation to infection. This aids in assessing the success of symptomatic surveillance-based control methods.

the interval of time between when a vector takes an infectious meal, and when it begins to transmit the pathogen, is referred to as the extrinsic incubation period.

The complete question is-

The interval of time between when a vector takes an infectious meal, and when it begins to transmit the pathogen, is referred to as the: (a) vectorial capacity; (b) intrinsic incubation period; (c) vectorial competence; (d) extrinsic incubation period.

learn more about the incubation period,

https://brainly.com/question/28830992

#SPJ4

Compound interest can be defined as the interest on a deposited amount, an investment that is compounded based on its principal and interest rate.

It will take about 3.239 years for the principal amount of $13,000 to double its initial value.

From the above question, we can deduce that we are to find the time "t"

The formula to find the time "t" in compound interest is given as:

t = ln(A/P) / r

where:

P = Principal = $13,000

R = Interest rate = 21.4%

A = Accumulated or final amount

From the question, the Amount "A" is said to be the double of the principla.

Hence,

A = $13,000 x 2

= $26,000

r = R/100

r = 21.4/100

r = 0.214 per year.

t = ln(A/P) / r

t = ln(26,000.00/13,000.00) / 0.214

t = 3.239 years

Therefore, it will take about 3.239 years for the principal amount of $13,000 to double its initial value.

To learn more, visit the link below:

https://brainly.com/question/22471957

Answer:

(9, -6)

Step-by-step explanation:

When rotating 270° counterclockwise about the origin,

\((x,y) \longrightarrow (y,-x)\)

The new cost after the discount and tax are applied is $872.10, which is option (d).

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

First, let's calculate the amount of discount Angel will receive using the coupon code:

Discount = 15% of $950 = 0.15 x $950 = $142.50

Next, let's calculate the new price of the jacket after the discount is applied:

New price = $950 - $142.50 = $807.50

Now, let's calculate the amount of tax that will be applied to the new price:

Tax = 8% of $807.50 = 0.08 x $807.50 = $64.60

Finally, let's add the tax to the new price to get the total cost:

Total cost = $807.50 + $64.60 = $872.10

Therefore, the new cost after the discount and tax are applied is $872.10, which is option (d).

To learn more about  discount from the given link:

https://brainly.com/question/31430480

#SPJ1

Answer:

-17/9

Step-by-step explanation:

You need to add 7 to both sides.

-9x - 7 = 10

-9x -7 + (7) = 10 + 7

-9x             = 17

Then both sides for (-9)

-9x/(-9) = 17/(-9)

          x = -17/9

Answer:

~50 bottles

Step-by-step explanation:

hope this helps

Answer:93

Step-by-step explanation:

To reach your fundraising goal of $75, you will need to sell 150 pencils for $0.50 each and 0 bracelets for $1.00 each.

To reach your fundraising goal of $75, you can sell pencils for $0.50 and bracelets for $1.00.

1. Calculate the total amount of money needed to reach the goal:
  Goal amount = $75

2. Determine the number of pencils and bracelets you need to sell to reach the goal:
  Let's assume you sell x number of pencils and y number of bracelets.

  The amount raised from selling pencils = x * $0.50
  The amount raised from selling bracelets = y * $1.00

  The total amount raised from both items should be equal to the goal amount:
  x * $0.50 + y * $1.00 = $75

3. Simplify the equation:
  0.50x + 1.00y = 75

4. Solve for one variable in terms of the other:
  Let's solve for x in terms of y:
  0.50x = 75 - 1.00y
  x = (75 - 1.00y) / 0.50

5. Substitute the value of x into the equation:
  (75 - 1.00y) / 0.50 * 0.50 + y * $1.00 = $75
  75 - 2y + y = 75
  -y = 0
  y = 0

6. Find the value of x:
  x = (75 - 1.00 * 0) / 0.50
  x = 75 / 0.50
  x = 150

To reach your fundraising goal of $75, you will need to sell 150 pencils for $0.50 each and 0 bracelets for $1.00 each.

To know more about fundraising goal visit:

https://brainly.com/question/28324495

#SPJ11

The argument is valid. The argument is valid based on the direct truth-table method.

To test the validity of the argument, we can use the direct truth-table method. Let's break down the argument and construct the truth table for the given premises and the conclusion:

Premises:

G ⊃ H

R ≡ G

~H v G

Conclusion:

R • H

Constructing the truth table:

We have three propositions: G, H, and R. Each proposition can have two truth values, true (T) or false (F). Therefore, we need 2^3 (8) rows in the truth table to evaluate all possible combinations.

By evaluating the truth table, we find that in all rows where the premises (1, 2, 3) are true, the conclusion (R • H) is also true. There is no row where the premises are true, but the conclusion is false. Therefore, the argument is valid.

The argument is valid based on the direct truth-table method. This means that if the premises (G ⊃ H, R ≡ G, ~H v G) are true, then the conclusion (R • H) must also be true.

To know  more about argument visit:

https://brainly.com/question/30148759

#SPJ11

the length of side OP of rhombus is 45 mm and PM + MN is equal to 90 mm.

We are given a rhombus MNOP

We know that, a rhombus is a quadrilateral in which there are 4 sides and all the sides are equal.

We are given the length of the side NO as:

NO = 45 mm

Now, we need to find the length of side OP.

OP = 45 mm ( as NO = OP)

Also, we need to find PM + MN

PM + MN = NO + NO ( as PM = MN = NO )

= 2 NO

= 2 × 45 mm

= 90 mm

Therefore, we get that, the length of side OP of rhombus is 45 mm and PM + MN is equal to 90 mm.

Learn more about rhombus here:

https://brainly.com/question/20627264

#SPJ9

a. The correct statement regarding the classification of the functions as exponential and linear is given as follows:

The total number of views for Video 1 are exponential because they grow by equal factors over equal intervals.

b. The average rate of change of the total number of views for Video 2 between July 12 and July 14 is of: 45,000 views a day.

The functions are classified depending if there is an equal factor or an equal difference between consecutive terms, as follows:

Hence the functions are classified as follows:

The average rate of change is given by the change in the output divided by the change in the input, hence it is of:

r = (190000 - 100000)/2 = 45,000 views a day.

More can be learned about exponential and linear functions at brainly.com/question/26095866

#SPJ1

Answer:

Let the number be x

so, x/4 = x-3

x = 4(x-3)

x= 4x-12

x-4x = -12

-3x = -12

x= 12/3

x = 4

Step-by-step explanation:

Hope this helps! (:

The derivative dy/dx of the equation ysin(x^2) = xsin(y^2) is given by (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).

In the given equation, y and x are both variables, and y is implicitly defined as a function of x. To find dy/dx, we differentiate each term using the chain rule and product rule as necessary.

Differentiating the left-hand side of the equation, we apply the product rule to ysin(x^2). The derivative of ysin(x^2) with respect to x is dy/dxsin(x^2) + ycos(x^2)*2x.

Differentiating the right-hand side of the equation, we apply the product rule to xsin(y^2). The derivative of xsin(y^2) with respect to x is sin(y^2) + x*cos(y^2)2ydy/dx.

Now we have two expression for the derivative of the left and right sides of the equation. To isolate dy/dx, we can rearrange the terms and solve for it.

Taking the derivative of ysin(x^2) = xsin(y^2) with respect to x using implicit differentiation yields:
dy/dxsin(x^2) + ycos(x^2)2x = sin(y^2) + xcos(y^2)2ydy/dx.

By rearranging the terms, we can solve for dy/dx:
dy/dx * (sin(x^2) - 2yxcos(y^2)) = sin(y^2) - y*cos(x^2)*2x.

Finally, we can obtain the value of dy/dx by dividing both sides by (sin(x^2) - 2yxcos(y^2)):
dy/dx = (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).

Learn more about implicit differentiation here brainly.com/question/31568657
#SPJ11

Answer:

119 is the value of x when y = 7

Step-by-step explanation:

Since y varies inversely with x, we can use the following equation to model this:

y = k/x, where

Step 1:  Find k by plugging in values:

Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality.  We can find k by plugging in 49 for y and 17 for x:

Plugging in the values in the inverse variation equation gives us:

49 = k/17

Solve for k by multiplying both sides by 17:

(49 = k / 17) * 17

833 = k

Thus, the constant of proportionality (k) is 833.

Step 2:  Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:

Plugging in the values in the inverse variation gives us:

7 = 833/x

Multiplying both sides by x gives us:

(7 = 833/x) * x

7x = 833

Dividing both sides by 7 gives us:

(7x = 833) / 7

x = 119

Thus, 119 is the value of x when y = 7.

Explanation

In the question, we are given that the millet seeds and the sunflowers seed are packaged in 5 pounds back.

We can assume that the pounds of millet seeds be x and the pounds of sunflower seeds be y. We can therefore create the equation;

Next, we know that a pound of sunflower seed cost $1.75 and a pound of millet seed cost $2.50 and the mixture is sold for $11.60. This will imply;

We will then solve the above equation simultaneously.

Insert equation 3 in equation 2

Since the weight of the sunflower seed is represented by y, therefore the answer is;

Answer: 1.2 pounds

Answer:

The shape has 8 vertices

Step-by-step explanation:

You would be able to solve this by counting the points of the shape.

Hope this helps :)

Answer:

No she is not correct

Step-by-step explanation:

Because when you add 1.25+0.45+2.50=4.14

not 4.2

No, every 2-approximation algorithm for finding a minimum vertex cover is not necessarily a 2-approximation algorithm for finding a maximum independent set.

The reason for this is that the two problems, minimum vertex cover and maximum independent set, are not symmetric in their definitions and objectives.

In the minimum vertex cover problem, the goal is to find the smallest possible set of vertices that covers all edges in the graph. On the other hand, in the maximum independent set problem, the objective is to find the largest possible set of vertices such that no two vertices in the set are adjacent.

An approximation algorithm for the minimum vertex cover problem guarantees that the size of the vertex cover found by the algorithm is at most twice the size of the optimal minimum vertex cover. This means that the algorithm provides a solution that is within a factor of 2 of the optimal solution.

However, this does not imply that the same algorithm will provide a solution within a factor of 2 of the optimal maximum independent set. The reason is that the concepts of vertex cover and independent set are complementary. A vertex cover is a set of vertices that covers all edges, whereas an independent set is a set of vertices with no adjacent vertices.

Therefore, while a 2-approximation algorithm for minimum vertex cover guarantees that the size of the vertex cover is at most twice the size of the optimal solution, it does not necessarily imply that the algorithm will find a maximum independent set with a size within a factor of 2 of the optimal solution.

For more such questions on algorithm visit:

https://brainly.com/question/30453328

#SPJ8