What is the discriminant of the quadratic equation 6x2
9x – 8 = 0?
-111
273
111
-273

To calculate the discharge through the circular channel, we can use Manning's equation, which relates the flow rate (Q) to the channel properties and flow conditions. Manning's equation is given by:

Q = (1/n) * A * R^(2/3) * S^(1/2)

where:

Q is the discharge (flow rate)

n is Manning's coefficient (0.014 in this case)

A is the cross-sectional area of the channel

R is the hydraulic radius of the channel

S is the slope of the channel bed

First, let's calculate the cross-sectional area (A) of the circular channel. The diameter of the channel is given as 6m, so the radius (r) is half of that, which is 3m. Therefore, the area can be calculated as:

A = π * r^2 = π * (3m)^2 = 9π m^2

Next, let's calculate the hydraulic radius (R) of the channel. For a circular channel, the hydraulic radius is equal to half of the diameter, which is:

R = r = 3m

Now, we can calculate the slope (S) of the channel bed. The given slope is 1 in 600, which means for every 600 units of horizontal distance, there is a 1-unit change in vertical distance. Therefore, the slope can be expressed as:

S = 1/600

Finally, we can substitute these values into Manning's equation to calculate the discharge (Q):

Q = (1/0.014) * (9π m^2) * (3m)^(2/3) * (1/600)^(1/2)

Using a calculator, the discharge can be evaluated to get the final result.

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What are the options?

A negative value indicates that more people would be attracted to Zone 3 than would be produced from it. Therefore, we cannot calculate the number of HBW trips that would be produced from Zone 3 after balancing productions and attractions.

Given the following estimates of zonal productions and attractions, it is possible to calculate the number of HBW (home-based work) trips that would be produced from Zone 3 after balancing the productions and attractions.

To balance the productions and attractions, we need to use the following formula:

Total productions - Zone 3 production = Total attractions - Zone 3 attraction

In this case, the total productions are 800 (240+400+160), and the total attractions are 600 (100+200+300). So, we can plug in the values we have:

800 - 160 = 600 - Zone 3 attraction

Simplifying this equation, we get:

Zone 3 attraction = 240

Now that we know the attraction from Zone 3 is 240, we can calculate the number of HBW trips that would be produced from Zone 3 using the formula:

HBW trips from Zone 3 = Zone 3 production - Zone 3 attraction

Plugging in the values we have:

HBW trips from Zone 3 = 160 - 240 = -80

A negative value indicates that more people would be attracted to Zone 3 than would be produced from it. Therefore, we cannot calculate the number of HBW trips that would be produced from Zone 3 after balancing productions and attractions.

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The final Exponential function is: y = 20(4)^x

To write an exponential function in the form y = ab^x that goes through two points, we need to first determine the values of a and b.

Given points (0, 20) and (2, 320), we can use the first point to determine the value of a:

y = ab^x

20 = ab^0  (when x = 0, y = 20)

20 = a(1)

a = 20

Now we can use the second point to determine the value of b:

y = ab^x

320 = 20b^2  (when x = 2, y = 320)

16 = b^2

b = 4 or -4

Since b cannot be negative in this case (as it is an exponential growth function), we can use b = 4.

Therefore, the exponential function that goes through the points (0, 20) and (2, 320) is:

y = 20(4)^x

We can check this by plugging in the x-values of the two given points:

y = 20(4)^0 = 20 (when x = 0, y = 20, as expected)

y = 20(4)^2 = 320 (when x = 2, y = 320, as expected)

So the final exponential function is: y = 20(4)^x

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The weight of the goods on the ship decreased by 50 percent.

To find the percentage decrease in the weight of goods on the ship, we need to calculate the difference between the initial weight and the final weight, divide it by the initial weight, and then multiply by 100 to get the percentage decrease.

The initial weight of the goods on the ship was 60,010 tons and the final weight after unloading was 30,005 tons.

The difference between the initial weight and the final weight is 60,010 - 30,005 = 30,005 tons.

To find the percentage decrease, we divide the difference by the initial weight:

30,005 / 60,010 = 0.5

Multiplying by 100 gives us the percentage:

0.5 x 100 = 50%

Therefore, the weight of goods on the ship has decreased by 50 percent.

In conclusion, the percentage decrease in the weight of goods on the ship is 50 percent. This means that the ship has unloaded half of its initial weight and now carries only half of the weight it carried when it left the port last week. This calculation can be helpful for the shipping company to determine the efficiency of their transportation and to plan for future shipments.

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Answer:

1031

Step-by-step explanation:

Answer:

~ 340

Step-by-step explanation:

A = pi * r^2

The big circle is r1 = 12cm so the small r2=6cm

A= A1 - A2 = (pi * r1^2)-( pi*r2^2) = 339,29 ~ 340 square cm

If the radius of the small circle is 12cm then: r1 = 24cm and r2 = 12cm and calculate it the same way

Answer:

The solutions are x = -6 or x = +2

Step-by-step explanation:

In this question, we are asked to get the series of the equation given. we can find this by equating what we have to zero

Mathematically, we proceed as follows;

(x +2)^2 -16 = 0

This can be rewritten as;

(x + 2)^2 - 4^2 = 0

we can then proceed to use the difference of two squares to finish this off

Thus, we have

(x + 2 + 4)(x + 2 - 4) = 0

(x + 6)(x-2) = 0

X + 6 = 0 or x-2 = 0

x = -6 or x = +2

Answer:

send the complete question . there are some missing signs .

Part A; Rebecca's current balance is $2500. Part B; Rebecca can save $27 by making the purchase on the last day of the billing cycle.

Part A:

Rebecca's finance charge is calculated using the following formula:

Finance charge = APR / 12 × (Average daily balance) × Number of days in billing cycle

Rebecca's APR is 24%, her average daily balance is x + $1400 / 28, and her billing cycle is 28 days. Her finance charge is $51.

Substituting these values into the formula:

$51 = (24 / 12) × ((x + $1400) / 28) × 28

Solving for x:

x = $2500

Therefore, Rebecca's current balance is $2500.

Part B:

If Rebecca makes the purchase on the first day of the billing cycle, her average daily balance will be $2500 + $1400 / 28 = $267.86.

Her finance charge will then be:

(24 / 12) × ($267.86) × 28 = $78

Therefore, Rebecca can save $78 - $51 = $27 by making the purchase on the last day of the billing cycle instead of the first day.

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The distance between successive fourth roots of the complex number √3/2 - 1/2i on the unit circle is 5π/24 units.

To find the distance between successive fourth roots of a complex number on the unit circle, we can use the concept of the angle between the roots. Let's proceed step by step:

The given complex number is √3/2 - 1/2i. This complex number lies on the unit circle because its magnitude is equal to 1.

1. Convert the given complex number to trigonometric form:

  √3/2 - 1/2i = cos(θ) + i*sin(θ)

  By comparing the real and imaginary parts, we can determine the angle θ:

  cos(θ) = √3/2

  sin(θ) = -1/2

  Using the unit circle, we can find that θ = 5π/6 (or 150 degrees). This angle represents the position of the given complex number on the unit circle.

2. Find the angle between successive fourth roots:

  Since we are interested in the fourth roots, we divide the angle θ by 4:

  θ/4 = (5π/6) / 4 = 5π/24

  This angle represents the angular distance between two successive fourth roots on the unit circle.

3. Calculate the distance between the two points:

  To find the distance, we multiply the angular distance by the radius of the unit circle (which is 1):

  Distance = (5π/24) * 1 = 5π/24

  Therefore, the distance between successive fourth roots of the complex number √3/2 - 1/2i on the unit circle is 5π/24 units.

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Answer:

A

Step-by-step explanation:

y = 9,958(0.972)x

Function which best models the given data is -150x + 9219.

A solution is an assignment of values to the unknown variables that makes the equality in the equation true.

According to the given question

y represents the number of bees.

and, x represents the number of days.

Since, we have to find the function to represent the given data.

As, we know the given data are the solution of any function, so they must satisfy the function. For this we will take any value of x and y and check whether it satisfy the given function or not.

From the given data,

Let check for the point (0, 1000).

Substitute (0, 1000) in the given function one by one.

For, y = 9,958(0.972)x

At, x = 0

We get y = 0

⇒ ( 0, 1000) is not the solution of the function 9958(0.72)x

For, y = 0.972(9,958)x

At, x = 0

we get y = 0

⇒ (0, 1000) is not the solution for the function 0.972(9958)x

For, y = 9219x - 150

At x = 0

we get y = -150

⇒ (0, 10000) is not the solution of function, 9219x -150

For, y = -150x + 9219

At x = 0

y = 9219 which is nearly equals to 10000 because y is the estimated number of bees.

⇒ (0, 10000) is the solution of the given function y = -150x + 9219 .

Hence, the function which best models the given data is -150x + 9219.

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In order to identify these mentioned terms, it is important that each of them is defined.

Diameter: It is a line that passes through the center of the circle from one endpoint to another. It is two times the radius of the circle

Radius: It is a line drawn from the center of the circle to one endpoint of the circle.

It is half of the diameter.

Chord: It is a line drawn from one endpoint of the circle to another but does not necessarily pass through the center. Diameter is an example of a chord, but a chord does not have to be a diameter

Arc: It is a segment of the circumference of a circle

Circumference: is the total distance around the circle

From the diagram above:

|AB| is a diameter

|OA| or |OB| is the radius

|CD| is the chord

Arc CD is indicated on the diagram

If a circle has a radius of 2 cm:

Diameter = 2 x radius

Diameter = 2 x 2

Diameter = 4 cm

Therefore, if a circle has a radius of 2 cm, the diameter is 4 cm

Answer:

2m - 5/4 ≤ -7/8

The given inequality can be written as 2m - 5/4 ≤ -7/8.

Inequality is of four types they are

a<b ⇒ a is less than b.

a≤b ⇒ a is less than or equal to b.

a>b ⇒ a is greater than b.

a≥b ⇒ a is greater than or equal to b.

According to the given question

An inequality -7/8 is at most the difference of twice a number m and 5/4 which is 2m - 5/4 ≤ -7/8.

Difference of twice a number 'm' and 5/4 is 2m - 5/4 and this is at most -7/8 means less than or equal to.

∴ The given statement can be written as 2m - 5/4 ≤ -7/8

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The answer is 41

Step-by-step explanation:

To solve this we must use the formula a^2+b^2=c^2. if we substitute in the values we get 9^2+40^2=c^2. The first variable is 81, then the b variable is 1600. The hypotenuse is the c value. 81+1600 is 1681, now we must find the square root of 1681. The answer is 41. Tell me if I'm wrong :)

Answer:   \(a_n=6n-2\)

Step-by-step explanation:

a₁, ____, 16, ____, a₅, _____, a₇

The difference of a₇ and a₅ is 2d (two steps to the next term).

It is given that 2d = 12  --> d = 6

We can subtract 6 from a₃ to find a₁

a₁ = 4, 10, 16, ____, a₅, _____, a₇

Input a₁ = 4, d = 6 into the explicit formula for an arithmetic equation.

\(a_n=a_1+d(n-1)\\\\a_n=4+6(n-1)\\\\a_n=4+6n-6\\\\\large\boxed{a_n=6n-2}\)

Answer:

it is b

Step-by-step explanation:

Answer:

x > 2

Step-by-step explanation:

I hope this helps

Answer:

you can pick any number less 31

some example numbers would be: \(6, 4, -18, 29\)

\(x\leq 31\\\) would be the equation for this type of problem.

Step-by-step explanation:

To explain the meaning it you need it:

"less than" is anything with a lesser value to that number and adding the "equal to" means it can be 31 or anything below it.

hope this helps :)

Answer:

Letter C: 1188

Step-by-step explanation:

$1000 plus the interest earned the first year = 1000 x 9%

Calculated like this $1000  x ( 1.09  interest) = 1090

then

that amount 1090 plus the interest earned the second year on that already compounded amount:

1090 x 9% interest =

Calculated like this 1090  x ( 1.09  interest) = 1188.1

rounding down to 1188 to match the answers

Answer:

Below.

Step-by-step explanation:

7)  c^2 = a^2 + b^2

15^2 = 11^2 + b^2

b^2 = 225 - 121 = 104

b = √104

= √4√26

= 2√26.m

8). 4^2 = a^2 + (√6)^2

a^2 = 16 - 6

a^2 = 10

a =  √10.

The following entropies are evaluated as H(X, Y ) = ∑p(x, y) log p(x, y), H(X|Y ) = ∑p(x, y) log p(x|y) = −E[ log(p(x|y)) .

We have the following joint probability distribution:

X/Y  0   1

0    1/3   1/3

1      0    1/3

The entropy of X is given by

H(X) = −p log p − (1 − p) log(1 − p) = H(p)

The entropy does not depend on the values that the random variable takes (0 and 1 in this case), but only depends on the probability distribution p(x).

The joint entropy is given by

H(X, Y ) = ∑p(x, y) log p(x, y).

The joint entropy measures how much uncertainty there is in the two random variables X and Y

taken together.

The conditional entropy of X given Y is

H(X|Y ) = ∑p(x, y) log p(x|y) = −E[ log(p(x|y))

The conditional entropy is a measure of how much uncertainty remains about the random variable

X when we know the value of Y.

For two variables, the chain rule becomes:

H(X, Y ) = H(X|Y ) + H(Y ) = = H(Y |X) + H(X).

Thus, the following entropies are evaluated as H(X, Y ) = ∑p(x, y) log p(x, y), H(X|Y ) = ∑p(x, y) log p(x|y) = −E[ log(p(x|y)) .

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The polynomial equation be x⁴ + 2x² - 63 then the factoring group exists  ( x² - 7) (x² + 9).

Factorization is the process of dividing a large number into smaller numbers that, when multiplied together, yield the original number. Factorization occurs when you divide a number into its factors or divisors.

Let the given polynomial equation be  x⁴ + 2x² - 63

By factoring the above polynomial equation, we get

Here the coefficient of the first term, x⁴, is 1.

The coefficient of the middle term, 2x², is 2.

The final term, "the constant," is -63.

To find -63 factors whose sum equals the middle term's coefficient, which is 2.

-63 + 1 = -62

-21 + 3 = -18

-9 + 7 = -2

-7 + 9 = 2

Split the middle term of the polynomial using the two factors found in step 2 above, -7 and 9 .

x⁴ - 7x² + 9x² - 63.

= ( x² - 7) (x² + 9)

∴ x⁴ + 2x² - 63 = ( x² - 7) (x² + 9) .

The polynomial equation be x⁴ + 2x² - 63 then the factoring group exists (x² - 7) (x² + 9).

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Answer:

A long history with corrected blemishes exhibits that though mistakes were made, they were corrected which allows for those viewing your credit history to know that you've learned to fix mistakes making you trustworthy and experienced.

Step-by-step explanation:

edge 2022

Answer:

C

Step-by-step explanation:

plz mark brainliest would really help

Answer:

$4956.23 approx

Step-by-step explanation:

Given data

P= $4860

R= 4%

T= 6 months = 0.5 years

Applying the compound interest formula we have

A=P(1+r)^t

Substitute

A=4860(1+0.04)^0.5

A= 4860(1.04)^0.5

A=4860*1.0198

A=4956.228

Hence the balance will be $4956.23 approx

Answer:

y=x doesent that mean 2=3 so what you do is the line that goes up thats y and the one that goes sideways thats x so at the to go to 2 then at the side go to 3

Answer:

Step-by-step explanation:

y=x doesent that mean 2=3