It took 5 hours to drive to Durham to Birmingham. The average speed was 48mph. What was the distance from Durham to Birmingham?

I need the explanation

Answer:

A

Step-by-step explanation:

To reparametrize the curve with respect to arc length, we need to find the arc length function s(t) and then solve for t in terms of s.

The arc length function is given by:

s(t) = ∫√[r'(t)·r'(t)] dt

where r'(t) is the derivative of r(t) with respect to t.

We can calculate r'(t) as:

r'(t) = (2e^(2t)cos(2t) - 4e^(2t)sin(2t))i + (12e^(2t)sin(2t))j + (2e^(2t)sin(2t) + 6e^(2t)cos(2t))k

Now we can substitute this into the arc length formula and integrate:

s(t) = ∫√[(2e^(2t)cos(2t) - 4e^(2t)sin(2t))^2 + (12e^(2t)sin(2t))^2 + (2e^(2t)sin(2t) + 6e^(2t)cos(2t))^2] dt

This integral looks quite complicated, so we will use a numerical integration method to approximate s(t).

We can use the trapezoidal rule to numerically integrate s(t) between t = 0 and some value t = T:

s(T) ≈ ∑[s(iΔt) + s((i+1)Δt)]/2 * Δt

where Δt = T/n is the step size, and n is the number of intervals we use.

Once we have approximated s(t), we can solve for t in terms of s using numerical methods such as the bisection method or Newton's method.

For example, if we want to find the value of t that corresponds to s = 10, we can solve:

s(t) = 10

for t using numerical methods. Once we have t, we can plug it back into r(t) to get the reparametrized curve in terms of arc length s.

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Answer:

what do you want the slope? The y cordinate is where the points are on the y axis.

Step-by-step explanation:

Answer:

$22,883

Step-by-step explanation:

Principal Amount ( P ) = $16250

Interest Rate ( r ) = 4.9% or 0.049( divide by 100)

Term ( t ) = 7

Compounded monthly( n ) = 12

Formula for Compound Interest:

A = P ( 1 + r/n)^nt

A = Future value

Solution:

Substitute the given values of P, r, n and t to the formula for the compound interest.

A = $16250 ( 1 + 0.049/12)^(7)(12)

A = $16250 ( 1.004083333)^(84)

A = $16250 ( 1.408184955 )

A = $22,883

Answer:

11

Step-by-step explanation:

3x + 4y - 7z + 11

The constant term is the term that has no variables ( letters)

11 is the constant term

Step-by-step explanation:

In order to rotate a coordinate point by 90° in the counterclockwise direction, follow the following transformation rule:

(x, y) ---> (-y, x)

Here is the list of the coordinates of the points on the fan blade and next to it is a list of points that are rotated by 90° in the counterclockwise direction:

Normal. Rotated

(x, y) (-y, x)

(3, 1) (-1, 3)

(5, 2) (-2, 5)

(8, 4) (-4, 8)

(9, 6) (-6, 9)

(8, 8) (-8, 8)

(6, 9) (-9, 6)

(4, 8) (-8, 4)

(2, 5) (-5, 2)

(1, 3) (-3, 1)

Simply repeat the pattern for the other two blades.

Answer:

positive

Step-by-step explanation:

because that's how math works

Answer:

5.3 inches

Step-by-step explanation:

The diagonal of a rectangle frame is 8 inches and the width of the frame is 6 inches. What is the length of this frame in inches?

Diagonal² = Length² + Width²

Length = √Diagonal² - Width

= √8² - 6²

= √64 - 36

= √(28)

Length = 5.2915026221 inches

Approximately = 5.3 Inches

Answer: ima try

Step-by-step explanation: how i always do it is the second number (-2) you start for the mid point (0,0) if its -2 go down 2 if it 2 go up 2 if its 0 stay there then you go to the first number(2/3) from where you landed thats now the new start point then you go (x,y) in this equation its (2/3) so go up 2 right three but watch out for the negatives. so if it was -2/3 you would go down 2 then right 3

i hoped this helped its hard to explain but I tried

The weighted mean for student 7 would be 398/5 = 79.6. To find the weighted mean of student 7's exam scores when exam 1 is weighted twice that of the other 3 exams, we first need to apply the weights to each exam score. We can do this by multiplying the exam 1 scores by 2, and leaving the other three exam scores as they are.

Once we have the weighted scores, we can calculate the weighted mean for student 7 by adding up their four scores (adjusted according to the weights) and dividing by the sum of the weights.

Specifically, for student 7, their adjusted scores would be: exam 1 = 82 x 2 = 164, exam 2 = 71, exam 3 = 78, exam 4 = 85.

Adding these together, we get a total of 398. The sum of the weights would be 2 + 1 + 1 + 1 = 5 (since exam 1 is weighted twice as much).

Therefore, the weighted mean for student 7 would be 398/5 = 79.6.

In summary, to calculate the weighted mean of student 7's exam scores when exam 1 is weighted twice that of the other 3 exams, we need to adjust each exam score according to the weights, add up the adjusted scores for student 7, and divide by the sum of the weights.

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The acceleration of the car with the given data would be [8.57] m/s². If the applied force were cut in half, I predict the acceleration would be [4.285] m/s².

Acceleration is calculated using the formula a = (v₂ - v₁) / (t₂ - t₁), where v₁ and v₂ are the initial and final velocities respectively, and t₁ and t₂ are the corresponding times. In the given table, the initial velocity is 0.13 m/s, the final velocity is 0.36 m/s, the time to travel 0.25 meters is 1.92 seconds, and the time to travel 0.5 meters is 2.61 seconds. By substituting these values into the acceleration formula, we find that the acceleration is approximately 8.57 m/s².

If the applied force is cut in half, it would result in a reduced net force acting on the car. According to Newton's second law of motion, F = ma, where F is the net force, m is the mass of the object, and a is the acceleration. If the force is halved while the mass remains constant, the resulting acceleration will also be halved. Therefore, I predict that the acceleration would be approximately 4.285 m/s² when the applied force is reduced by half.

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The distance from point A to point B rounded to the nearest foot is; 887 ft

The vertical change is 126 feet.

At point A, the angle is 6º, while the horizontal position is of a. Thus;

tan 6 = 126/a

a = 126/(tan 6)

a = 1198.8 ft

At point B, the angle is of 22º, while the horizontal position is b. Thus;

b = 126/tan 22

b = 311.9 ft

Thus;

Distance from point A to point B is;

a - b = 1198.8 - 311.9

⇒ 887 ft

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Answer:

I'm not sure of the answer

If you have a required return of 6% per year, compounded monthly, and you are offered an investment that will pay you $800 a month for 40 years, you would be willing to pay approximately $206,595.71 for this investment.

To determine the value you would be willing to pay for this investment, we can use the concept of present value. The present value of an investment is the current worth of the future cash flows it will generate. In this case, the investment will pay you $800 a month for 40 years.

To calculate the present value, we can use the formula:

\(PV = CF / (1 + r)^n\)

Where PV is the present value, CF is the cash flow, r is the required return per period, and n is the number of periods.

In this case, the cash flow is $800 per month, the required return is 6% per year (or 0.06/12 = 0.005 per month), and the number of periods is 40 years * 12 months = 480 months.

Plugging these values into the formula, we have:

PV = $800 / \((1 + 0.005)^(480)\)

Calculating this expression, we find that the present value is approximately $206,595.71. Therefore, you would be willing to pay approximately $206,595.71 for this investment to achieve your required return of 6% per year, compounded monthly.

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The reason why x ≥ 0 and y ≥ 0 is simply because the number of DVDs and the number of CDs cannot not be less than zero and the shop cannot have zero products.

A graph which shows the region that satisfies all three inequalities is shown below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of DVDs and the number of CDs, and then translate the word problem into an algebraic equation (linear inequalities) as follows:

Since the cost of a DVD is $10 and the cost of a CD is $8 and Andrew goes into the shop with $40 to spend, a system of linear inequalities that models the situation and constraints is given by;

x ≥ 0

y ≥ 0

10x + 8y ≤ 40

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Answer:

17.5%

Step-by-step explanation:

Subtract one value from the other. (i does not matter the sign)  

 400 − 330 = 70, so his error is 70

Now  find the Percentage Error:

Divide by the exact value and make it a percentage:

70/400 = 0.175 = 17.5%

The equation of the ellipse is: \((x^2/27) + (y^2/36) = 1\)

What is equation?

An equation is a statement in mathematics asserting that two expressions have the same value. It consists of different mathematical operations like addition, subtraction, multiplication, and division, as well as constants and variables.

The equation for an ellipse with vertical major axis and center at the origin is given by:

\((x^2/b^2) + (y^2/a^2) = 1\)

where a is the length of the semi-major axis and b is the length of the semi-minor axis.

For an ellipse with eccentricity e, we have:

\(e = sqrt(1 - (b^2/a^2))\)

In this case, the foci are at (0, +3) and (0, -3), which means that the distance between the foci is:

2c = 6

And since the eccentricity is 1/2, we have:

e = 1/2 = c/a

Solving for c, we get:

c = a/2

Substituting this into the equation for the distance between the foci, we get:

2c = 6

2(a/2) = 6

a = 6

Now we can find b using the equation for eccentricity:

\(e = \sqrt{(1 - (b^2/a^2))}\\\\1/2 = \sqrt{(1 - (b^2/36))}\\\\1/4 = 1 - (b^2/36)\\\\b^2/36 = 3/4\\\\b^2 = 27\\\\b = \sqrt{(27)}\)

Therefore, the equation of the ellipse is:

\((x^2/27) + (y^2/36) = 1\)

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To determine which differential equation(s) are linear, we need to examine the form of each equation. A linear differential equation is one that can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x), b(x), c(x), and g(x) are functions of x.

The differential equation 2xy" - 5xy' + y = sin(3x) is linear. It can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x) = 2x, b(x) = -5x, c(x) = 1, and g(x) = sin(3x).
The differential equation (v)² + xy = In(x) is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (v)², where v represents the derivative of y with respect to x. This term does not have a linear coefficient.
The differential equation y' + sin(y) = e^(3x) is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = sin(y), and g(x) = e^(3x).
The differential equation (x²+1)y" - 3y - 2x³y = -x - 9 is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (x²+1)y", where the coefficient is a function of x.
The differential equation y' + xy = y" is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = x, and g(x) = y".

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Given :

Two pyramid with same volume .

To Find :

If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B .

Solution :

\(V_a=V_b\)

Volume of pyramid is given by :

\(V=\dfrac{\text{Area of base}\times height}{3}\\\\V=\dfrac{Ah}{3}\)

Now , h'=3h

\(V'_b=\dfrac{Ah'}{3}\\\\V'_b=3\dfrac{Ah}{3}\\\\V'_b=3V_a\)

Therefore , new volume of pyramid B is 3 times the value of pyramid A .

Hence , this is the required solution .

Answer:

Total area of the fabric = 66 in.²

Step-by-step explanation:

The diagram of the stretched fabric shown takes the shape of a kite having two diagonals that intersect each other.

Total area of the fabric = area of the kite = ½(product of the two diagonals)

= ½(AC × BD)

We need to find AC and BD

BE = DE = 6 in. (Equal lengths)

BD = BE + DE

BD = 6 + 6 = 12 in.

AC = AE + CE

Apply Pythagorean theorem to find AE and CE

✔️AE = √(AB² - BE²) = √((√45)² - 6²) = √(45 - 36) = √9 = 3 in.

✔️CE = √(CD² - DE²) = √(10² - 6²) = √(100 - 36) = √64 = 8 in.

FIND AC:

✔️AC = AE + CE

AC = 3 + 8

AC = 11 in.

FIND the total area of the fabric:

✔️Total area = ½(AC × BD) = ½(11 × 12)

= ½(132)

= 66 in.²

Kevin is correct. He needs to know how much of his college expenses will be covered so he knows how much he should save.

Kevin is correct. By filling out the FAFSA and sending it in, he will not have to pay anything because grants and scholarships will cover the costs.

Kevin is incorrect." Beacause It is never too early to start saving for college. Even if he earns scholarships, he could use the money for other expenses.

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Answer:

y = 1/5x + 5

Step-by-step explanation:

If you plot (5,6) on a graph, and count down 1 point, and over to the left 5 points, you will get to the y-axis. Then, the point that is on the y-axis is the y-intercept. That is 5. The 5 goes at the end of the equation.

Answer: max has a tail

Step-by-step explanation:

if all cats have tails and max is a cat then he has a tail

The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;

A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;

Solving the above inequality, we have;

2•x + 3 ≤ -3

2•x ≤ -3 - 3 = -6

2•x ≤ -6

Therefore;

x ≤ -6 ÷ 2 = -3

x ≤ -3

Which gives;

-∞ < x ≤ -3 in interval notation is (-∞, -3]

The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;

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1° and 14° are acute angles.  

An acute angle is one that is less than 90°, or one that is between 0° and 90°.  

The opposite of an acute angle is an obtuse angle. In other terms, an obtuse angle is one that is larger than 90° and less than 180°. It is the angle that is between 90° and 180°.

90° is the standard for a right angle. Any angle that is less than 90° is called acute, and any angle that is larger than 90° is called obtuse.

∠1 and ∠14 are less than 90° therefore, they are acute angles.

Correct question :

What type of angle are 1° and 14°?

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Luiza route after plotting the points on cartesian planes it cover 16 miles.

A coordinate plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis.

The first thing to do in this case is to draw the ordered pairs in the Cartesian plane and join the points.

We have then that the resulting figure is a rectangle.

We must find the perimeter of the rectangle that is given by:

P = 2L + 2W

Where,

L: length

W: width

Restoring the values:

P = 2 * (5) + 2 * (3)

P = 16

So therefore her route cover 16 miles.

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