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To evaluate the line integral, calculate the arclength element and substitute it into the integral. Expand the expression inside the square root, multiply it by (2x+9z), and integrate term by term.

To evaluate the line integral of (2x+9z) ds where the curve is given by the parametric equations x=t, y=t^2, z=t^3 for t between 0 and 1, we need to find the arclength element ds and substitute it into the integral. The arclength element ds can be calculated using the formula ds = sqrt(dx^2 + dy^2 + dz^2). In this case, dx = dt, dy = 2t dt, and dz = 3t^2 dt. Substituting these values into the arclength element formula, we get ds = sqrt(dt^2 + 4t^2 dt^2 + 9t^4 dt^2) = sqrt(1 + 4t^2 + 9t^4) dt.

Substituting ds into the line integral, we get the integral of (2x+9z) * sqrt(1 + 4t^2 + 9t^4) dt. To evaluate this integral, you can expand the expression inside the square root, multiply it by (2x+9z), and integrate term by term.

However, it seems that there might be a typo in the original question regarding the curve parametrization. The curve given by x=t, y=t^2, z=t^3 is actually a parabolic curve, not a line. If you need further clarification or assistance, please let me know.

A piecewise equation to model the total weekly pay for an engineering technician who earns different rates for hours within and beyond 40 hours is P(h) = {25h if h ≤ 40, 1000 + 32(h - 40) if h > 40}.

The question asks for a piecewise equation to model the total weekly pay of an engineering technician who makes $25 per hour for the first 40 hours and $32 an hour for each hour over 40 hours. The piecewise function is made up of two parts:

When written as a piecewise function, it will look something like this:

P(h) =
 \{
 \begin{array}{ll}
 25h & \text{if } h ≤ 40,\\
 1000 + 32(h - 40) & \text{if } h > 40.
 \end{array}
 \}

Answer: 2119 shirts

Step-by-step explanation:

Given : There were 3,515 shirts at the stadium store before the game.

After the game, there were 1,396 shirts left.

The by using SUBTRACTION OPERATION, the number of shirts were sold during the game will be:-

[tex]3515-1396=2119[/tex]

Hence, 2119 shirts were sold during the game.

Answer:

[tex]\sqrt{31}[/tex]

Step-by-step explanation:

A.[tex]-5 \frac{4}{11} =\frac{-59}{11}[/tex]

Since it in in p/q form so it is a rational number

B. [tex]\sqrt{31} =5.5677643.......[/tex]

Since it cannot be represented in the form of p/q . So, it is irrational number .

C. 7.608

[tex]\frac{7608}{1000}[/tex]  

Since it can be represented in p/q form . So, it is rational number.

D. 18.46...

18.4666.. Since 6 is repeating in decimal place . So, 18.46.. can be written in p/q form .

Hence Option B sqrt of 31 is not a rational number .

In an area that is 5 km by 3 km, with an ocotillo population density of 15 plants per square kilometer, we would expect to find 225 ocotillo plants.

The student's question pertains to calculating the expected number of ocotillo plants in a given area based on the known population density. First, we need to find the total area of the region in question, which in this case is a desert area that measures 5 km by 3 km. We calculate the area by multiplying the length by the width: 5 km x 3 km = 15 km2.

Since the population density of ocotillo is given as 15 plants per square kilometer, we can find the total number of ocotillos by multiplying the density by the total area:

15 plants/km2 x 15 km2 = 225 plants.

Therefore, in an area that is 5 km by 3 km, we would expect to find 225 ocotillo plants.

To find the positive difference between the solutions of the quadratic equation x^2-4x-14=3x+16, we simplify it to x^2-7x-30=0 and use the quadratic formula. Calculating the solutions, we get 10 and -3, and the positive difference between these solutions is 13.

To find the positive difference between the solutions of the quadratic equation x2-4x-14=3x+16, we first need to simplify the equation by subtracting 3x and 16 from both sides to set it equal to zero.

x2 - 7x - 30 = 0

Now, we use the quadratic formula, which is x = ∛(-b ± √(b2 - 4ac))/(2a), to find the solutions for x, where a = 1, b = -7, and c = -30.

∛(-(-7) ± √((-7)2 - 4*1*(-30)))/(2*1)

The solutions are:

Calculating the square root and simplifying, we find:

The solutions then become:

The positive difference between the solutions 10 and -3 is:

10 - (-3) = 13

Therefore, the positive difference between the solutions is 13.

The positive difference between the two solutions is 13.

Start by rearranging the equation [tex]\(x^2 - 4x - 14 = 3x + 16\)[/tex] into standard quadratic form:

[tex]\[ x^2 - 4x - 14 = 3x + 16 \][/tex]

Combine like terms:

[tex]\[ x^2 - 4x - 14 - 3x - 16 = 0 \][/tex]

[tex]\[ x^2 - 7x - 30 = 0 \][/tex]

Now, to find the solutions to this quadratic equation, we can use the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

For the equation [tex]\(x^2 - 7x - 30 = 0\)[/tex], the coefficients are:

[tex]\[ a = 1, \quad b = -7, \quad c = -30 \][/tex]

Let's substitute these values into the quadratic formula:

[tex]\[ x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(1)(-30)}}{2(1)} \ \\\\\\[ x = \frac{7 \pm \sqrt{49 + 120}}{2} \ \\\\\\[ x = \frac{7 \pm \sqrt{169}}{2} \ \\\\\\[ x = \frac{7 \pm 13}{2} \][/tex]

So, the solutions are:

[tex]\[ x = \frac{7 + 13}{2} = 10 \ \\\\\\[ x = \frac{7 - 13}{2} = -3 \][/tex]

The positive difference between these solutions is:

[tex]\[ \text{Positive difference} = |10 - (-3)| = |10 + 3| = 13 \][/tex]

Therefore, the positive difference between the two solutions is 13.

Each bouquet contains 16 roses, 4 tulips, and 4 lilies.

To determine the number of roses, tulips, and lilies in each bouquet, we need to set up a system of equations based on the given information. Let's denote the number of roses as 'r', the number of tulips as 't', and the number of lilies as 'l'.

From the problem, we are told that there are twice as many roses as the other two flowers combined in each bouquet. This can be represented by the equation:

r = 2(t + l)

Next, we are given that the florist wants 24 flowers in each bouquet. So the total number of flowers is:

r + t + l = 24

Now we can solve these two equations simultaneously to find the values of 'r', 't', and 'l'.

Substituting the first equation into the second equation, we get:

2(t + l) + t + l = 24

3t + 3l = 24

t + l = 8

Solving this equation, we find t = 4 and l = 4. Plugging these values back into the first equation, we get:

r = 2(4 + 4)

r = 16

So each bouquet contains 16 roses, 4 tulips, and 4 lilies.

Final answer:

The two integers that satisfy the conditions of being twice of each other and having a product of 32 are either (4, 8) or (-4, -8).

Explanation:

The two integers as x and y, with y being 2 times x (y = 2x). According to the problem, the product of these two integers is 32 (x * y = 32). If we substitute y in the equation with 2x, we obtain the following: x * 2x = 32. Simplifying this equation gives us a quadratic equation, x² = 16.

To find x, we take the square root of both sides. The square root of 16 is 4, so x can be either 4 or -4. Consequently, y can be either 8 or -8, depending on whether x is positive or negative.

Therefore, the two sets of integers that satisfy the equation x*y = 32 are (4, 8) and (-4, -8), as both pairs have a product of 32 and one integer is exactly twice the other.

I would be $3.41 first you figure out how much one cost by dividing 0.93 by 6 then you multiply your answer by 22

Answer:

Option B

Step-by-step explanation:

Given are 4 sequences and we have to find which one represents a geometric sequence.

We know that geometric sequence will be of the form

a, ar, ar^2,....

On scrutinising the options we get first option does not have the term multiplied by common ratio

OPtion I is incorrect

Option II is a geometric sequence with common ratio (1+i)

Option III is not a geometric sequence since the exponents are all real numbers

Option IV is also incorrect.

The function that represents a geometric sequence is [tex]A(n) = P(1 + i)^{n- 1}[/tex]

A geometric function is represented as:

[tex]A(n) = ar^n[/tex]

The above function can be modified as follows:

[tex]A(n) = a(r)^n[/tex]

Looking through the options, we have:

[tex]A(n) = a(r)^n[/tex] is similar to [tex]A(n) = P(1 + i)^{n- 1}[/tex]

Hence, the function that represents a geometric sequence is [tex]A(n) = P(1 + i)^{n- 1}[/tex]

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An equation regarding the length of the sides of an isosceles right triangle is required.

The required equation is [tex]2x^2=h^2[/tex]

The length of the legs of triangle which are equal in length is [tex]x[/tex]

The length of the hypotenuse is [tex]h[/tex]

From the Pythagoras theorem we have

[tex]x^2+x^2=h^2\\\Rightarrow 2x^2=h^2[/tex]

Hence, in the above equation the length of the legs and the hypotenuse lengths are related.

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Joe is positive 986 yards

Ziggy is negative 118 yards

the total difference is 986 +118 = 1,104 yards

To find the dimensions of the rectangle, we set up an equation using the area formula and solve for 'x'.

Let's assume that the width of the rectangle is 'x' yards. Since the length is 5 yards less than twice the width, we can express the length as (2x - 5) yards. The area of a rectangle is given by the formula A = length * width, so we can set up the equation:

A = (2x - 5) * x = 52

Expanding the equation:

2x^2 - 5x - 52 = 0

Using the quadratic formula or factoring, we can solve for 'x'. Once we find the value of 'x', we can substitute it back into the expressions for length and width to find the dimensions of the rectangle.

Dimensions of the rectangle: Width = x yards, Length = (2x - 5) yards

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Answer:

990

Step-by-step explanation: