A parachutist's rate during a free fall reaches 165 feet per second. What is this rate in meters per second? At this rate, how many meters will the parachutist fall during 5 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.

Answer:

Any rational number.

Step-by-step explanation:

∴ [tex]x+0.5[/tex] is rational if and only if x is rational.

To proveL:  we proceed as follows:

Suppose that  [tex]x+0.5[/tex] is rational.

Then there are some integers p , q with [tex]q\neq 0[/tex] such that

[tex]x+\frac{1}{2}=\frac{p}{q}[/tex]

Subtract both sides by [tex]\frac{1}{2}[/tex], we get

[tex]x=\frac{p}{q}-\frac{1}{2}=\frac{2p-q}{2q}[/tex] which is rational.

Conversely, if x is rational, then there are integers a,b with b>0 such that    [tex]x=\frac{a}{b}[/tex]  then we have,  

[tex]x+\frac{1}{2}=\frac{a}{b}+\frac{1}{2}=\frac{2a+b}{2b}[/tex] which is also a rational.

Answer:

5y-y =360

4y =360

y= 90 sandwiches by Pete's deli

x= 5(90) = 450 sandwiches by Bills Roast Beef

Step-by-step explanation:

Answer:

[tex](-5,2)[/tex]

Step-by-step explanation:

We have been given that a figure has a vertex at (5,2). The figure has line symmetry about the y-axis.

We know that if a figure is symmetric about y-axis, then its x-coordinate changes to opposite sign and y-coordinate remains same.

We can see that x-coordinate of our given point is 5, so x-coordinate of another vertex of the figure would be -5.

Therefore, the point [tex](-5,2)[/tex] is symmetric about y-axis for our given point.

Using algebra, we find that 225 adult tickets were sold out of a total of 504 tickets.

Let's denote the number of adult tickets as x. Since there were 54 more student tickets sold than adult tickets, we can represent the number of student tickets as x + 54. The total number of tickets sold is 504, so we set up the equation x + (x + 54) = 504.

Combining like terms, we get 2x + 54 = 504. Subtracting 54 from both sides gives us 2x = 450. Finally, dividing both sides by 2 gives us x = 225.

Therefore, 225 adult tickets were sold.

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The approximation of the area of the region R under the graph of the function is 18.625 square units.

In this question we must calculate the approximate area ([tex]A[/tex]) below the curve by means of Riemann sums with left endpoints, whose expression is described below:

[tex]A = \Delta x \cdot \Sigma\limits^{n-1}_{i=0} f(a + i\cdot \Delta x)[/tex], for [tex]x \in [a,b][/tex] (1)

[tex]\Delta x = \frac{b-a}{n}[/tex] (2)

Where:

If we know that [tex]a = -1[/tex], [tex]b = 2[/tex], [tex]n = 6[/tex] and [tex]f(x) = 7 - x^{2}[/tex], then the approximate area is:

[tex]\Delta x = \frac{2-(-1)}{6}[/tex]

[tex]\Delta x = 0.5[/tex]

[tex]A = 0.5\cdot [f(-1) + f(-0.5)+f(0)+f(0.5)+f(1)+f(1.5)][/tex]

[tex]A = 0.5\cdot (6+6.75+7+6.75+6+4.75)[/tex]

[tex]A = 18.625[/tex]

The approximation of the area of the region R under the graph of the function is 18.625 square units.

To learn more on Riemann sums, we kindly invite to check this verified question: https://brainly.com/question/21847158

The arc length of the curve on the given interval −1 ≤ t ≤ 3 with parametric equation x = 6t + 5 and y = 7 − 7t −1 is 4√85.

It is the reverse of differentiation.

The arc length of the curve on the given interval.

Parametric equations interval

x = 6t + 5,  −1 ≤ t ≤ 3

y = 7 − 7t,  −1 ≤ t ≤ 3

We know that the parametric form of the arc length will be given as

[tex]\rm \int _{-1}^3 \sqrt{(\dfrac{dx}{dt})^2 + (\dfrac{dy}{dt})^2} \ dt[/tex]

Then we have

[tex]\rm \dfrac{dx}{dt} = 6\\\\\dfrac{dy}{dt} = -7[/tex]

Then the arc length will be

[tex]\rightarrow \rm \int _{-1}^3 \sqrt{(3)^2 + (-7)^2} \ dt\\\\\rightarrow \sqrt{85} [t]_{-1}^3 \\\\\rightarrow 4 \sqrt{85}[/tex]

More about the integration link is given below.

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Final answer:

To determine the number of adult tickets sold for the school play, a system of equations is set up and solved, revealing that 275 adult tickets were sold.

Explanation:

To find the number of adult tickets sold for the school play, we need to set up a system of equations based on the information given. Let x represent the number of adult tickets and y represent the number of student tickets. According to the problem, the following two statements are true:

The total number of tickets sold is 487: x + y = 487

There were 63 fewer student tickets sold than adult tickets: y = x - 63

We can substitute the second equation into the first to find the value of x:

x + (x - 63) = 487

2x - 63 = 487

2x = 487 + 63

2x = 550

x = 275

Therefore, 275 adult tickets were sold.

The sum of the angle of a triangle is 180 degrees. If you are to draw a pattern of equilateral triangles then you know that an equilateral triangle has three equal sides. Also, its angles are the same, having 60 degrees at each corner of the triangle. A triangle cannot qualify as an equilateral triangle if it is greater than 180 degrees or less than 180 degrees as a total angle. Also if a triangle that has no two right angles, then it is called a scalene triangle.  If the triangle has two right angles, it is called isosceles triangle. A triangle with equal sides is called an equilateral triangle.

The total energy of the beam just as it hits the ground would be equivalent to the initial potential energy when it was held at a height of 40 m, assuming no air resistance.

The question is about understanding the concept of conservation of energy, specifically the transformation of potential energy to kinetic energy. When the beam was held at a height of 40 m, it had potential energy given by the formula:

PE = mgh

where m is the mass of the beam, g is the acceleration due to gravity, and h is the height. Assuming no air resistance, when the beam falls, all of its potential energy will be converted to kinetic energy, which can be determined by the formula:

KE = 1/2 mv^2

However, as we don't know the exact speed of the beam just as it's hitting the ground, we don't need it because the total energy remains constant. So, just as the beam hits the ground the total energy will be the same as the initial potential energy when it was still.

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volume = pi x r^2x h

100 = 3.14 x 2^2 x h

100 =3.14 x 4 x h

100 = 12.56 x h

h = 100/12.56 = 7.9617

the height is approximately 8 inches tall

Answer:

The dosage will be 238 MGS after decrease.

Step-by-step explanation:

The current dosage of the medication of the patient = 340 MGS

patient requires 30% decrease in the dosage of the medication.

Now her new dosage after decrease = 340 -(30% × 340)

                                                              = 340 -(0.30 × 340)

                                                              = 340 - 102

                                                              = 238 MGS

The dosage will be 238 MGS after decrease.

Hello!

Step-by-step explanation:

Slope: [tex]\frac{Y^2-Y^1}{X^2-X^1}=\frac{rise}{run}[/tex]

[tex]\frac{1-8=-7}{2-(-3)=2+3=5}=\frac{-7}{5}=-\frac{7}{5}[/tex]

Slope is -7/5

Answer is -7/5

Hope this helps!

Thanks!

-Charlie

:)

:D