The registration fee for a used car is 0.8% of the sale price of $5,700. How much is the fee?

The question deals with a physics scenario involving a subway train applying brakes, kinetic friction, and requires calculating stopping distances and average acceleration using mechanical principles.

The question involves a subway train traveling at a certain speed and then applying brakes on specific cars, leading to a scenario involving kinetic friction. It asks for an analysis of the situation using physics concepts such as speed conversion, coefficient of kinetic friction, and acceleration. A comprehensive understanding of these topics would be necessary to calculate quantities like stopping distance and average acceleration.

The provided references suggest that the problems are focusing on converting speeds from miles per hour to meters per second, the effects of friction on motion, and using equations of motion to determine the stopping distance of a vehicle with locked wheels on a wet surface. These problems demonstrate applications of concepts in mechanics, specifically Newton's laws of motion, frictional forces, and energy conservation.

The subway train will travel approximately 26.2 meters before coming to a stop due to the brakes causing the wheels to slide on the track with a coefficient of kinetic friction of 0.35.

To solve this problem, we need to use principles of physics, specifically those related to friction and acceleration.

Convert the Speed: First, convert the speed from miles per hour (mi/h) to meters per second (m/s) for ease of calculation.

30 mi/h = 30 * 1609 / 3600 m/s ≈ 13.4 m/s.

Identify the Variables:

Initial speed (u): 13.4 m/s

Final speed (v): 0 m/s (since the train stops)

Coefficient of kinetic friction (μ): 0.35

Calculate the Frictional Force: The kinetic frictional force can be calculated using the formula:

Frictional force (f_k) = μ * N, where N (the normal force) equals the weight of the sliding cars. Assuming we only need to calculate the proportion without specific mass of cars, we can denote N as m * g (mass * gravity). Therefore, f_k = 0.35 * m * g.

Determine the Deceleration: Using Newton's second law, f_k = m * a (mass * acceleration), we can solve for acceleration (a):

0.35 * m * g = m * a,

a = 0.35 * g (since m cancels out), where g is the acceleration due to gravity (≈ 9.8 m/s²).

a = 0.35 * 9.8 m/s² ≈ 3.43 m/s².

Use the Kinematic Equation: To find the stopping distance, we use the kinematic equation: v² = u² + 2 * a * s (where s is the stopping distance):

0 = (13.4)² + 2 * (-3.43) * s

0 = 179.56 - 6.86 * s

s = 179.56 / 6.86

s ≈ 26.2 meters.

To find the area of the walk around a circular swimming pool with a given diameter and width, calculate the radius, add the walk width to it, and then compute the area of the walk using the area of a circle formula.

The area of the walk around the pool is:

Find the radius of the pool by dividing the diameter by 2. Radius = 17 yd / 2 = 8.5 yd.

Find the radius of the walk by adding 2 yards to the pool's radius. Walk's radius = 8.5 yd + 2 yd = 10.5 yd.

Calculate the area of the walk using the formula for the area of a circle: A = πr². Area = 3.14 x (10.5)² = 346.185 square yards.

you add -2 1/4 + -4 1/2 = -6 3/4

so, your answer is -6 3/4

Answer:

10 1/4

Step-by-step explanation:

The area of the rectangular field is 120,000 square meters.

We shall multiply the length by its width, to find the area of the rectangular field.

We can calculate like this:

Area = Length x Width

Area = 0.4 kilometers x 0.3 kilometers

Next, we convert the measurements to square meters, recalling that 1 kilometer = 1000 meters:

Area = (0.4 km * 1000 m/km) x (0.3 km * 1000 m/km)

Area = (400 m) x (300 m)

Then, multiplying the values, we have:

Area = 120,000 square meters

Hence, the area of the rectangular field is 120,000 square meters.

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Final answer:

The company should produce 1,200 boxes of Assortment I per week to maximize its profit.

Explanation:

In order to maximize profit, the company should produce the assortment that yields the highest profit per candy sold. Let's calculate the profit per candy for each assortment:

From the calculations above, we can see that Assortment I has the highest profit per cherry candy. Therefore, the company should produce as many boxes of Assortment I as possible, given the available resources. To determine the number of boxes to produce, we need to calculate the maximum number of cherry candies that can be produced with the available resources:

Assortment I contains 4 cherry candies per box, so the maximum number of boxes of Assortment I that can be produced is 4,800/4 = 1,200 boxes. The company should produce 1,200 boxes of Assortment I per week to maximize its profit.

Answer: The price today = $250

Step-by-step explanation:

Given : The original price of apple was  $200.

The price of a new apple ipod has increased by 1/4.

Then , the new price =(Original price)  +([tex]\dfrac{1}{4}[/tex]) x (Original price)

= (Original price) ( [tex]1+\dfrac{1}{4}[/tex] )

[tex](\$200)(\dfrac{5}{4})=\$250[/tex]

Hence, the price of ipod today = $250

The value of x on solving the equation 5/6 (3/8 - x) = 16 is - 251 / 5.

In other terms, it is a mathematical statement stating that "this is equivalent to that." It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.

Given:

5/6 (3/8 - x) = 16

Solve the above equation as shown below,

Use the distributive property to solve the equation,

5 / 6 × 3 / 8 - 5 / 6 x = 16

15 / 48 - 5 / 6 x = 16

5 / 16 - 5 / 6 x = 16

5 / 6 x = 5 / 16 - 16

5 / 6x = -251 / 16

x = -251 / 16 × 6 / 5

x = - 251 / 5

Thus, the value of x is - 251 / 5.

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Final answer:

Kyle is currently 21 years old. This was determined by setting up equations based on the information given and solving for Melissa's age first, which allowed us to find Kyle's age.

Explanation:

We are given that Kyle is six years older than Melissa. Also, nine years ago, he was twice her age. Let's represent Melissa's current age as M and Kyle's current age as K.

From the first piece of information, we can formulate the following equation:

1) K = M + 6

From the second piece of information, we get:

2) K - 9 = 2 * (M - 9)

Now, we substitute the expression from equation 1 into equation 2:

(M + 6) - 9 = 2 * (M - 9)

M - 3 = 2M - 18

After simplifying the equation, we find Melissa's current age:

M = 15

Using equation 1, we then calculate Kyle's current age:

K = 15 + 6

K = 21

Hence, Kyle is currently 21 years old.

Answer:

10

Step-by-step explanation:

The radius is the magnitude of the complex number that is the difference between any point on the circle and the center point. A suitable calculator can tell you that magnitude:

║(8+7i) - (2-i)║ = √((8-2)² +(7-(-1))²) = √(36+64) = √100 = 10

Answer:

10

Step-by-step explanation:

Answer:

Step-by-step explanation:

A convergent sequence is a sequence that approach to a specific limit. If the sequence doesn't approach to a limit, then it's a divergent sequence.

Now, if we have a sequence apparently convergent where we just analyse the first 1000 terms, that information won't be enough to actually consider the complete sequence as convergent, because those 1000 terms are not representative of the actual limit.

Therefore, the answer is false.

Step-by-step explanation:

How are we expected to find values of the numbers without any other information??

The floor function rounds down decimal or fractional numbers to the nearest integer.

(a) ⌊1.1⌋ = 1

(b) ⌈1.1⌉ = 2

(c) ⌊-0.1⌋ = -1

(d) ⌈-0.1⌉ = 0

(e) ⌈2.99⌉ = 3

(f) ⌈-2.99⌉ = -2

(g) ⌊1/2 + ⌈1/2⌉⌋ = 1

(h) ⌈⌊1/2⌋ + ⌈1/2⌉ + 1/2⌉ = 2

The values enclosed in square brackets represent the floor function, which rounds a decimal number down to the nearest integer. Here are the values for the given expressions:

(a) ⌊1.1⌋ = The floor function ⌊x⌋ rounds down to the nearest integer, so ⌊1.1⌋ = 1.

(b) ⌈1.1⌉ = The ceiling function ⌈x⌉ rounds up to the nearest integer, so ⌈1.1⌉ = 2.

(c) ⌊-0.1⌋ = ⌊x⌋ rounds down to the nearest integer, so ⌊-0.1⌋ = -1.

(d) ⌈-0.1⌉ = ⌈x⌉ rounds up to the nearest integer, so ⌈-0.1⌉ = 0.

(e) ⌈2.99⌉ = ⌈x⌉ rounds up to the nearest integer, so ⌈2.99⌉ = 3.

(f) ⌈-2.99⌉ = ⌈x⌉ rounds up to the nearest integer, so ⌈-2.99⌉ = -2.

(g) ⌊1/2 + ⌈1/2⌉⌋ = ⌊1/2 + 1⌋ = ⌊1.5⌋ = 1.

(h) ⌈⌊1/2⌋ + ⌈1/2⌉ + 1/2⌉ = ⌈0 + 1 + 0.5⌉ = ⌈1.5⌉ = 2.

So, these are the integer values obtained by applying the floor function to the given decimal or fractional numbers, and in some cases, applying it multiple times.

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Que. Find the following values.

(a) ⌊1.1⌋

(b) ⌈1.1⌉

(c) ⌊−0.1⌋

(d) ⌈−0.1⌉

(e) ⌈2.99⌉

(f) ⌈−2.99⌉

(g) ⌊1/2+⌈1/2⌉⌋

(h) ⌈⌊1/2⌋+⌈1/2⌉+1/2⌉

Final answer:

The function [tex]N(t) = 110,000(1.034)^t[/tex] models patent applications yearly after 1980; in 2015 (t = 35), it predicts 354,496 applications. Doubling time, found when N(t) doubles from the initial value, is approximately 21 years

Explanation:

The given function  [tex]N(t) = 110,000(1.034)^t[/tex] models the number of patent applications received at any year t after 1980, where t represents the number of years. In 2015, t = 35, so  [tex]N(35) = 110,000(1.034)^35 = 354,496[/tex]. To find the doubling time, we set N(t) equal to twice the initial value: 2(110,000) = 220,000. Solving [tex]220,000 = 110,000(1.034)^t[/tex] yields [tex](1.034)^t = 2,[/tex]then log(1.034)t = log(2). Hence, t = log(2) / log(1.034) ≈ 20.73. Thus, the doubling time for N(t) is approximately 21 years.

The circumference of a circle with a radius of 9 yards is calculated using the formula C = 2πr, with π approximated as 3.14. After substituting the values, the circumference is found to be 56.52 yards to the nearest hundredth.

To calculate the circumference of a circle with a radius (r) of 9 yards, you'll use the formula for the circumference of a circle, which is C = 2πr. Given that π (pi) is approximately 3.14, as the question suggests, you'll substitute this value and the given radius into the formula.

Step-by-step calculation:

Therefore, the circumference of the circle to the nearest hundredth of a yard is 56.52 yards.

The volume of the solid that lies within both the cylinder and the sphere is [tex]\( \pi \cdot 39^{3/2} \)[/tex].

To find the volume of the solid that lies within both the cylinder

[tex]\(x^2 + y^2 = 25\)[/tex] and the sphere [tex]\(x^2 + y^2 + z^2 = 64\)[/tex], we'll use cylindrical coordinates. The equations in cylindrical coordinates are

[tex]\(x = r\cos(\theta)\), \(y = r\sin(\theta)\), and \(z = z\)[/tex].

First, let's find the limits of integration for (r), [tex]\(\theta\)[/tex], and (z):

Limits for (r): The cylinder has a radius of 5 (r = 5), so [tex]\(0 \leq r \leq 5\)[/tex].

Limits for [tex]\(\theta\)[/tex]: Since the solid lies within the entire cylinder, [tex]\(0 \leq \theta \leq 2\pi\).[/tex]

Limits for (z): The sphere has a radius of [tex]\(\sqrt{64} = 8\)[/tex], so [tex]\(0 \leq z \leq \sqrt{64 - r^2}\)[/tex].

Now, the volume element (dV) in cylindrical coordinates is [tex]\(r \, dr \, d\theta \, dz\)[/tex].

So, the volume (V) is given by:

[tex]\[ V = \int_0^{2\pi} \int_0^5 \int_0^{\sqrt{64-r^2}} r \, dz \, dr \, d\theta \][/tex]

Let's calculate this:

[tex]\[ V = \int_0^{2\pi} \int_0^5 \left[ z \right]_0^{\sqrt{64-r^2}} \, dr \, d\theta \][/tex]

[tex]\[ V = \int_0^{2\pi} \int_0^5 \sqrt{64-r^2} \, dr \, d\theta \][/tex]

[tex]\[ V = \int_0^{2\pi} \left[ \frac{1}{2} (64-r^2)^{3/2} \right]_0^5 \, d\theta \][/tex]

[tex]\[ V = \int_0^{2\pi} \frac{1}{2} (64-25)^{3/2} \, d\theta \][/tex]

[tex]\[ V = \int_0^{2\pi} \frac{1}{2} (39)^{3/2} \, d\theta \][/tex]

[tex]\[ V = \frac{39^{3/2}}{2} \int_0^{2\pi} d\theta \][/tex]

[tex]\[ V = \frac{39^{3/2}}{2} \cdot 2\pi \][/tex]

[tex]\[ V = \pi \cdot 39^{3/2} \][/tex]

So, the volume of the solid that lies within both the cylinder and the sphere is [tex]\( \pi \cdot 39^{3/2} \)[/tex].

The volume of the solid that lies within both the cylinder [tex]\(x^2 + y^2 = 25\)[/tex] and the sphere[tex]\(x^2 + y^2 + z^2 = 64\) is \( \frac{40\pi}{3} \).[/tex]

To find the volume of the solid that lies within both the cylinder [tex]\(x^2 + y^2 = 25\)[/tex] and the sphere [tex]\(x^2 + y^2 + z^2 = 64\)[/tex], we can use cylindrical coordinates.

In cylindrical coordinates, the equations of the cylinder and the sphere become:

Cylinder: [tex]\(r^2 = 25\)[/tex]

Sphere: [tex]\(r^2 + z^2 = 64\)[/tex]

The limits of integration for r will be from 0 to 5 (since [tex]\(r^2 = 25\)[/tex] gives r = 5 in cylindrical coordinates). The limits of integration for z will be from [tex]\(-\sqrt{64 - r^2}\) to \(\sqrt{64 - r^2}\).[/tex]

The volume element dV in cylindrical coordinates is [tex]\(r \, dr \, dz \, d\theta\).[/tex]

So, the volume V of the solid is given by the triple integral:

[tex]\[V = \iiint dV = \int_{0}^{2\pi} \int_{0}^{5} \int_{-\sqrt{64 - r^2}}^{\sqrt{64 - r^2}} r \, dz \, dr \, d\theta\][/tex]

Let's evaluate this triple integral:

[tex]\[V = \int_{0}^{2\pi} \int_{0}^{5} \left[ r\sqrt{64 - r^2} - (-r\sqrt{64 - r^2}) \right] \, dr \, d\theta\]\[V = 2\pi \int_{0}^{5} 2r\sqrt{64 - r^2} \, dr\][/tex]

Now, we can use a substitution to solve this integral. Let [tex]\(u = 64 - r^2\),[/tex]then [tex]\(du = -2r \, dr\):[/tex]

[tex]\[V = -4\pi \int_{64}^{39} \sqrt{u} \, du\]\[V = -4\pi \left[ \frac{2}{3}u^{3/2} \right]_{64}^{39}\]\[V = -\frac{8\pi}{3} \left[ 39^{3/2} - 64^{3/2} \right]\]\[V = -\frac{8\pi}{3} \left[ 59 - 64 \right]\]\[V = \frac{40\pi}{3}\][/tex]

Thus, the volume of the solid that lies within both the cylinder [tex]\(x^2 + y^2 = 25\)[/tex] and the sphere[tex]\(x^2 + y^2 + z^2 = 64\) is \( \frac{40\pi}{3} \).[/tex]

Answer:

c would be the right answer

Step-by-step explanation:

A repeating mixed number is a mixed fraction, which after converted to decimal; the numbers after the decimal point repeat without end.

1.12 as a repeating mixed number is [tex]1\frac{13}{99}[/tex]

Given that

[tex]Number = 1.12[/tex]

First, we represent as a fraction

[tex]Number = \frac{112}{100}[/tex]

To represent the number as a repeating mixed number, we simply subtract 1 from the numerator

[tex]Number = \frac{112}{100 - 1}[/tex]

[tex]Number = \frac{112}{99}[/tex]

Represent as a mixed number

[tex]Number = 1\frac{13}{99}[/tex]

Hence, 1.12 as a repeating mixed number is [tex]1\frac{13}{99}[/tex]

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