A loan of $2200 is due in 5 years. If money is worth 5.4% compounded annually, find the equivalent payments that would settle the debt at the times shown below (a) now (b) in 3 years (c) in 5 years (d) in 10 years

Answer:

9

Step-by-step explanation:

10-4*sqrt(1/16)

=10-4[sqrt(1)/sqrt(16)]

=10-4[1/4]

=10-4(1/4)

=10-4/4

=10-1

=9

In a circle with a radius of 12 m, the length of the arc that subtends a central angle of measure 70° is roughly 8.37 m.

To find the length of the arc that subtends a central angle of measure 70° in a circle of radius 12 m, we can use the formula:

Length of arc = (Angle measure/360°) * 2 * π * radius

In this case, the angle measure is 70° and the radius is 12 m. Plugging these values into the formula, we get:

Length of arc = (70°/360°) * 2 * π * 12 m

Simplifying this expression, we have:

Length of arc = (7/36) * 2 * π * 12 m

To evaluate this expression, we can first simplify the fraction:

Length of arc = (7/18) * 2 * π * 12 m

Multiplying the fraction by 2, we get:

Length of arc = (7/18) * 2 * π * 12 m

Length of arc = (14/18) * π * 12 m

Next, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:

Length of arc = (7/9) * π * 12 m

Finally, multiplying the remaining terms, we have:

Length of arc = 7/9 * 12 * π m

Length of arc ≈ 8.37 m

Therefore, the length of the arc that subtends a central angle of measure 70° in a circle of radius 12 m is approximately 8.37 m.

To learn more about "Length Of The Arc" visit: https://brainly.com/question/28108430

#SPJ11

The magnitude of the force required to prevent the car from rolling down the hill is 1578.88 Newton.

In accordance with Newton's Second Law of Motion, the force acting on this car is equal to the horizontal component of the force (Fx) that is parallel to the slope:

Fx = mgcosθ

Fx = Fcosθ

Where:

Note: 3500 lbs to kg = 3500/2.205 = 1587.573 kg

By substituting the given parameters into the formula for the horizontal component of the force (Fx), we have;

Fx = 1587.573cos(6)

Fx = 1578.88 Newton.

Read more on force here: https://brainly.com/question/25961211

#SPJ4

The magnitude of the force required to prevent the car from rolling down the hill is approximately 367.01 lbs.

To find the magnitude of the force required to prevent the car from rolling down the inclined hill, we can analyze the forces acting on the car.

The weight of the car acts vertically downward with a magnitude of 3500 lbs. We can decompose this weight into two components: one perpendicular to the incline and one parallel to the incline.

The component perpendicular to the incline can be calculated as W_perpendicular = 3500 * cos(6°).

The component parallel to the incline represents the force that tends to make the car roll down the hill. To prevent this, an equal and opposite force is required, which is the force we need to find.

Since we are ignoring friction, the force required to prevent rolling is equal to the parallel component of the weight: F_required = 3500 * sin(6°).

Calculating this value gives:

F_required = 3500 * sin(6°) ≈ 367.01 lbs (rounded to 2 decimal places).

Therefore, the magnitude of the force required to prevent the car from rolling down the hill is approximately 367.01 lbs.

Learn more about magnitude here:

https://brainly.com/question/30337362

#SPJ11

The answer is: The width of the walkway should be 5 feet.

We are given a diagram below that represents the given data. Julieta is constructing a walkway around a rectangular swimming pool which measures 11 feet by 8 feet.

She wants the total area of the pool and the walkway to be 460 square feet. Our task is to determine the width of the walkway.

Let's assume that the width of the walkway is x feet. Then, the length of the rectangle formed by the walkway and pool together will be 11+2x and the width will be 8+2x.

The area of the rectangle is given as: Area of rectangle = Length × Width⇒(11+2x)×(8+2x) = 460⇒88 + 22x + 16x + 4x² = 460⇒4x² + 38x - 372 = 0 Dividing the entire equation by 2, we get: 2x² + 19x - 186 = 0 To solve this quadratic equation, we will use the quadratic formula: x = [-b ± √(b²-4ac)] / 2awhere a = 2, b = 19, and c = -186.

On substituting these values in the above formula, we get: x = (-19 ± √(19²-4×2×(-186))) / 2×2 Simplifying this expression further, we get: x = (-19 ± √1521) / 4⇒x = (-19 ± 39) / 4⇒x = 5 or x = -9.5

Since the width cannot be negative, the width of the walkway should be 5 feet. Therefore, the answer is: The width of the walkway should be 5 feet.

For more such questions on walkway

https://brainly.com/question/21284095

#SPJ8

The solution to the equation 3 ln x - ln 2 = 4 is x ≈ 4.937.

To solve the equation 3 ln x - ln 2 = 4, we can use the properties of logarithms.

First, we can combine the two logarithms on the left side using the quotient property of logarithms. According to this property, ln(a) - ln(b) is equal to ln(a/b):

So, we can rewrite the equation as ln(x^3/2) = 4.

Next, we can convert the logarithmic equation into an exponential equation. The exponential form of ln(x) = y is e^y = x, where, e is the base of the natural logarithm.

Applying this to our equation, we get e^4 = x^3/2.

To isolate x, we can multiply both sides of the equation by 2 and then take the square root of both sides.

2 * e^4 = x^3
x = (2 * e^4)^(1/3)

Rounding to the nearest thousandth, x ≈ 4.937.

Learn more about logarithm from the given link!

https://brainly.com/question/31525992

#SPJ11

Answer:

Step-by-step explanation:

If the related function is decreasing when x < 0, it means that as x decreases (moves to the left on the x-axis), the corresponding y-values of the function decrease as well. In other words, the function is getting smaller as x becomes more negative.

Given that the zeros of the function are -2 and 2, it means that when x = -2 or x = 2, the function evaluates to zero. This means that the graph of the function intersects the x-axis at x = -2 and x = 2.

Based on this information, we can conclude that the related function starts from positive values, decreases as x moves to the left (x < 0), and intersects the x-axis at x = -2 and x = 2.

Answer:

To find the solutions to the equation f(x) = g(x), we need to set the two functions equal to each other and solve for x.

Setting f(x) = g(x), we have:

−0.2x − 3 + 2.3x − 2 + 7x − 10.3 = −|0.2x| + 4.1

Combining like terms, we get:

8.1x - 15.3 = -|0.2x| + 4.1

Next, we'll consider two cases for the absolute value term.

Case 1: 0.2x ≥ 0

In this case, the absolute value can be removed, and the equation becomes:

8.1x - 15.3 = -0.2x + 4.1

Combining like terms again:

8.3x - 15.3 = 4.1

Adding 15.3 to both sides:

8.3x = 19.4

Dividing both sides by 8.3:

x ≈ 2.34 (rounded to the nearest hundredth)

Case 2: 0.2x < 0

In this case, we need to change the sign of the absolute value term and solve separately:

8.1x - 15.3 = 0.2x + 4.1

Combining like terms:

7.9x - 15.3 = 4.1

Adding 15.3 to both sides:

7.9x = 19.4

Dividing both sides by 7.9:

x ≈ 2.46 (rounded to the nearest hundredth)

Therefore, the solutions to the equation f(x) = g(x) to the nearest hundredth are x ≈ 2.34 and x ≈ 2.46.

The equation log₁₀ 0.001 = x can be solved by rewriting it in exponential form: 10^x = 0.001. Taking the logarithm of both sides with base 10, we find that x = -3.

To solve the equation log₁₀ 0.001 = x, we need to convert it to exponential form. The logarithm with base 10 is equivalent to an exponentiation with base 10. In this case, the logarithm of 0.001 with base 10 is equal to x.

To rewrite the equation in exponential form, we raise 10 to the power of both sides: 10^x = 0.001. This equation states that 10 raised to the power of x is equal to 0.001.

To find the value of x, we need to determine the exponent that yields 0.001 when 10 is raised to that power. By calculating the value of 10^x, we find that x = -3.

Therefore, the solution to the equation log₁₀ 0.001 = x is x = -3. This means that the logarithm of 0.001 with base 10 is equal to -3.

Learn more about Logarithm

brainly.com/question/30226560

brainly.com/question/32351461

#SPJ11

Approximately 83%` of the members voted against the measure.

Let the number of members of the legislature be x.Since 1/4 of the members of the legislature did not vote on the measure, then the fraction of those who voted is 1 - 1/4 = 3/4.3/4 of the members of the legislature voted.

Since the fraction of members of the legislature voting against the measure would have been 1/3 if 5 additional members had voted against it, then let the number of members who voted against it be y.

Thus, `(y + 5)/(x - 1) = 1/3`.

Solving for y:`(y + 5)/(3x/4) = 1/3`

Cross-multiplying and solving for y:`3(y + 5) = x/4``y + 5 = x/12`

Since y voted against the measure, and 3/4 of the members voted, then 1 - 3/4 = 1/4 of the members abstained from voting.

Thus, `(x - y - 5)/4 = x/4 - y - 5/4` members voted against the measure originally, which we know is equal to `3/4x - y`.

Equating the two expressions:`3/4x - y = x/4 - y - 5/4`

Simplifying:`x/2 = 5`

Therefore, `x = 10`.

Substituting back to find y:`y + 5 = x/12``y + 5 = 10/12``y = 5/6`

So, `5/6` of the members voted against the measure, which is `0.8333...` as a decimal.

Rounded to the nearest whole number, `83%` of the members voted against the measure.

Learn more about voting at

https://brainly.com/question/14341203

#SPJ11

Using elimination method, the solutions of the given system of equations are (x, y) =( 3√2/2, √10 / 2), (-3√2/2, -√10 / 2), (-3√2/2, √10 / 2), (3√2/2, -√10 / 2).

Given system of equations is:x² + y² = 7 --- equation (1)x² - y² = 2 --- equation (2)

Elimination method: In this method, we eliminate one variable first by adding or subtracting the equations and then solve the other variable. After solving one variable, we substitute its value in one of the given equations to get the value of the other variable. Let's solve it:x² + y² = 7x² - y² = 2

Add both equations: 2x² = 9 ⇒ x² = 9/2⇒ x = ± 3/√2 = ± 3√2 / 2

Substitute x = + 3√2 / 2 in equation (1) ⇒ y² = 7 - x² = 7 - (9/2) = 5/2⇒ y = ± √5/√2 = ± √10 / 2

So, the solutions of the given system of equations are (x, y) =( 3√2/2, √10 / 2), (-3√2/2, -√10 / 2), (-3√2/2, √10 / 2), (3√2/2, -√10 / 2).

More on elimination method: https://brainly.com/question/11764765

#SPJ11

The formula to find the sum of the measures of the exterior angles of a polygon is 360 degrees.

The sum of the measures of the exterior angles of any polygon, regardless of the number of sides it has, is always 360 degrees.

An exterior angle of a polygon is an angle formed by one side of the polygon and the extension of an adjacent side. For example, in a triangle, each exterior angle is formed by one side of the triangle and the extension of the adjacent side.

To find the sum of the measures of the exterior angles, we add up the measures of all the exterior angles of the polygon. The sum will always equal 360 degrees.

This property holds true for polygons of any shape or size. Whether it is a triangle, quadrilateral, pentagon, hexagon, or any other polygon, the sum of the measures of the exterior angles will always be 360 degrees.

Understanding this formula helps us determine the total measure of the exterior angles of a polygon, which can be useful in various geometric calculations and proofs.

Learn more about Polygon

brainly.com/question/17756657

brainly.com/question/28276384

#SPJ11

Here is a diagram of the points described:

(2,3)      (2, -3)

  |             |

  |             |

  c----------d

Based on the given points, let's consider the following:

Point A: A (2, 3)

Point B: B (2, -3)

Points A and B have the same x-coordinate, indicating that they lie on a vertical line. The y-coordinate of A is greater than the y-coordinate of B, suggesting that A is located above B on the y-axis.

Now, you mentioned that points C and D are collinear. Collinear points lie on the same line. Assuming that points C and D lie on the same vertical line as A and B, but at different positions.

The points A (2,3) and B (2, -3) are collinear, but the points A, B, C, D, and F are not. This is because the points A and B have the same x-coordinate, so they lie on the same vertical line. The points C and D also have the same x-coordinate, so they lie on the same vertical line. However, the point F does not have the same x-coordinate as any of the other points, so it does not lie on the same vertical line as any of them.

Learn more about points here:

brainly.com/question/18481071

#SPJ11

The highest degree of the equation is 3. As t approaches infinity, the value of the equation also tends to infinity as the degree of the equation is odd.

The given initial value problem is:

y(4) − 12y′′′ + 36y′′ = 0,

y(1) = 14 + e6,

y′(1) = 9 + 6e6,

y′′(1) = 36e6,

y′′′(1) = 216e6

To find the solution of the given initial value problem, we proceed as follows:

Let y(t) = et

Now, y′(t) = et,

y′′(t) = et,

y′′′(t) = et and

y(4)(t) = et

Substituting the above values in the given equation, we have:

et − 12et + 36et = 0et(1 − 12 + 36)

= 0et

= 0 and

y(t) = c1 + c2t + c3t² + c4t³

Where c1, c2, c3, and c4 are constants.

To determine these constants, we apply the given initial conditions.

y(1) = 14 + e6 gives

c1 + c2 + c3 + c4 = 14 + e6y′(1)

                           = 9 + 6e6 gives c2 + 2c3 + 3c4 = 9 + 6e6y′′(1)

                           = 36e6 gives 2c3 + 6c4 = 36e6

y′′′(1) = 216e6

gives 6c4 = 216e6

Solving these equations, we get:

c1 = 14, c2 = 12 + 5e6,

c3 = 12e6,

c4 = 36e6

Thus, the solution of the given initial value problem is:

y(t) = 14 + (12 + 5e6)t + 12e6t² + 36e6t³y(t)

= 36t³ + 12e6t² + (12 + 5e6)t + 14

Hence, the solution of the given initial value problem is 36t³ + 12e6t² + (12 + 5e6)t + 14.

As t approaches infinity, the behavior of the solution can be determined by analyzing the highest degree of the equation.

To learn more on constants:

https://brainly.com/question/27983400

#SPJ11

The volume of the solid that lies within the sphere x^2+y^2+z^2= 36, above the xy-plane, and below the cone z=x^2+y^2 is 96π cubic units. The calculation was done using spherical coordinates.

To find the volume of the solid that lies within the sphere x^2+y^2+z^2= 36, above the xy-plane, and below the cone z=x^2+y^2, we can use spherical coordinates.

The sphere has radius 6, so we have:

0 ≤ ρ ≤ 6

The cone has equation z = ρ^2, so we have:

ρ cos(φ) = ρ^2 sin(φ)

cos(φ) = ρ sin(φ)

tan(φ) = 1/ρ

φ = π/4

Therefore, we have:

π/4 ≤ φ ≤ π/2

0 ≤ θ ≤ 2π

Using the formula for the volume element in spherical coordinates, we have:

dV = ρ^2 sin(φ) dρ dφ dθ

Integrating over the given limits, we get:

V = ∫(θ=0 to 2π) ∫(φ=π/4 to π/2) ∫(ρ=0 to 6) ρ^2 sin(φ) dρ dφ dθ

V = ∫(θ=0 to 2π) ∫(φ=π/4 to π/2) [ρ^3 sin(φ) / 3] |_ρ=0 to 6 dφ dθ

V = ∫(θ=0 to 2π) ∫(φ=π/4 to π/2) 72 sin(φ) / 3 dφ dθ

V = ∫(θ=0 to 2π) [72 cos(φ)]|φ=π/4 to π/2 dθ

V = ∫(θ=0 to 2π) 48 dθ

V = 96π

Therefore, the volume of the solid is 96π cubic units.

The solid is a spherical cap above the xy-plane and below the cone z=x^2+y^2.

picture:

                /|

               / |

              /  |

             /   |

            /    |

           /     |

          /      |

         /___|

         |       |

         |       |

         |       |

         |       |

To know more about volume, visit:
brainly.com/question/28058531
#SPJ11

10g is equal to 0.01 Kg.

32km is equal to 32,000 meters.

12 m² is equal to 12,000 mm².

50,000mm³ is equal to 0.05 m³.

2.36hrs is equal to 2 hours, 21 minutes, and 36 seconds.

The distance exactly halfway between town A and town B is 8.25 km.

To convert grams to kilograms, divide the given value by 1000 since there are 1000 grams in a kilogram.

To convert kilometers to meters, multiply the given value by 1000 since there are 1000 meters in a kilometer.

To convert square meters to square millimeters, multiply the given value by 1,000,000 since there are 1,000,000 square millimeters in a square meter.

To convert cubic millimeters to cubic meters, divide the given value by 1,000,000,000 since there are 1,000,000,000 cubic millimeters in a cubic meter.

To convert hours to hours, minutes, and seconds, the given value can be expressed as 2 hours and 0.36 hours. The decimal part represents the minutes and seconds. Multiply 0.36 by 60 to get 21.6 minutes, and then convert 0.6 minutes to seconds, which is 36 seconds.

For the second part of the question, to find the distance exactly halfway between town A and town B, divide the total distance (16500m) by 2 to get 8250m. Since the answer should be in kilometers, divide 8250 by 1000 to get 8.25 Km.

You can learn more about kilograms at

https://brainly.com/question/9301317

#SPJ11

A solution is made by combining 54 kg of salt water with 76 kg of clear water, producing water that contains 2.7 percent salt. The percentage of salt in the saltwater is 41.5%.

The problem is asking us to calculate the percentage of salt present in saltwater. We are given the amount of saltwater and clear water used to create a solution with 2.7% salt. 54 kg of salt water and 76 kg of clear water are combined to make a solution. We want to know what percentage of the salt water is salt.
As we know, the percentage of salt in the saltwater is (mass of salt / total mass of saltwater) × 100. Let us assume that the mass of salt present in the salt water is x kg. Therefore, the mass of salt water (salt + water) is 54 kg. So, the mass of salt is x kg and the mass of water is (54 - x) kg. Since the solution contains 2.7% salt, we can write:
(mass of salt / total mass of saltwater) × 100 = 2.7%. Also, we have the total mass of the solution:
The total mass of solution = Mass of salt water + mass of clear water = 54 + 76 = 130 kg.
Now we can write the equation as: [tex]\frac{x}{54} \times 100 = 2.7 \%[/tex]. And we know that the total mass of the solution is 130 kg:
x + (54 - x) = 130 kg. By solving the above equation we get,x = 30.6 kg. So, the percentage of salt in the saltwater is [tex]\frac{30.6 }{54} \times 100 = 56.67 \%[/tex]. Approximately 56.67% of the saltwater is salt.

Learn more about percentages here:

https://brainly.com/question/843074

#SPJ11

Answer: Therefore, the angle between the kayakers is approximately 63 degrees. The closest answer choice is 78°.

Step-by-step explanation:

To find the angle between the kayakers, we can use the dot product formula:

F sub 1 · F sub 2 = ||F sub 1|| ||F sub 2|| cos θ

where · denotes the dot product, || || denotes the magnitude, and θ is the angle between the two vectors.

First, we need to find the magnitudes of F sub 1 and F sub 2:

||F sub 1|| = sqrt(190^2 + 160^2) = 247.79

||F sub 2|| = sqrt(128^2 + (-121)^2) = 170.10

Next, we need to find the dot product of F sub 1 and F sub 2:

F sub 1 · F sub 2 = (190)(128) + (160)(-121) = -12080

Substituting these values into the dot product formula, we get:

-12080 = (247.79)(170.10) cos θ

Solving for cos θ, we get:

cos θ = -0.424

Taking the inverse cosine of both sides, we get:

θ ≈ 116.8°

However, this is the angle between the two vectors in standard position (i.e., with initial points at the origin). To find the angle between the kayakers, we need to subtract this angle from 180°:

180° - θ ≈ 63.2°