A principal of $400 is invested in an account at 6% per year compounded annually. What is the total amount of money in the account after 5 years? A. $526.00 B. $531.37 C. $535.29 D. $520.00

To model the pressure function in the pipe that oscillates between 40 and 280 ten times an hour, we can use a sine function. The formula is P = f(t) = 120 sin(π/3 t) + 160.

The pressure in the pipe oscillates between 40 and 280 ten times an hour, this is a trigonometric function scenario. Assuming the oscillation is sinusoidal, we can use a sine function to model the pressure in the pipe. The oscillation's period is 6 minutes because the pressure changes happen 10 times per hour. Thus, the function modelling this pressure will be of the form

P = a sin(b(t - c)) + d.

Given that the middle value of the pressure (between the max of 280 and the minimum of 40) is 160, this makes

'd' = 160.

The amplitude 'a' is half the total swing of the pressure which is 120.

To find 'b', we use the fact that the period of a sinusoid in this form is (2π/b).

As our period is 6 minutes, that makes 'b' = π/3.

The pressure is at a minima at t=0 so the phase shift 'c' = 0

Hence the formula P = f(t) = 120 sin(π/3 t) + 160.

https://brainly.com/question/4116396

#SPJ11

The equation of line passes through the points (2, -1) and (5, -10) will be;

⇒ y = - 3x + 5

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (2, -1) and (5, -10)

Now,

Since, The equation of line passes through the points (2, -1) and (5, -10)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 10 - (-1)) / (5 - 2)

m = - 9 / 3

m = - 3

Thus, The equation of line with slope - 3 is,

⇒ y - (-1)= - 3 (x - 2)

⇒ y + 1 = - 3x + 6

⇒ y = - 3x + 6 - 1

⇒ y = - 3x + 5

Therefore, The equation of line passes through the points (2, -1) and

(5, -10) will be;

⇒ y = - 3x + 5

Learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ5

In this problem, you are asked to compute for the value of y when x = 21. The function shows how the value of y changes with the given value of x.

Y = 2/3x + 20

Y = 2/3 (21) + 20

Y = 14 + 20

Y = 34

Answer:

5

Step-by-step explanation:

just trust me

The approximate diameter of the circle is 80 feet, the circumference is approximately 251.327 feet, and the area is approximately 5026.548 square feet.

To find the diameter, circumference, and area of the circle watered by the lawn sprinkler, we can use the formulas:

1. **Diameter [tex](\(d\)) = \(2 \times \text{radius}\)[/tex]

2. **Circumference [tex](\(C\)) = \(2 \times \pi \times \text{radius}\)[/tex]

3. **Area [tex](\(A\)) = \(\pi \times \text{radius}^2\)[/tex]

Given:

Radius[tex](\(r\)) = 40 feet[/tex]

1. Diameter:

[tex]\[d = 2 \times r\]\[d = 2 \times 40 \text{ feet}\]\[d = 80 \text{ feet}\][/tex]

2. Circumference:

[tex]\[C = 2 \times \pi \times r\]\[C = 2 \times \pi \times 40 \text{ feet}\]\[C \approx 2 \times 3.14159 \times 40 \text{ feet}\]\[C \approx 251.327 \text{ feet}\][/tex]

3. Area:

[tex]\[A = \pi \times r^2\]\[A = 3.14159 \times 40^2 \text{ square feet}\]\[A = 3.14159 \times 1600 \text{ square feet}\]\[A \approx 5026.548 \text{ square feet}\][/tex]

Answer:

The approximate diameter of the circle is 80 feet, the circumference is approximately 251.327 feet, and the area is approximately 5026.548 square feet.

The equation y - 5x = -9 defines a line that none of the given points (1,5), (2,10), (3,7), and (4,14) lie on, as substituting their x-values in the equation doesn't yield the corresponding y-values.

The question involves identifying points on a line described by the equation y - 5x = -9. To verify which points belong to this line, we can substitute the x-values of the given points into the equation and see if the resulting y-values match those in the points. We solve for y in the equation to get y as a function of x (dependence of y on x): y = 5x - 9.

Now, let's examine the points (1,5), (2,10), (3,7), and (4,14) to see if they satisfy this equation:

None of these points lie on the line defined by y = 5x - 9. For a point to be on the line, plugging its x-coordinate into the equation must result in its corresponding y-coordinate.

To simplify the given rational expression, we factor both the numerator and the denominator, cancel out the common factor, and express the result as (n^2 - 6) / (n^2 - 2), with restrictions on n that it can't equate to the square roots of 5 or 2.

The question involves simplifying the rational expression n^4 - 11n^2 + 30 divided by n^4 - 7n^2 + 10, and stating any restrictions on the variable. To simplify this, we first factor both the numerator and the denominator.

Numerator: (n^2 - 5)(n^2 - 6)
Denominator: (n^2 - 5)(n^2 - 2)

After factoring, we can cancel out the common factor (n^2 - 5) from both the numerator and the denominator. This leaves us with (n^2 - 6) / (n^2 - 2).

However, we must state the restrictions on the variable n. The original denominator cannot be equal to zero, thus n^2 cannot be equal to 5 or 2, leading to restrictions of n != sqrt(5) and n != sqrt(2).

Answer:

x = 8.4 cm

Step-by-step explanation:

Here we have to use the tan ratio to find the value of x.

tan = opposite/adjacent

tan 35 = x/12

Multiplying both sides by 12, we get

x = 12 tan 35               [tan 35 = 0.7]

x = 12*0.7

x = 8.4

Therefore, the value of x = 8.4 cm

Hope this will helpful.

Thank you.

Answer:

$144

Step-by-step explanation:

Just did test

The correct answer is:

$38.75

Explanation:

35 feet of trim at $1.75 per foot would give us a cost of

35(1.75) = 61.25.

Paying with a $100 bill, he would receive

100-61.25 = $38.75 in change.

Answer:

Step-by-step explanation:

We plot the points on a graph with months on x-axis and Revenue/expenses on y-axis.

A straight line shows the decrease in expenses and another line showing increase in revenue.

The point of intersection shows the common point where the revenue and expenses become equal. This point of intersection we get at 6.5 months as shown in the graph attached.

Answer:

Week 7

Step-by-step explanation:

You can solve this problem by graphing the revenue and the expenses and it's asking on which week the lines intersect.

R measures 42.8 degrees, which is around average.

The properties of the triangle are:

1. The sum of all the angles of a triangle (of all types) is equal to 180°.

2. The sum of the length of the two sides of a triangle is greater than the length of the third side.

3. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

The sine rule states that for a triangle with sides a, b, and c opposite to angles A, B, and C respectively,

a/sinA = b/sinB = c/sinC

Using this rule, we can find the measure of angle R as follows:

a = ST = 30

b = RT = 35

c = RS

Let angle R be opposite to side b.

sinR/sinS = b/c

sinR/sin69 = 35/c

c = 35/sin69 x sinR

Now we can use the sine rule to find c:

a/sinA = b/sinB = c/sinC

30/sin69 = 35/sinR = c/sin42

c = 35/sinR x sin42

Equating the two expressions for c, we get:

35/sin69 x sinR = 35/sinR x sin42

Simplifying this equation, we get:

sinR/sin69 = sin42

sinR = sin69 x sin42

sinR = 0.672

Taking the inverse sine of both sides, we get:

R = sin^{-1}(0.672)

R ≈ 42.8 degrees

Therefore, the measure of angle R is approximately 42.8 degrees.

Learn more about triangles here:

https://brainly.com/question/2773823

#SPJ2

Answer:

'The product of two rational numbers is rational'                        

Step-by-step explanation:

Statement 'The product of two rational numbers'.

We know that, 'The product of two rational numbers is rational'.

We can prove it,

Let [tex]\frac{a}{b}[/tex] and [tex]\frac{p}{q}[/tex] are two rational number.

Where, a,b,p,q are integers and [tex]b,q\neq 0[/tex]

Now, Product the two rational number

[tex]\frac{a}{b}\times \frac{p}{q}=\frac{ap}{bq}[/tex]

Since, ap and bq are integers and [tex]bq\neq 0[/tex]

Thus, [tex]\frac{ap}{bq}[/tex] is an fraction with integers in the numerator and denominator making it a rational number.

Therefore, 'The product of two rational numbers is rational' is true.

Answer:

The volume is 180 cube cm.

Step-by-step explanation:

By the given diagram,

The composite figure is made by the two cuboids,

First having dimensions, 2 cm × 5 cm × 6 cm,

And second having dimensions, 8 cm × 5 cm × 3 cm,

So, the volume of the given composite figure = the volume of first cuboid + the volume of second cuboid

= 2 × 5 × 6 + 8 × 5 × 3,

= 60 + 120

= 180 cube cm

The volume of the composite space figure to the nearest whole number is: 180 cube cm.

Here, we have,

from the given information, we get,

By the given diagram,

The composite figure is made by the two cuboids,

First having dimensions, 2 cm × 5 cm × 6 cm,

And second having dimensions, 8 cm × 5 cm × 3 cm,

So, the volume of the given composite figure

= the volume of first cuboid + the volume of second cuboid

= 2 × 5 × 6 + 8 × 5 × 3,

= 60 + 120

= 180 cube cm

Hence, the volume of the composite space figure to the nearest whole number is: 180 cube cm.

To learn more on volume click :

brainly.com/question/1578538

#SPJ6

Answer:

hudadagra what does a say im sorry for putting this in answer but it wont let me comment.

Step-by-step explanation:

i cant see the pic

Final answer:

The solutions to the equation 2sin^2x = sinx in the interval [0, 2π) are x = 0, π, π/6, 5π/6 and x = π/6, 5π/6.

Explanation:

The given equation is: 2sin^2x = sinx.

To solve this equation, we can first factor out sinx:

sinx(2sinx - 1) = 0.

Setting each factor equal to zero, we get two equations:

Solving for x, we find:

In geometry, a chord, radius, diameter, tangent, secant, and the point of tangency are all parts related to a circle. A radius can also be an axis, a minor arc is the smaller arc between two points on a circle, and a major arc is the larger one. These terms help in understanding the properties and relations of lines to a circle.

In the context of circles in geometry, various terms define specific parts or aspects of a circle. Here's what each term represents:

A minor arc is the shortest arc connecting two endpoints on a circle, and a major arc is the longer arc connecting the same two endpoints. The length of an arc is proportional to the size of its associated angle at the center of the circle.

When drawing or labeling the parts of a circle, it's important to note these definitions. For instance, if given a diagram with a point on the circle labeled 'A' and the center labeled 'O', the segment OA would be a radius. If there's a straight line that touches the circle at point A and doesn't cross through it, that would be your tangent, and point A is the point of tangency. Any straight line through A that crosses through another point on the circle, say, point B, would be a secant, and the line OAB (if extended through O) would be a diameter. The arc's size determines if it is a minor or major arc, depending on whether it is more or less than half the circle's circumference.

Answer:

A rotation

Explanation:

A reflection across the y-axis would map trapezoid 1 to trapezoid 8.

A horizontal translation would also map trapezoid 1 to trapezoid 8.

However, a rotation would map trapezoid 1 to trapezoid 7; it would not map it to trapezoid 8.

Answer: The answer is (c) rotation.

Step-by-step explanation: We are given a figure where 8 trapezoid are drawn on the coordinate plane. We are to select from the given option the transformation that will not map trapezoid 1 to trapezoid 8.

We can easily check that by reflecting and translating that both these transformations will definitely map trapezoid 1 to trapezoid 8.

Only the rotation will not work here. If we rotate trapezoid 1 by 180° taking origin as the centre of rotation, the the image will be opposite of trapezoid 8. Therefore, rotation will not map trapezoid 1 to trapezoid 8.

Thus, (c) is the correct option.