Solve (sin2x)/(cosx)=2 for 0≤x≤2π

The minimum time required to depreciate the value of the car is 12 years.

Let us assumed the time to be t. Representing the formula for calculation of time-

Final value = Principal value × [tex] {(1 - rate of depreciation)}^{t} [/tex]

Keeping the values in formula to find the time period

3000 = 18700 × [tex] {(1 - 14.25%)}^{t} [/tex]

Solving the expression

[tex] {(0.8575)}^{t} [/tex] = 3000/18700

Cancelling zeroes common in numerator and denominator

3000/18700 = [tex] {(0.8575)}^{t} [/tex]

Taking log on both sides of the equation

t log 0.8575 = 30/187

Keep the value

t = log 0.8575 30/187

t = 12 years

Hence, it will take 12 years for value depreciation.

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Answer:

Step-by-step explanation:

To answer this question, we need to calculate the mean and median of the given data set and then see how the additional earnings affect them.

First, let's calculate the mean of the original data set:

Mean = (50 + 82 + 39 + 50 + 31 + 70) / 6 = 322 / 6 = 53.67

Next, let's calculate the median of the original data set. To do this, we need to arrange the data set in order:

31, 39, 50, 50, 70, 82

The median is the middle value, which is 50.

Now, let's add Becky's earnings of $23 to the data set:

31, 39, 50, 50, 70, 82, 23

The new data set has 7 values. Let's calculate the new mean:

Mean = (50 + 82 + 39 + 50 + 31 + 70 + 23) / 7 = 365 / 7 = 52.14

The new mean is less than the original mean, so we can eliminate options A and C.

Now let's calculate the new median. We need to arrange the data set in order:

23, 31, 39, 50, 50, 70, 82

The median is still 50.

Therefore, the answer is option D: The mean decreases and the median remains the same.

The graph of the inequality is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y < -2 + 7

The above expression is an inequality that implies that

The value of y is less than the sum of -2 and 7

Next, we plot the graph

See attachment for the graph of the inequality

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In mathematics, the expression "to the power of" pertains to the exponent, signifying how many times a key number is to be multiplied by itself.

Expressing this idea in English can be done well by using the term "to the power of." To show this, 2 raised to the third power can be interpreted as 2 multiplied by itself three times, resulting in 8.

Therefore, the possible reason behind using the word "power" is probably due to the fact that when the exponent rises, the outcome number is wide, either being greater or smaller, made on the base being above or below 1. This implies that the figure holds more significant value.

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Using the given information, the cost of Max's electricity bill is R551.10

From the question, we are to calculate the cost of Max's monthly electricity bill

From the given information,

"Max's monthly electricity budget only allows him to use 250.50 kWh"

and

"The cost for 1 kWh is R2.20"

To determine the cost of Max's monthly electricity bill, we will multiply his monthly electricity budget by the cost for 1 KWh

That is,

Max's monthly electricity bill = 250.50 × R2.20

Max's monthly electricity bill = R551.10

Hence,

The cost of Max's monthly electricity bill is R551.10

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The equation for total cost of buying and shipping the records is

76.4x + 80

We have,

She buys 3 in good condition

So, the cost for 3 good condition

= 3 (10.5x)

= 31.5 x

and, She buys 1 in Fair condition

So, the for 1 fair condition

= 5x

and, She buy 2 new condition then the price is

= 39.9 x

So, the equation for total cost of buying and shipping the records is

= 31.5x + 5x + 39.9x + 8

= 76.4x + 8

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Answer: a. d. f.

Step-by-step explanation:

The volume of a right circular cone which has a height of 11.9 ft and a base with a radius of 16.3 ft as required is;

As evident in the task content; the volume of a right circular cone a height of 11.9 ft and a base with a radius of 16.3 ft is to be determined.

Recall, the volume of the cone is;

V = (1/3) × πr²h

V = (1/3) × π × 16.3² × 11.9

V = 3310.9 ft³.

Ultimately, the volume of the right circular cone is; 3310.9 ft³.

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Answer:

3310.9

Step-by-step explanation:

The equations that can be used to solve for y, the length of the room are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0

From the question, we have the following parameters that can be used in our computation:

Area = 750

Length = y

Width = y - 5

The area is the product of the length and the width

So, we have

y * (y - 5) = 750

When expanded. we have

y^2 - 5y = 750

Lastly, we have

(y + 25)(y – 30) = 0 -- when factored

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The amount of sand Eloise will put in each sandbox is 7.5 pounds (30 divided by 4).

Answer:

  u = -4

Step-by-step explanation:

You want the solution to the equation 16u -5u +18 = 3u -14.

The equation can be simplified by combining like terms:

  11u +18 = 3u -14

Adding (-18-3u) to both sides, we have ...

  8u = -32

  u = -32/8 = -4 . . . . . . divide by the coefficient of u

The solution is u = -4.

The area of the entire rectangle as polynomial is x^2 + 8x + 12

From the question, we have the following parameters that can be used in our computation:

Height = x + 2; Width = x + 6

Broken rectangles

The area of the rectangle is the product of the dimensions

Adding the heights and the width of the individual rectangles, we have

Height = x + 2; Width = x + 6

So, the area is

Area = (x + 2)(x + 6)

Expand

Area = x^2 + 8x + 12

Hence, the area expression is x^2 + 8x + 12

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The triangles are classified according to their sides as:

1. equilateral 2. Scalene   3. and 4. Isosceles   5. equilateral     6. and 7. scalene triangle.      8. Isosceles   9. and 10. Equilateral

Recall the following:

A triangle is equilateral if all three sides are equal.

It is isosceles if it has two equal sides.

A triangle is scalene if all three sides are of different lengths.

1. The triangle is equilateral because all sides are equal.

2. Scalene

3. and 4. Isosceles (two sides are equal)

5. All sides are equal, so it is an equilateral triangle.

6. and 7. The three sides have different lengths, therefore, it is a scalene triangle.

8. Isosceles

9. and 10. Equilateral

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Answer:

452 square centimeters.

Step-by-step explanation:

To find the area of a circle, we use the formula:

A = πr^2

Where A is the area of the circle, r is the radius, and π is a mathematical constant (approx. 3.14).

Given that the radius of the circle is 12 cm, we can substitute r = 12 in the formula:

A = π(12)^2

A = 3.14 x 144

A = 452.16

Therefore, the area of the circle is approximately 452.16 square centimeters. However, we need to round the answer to the nearest whole number.

Since the decimal part of the answer is less than 0.5, we round the answer down to the nearest whole number. Therefore, the area of the circle nearest the whole number is 452 square centimeters.

The angles that you get when a circle is divided into 4 equal parts, would be four 90 degree angles.

The reason these angles are called 'right angles' is because they create an exact 90-degree angle, signifying one fourth of a complete circle. Every specific angle is named as a 'quadrant,' as it covers a quarter or a quadrant of the circle.

These four perpendicular angles stand side by side - having in common not just one diameter of the circle but also a shared vertex, which is at the center of the circle. Together, they share uniformly the circle into four unique sections - each turning toward a distinct quadrant of the circle parallel to their placement.

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The value of 5cos(tetha) + 4/sin(beta) is 9

Complementary angles are two angles that sum up to 90°. This means that in a right angled triangle sin( beta) is thesame as cos(90-tetha) and cos (beta) is sin(90-tetha).

Examples of complementary angles include: 30 and 60, 50 and 40 e.t.c

Therefore if tan ( tetha ) = 3/4, and tan(tetha) = opp/adj. This means opp is 3 and adj is 4

therefore hyp = √3²+4²

= √9+16 = √25

= 5

therefore cos(tetha) = 4/5

and sin beta = 4/5

therefore 5cos(tetha) + 4/sin(beta) = 5 × 4/5 +(4÷4/5)

= 4+5 = 9

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The largest interior angle of the triangle is the angle A

The side lengths of the triangles are given as

b = 10 cm

a = 14 cm

The other side length is not given

So, we solve the question using the two side lengths

Having said that:

The general rule is that; the higher the side length, the larger the angle

14 cm is greater than 10 cm

This means that the angle A is greater than the angle B

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Part A: Note that the best graphical representation to use for this kind of data is a Histogram.

Part B : Creating the historgram means you have to first chose the intervals for the data.

When it comes to displaying the distribution of a set of continuous data, histograms offer an appropriate visualization method.

This display type divides the data into intervals and plots the number of observations that fall within each interval, hence providing frequency distribution information.

For instance, in creating a histogram for this particular dataset, one can choose intervals or bins with sizes e.g. 5 units covering a range between 0 and 30 before tabulating the count of observed variables in each bin and plotting these counts on the chart's vertical axis.

A histogram illustrates how often students ate breakfast within a 30-day timeframe. This frequency distribution features labeled axes, with the vertical axis representing "Frequency" and the horizontal axis depicting "Number of times students ate breakfast."

Each bar on the horizontal axis corresponds to an interval and shows its frequency on a scaled height basis.

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Using an equation, the number of children, parents, and grandparents in attendance were:

An equation is an algebraic statement showing the equality or equivalence of two or more mathematical expressions.

Mathematical expressions combine variables, numbers, values, and constants using mathematical operands.

The total number of people in attendance at the family reunion = 400

Let the number of grandparents = x

Let the number of parents = 2x

Let the number of children = 2x + 50

x + 2x + 2x + 50 = 400

5x = 350

x = 70

Grandparents = 70

Parents = 140 (2 x 70)

Children = 190 (2 x 70 + 50)

Total = 400 (70 + 140 + 190)

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Answer: Angle one equals -15, and angle two equals 14, if the +7 equals a positive seven.

Step-by-step explanation:

There are more negatives than positives, so we make the ending answer negative, giving us -15. And the second one is simple multiplication, you double the 7 times two, or vice versa.

Hope this helps!

92 more students favor visiting Florida than Colorado

From the question, we have the following parameters that can be used in our computation:

Students = 400

Florida = 38%

Colorado = 15%

The percentage difference is

Difference = 38% - 15%

So, we have

Difference = 23%

This means that

Students = 23% * 400

Evaluate

Students = 92

Hence, the number of students is 92

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Answer:

The function f(x,y) = x^2 + y^2 represents the equation of a paraboloid with its vertex at the origin. Since the function increases as we move away from the origin, there are no maximum points, but there is a minimum point at the origin.

To find this minimum point, we can take the partial derivatives of f(x,y) with respect to x and y, and set them equal to zero:

df/dx = 2x = 0

df/dy = 2y = 0

Solving these equations simultaneously gives us x = 0 and y = 0, which is the only critical point of the function. To determine whether this point is a minimum or maximum, we can use the second partial derivative test.

Taking the second partial derivatives, we have:

d^2f/dx^2 = 2

d^2f/dy^2 = 2

d^2f/dxdy = 0

At the point (0,0), both second partial derivatives are positive, which indicates that the point is a minimum. Therefore, the function f(x,y) = x^2 + y^2 has a minimum value of 0 at the point (0,0).

Answer:

53,352 cm

Step-by-step explanation:

1. The first step is to draw the rectangle draw one rectangle over the other and start labeling the sides.

2. After labeling use the rectangle prism formula: L times W times H in this case it would be 38 times 18 times 13 this is equal to 8,892.

3. From there, we know that there are six sides so we can multiply this value by 6 so it would be 8,892 times 6 = 53,352 cm.

If I made a mistake or if have any questions feel free to tell me!

-Mathematics and Science Major for Middle School Students at Harvard University

Answer:

B. 122.88

Step-by-step explanation:

Since t is the number of years since 1910, we can find the t value we need for the equation by subtracting 1910 from 1980:

t = 1980 - 1910 = 70

Now, we can plug in 70 for t to find the amount of currency in 1980:

[tex]M(t)=2.08(1.06)^t\\M(70)=2.08(1.06)^7^0\\M(70)=122.8779348\\M(70)=122.88[/tex]

Thus, the amount of currency in 1980 according to the model was $122.88 billion

In 58 seconds after starting its descent, the aircraft will touch down.

The plane will land when its altitude y is zero.

So we can set y = 0 in the equation:

0 = 464 - 8x

Solving for x:

8x = 464

x = 58

Therefore, the plane will land 58 seconds after it begins its descent.

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Answer:

b[tex]\sqrt{a}[/tex]

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] , then

[tex]\sqrt{ab^2}[/tex]

= [tex]\sqrt{a}[/tex] × [tex]\sqrt{b^2}[/tex]

= [tex]\sqrt{a}[/tex] × b

= b[tex]\sqrt{a}[/tex]

The equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.

To find the equation of the line perpendicular to y=1/2x-1, we need to determine its slope. We can recall that the slope of a line in slope-intercept form, y = mx + b, is given by m, the coefficient of x. So in the given equation y=1/2x-1, the slope is 1/2.

The slope of a line perpendicular to this line will be the negative reciprocal of the slope, which means it will be -2. To see why this is true, remember that the product of the slopes of two perpendicular lines is always -1. So if the slope of the original line is m, the slope of the perpendicular line will be -1/m.

Now that we know the slope of the perpendicular line is -2, we can use the point-slope form of the equation of a line to find its equation. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

We are given a point on the perpendicular line, (5, 6), so we can substitute that into the equation and also substitute in the slope, -2:

y - 6 = -2(x - 5)

y - 6 = -2x + 10

y = -2x + 16

Hence, the equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.

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The ordered pairs to a solution for the given linear equation are (-1, 3.5) and (4, -4).

To find the ordered pair that is a solution to the equation 6x + 4y = 8, we can substitute the given value of x or y and solve for the other variable.

For the first option, substituting x = -1, we get:

6(-1) + 4y = 8

-6 + 4y = 8

4y = 14

y = 3.5

So, the ordered pair (-1, 3.5) is a solution to the equation.

For the second option, substituting y = -4, we get:

6x + 4(-4) = 8

6x - 16 = 8

6x = 24

x = 4

So, the ordered pair (4, -4) is a solution to the equation.

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