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barxatty [35]
3 years ago
10

Write the recursive formula of 13, 9, 5...

Mathematics
1 answer:
lukranit [14]3 years ago
7 0

Step-by-step explanation:

a(n) = a +(n-1)d

a=13

d=9-13=5-9=-4

°.° a(n) = 13 +(n–1)-4

hope this helps

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ahmed is sitting on a dock watching a float plane in a harbour. At a certain time, the plane is 350 m above the water and 470 m
Pavel [41]

Answer:

The angle of elevation of the plane measured from Ahmed is approximately 36.67°

Step-by-step explanation:

The given parameters of the float plane are;

The height of the float plane above the water, y = 350 m

The horizontal distance of the float plane from Ahmed, x = 470 m

Given that Ahmed is sitting on the dock, by the water, by trigonometric ratios, we have;

The height of the float plane, the distance of the plane from Ahmed and the line of sight forming the angle of elevation of the plane measured from Ahmed, form a right triangle

tan\angle X = \dfrac{Opposite \ leg \ length}{Adjacent \ Leg\ length}

Therefore

tan(\theta) = \dfrac{y}{x}

Where;

θ = The angle of elevation of the plane measured from Ahmed

y = The leg of the right triangle opposite the reference angle

x = The leg  of the right adjacent to reference angle

Therefore;

θ = arctan(y/x) which gives;

θ = arctan(350/470) ≈ 36.67°

The angle of elevation of the plane measured from Ahmed, θ ≈ 36.67°.

8 0
3 years ago
What is the slope of a line that is perpendicular to the graphed line?
Lemur [1.5K]

Answer:

2

Step-by-step explanation:

To find the slope of the graphed line, you take two points. I have chosen (0, 4) and (8, 0)

The formula of a slope is (y value of second point -y value of first point) divided by (x value of second point -x value of first point):

\frac{0-4}{8-0} =-\frac{1}{2}

------------------------------------------------------------------------

The slope for a perpendicular line is 2.

6 0
3 years ago
John wants to make a 100 ml of 6% alcohol solution mixing a quantity of a 3% alcohol solution with an 8% alcohol solution. What
mart [117]

Answer:

-50 ml of 3% alcohol solution and 150 ml of 8% alcohol solution

Step-by-step explanation:

For us to solve this type of mixture problem, we must represent the problem in equations. This will be possible by interpreting the question.

Let the original volume of the first alcohol solution be represented with x.

The quantity of the first alcohol solution needed for the mixture is 3% of x

                   ⇒ \frac{3}{100} * x

                       = 0.03x

Let the original volume of the second alcohol solution be represented with y.

The quantity of the second alcohol solution needed for the mixture is 5% of y

                   ⇒ \frac{5}{100} * y

                       = 0.05y

The final mixture of alcohol solution is 6% of 100 ml

                 ⇒ \frac{6}{100} * 100 ml

                       = 6 ml

Sum of values of two alcohol solutions = Value of the final mixture

                     0.03x + 0.05y = 6 ml               ..........(1)

Sum of original quantity of each alcohol solution = Original volume of the of mixture

                     x + y = 100 ml                          ..........(2)      

For easy interpretation, I will be setting up a table to capture all information given in the question.

Component                       Unit Value      Quantity(ml)       Value

3% of Alcohol solution        0.03                 x                     0.03x

8% of Alcohol solution        0.08                 y                     0.08y

Mixture of 100ml of 6%        0.06               100                       6    

                                                                x + y = 100       0.03x + 0.08y =6

Looking at the equations we derived, we have two unknowns in two equations which is a simultaneous equation.

                                0.03x + 0.05y = 6 ml               ..........(1)

                                x + y = 100 ml                           ..........(2)    

Using substitution method to solve the simultaneous equation.

Making x the subject of formula from equation (2), we have,

                                x  = 100 - y                                 ..........(3)

Substituting  x  = 100 - y from equation (3) into equation (1)

                               0.03(100 - y) + 0.05y = 6  

                               3 - 0.03y + 0.05y = 6  

Rearranging the equation,            

                               0.05y - 0.03y = 6 - 3

                               0.02y = 3

                               y = \frac{3}{0.02}

                               y = 150 ml

Substituting y = 150 ml into equation (3) to get x

                              x  = 100 - 150 ml

                              x = - 50 ml

The quantity of the first alcohol solution needed for the mixture for 3% is - 50 ml

The quantity of the second alcohol solution needed for the mixture for 5% is 150 ml

This solution means 50 ml of the first alcohol solution must be removed from the mixture with 150 ml of the second alcohol solution to get a final mixture of 100 ml of 6% alcohol solution.

3 0
2 years ago
of the students in your class, 12% are left-handed. What fraction of the students are left-handed? Are there more right-handed o
Ksivusya [100]

Answer:

<em><u>The answer here is 3/25, more left handed students.</u></em>

Step-by-step explanation:

12/100 are left handed, which reduces to 3/25. This means that there are only 3 left handed kids for every 22 right handed kids, showing that there are more right handed students than left handed.

7 0
2 years ago
Find the area of a parallelogram whose base is 12cm and altitude is 8cm. Also find the other base of its corresponding altitude
lukranit [14]

Answer:

Step-by-step explanation:

Area of parallelogram = base * height

                                    = 12 * 8

                                    = 96 cm²

Area of parallelogram = 96

base * height = 96

          base = 96/height

          base = 96/16

         base = 6 cm

6 0
2 years ago
Read 2 more answers
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