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Oksanka [162]
3 years ago
6

What number pattern is generated by the following

Mathematics
1 answer:
jenyasd209 [6]3 years ago
3 0

Answer:

nth term = 1 + n(13/4)

Step-by-step explanation:

3n + n/4 + 1

n = 1, 3(1) + (1)/4 + 1 = 4 + ¼ = 17/4

n = 2, 3(2) + (2)/4 + 1 = 7 + ½ = 30/4

n = 3, 3(3) + (3)/4 + 1 = 10 + ¾ = 43/4

n = 4, 3(4) + (4)/4 + 1 = 14 = 56/4

The difference between consecutive terms is 13/4

At n = 1, 17/4 = 1 + 1(13/4)

At n = 2, 30/4 = 1 + 2(13/4)

nth term = 1 + n(13/4)

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There are 3 islands A,B,C. Island B is east of island A, 8 miles away. Island C is northeast of A, 5 miles away and northwest of
Nostrana [21]

Answer:

The bearing needed to navigate from island B to island C is approximately 38.213º.

Step-by-step explanation:

The geometrical diagram representing the statement is introduced below as attachment, and from Trigonometry we determine that bearing needed to navigate from island B to C by the Cosine Law:

AC^{2} = AB^{2}+BC^{2}-2\cdot AB\cdot BC\cdot \cos \theta (1)

Where:

AC - The distance from A to C, measured in miles.

AB - The distance from A to B, measured in miles.

BC - The distance from B to C, measured in miles.

\theta - Bearing from island B to island C, measured in sexagesimal degrees.

Then, we clear the bearing angle within the equation:

AC^{2}-AB^{2}-BC^{2}=-2\cdot AB\cdot BC\cdot \cos \theta

\cos \theta = \frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC}

\theta = \cos^{-1}\left(\frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC} \right) (2)

If we know that BC = 7\,mi, AB = 8\,mi, AC = 5\,mi, then the bearing from island B to island C:

\theta = \cos^{-1}\left[\frac{(7\mi)^{2}+(8\,mi)^{2}-(5\,mi)^{2}}{2\cdot (8\,mi)\cdot (7\,mi)} \right]

\theta \approx 38.213^{\circ}

The bearing needed to navigate from island B to island C is approximately 38.213º.

8 0
3 years ago
Simplify the following expression.
HACTEHA [7]
Remember that exponentioal rule
x^m times x^n=x^(m+n)
therefor
7^4 times 7^-6=7^(4-6)=7^(-2)
remember the other rule
x^-m=1/(x^m) so
7^-2=1/(7^2)=1/49
answe ris A
5 0
3 years ago
Which answer is correct and why?
Ivanshal [37]
The answer is C.) 62.
Subtract 28 from 180, leaving 152, then subtract 90 since it's a right triangle because 2 sides are equivalent, leaving 62.
3 0
3 years ago
Read 2 more answers
4(4-w)=3(2w+2)<br>find w​
Travka [436]

Answer:

1

Step-by-step explanation:

4(4-w) = 3(2w+2)

Use distributive property:

16 - 4w = 6w + 6

    +4w  +4w

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

     16 = 10w + 6

    -6              -6

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

        10 = 10w

        ----    -----

        10      10

         1 = w

Hope this helped.

7 0
3 years ago
Read 2 more answers
Solve number 8 please
beks73 [17]

Answer:

see explanation

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² - 8x + 8y + 23 = 0

collect the x and y terms together and subtract 23 from both sides

x² - 8x + y² + 8y = - 23

using the method of completing the square

add ( half the coefficient of the x / y terms )² to both sides

x² + 2(- 4)x + 16 + y² + 2(4)y + 16 = - 23 + 16 + 16

(x - 4)² + (y + 4)² = 9 ← in standard form

with centre = (4, - 4 ) and r = \sqrt{9} = 3

this is shown in graph b

7 0
1 year ago
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