MATHEMATICS COLLEGE

The third and the sixth term of a geometric progression are 24 and 64/9 respectively. Finda) the first term and common ratio
b) the sum of the first five terms

Answers

Answer 1

Answer:

Ai. Common ratio = 2/3

Aii. First term = 54

B. Sum of the first five terms = 422/3

Step-by-step explanation:

From the question given above, the following data were obtained:

3rd term (T3) = 24

6Th term (T6) = 64/9

First term (a) =?

Common ratio (r) =?

Sum of the first five terms (S5) =?

Ai. Determination of the common ratio (r).

T3 = ar²

T3 = 24

24 = ar²....... (1)

T6 = ar⁵

T6 = 64/9

64/9 = ar⁵......... (2)

The equation are:

24 = ar²....... (1)

64/9 = ar⁵......... (2)

Divide equation 2 by equation 1.

64/9 ÷ 24 = ar⁵ / ar²

64/9 × 1/24 = r³

8/27 = r³

Take the cube root of both side

r = 3√(8/27)

r = 2/3

Thus, the common ratio is 2/3

Aii. Determination of the first term (a).

T3 = ar²

3rd term (T3) = 24

Common ratio (r) = 2/3

First term (a) =?

24 = a(2/3)²

24 = 4a/9

Cross multiply

24 × 9 = 4a

216 = 4a

Divide both side by 4

a = 216/4

a = 54

Thus, the first term (a) is 54

B. Determination of the sum of the first five terms.

Common ratio (r) = 2/3

First term (a) = 54

Number of term (n) = 5

Sum of first five terms (S5) =?

Sn = a[1 –rⁿ] / 1 – r

S5 = 54[1 – (⅔)⁵] / 1 – ⅔

S5 = 54 [1 – 32/243] / ⅓

S5 = 54 (211/243) × 3

S5 = 54 × 211/81

S5 = 6 × 211/9

S5 = 2 × 211/3

S5 = 422/3

Thus, the sum of the first five terms is 422/3

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Answers

B, A, B, D

to calculate the slope m use the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 7, - 2) and (x₂, y₂ ) = (9, 4)

m = $(4+2)/(9+7)$ = $(6)/(16)$ = $(3)/(8)$

repeat with (x₁, y₁ ) = (5, - 6) and (x₂, y₂) = (- 1, 8)

m = $(8+6)/(-1-5)$ = $(14)/(-6)$ = - $(7)/(3)$

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = $(1)/(8)$ x - 1 is in this form

with slope m = $(1)/(8)$

To find the y- intercept , let x = 0, in the equation

x = 0 : y = 0 - $(10)/(7)$ = - $(10)/(7)$ ← y- intercept

Final answer:

The slopes of the lines between the given pairs of points are 3/8 and -7/3 respectively. The slope of the line Y = 1 / 8x - 1 is 1 / 8 and the y-intercept of the equation Y = 7 / 2x - 10 / 7 is -10 / 7.

Explanation:

The slope between two points is found by using the formula m = (y2 - y1) / (x2 - x1). Let's calculate for the first two. For (-7, -2) and (9, 4), the slope m = (4 - (-2)) / (9 - (-7)) = 6 / 16 =

3 / 8

. So, the correct answer is B. For the second pair of points (5, -6) and (-1, 8), m = (8 - (-6)) / (-1 - 5) = 14 / -6 = -

7 / 3

. So, the answer is A. The slope of the line of an equation in the form of y = mx + b is the coefficient of x (m), so for the line Y = 1 / 8x - 1, the slope is

1 / 8

. The answer is B. The y-intercept (b) is the constant term in the equation y = mx + b, so for the equation y = 7 / 2x - 10 / 7, the y-intercept is -

10 / 7

. The answer is D.

Learn more about Slope and Intercept here:

brainly.com/question/31471561

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Someone help me simplify this 3t+12-9=

Answers

it's simple

3t+3

just this

You would subtract 9 from 12 which would give you 3 which would lead you to 3t+3

David has four bags of apples and two bagsof mangoes. The first four bags contain
6 apples each and the bags with mangoes
contain 3 mangoes each. If David and his
friends ate 2 apples from each bag and 2
mangoes from each bag, what is the total
number of fruits left over?

Answers

Answer:

Step-by-step explanation: the step by step explanation is 6*4=24 so 24 apples then 3*2=6 so 6 mangoes then if 8 apples are ate then 4 mangoes are ate then (24+6)-(8+4)=30-12 so the answer is 18.

18 fruits left over
6 bags in total
4 bags x 6 apples each = 24 fruits
2 bags with 3 mangoes each= 6 fruits
Total 30 fruits
Friends ate 2 fruits from each of the 6 bags
They ate 12 fruits

30-12 = 18

A town interested in installing wind turbines to generate electricity measures the speed of the wind in the town over the course of a year. They find that most of the time, the wind speed is pretty slow, while only rarely does the wind blow very fast during a storm. What would be the best measure of the central wind speed they should report to the mayor? The mean, because the distribution of wind speeds is skewed. The median, because the distribution of wind speeds is symmetric. The mean, because the distribution of wind speeds is symmetric. The median, because the distribution of wind speeds is skewed. The proportion, because the distribution of wind speeds is skewed. The proportion, because the distribution of wind speeds is symmetric.

Answers

9514 1404 393

Answer:

The median, because the distribution of wind speeds is skewed.

Step-by-step explanation:

A few higher speeds will raise the mean. For a skewed distribution, the median may be a more appropriate measure of center.

Additional comment

From an engineering point of view, one might have to consider speeds only within some range, as the wind turbines may be shut down for speeds too low or too high. Likely the power generated is not proportional to speed, so a weighted average (of the square of speed) would probably be more useful. Unfortunately, this question does not get into such subtleties.

you had $20 at the beginning of the week you worked 10 hours during the week having $70 how much do you earn each hour