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2 years ago

1) -24, -4, 16, 36, ... Find a23

Mathematics

1 answer:

viktelen [127]2 years ago

7 0

We're given the Arithmetic Progression <em>-24, -4, 16, 36 ...</em> .

We know that a term in an AP is generally represented as:

$\bf a_n\ =\ a\ +\ (n\ -\ 1)d$

where,

a = the first term in the sequence
n = the number of the term/number of terms
d = difference between two terms

We need to find $\sf a_2_3$ .

From the given progression, we have:

a = -24
n = 23
d = (-24 - (-4) = -20

Using these in the formula,

$\sf a_2_3\ =\ a\ +\ (n\ -\ 1)d\\\\\\a_2_3\ =\ -24\ +\ (23\ -\ 1)\ \times\ (-20)\\\\\\a_2_3\ =\ -24\ +\ 22\ \times (-20)\\\\\\a_2_3\ =\ -24\ -\ 440\\\\\\\bf a_2_3\ =\ -464$

Therefore, the 23rd term in the AP is -464.

Hope it helps. :)

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Identify the lateral area and the surface area of a right rectangular prism with an 8 cm by 9 cm base and a height of 13 cm.

stepan [7]

It's A: L =704cm2; S =936cm2
because your multiplying your length and width (8x9) =72
multiply 72 by the height and you get your answer for S = 936cm2

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2 years ago

Find the angle between the given vector in degrees. u=<6, 4>, v=<7, 5> HELPPPPPPPPPP

Paladinen [302]

Recall that

$\vec a\cdot\vec b=\|\vec a\|\|\vec b\|\cos\theta$

where $\theta$ is the angle between the vectors $\vec a,\vec b$ whose magnitudes are $\|\vec a\|,\|\vec b\|$ , respectively.

We have

$\langle6,4\rangle\cdot\langle7,5\rangle=\sqrt{6^2+4^2}\sqrt{7^2+5^2}\cos\theta$

$\cos\theta=\dfrac{31}{\sqrt{962}}\implies\theta\approx88.2^\circ$

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2 years ago

Calculate the mean, median, mode, range, and 5 Number Summary of the following data set: 5,6,8,4,7,5,4,2,5,6,5,2,1,4

Artist 52 [7]

Answer:

mean = 4.57, median = 5 , mode = 5, range =7 ,

five number summary: Minimum value= 1 , First Quartile = 4, Median = 5

Third Quartile = 6, Maximum value = 8

Step-by-step explanation:

First arrange the data in ascending order.

1,2,2,4,4,4,5,5,5,5,6,6,7,8

Mean = sum of all numbers / total numbers

= 1+2+2+4+4+4+5+5+5+5+6+6+7+8 / 14

= 64 / 14

= 4.57

Median:

Since the given data is even number so, we can find median by taking mean of 2 middle numbers.

so the middle numbers are 7th and 8th data i.e, 5 and 5

Median =(5+5)/2

= 5

Mode:

The most repetitive number in the data set is mode

So Mode = 5

Range:

Range can be found by subtracting smallest number from largest number in the data set.

Smallest number = 1, Largest number = 8

Range= Largest number - Smallest number

= 8-1 = 7

Five no Summary

Minimum value= 1

First Quartile ( 25 % mark )= 4

Median = 5

Third Quartile (75 % mark) = 6

Maximum value = 8

First quartile can be found by : consider the data on left of the median and find median among them

Third quartile can be found by: consider the data on right of the median and find median among them

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2 years ago

What is the surface area of the right prism?

madreJ [45]

Answer:

The surface area of right prism is 12 feet² , option D

Step-by-step explanation:

Given as :

The measure of base = 4 ft

The height of base = 0.5 ft

The surface area of right prism = perimeter of base × height + 2 × base

Now ,

Perimeter of base = 4 + 4 = 8 ft

So, The surface area of right prism = 8 × 0.5 + 2 × 4

Or, The surface area of right prism = 4 + 8

∴ , The surface area of right prism = 12 feet²

Hence The surface area of right prism is 12 feet² . Answer

4 0

2 years ago

Read 2 more answers

What is the nth term rule of the quadratic sequence below? 4,15,30,49,72,99,130,...

navik [9.2K]

Answer:

The nth term rule of the quadratic sequence is $2n^{2} +5n-3$ .

Step-by-step explanation:

We are given the following quadratic sequence below;

4, 15, 30, 49, 72, 99, 130,...

As we know that the formula for the nth term of the quadratic sequence is given by = $an^{2}+bn+c$

Firstly, we will find the difference between the term of the given sequence;

1st difference of the given sequence;

(2nd term - 1st term), (3rd term - 2nd term), (4th term - 3rd term), (5th term - 4th term), (6th term - 5th term), (7th term - 6th term)

= (15 - 4), (30 - 15), (49 - 30), (72 - 49), (99 - 72), (130 - 99),....

= (11, 15, 19, 23, 27, 31,.....)

Now, we will find the second difference of the given sequence, i.e;

= (15 - 11), (19 - 15), (23 - 19), (27 - 23), (31 - 27),....

= (4, 4, 4, 4, 4)

Since the differences are same now, so to find the value of a we have to divide the value of second difference by 2, i.e;

The value of a = $\dfrac{4}{2}$ = 2

SO, the first term of the nth term rule equation is $an^{2}$ = $2n^{2}$ .

Now, in the term $2n^{2}$ , put the value of n = 1, 2, 3, 4 and 5 and then form the sequence, i.e;

If n = 1, then $2n^{2}$ = $2 \times (1)^{2}$ = 2

If n = 2, then $2n^{2}$ = $2 \times (2)^{2}$ = 8

If n = 3, then $2n^{2}$ = $2 \times (3)^{2}$ = 18

If n = 4, then $2n^{2}$ = $2 \times (4)^{2}$ = 32

If n = 5, then $2n^{2}$ = $2 \times (5)^{2}$ = 50

SO, the sequence formed is (2, 8, 18, 32, 50).

Now, find the difference of this sequence and the original quadratic sequence, i.e;

= (4 - 2), (15 - 8), (30 - 18), (49 - 32), (72 - 50)

= (2, 7, 12, 17, 22)

Now, as we can see that the above sequence resembles the general form of (5n - 3) because:

If we put n = 1, then (5n - 3) = 5 - 3 = 2

If we put n = 2, then (5n - 3) = 10 - 3 = 7 and so on....

From this, we concluded that the value of b and c are 5 and (-3) respectively.

Hence, the nth term rule for the given quadratic sequence is $2n^{2} +5n-3$ .

7 0

2 years ago