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Kisachek [45]
3 years ago
5

Find the sum of first seventeen numbers of an ap whose 4th and 9th tearm are -15 and -30

Mathematics
1 answer:
Radda [10]3 years ago
4 0

Answer:

The sum of first seventeen terms is - 510

Step-by-step explanation:

Given as :

The 4th term of an A.P =  t_4 =  - 15

The 9th term of an A.P =  t_9 =  - 30

For an arithmetic progression

The nth term is given as t_n = a + ( n - 1)×d

Where a is the first term and d is the common difference between numbers

<u>So, For 4th term </u>

t_n = a + ( n - 1)×d

Or, t_4 = a + ( n - 1)×d

- 15 = a + ( 4 - 1)×d

Or, - 15 = a + 3 d            .........1

<u>So, For 9th term </u>

t_n = a + ( n - 1)×d

t_9 = a + ( n - 1)×d

- 30 = a + ( 9 - 1)×d

Or, - 30 = a + 8 d            .........2

Solve eq 1 and 2

( a + 8 d ) - ( a + 3 d ) = - 30 - ( - 15)

or, ( a - a ) + ( 8 d - 3 d ) = - 30 + 15

or, 0 + 5 d = - 15

∴ d = - \frac{15}{5} = - 3

Now, put the value of d in eq 1

I.e - 15 = a + 3 × ( - 3)  

Or. - 15 = a - 9

∴ a = -15 + 9 = - 6

Now The sum of nth term is written as :

s_n = \frac{n}{2} × [ 2 × a + ( n - 1 )×d ]

Where n is the nth term

a is the first term

d is the common difference

So<u> For n = 17th term </u>

s_17 = \frac{17}{2} × [ 2 × ( - 6) + ( 17 - 1 )×( - 3) ]

Or, s_17 = \frac{17}{2} × [ - 12 - 48 ]

Or, s_17 = \frac{17}{2} × ( - 60 )

Or, s_17 = 17 × ( - 30)

∴  s_17 = - 510

Hence The sum of first seventeen terms is - 510  Answer

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In ∆ABC with m∠C = 90° the sides satisfy the ratio BC:AC:AB = 4:3:5. If the side with middle length is 12 cm, find: 1) The perim
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*The side with the middle length is 12cm, therefore BC must be 12 cm

------------------------------------------------------------<span>
Ratio 
------------------------</span>---------------------------------<span>--
BC:AC:AB
  4 : 3 : 5

</span>-----------------------------------------------------------
<span>Find 1 share
</span>-----------------------------------------------------------<span>
Given that BC = 12 cm
4 shares = 12 cm
1 share = 12 ÷ 4 = 3cm

</span>-----------------------------------------------------------
Find AC (4 shares)
-----------------------------------------------------------<span>
3 shares = 3 x 3 = 9 cm
BC = 9cm

</span>-----------------------------------------------------------
<span>Find AB (5 shares)
</span>-----------------------------------------------------------<span>
5 shares = 5 x 3 = 15cm
AB = 15cm

</span>------------------------------------------------------------
Length
-----------------------------------------------------------
   BC   :  AC   :  AB
12cm  :  9cm : 15cm<span>

---------------------------------</span>---------------------------------<span>
Perimeter
</span>------------------------------------------------------------------
<span>12 + 9 + 15 = 36cm

</span>------------------------------------------------------------------
<span>Answer: The perimeter is 36cm
</span>------------------------------------------------------------------<span>

</span>------------------------------------------------------------------
<span>Area
</span>------------------------------------------------------------------
1/2 x 9 x 12 = 54cm²<span>

</span>------------------------------------------------------------------
Answer: Area = 54cm²
------------------------------------------------------------------<span>

Given that the biggest ratio is AB
</span>⇒AB is the hypotenuse
AB = 15 cm

------------------------------------------------------------------
Answer: Hypotenuse = AB = 15cm
------------------------------------------------------------------
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Write the negation of: If we lose electricity, then the data will be lost.
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Step-by-step explanation:

Consider the provided statement.

If we lose electricity, then the data will be lost.

We are need to write the negation of the above statement.

First divide the whole statement in two parts

Let us consider p = We lose electricity and q = The data will be lost.

The symbol use for negation is tilde \sim

\sim(p\rightarrow q)

p\wedge \sim q

Represent T for true and F for False.

The required table is shown below:

p           q           (p\wedge \sim q)

F            F                F

F            T                F

T            F                T

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Give at least five problems solving about area of a sector of a circle.
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See below for the examples of sectors and arcs of a circle

<h3>Area of sector of a circle</h3>

The area of a sector is calculated as:

A = \frac{\theta}{360} * \pi r^2 ---- when the angle is in degrees

A = \frac{\theta}{2} *r^2 ---- when the angle is in radians

Take for instance, we have the following problems involving sector areas

Calculate the area of a sector where the radius of the circle is 7, and

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  2. The central angle is π/12 rad
  3. The central angle is 90 degrees
  4. The central angle is π/4 rad
  5. The central angle is 180 degrees

Using the above formulas, the sector areas are:

1. A = \frac{30}{360}* \frac{22}{7} * 7^2 = 12.83

2.  A = \frac{\pi}{12} * 7^2 = 12.83

3. A = \frac{90}{360}* \frac{22}{7} * 7^2 = 38.5

4. A = \frac{\pi}{2} * 7^2 = 38.5

5. A = \frac{180}{360}* \frac{22}{7} * 7^2 = 77

<h3>Examples of arc length</h3>

The length of an arc is calculated as:

L= \frac{\theta}{360} * 2\pi r ---- when the angle is in degrees

L = r\theta ---- when the angle is in radians

Take for instance, we have the following problems involving arc lengths

Calculate the length of an arc where the radius of the circle is 7, and

  1. The central angle is 30 degrees
  2. The central angle is π/12 rad
  3. The central angle is 90 degrees
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  5. The central angle is 180 degrees

Using the above formulas, the arc lengths are:

1. L = \frac{30}{360}* 2 * \frac{22}{7} * 7 = 3.7

2.  L = \frac{\pi}{12} * 7 = 3.7

3. L = \frac{90}{360}*2 * \frac{22}{7} * 7 = 11.0

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5. L = \frac{180}{360}*2 * \frac{22}{7} * 7 = 22

<h3>Examples of the arcs of a circle</h3>

The examples include:

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  • Pizza
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Read more about arc and sectors at:

brainly.com/question/15955580

#SPJ1

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