Ask question

Ask question

All categories

Dahasolnce [82]

1 year ago

15

The 16th term of an AP is three times the 5th term.If the 12th term is 20 more the 7th term.Find the first term and the common d

ifference

1 answer:

Vlad1618 [11]1 year ago

3 0

<h3><u>Answer:</u></h3>

First term = 6
Common difference= 4

<h3><u>Solution</u><u>:</u></h3>

Let's take the first term as <u>a</u> and the common difference be <u>d</u>

The formula to find the nth term of an arithmetic progression is given by :

an = a + ( n - 1 ) d

<u>According to question, we have :</u>

16th term of an AP is three times the 5th term.

➝ a16 = 3 ( a5 )

➝ a + ( 16 - 1 )d = 3 ( a + ( 5 - 1 )d )

➝ a + 15d = 3 ( a + 4d )

➝ a + 15d = 3a + 12d

➝ 15d - 12d = 3a - a

➝ 3d = 2a

➝ 2a = 3d

➝ <u>a = 3d/2</u><u>‎</u>ㅤ‎ㅤ‎ㅤ⸻ ( 1 )

And, the 12th term is 20 more the 7th term.

➝ a12 - ( a7 ) = 20

➝ a + ( n - 1 )d -( a + ( n - 1 )d ) = 20

➝ a + ( 12 - 1 )d - + a + ( 7 - 1 )d ) = 20

➝ a + 11d - ( a + 6d ) = 20

➝ a - a + 11d - 6d = 20

➝ 5d = 20

➝ d = 20/ 5

➝<u> d = 4</u>

<u>Using</u><u> equation</u><u> (</u><u> </u><u>1</u><u> </u><u>)</u>

➝ a = 3d / 2

➝ a = ( 3 × 4 ) / 2

➝ a = 12 / 2

➝<u> a = 6</u>

You might be interested in

I don't need you to work it out, just theorem(s) i need to reach the answer :)

VikaD [51]

Not sure why such an old question is showing up on my feed...

Anyway, let $x=\tan^{-1}\dfrac43$ and $y=\sin^{-1}\dfrac35$ . Then we want to find the exact value of $\cos(x-y)$ .

Use the angle difference identity:

$\cos(x-y)=\cos x\cos y+\sin x\sin y$

and right away we find $\sin y=\dfrac35$ . By the Pythagorean theorem, we also find $\cos y=\dfrac45$ . (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)

Meanwhile, if $\tan x=\dfrac43$ , then (by Pythagorean theorem) $\sec x=\dfrac53$ , so $\cos x=\dfrac35$ . And from this, $\sin x=\dfrac45$ .

So,

$\cos\left(\tan^{-1}\dfrac43-\sin^{-1}\dfrac35\right)=\dfrac35\cdot\dfrac45+\dfrac45\cdot\dfrac35=\dfrac{24}{25}$

7 0

3 years ago

Applying properties of Exponents in exercise,use the properties of exponents to simplify the expression.See example 1.

evablogger [386]

Answer: a) 15625, b) 0.2, c) 625, d) 0.008.

Step-by-step explanation:

Since we have given that

a) $(5^2)(5^3)$

As we know that

$a^m\times a^n=a^{m+n}$

So, it becomes,

$5^2\times 5^3=5^{2+3}=5^6=15625$

(b) $(5^2)(5^{-3})$

So, it becomes,

$5^2\times 5^{-3}=5^{2-3}=5^{-1}=\dfrac{1}{5}=0.2$

(c) $(5^2)^2$

As we know that

$(a^m)^n=a^{mn}$

So, it becomes,

$5^{2\times 2}=5^4=625$

(d) $5^{-3}$

$a^{-m}=\dfrac{1}{a^m}\\\\5^{-3}=\dfrac{1}{5^3}=\dfrac{1}{125}=0.008$

Hence, a) 15625, b) 0.2, c) 625, d) 0.008.

4 0

2 years ago

Answer quickly for 50 points, thank you.

Kaylis [27]

The incorrect answer is B.

All you have to do is plug in x to the formulas and see if the are equal.

4x - 2 = 3x + 6

4(8) - 2 = 3(8) + 6

30 = 30

CORRECT

The second is not only not equal, but it is the wrong kind of formula for what you are trying to prove there.

Hope that helps!

6 0

2 years ago

Read 2 more answers

Graph the given relation or equation and find the domain and range. Then

vredina [299]

X=1 Hopefully that helped

6 0

2 years ago

75% of the 40 beverages in the vending machine are sports drinks. How many of the beverages are sports drinks?

GrogVix [38]

There are 30 sports drinks
40/100 = 0,4x75 = 30

4 0

2 years ago