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Mandarinka [93]
3 years ago
5

Find the sum of the first six terms of the sequence for which a2=0.7 and a3=0.49.

Mathematics
2 answers:
alina1380 [7]3 years ago
8 0
A1 = 0.91
a6 = -0.14
sum = (0.91+-0.14) /2
sum = 2.31
Sloan [31]3 years ago
3 0

Answer:  Sum of the first six terms is 2.31.

Step-by-step explanation:

Since we have given that

a_2=0.7\\\\and\\\\a_3=0.49

Since we know the formula for "Arithmetic Progression":

a_2=a+d=0.7\implies a=0.7-d\\\\a_3=a+2d=0.49

Now, solving the above two equations:

a+2d=0.49\\\\0.7-d+2d=0.49\\\\0.7+d=0.49\\\\d=0.49-0.70\\\\d=-0.21

So, when we put the value of d in the first equation, we get that

a=0.7-d\\\\a=0.7+0.21\\\\a=0.91

so, Sum of first six terms would be

S_6=\dfrac{6}{2}(2\times 0.91+(6-1)\times -0.21)\\\\S_6=3(1.82+5\times -0.21)\\\\S_6=3(1.82-1.05)\\\\S_6=2.31

Hence, Sum of the first six terms is 2.31.

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Which pair of numbers is relatively prime
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Without any calculations it's evident it can't be neither B (both numbers are even, so they're divisible by 2) nor C (the numbers end in 0 and 5, so they're divisible by 5).

A.
57=3\cdot19\\
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Both numbers have a factor of 3, so they're not relatively prime.
That means it must be D. But, let's check it.

143=11\cdot13\\
323=17\cdot19

Indeed, those two numbers are relatively prime.

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3 years ago
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1. A plane is flying at an altitude of 13000 feet. The angle of depression from the plane to a control tower is 20 degrees. The
Mariulka [41]

Answer:

see explanation

Step-by-step explanation:

There is a right triangle formed between the height above the tower to the plane, the horizontal and the line from the tower to the plane.

The height above the tower to the plane = 13000 - 150 = 12850 ft

The angle between the plane and the tower is 20° , angle of depression.

Using the tangent ratio in the right triangle formed, with the adjacent side being the horizontal ( hor ) distance, then

tan20° = \frac{opposite}{adjacent} = \frac{12850}{hor} ( multiply both sides by hor)

hor × tan20° = 12850 ( divide both sides by tan20° )

hor = \frac{12850}{tan20} ≈ 35305 ft ( to the nearest foot )

(2)

Arianna is 60 + 5 = 65 ft above the ground ( to her eye level )

Using the right triangle formed with legs 65 and 37  and angle of depression x, then

tanx° = \frac{opposite}{adjacent} = \frac{37}{65} , thus

x = tan^{-1} (\frac{37}{65} ) ≈ 30° ( to the nearest degree )

4 0
3 years ago
Read 2 more answers
two trains leaves stations 320miles apart at the same time and travel toward eachother. One train travels at 110 miles per hour
I am Lyosha [343]

x/110 = (320-x)/90

<span> Cross multiply</span>

90x = 35200-110x

200x=35200

X = 35200/200 = 176 (distance traveled by train going 110 mph

176/110 = 1.6 hours = 1 hour and 36 minutes

 

Check: 110*1.6 = 176, 90*1.6 = 144

176+144 = 320

it will take 1.6 hours ( 1 hour 36 minutes) for the trains to meet
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You're given two side lengths of 6 centimeters and 9 centimeters. Which measurement can you use for the length of the third side
Zarrin [17]
Does it have to be a different number if not do nine cause then the bottom line soul be 6 and the sides would be 9
7 0
3 years ago
If you add 21 to my number and then multiply the result by 3, you will get 84 more than two-thirds of my number. Find my number.
Ksivusya [100]

Based on the calculations, the unknown number is equal to \frac{-45}{7}

  • Let the unknown number be x.

<h3>How to find an unknown number:</h3>

Translate the word problem into an algebraic expression, we have;

Adding 21 to the unknown number:

21 +x

Multiplying the result by 3:

3\times (21+x)

84 more than two-thirds of the unknown number:

\frac{2x}{3} +84

Equating the equations, we have:

3\times (21+x) = \frac{2x}{3} +84\\\\43+3x=\frac{2x}{3} +84

Cross-multiplying, we have:

43+3x=\frac{2x}{3} +84\\\\129+9x=2x+84\\\\9x-2x=84-129\\\\7x=-45\\\\x=\frac{-45}{7}

Read more on word problems here: brainly.com/question/13170908

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