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svp [43]
3 years ago
9

Find the sum of the first 6 terms of the following series, to the nearest integer.

Mathematics
1 answer:
natka813 [3]3 years ago
8 0

Answer:

1008

Step-by-step explanation:

geometric sequence:

a=16

r=32/16=2

Sum of GS:

s=a(1-r^n)/(1-r)

S(6)=16(1-2^6)/(1-2)

=1008

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Somebody please help! And show your work!
VARVARA [1.3K]

a= 34 degrees

b= 28 degrees

c= 62 degrees

Step-by-step explanation:

First you know that b is 1/2 of 56 degrees or 28.

The triangle with the a in it is isoceles because the two sides are both radii.

In the triangle the top angle = 112 because it is a centeral angle to the 112 arc.

Angle a and opposite to a are equal and then have to be 34 degrees to equal 180.

We know two arc lengths are 112 and 56 and the one with angle a has to be 34x2 or 68.

a whole circle equals 360.

360-56-68-112 = 124

Angle c = 1/2 of 124, or 62 degrees

6 0
3 years ago
Jackie loves to cook fried foods. She recorded the total amount of oil that she used each month in the table below.
SpyIntel [72]
Answer

She used 6/15 litres of oil in January

Explanation

We are given that, in January, she used 3/5 of the amount of oil she used in February.

We are also given that, she used 2/3 litres of oil in February.

Therefore, amount of oil used in January is:

3/5 • 2/3 = 6/15

She used 6/15 litres of oil in January
6 0
3 years ago
Read 2 more answers
) A watershed experiences a rainfall of 8 inches. What is the runoff volume when the curve number is 80
finlep [7]

Answer:

5.625 inches

Step-by-step explanation:

Given that:

Total Rainfall in inches (P) = 8 inches

The runoff volume (in inches) Q = ???

The curve number CN = 80

Recall that: The runoff volume can be calculated by using the formula:

Q = \dfrac{(P-0.2S)^2}{(P+0.8S)}    for P > 0.2S

Q = 0                     for P < 0.2S

S = \dfrac{1000}{CN}-10

where:

curve number CN = 80

S = \dfrac{1000}{80}-10

S = 2.5 inches

Since the rainfall (P) is greater than 0.25

Then:

Q = \dfrac{(P-0.2S)^2}{(P+0.8S)}  

Q = \dfrac{(8-0.2(2.5))^2}{(8+0.8(2.5))}

Q = \dfrac{(8-0.5)^2}{(8+2)}

Q = \dfrac{(7.5)^2}{(10)}

Q = \dfrac{(56.25)}{(10)}

Q = 5.625 inches

Thus, the runoff volume = 5.625 inches

4 0
3 years ago
Need help with this problem2(–2x – 4) + 6 = 5 – 3(x + 1) <br> I need the answer to this asap
Jet001 [13]
-4x-8+6=5-3x-3 distribute -4x-2=2-3x combine like terms -4=x combine like terms with addition and subtraction x=-4 final answer
4 0
3 years ago
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Question 20
Alexxandr [17]

Answer:

The camera had to cover the greatest angle is CAMERA 3 because it had the largest angle of 71.47°

Step-by-step explanation:

From the above question,

We have:

Camera 1 = Angle A

Camera 2= Angle B

Camera 3 = Angle C

A = 210ft

B = 234ft

C = 260ft

We need to find Angle A( angle of camera 1) using the cosine rule

A=(B² + C² - 2BCCosA)

210² = 234² + 260² - 2 × 234 × 260 × CosA

210² = 122356 - 121680CosA

Square both sides

210² = 122356 - 121680CosA

44100 = 122356 - 121680CosA

121680CosA = 122356 - 44100

121680CosA = 78256

Cos A = 78256/121680

Cos A = 0.6431295201

A = arc cos (0.6431295201)

A = 49.974422249°

Angle A approximately = 49.97°

Using the Sine rule to find the Angle B

A/Sine A = B/Sine B

210ft/Sine 49.97° = 234ft/Sine B

210ft × Sine B = 49.97° × 234ft

Sine B =( Sine 49.97° × 234ft)/210ft

B = arc sin (0.8532172354)

Angle B = 58.56334

Approximately = 58.56°

Angle C = 180 - (49.97 + 58.56)°

Angle C = 71.47°

Therefore, the camera had to cover the greatest angle is Camera 3 because it had the largest angle of 71.47°

6 0
3 years ago
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