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1 year ago

The second quadrant contains which point? Choose one below.

Mathematics

1 answer:

siniylev [52]1 year ago

3 0

Answer:

Step-by-step explanation:

In quadrant 2 (second quadrant) the X is negative and the Y is positive.

So C is the answer.

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Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms

miv72 [106K]

Hint :-

Break the given sequence into two parts .
Notice the terms at gap of one term beginning from the first term .They are like $\dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ . Next term is obtained by multiplying half to the previous term .
Notice the terms beginning from 2nd term , $4,7,10,13$ . Next term is obtained by adding 3 to the previous term .

Solution :- 

We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,

$\implies S_1 = \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ .

We can see that this is in Geometric Progression where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,

$\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]$

Notice the term $\dfrac{1}{2^{25}}$ will be too small , so we can neglect it and take its approximation as 0 .

$\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]$

$\\\implies \boxed{ S_1 \approx 1 }$

$\rule{200}2$

Now the second sequence is in Arithmetic Progression , with common difference = 3 .

$\implies S_2=\dfrac{n}{2}[2a + (n-1)d]$

Substitute ,

$\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}$

Hence sum = 908 + 1 = 909

7 0

3 years ago

Using geometry, calculate the volume of the solid under z=64−x2−y2and over the circular disk x2+y2≤64

Anarel [89]

Perhaps you mean to find the volume under $z=\sqrt{64-x^2-y^2}$ ? It seems like you have to rely on calculus otherwise (in the case that you indeed mean $z=64-x^2-y^2$ ).

Assuming this, note that $z=\sqrt{64-x^2-y^2}$ describes the top half of a sphere with radius 8, which means the volume below this surface over the disk $x^2+y^2\le64$ is simply half the volume of the sphere. Thus the volume is

$\dfrac43\pi8^3=\dfrac{2048}3\pi$

3 0

3 years ago

Animals and people that take in more energy than they expend will get fatter. Here are data on 12 rhesus monkeys: 6 lean monkeys

In-s [12.5K]

Answer:

mean lean body mass of the lean monkeys = 8.4kg

mean lean body mass of the obese monkeys = 10.4kg

Step-by-step explanation:

a) Mean = Sum of Body mass/number of body mass

For lean monkeys, mean = (6+7.5+9.2+9.7+9.1+9.1)/6

Mean = 50.6/6

Mean = 8.4

for obese monkeys, mean = (8+9.1+10.3+12+11.9+11.2)/6

Mean = 62.5/6

Mean = 10.4

3 0

3 years ago

Carmen rolls a cube with sides labeled A, B, C, D, E, and F.

Sav [38]

The number of possible outcomes is 29. ! hope this help hun <3

5 0

3 years ago

What is the value of x ? 6.75 + 3/8x = 13 1/4

Bad White [126]

Let's solve your equation step-by-step.

6.75+38x=1314

Step 1: Simplify both sides of the equation.

38x+6.75=534

Step 2: Subtract 6.75 from both sides.

38x+6.75−6.75=534−6.75

38x=132

Step 3: Multiply both sides by 8/3.

(83)*(38x)=(83)*(132)

x=523

Answer:

x=1713

7 0

3 years ago