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1 year ago

Must show work, please helppp

Mathematics

2 answers:

katrin [286]1 year ago

8 0

9514 1404 393

Answer:

1/2

Step-by-step explanation:

The base of the exponent tells us the common ratio of this geometric series is 1/2. The start value of n=7 tells us the first term in the series we're evaluating is ...

a1 = 2(1/2)^(7-4) = 2·(1/2)^3 = 2/8 = 1/4

The formula for the infinite sum of a geometric series is ...

S = a1(1/(1-r))

Filling in the values we know, this is ...

S = (1/4)(1/(1 -1/2)) = (1/4)(2) = 1/2

The infinite sum is 1/2.

katovenus [111]1 year ago

7 0

i can't see the photo.

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Unsure how to do this calculus, the book isn't explaining it well. Thanks

krok68 [10]

One way to capture the domain of integration is with the set

$D = \left\{(x,y) \mid 0 \le x \le 1 \text{ and } -x \le y \le 0\right\}$

Then we can write the double integral as the iterated integral

$\displaystyle \iint_D \cos(y+x) \, dA = \int_0^1 \int_{-x}^0 \cos(y+x) \, dy \, dx$

Compute the integral with respect to $y$ .

$\displaystyle \int_{-x}^0 \cos(y+x) \, dy = \sin(y+x)\bigg|_{y=-x}^{y=0} = \sin(0+x) - \sin(-x+x) = \sin(x)$

Compute the remaining integral.

$\displaystyle \int_0^1 \sin(x) \, dx = -\cos(x) \bigg|_{x=0}^{x=1} = -\cos(1) + \cos(0) = \boxed{1 - \cos(1)}$

We could also swap the order of integration variables by writing

$D = \left\{(x,y) \mid -1 \le y \le 0 \text{ and } -y \le x \le 1\right\}$

and

$\displaystyle \iint_D \cos(y+x) \, dA = \int_{-1}^0 \int_{-y}^1 \cos(y+x) \, dx\, dy$

and this would have led to the same result.

$\displaystyle \int_{-y}^1 \cos(y+x) \, dx = \sin(y+x)\bigg|_{x=-y}^{x=1} = \sin(y+1) - \sin(y-y) = \sin(y+1)$

$\displaystyle \int_{-1}^0 \sin(y+1) \, dy = -\cos(y+1)\bigg|_{y=-1}^{y=0} = -\cos(0+1) + \cos(-1+1) = 1 - \cos(1)$

7 0

8 months ago

A radio station advertises a contest with ten cash prizes totaling $5510. There is to be a $100 difference between each successi

My name is Ann [436]

Answer:

option C

c. least: $101

greatest: $1001

Step-by-step explanation:

A radio station advertises a contest with ten cash prizes totaling $5510. There is to be a $100 difference between each successive prize.

Sum of 10 prizes = 5510

100 is the difference. there is a common difference d=100

So its a arithmetic sequence

the sum formula for arithmetic sequence is

$S_n = \frac{n}{2}(2a_1 +(n-1)d)$

Sn = 5510, n=10 n d= 100 we need to find out first term a1

$5510 = \frac{10}{2}(2a_1 +(10-1)100)$

5510 = 5 (2a1 + 900)

5510 = 10a1 + 4500

Subtract 4500 on both sides

1010= 10a1

divide by 10 on both sides

a1 = 101

so first term that is least term is 101

To find out greatest term we use formula

$a_n = a_1 + (n-1) d$

a(10) = 101 + (10-1)100

= 101 + 900= 1001

greatest is 1001

4 0

3 years ago

Y=2x+6 and y=-3x+16 for solving the system

Butoxors [25]

Substitution

Step 1: Solve for x or y in either of the two equations. In the equations that you are given, y is already solved for you.

Step 2: Plug in 2x + 6 into the opposite equation.

2x + 6 = -3x + 16
   - 6 - 6
------------------------------
2x = -3x + 10
+ 3x + 3x
------------------------------
5x = 10
------   ------
5    5

x = 2

Step 3: Plug in the x value into either equation.

y = 2(2) + 6
y = 4 + 6
y = 10

The final answer gets expressed as a coordinate pair: (x,y) (2,10)

I hope this helps you :)

4 0

2 years ago

Shobo's mother's present age is six times Shobo's present age. Shobo's age five

andre [41]

Shobo's age = x years

His mother's age = 6 times of Shobo's age

= 6x years

Five years from now

________________

Shobo's age = ( x + 5 ) years

According to the problem given,

x + 5 = one by third of his mother's

present age

x + 5 = 6x / 3

x + 5 = 2x

5 = 2x - x

5 = x

Therefore ,

Shobo's present age = x = 5 years

His mother's age = 6x

= 6 × 5

= 30 years

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2 years ago

Find the probability of getting the results shown on the spinners. Express your answer as a fraction in simplest form.

iragen [17]

1/5 and 1/4 is the answer

8 0

2 years ago

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