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Artyom0805 [142]
3 years ago
6

Evaluate the series

Mathematics
1 answer:
lesantik [10]3 years ago
8 0
S=\displaystyle\sum_{n=1}^7\left(\frac14\right)^n

\displaystyle S=\frac14+\left(\frac14\right)^2+\cdots+\left(\frac14\right)^7
\displaystyle\frac14S=\left(\frac14\right)^2+\left(\frac14\right)^3+\cdots+\left(\frac14\right)^8
\displaystyle S-\frac14S=\frac14+\left(\left(\frac14\right)^2-\left(\frac14\right)^2\right)+\cdots+\left(\left(\frac14\right)^7-\left(\frac14\right)^7\right)-\left(\frac14\right)^8
\displaystyle\frac34S=\frac14-\left(\frac14\right)^8
\displaystyle S=\frac{\frac14-\left(\frac14\right)^8}{\frac34}=\frac{5461}{16384}
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xenn [34]

Answer:

The speed is still water is v = \frac{d}{h} - c.

Step-by-step explanation:

Dimentionally speaking, speed is distance divided by time. Since, the person is travelling downstream, absolute speed is equal to the sum of current speed and speed of the person regarding current. Both components are constant. That is:

c + v = \frac{d}{h}

Where:

c - Current speed, measured in miles per hour.

v - Speed of the person regarding current, measured in miles per hour.

d - Distance travelled downstream, measured in miles.

h - Time spent on travelling, measured in hours.

Speed in still water occurs when current speed is zero. Then, such variable is obtained after subtracting current speed on both sides of the expression. Hence:

v = \frac{d}{h} - c

The speed is still water is v = \frac{d}{h} - c.

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4 years ago
Evaluate the expression for a^2 + b ÷3 when a = 3 and b = 6
Flura [38]

Answer:

11

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3 years ago
What is 20/10 as a <br><br> mixed number
Lostsunrise [7]
It will just be 2 since 10 goes into 20 2 times

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4 years ago
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Aleksandr-060686 [28]

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

7*x-4-(21)=0

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Divide both sides of the equation by 7:

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6 0
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Sidana [21]

Answer:

(a) y = 6250x +17850 --- The function

(b) y = 49100 --- The salary in 5 years

Step-by-step explanation:

Given

y = 1250x + 22850

Solving (a): Model the function around (1,24100) and (3,36600)

First, we calculate the slope

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{36600 - 24100}{3 - 1}

m = \frac{12500}{2}

m = 6250

The function is then calculated as:

y = m(x - x_1) + y_1

y = 6250(x - 1) + 24100

y = 6250x - 6250 + 24100

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Here:

x = 5

So:

y = 6250x +17850

y = 6250*5 +17850

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