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3 years ago

The midpoint of the line segment at (1,7) and (5,5) is A) (3,6) B) (2,6) C) (3,1) D) (2,1)

Mathematics

1 answer:

hammer [34]3 years ago

5 0

Answer:

A) (3,6)

Step-by-step explanation:

Let M be the midpoint of the line segment at (1,7) and (5,5). Then:

$\mathsf{M\left(\dfrac{1+5}{2},\dfrac{7+5}{2}\right)}=\\=\mathsf{M\left(\dfrac{6}{2},\dfrac{12}{2}\right)}=\\=\mathsf{M\left(3,\,6\right)}$

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A water storage tank has the shape of a cylinder with diameter 14 ft. It is mounted so that the circular cross-sections are vert

andrezito [222]

Answer:

percentage of the total capacity is 75.6%

Step-by-step explanation:

Hello! To solve this problem we follow the following steps

1. draw the complete scheme of the problem (see attached image)

2. To solve this problem we must find the area of the circular sector using the following equation.(c in the second attached image)

$A=\frac{R^2}{2} (\alpha -sin\alpha )$

$\alpha =2arccos(\frac{d}{R})$

3. observing the attached images we replace the values in the equations and find the area of the circular sector, remember that you must transform the angle to radians

$\alpha =2arccos(\frac{5}{7})=88.83$

$A=\frac{R^2}{2} (\alpha -sin\alpha )\\A=\frac{7^2}{2} (88.83-sen88.83)*\frac{\pi rad}{180} =37.57ft^2$

4.we calculate the area of the total circle (At), then subtract the area of the circular sector (Ac) to find the area occupied by water (Aw)

$At=\frac{\pi }{4} (14ft)^2=153.93ft^2$

Aw=At-Ac=153.93-37.57=116.36ft^2

5.Finally, we calculate the percentage that represents the water in the tank by dividing the area of the water over the total area of the tank

$\frac{116.36}{153.93} *100=75.6$

percentage of the total capacity is 75.6%

3 0

2 years ago

PLEASE HELP 7TH GRADE 100 PTS!!!

MariettaO [177]

f(x) = 5x is linear. Just a straight line with a slope of +5. So if the intervals are both a difference of 1, then the average rate of change will be the same.

f(x2) - f(x1) over x2 - x1. That's the formula for average rate of change.

So for Section A:

f(x) = 5x, (0,1)

[f(1) - f(0)]/(1-0)

= [5(1) - 5(0)]/1

=(5)/1

Do the same for section B and you'll get 5 as well.

I hope this helps you because I have no clue if my answer is right

6 0

3 years ago

Use f(x)=1/2x and f^-1(x)=2x to solve the problems f^1(-2), f(-4), f(f^-1(-2)?

neonofarm [45]