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Katyanochek1 [597]
3 years ago
13

What is the midpoint of the following coordinates:

Mathematics
1 answer:
igor_vitrenko [27]3 years ago
4 0
To find the midpoint if you have the points
(x,y) and (z,t) and you wnat to finnd the midpoint you do
midpoint=(\frac{x+z}{2} , \frac{y+t}{2})
so

1. (4,7) and (-3,11)
midpoint=(\frac{4-3}{2} , \frac{7+11}{2} )=(1/2,9)
 


2. (-8,3) ad (-6,-3)
midpoint=(\frac{-8-6}{2} , \frac{3+11}{2})=(-7,7)




3. (-8,5) and (-3,-5)
(-3,-5)=(\frac{-8+x}{2} , \frac{5+y}{2})
so
-3=\frac{-8+x}{2}
-6=-8+x
2=x


-5=\frac{5+y}{2}
-10=5+y
-15=y
B=(2,-15)


4. (9,-2) and (5,7)
(5,7)=(\frac{9+x}{2} , \frac{-2+y}{2})

5=\frac{9+x}{2}
10=9+x
1=x

7=\frac{-2+y}{2}
14=-2+y
16=y

A=(1,16)





1. M=(1/2,9)
2. M=(-7,7)
3.B=(2,-15)
4. A=(1,16)





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If a ball is thrown straight up into the air with an initial velocity of 70 ft/s, its height in feet after t seconds is given by
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Answer:

a) Average velocity at 0.1 s is 696 ft/s.

b) Average velocity at 0.01 s is 7536 ft/s.

c) Average velocity at 0.001 s is 75936 ft/s.

Step-by-step explanation:

Given : If a ball is thrown straight up into the air with an initial velocity of 70 ft/s, its height in feet after t seconds is given by y = 70t-16t^2.

To find : The average velocity for the time period beginning when t = 2 and lasting.  a. 0.1 s. , b. 0.01 s. , c. 0.001 s.

Solution :    

a) The average velocity for the time period beginning when t = 2 and lasting 0.1 s.

(\text{Average velocity})_{0.1\ s}=\frac{\text{Change in height}}{0.1}

(\text{Average velocity})_{0.1\ s}=\frac{h_{2.1}-h_2}{0.1}

(\text{Average velocity})_{0.1\ s}=\frac{(70(2.1)-16(2.1)^2)-(70(0.1)-16(0.1)^2)}{0.1}

(\text{Average velocity})_{0.1\ s}=\frac{69.6}{0.1}

(\text{Average velocity})_{0.1\ s}=696\ ft/s

b) The average velocity for the time period beginning when t = 2 and lasting 0.01 s.

(\text{Average velocity})_{0.01\ s}=\frac{\text{Change in height}}{0.01}

(\text{Average velocity})_{0.01\ s}=\frac{h_{2.01}-h_2}{0.01}

(\text{Average velocity})_{0.01\ s}=\frac{(70(2.01)-16(2.01)^2)-(70(0.01)-16(0.01)^2)}{0.01}

(\text{Average velocity})_{0.01\ s}=\frac{75.36}{0.01}

(\text{Average velocity})_{0.01\ s}=7536\ ft/s

c) The average velocity for the time period beginning when t = 2 and lasting 0.001 s.

(\text{Average velocity})_{0.001\ s}=\frac{\text{Change in height}}{0.001}  

(\text{Average velocity})_{0.001\ s}=\frac{h_{2.001}-h_2}{0.001}

(\text{Average velocity})_{0.001\ s}=\frac{(70(2.001)-16(2.001)^2)-(70(0.001)-16(0.001)^2)}{0.001}

(\text{Average velocity})_{0.001\ s}=\frac{75.936}{0.001}

(\text{Average velocity})_{0.001\ s}=75936\ ft/s

5 0
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Braden biked 10 8/9 miles on Monday. On Tuesday, he biked 3/ 4 as far as Monday. How many total miles did he bike over the two d
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Answer:

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Step-by-step explanation:

For Tuesday's ride we need to multiply 10 8/9 by 3/4.

10 8/9 = (9*10+8) / 9 =  98/9 miles.

98 / 9  * 3/4

= 98/3 * 1/4

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= 8 1/6 miles.

Total miles over 2 days = 10 8/9 + 8 1/6

= 18 + 8/9 + 1/6

= 18 +  48/54 + 9/54

= 18 57/54

= 19 3/54

= 19 1/18 miles.

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