She invited 150 friends. But she only had 5 activities for her friends and her party only lasted 4 hours. How much time will eac
1 answer:
Answer:
19.20 seconds.
Step-by-step explanation:
Given:
She invited 150 friends.
But she only had 5 activities for her friends and her party only lasted 4 hours.
Question asked:
How much time will each friend get on each activity ?
Solution:
First of all convert 4 hours into seconds:-
1 hour = 3600 seconds
4 hours = 3600 4 = 14400 seconds
<u>By unitary method:</u>
150 friends get time in 5 activities = 14400
1 friend get time in 5 activities = 14400 150 = 96 seconds
That means <u>each friend get 96 seconds in all 5 activities.</u>
Each friend get time on each activity = ?
Each friend get time on 5 activities = 96
Each friend get time on 1 activity = 96 5 = 19.20 seconds
Thus, each friend will get 19.20 seconds on each activity.
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Answer:
a)
b) yes the two lines are perpendicular
c)
Step-by-step explanation:
a) All this is asking if to find a line that is perpendicular to 2x + 5y = 7 AND passes through the origin.
so first we'll find the gradient(or slope) of 2x + 5y = 7, this can be done by simply rearranging this equation to the form
this is changed into the , and we easily see that -2/5 is in the place of m, hence
is the slope of the line 2x + 5y = 7.
Now, we need to find the slope of its perpendicular. We'll use:
.
here both slopes and
are slopes that are perpendicular to each other, so by plugging the value -2/5 we'll find its perpendicular!
.
.
Finally, we can find the equation of the line of the perpendicular using:
we know that the line passes through origin(0,0) and its slope is 5/2
is the equation of the the line!
b) For this we need to find the slopes of both lines and see whether their product equals -1?
mathematically, we need to see whether ?
the slopes can be easily found through rearranging both equations to
Line:1
Line:2
this equation is already in the form we need.
the slopes of both equations are
and
using
since the product does equal -1, the two lines are indeed perpendicular!
c)if two perpendicular lines have the same intercept, that also means that the two lines meet at that intercept.
we can easily find the slope of the given line, y = − 4 / 5 x + 6 to be and the y-intercept is
the coordinate at the y-intercept will be (0,6) since this point only lies in the y-axis.
we'll first find the slope of the perpendicular using:
we have all the ingredients to find the equation of the line now. i.e (0,6) and m
this is the equation of the second line.
side note:
this could also have been done by simply replacing the slope(m1) of the y = − 4 / 5 x + 6 by the slope of the perpendicular(m2): y = 5 / 4 x + 6
Answer:
2 times
Step-by-step explanation:
Well let's first graph the quadratic equation,
Look at the image below ↓
By looking at the image below we can tell that the graph touches the x axis 2 times at,
<u>(-1,0)</u>
<u>(1 1/3,0)</u>
<em />
<em>Thus,</em>
<em>the parabola touches the x axis twice.</em>
<em />
<em>Hope this helps :)</em>
