From the information, it seems the runner is slowing down because the speed at 1st hour is 5km/h but at 3rd hour become 3km/h.
If v= velocity, v0= initial speed, t= time, and the a=acceleration then the function would be:
v= v0 + a * t
To find the acceleration you need to do this equation:
acceleration= velocity1- velocity3 / t3-t1
a = (3km/h-5km/h)/ (3 hour- 1 hour)
a = (-2km/h)/2hour= -1 km/hour^2
After that you need to find the initial speed. Try to put the 1st hour variable into the full equation. It would look like this
v= v0 + a * t
5km/h= v0 + (-1 km/hour^2 * 1 hour)
v0= 5km/h + 1km/h
v0= 6km/h
Then the full function would be:
v= 6km/h - 1km/h^2 * t
The graph would look like a backslash(\) from 6 gradually go down to 1.
Answer:
Step-by-step explanation:
Given that a tangent is drawn from P (6,2) to unit circle with center at the origin.
The tangent passing through (6,2) would have equaiton of the form
for suitable m.
Because this line is tangent, distance of centre of circle namely origin is the radius 1.
i.e. ![|\frac{-2m+6}{\sqrt{1+m^2} } |=1\\(-2m+6 )^2 = 1+m^2\\3m^2-24m+35=0\\\\m=1.918, 6.082](https://tex.z-dn.net/?f=%7C%5Cfrac%7B-2m%2B6%7D%7B%5Csqrt%7B1%2Bm%5E2%7D%20%7D%20%7C%3D1%5C%5C%28-2m%2B6%20%29%5E2%20%3D%201%2Bm%5E2%5C%5C3m%5E2-24m%2B35%3D0%5C%5C%5C%5Cm%3D1.918%2C%206.082)
the coordinates are the intersection of the tangent with the circle
They are (-0.162, 0.987) and (0.462,-0.887)
Answer:
Step-by-step explanation:
From the figure attached,
Coordinates of the vertices of the given rectangle ABCD,
A(3, 6), B(12, 6), C(12, 1) and D(3, 1)
Rule for the reflection of a point across x-axis,
(x, y) → (x, -y)
After reflection of the given rectangle across x-axis image points will be,
A(3, 6) → A'(3, -6)
B(12, 6) → B'(12, -6)
C(12, 1) → C'(12, -1)
D(3, 1) → D'(3, -1)
Now we can plot these points on the graph to get the image of rectangle ABCD.
Answer:
252
Step-by-step explanation:
The order of the books isn't important, so we'll use combinations.
The number of ways to choose 5 books from 10 is:
₁₀C₅ = 10! / (5! (10 − 5)!)
₁₀C₅ = 10! / (5! 5!)
₁₀C₅ = 10×9×8×7×6 / (5×4×3×2×1)
₁₀C₅ = 252
Answer:
B.) is the best deal
Step-by-step explanation:
A.) three six packs is $3 for each pack minus $2
$3 + $3 + $3 = $9
$9 - $2 = $7
B.) guessing the three six packs is $3 then minusing 25%
$3 - 25% = $2.25