Answer:
25
Step-by-step explanation:
The parallel lines divide the sides proportionally, so ...
DC/DQ = CR/QB
x/40 = 15/24
x = 40(15/24) . . . . multiply by 40
x = 25
Answer:
<em>Option: C. (6,7)</em>
Step-by-step explanation:
<u>Acute Triangle</u>
An acute triangle is a type of triangle with three angles that measure less than 90°. If one of the angles is 90°, then it's a right triangle.
In the given figure, we must find what point makes an acute triangle with the red colored segment. Let's analyze the options
The point (7,7) has the same x-coordinate as the right vertex, thus it will form a reight triangle, not an acute triangle
The point (8,5) would form an angle of more than 90°. It's not the correct option. The same situation applies to the point (2,4)
The only valid option is the point (6,7) because the x-coordinate is inside of the x-coordinates of the given segment.
Option: C. (6,7)
Answer:
The Acceleration of bike after 3 minutes of ride is 14 meter² per minutes
Step-by-step explanation:
Given as :
The displacement of bike is the function of time
i.e s(t) = t³ - 2 t² + 3 meters
The Time of bike acceleration = t = 3 minutes
Let The Acceleration of bike = a meter² per minutes
Now, According to question
∵ <u>Acceleration is define as the rate of change of velocity</u>
i.e acceleration = ![\dfrac{\textrm velocity}{\textrm time}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20velocity%7D%7B%5Ctextrm%20time%7D)
or, a = ![\dfrac{\textrm v}{\textrm t}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20v%7D%7B%5Ctextrm%20t%7D)
And
<u>Velocity is define as rate of change of displacement</u>
i.e velocity = ![\dfrac{\textrm displacement}{\textrm time}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20displacement%7D%7B%5Ctextrm%20time%7D)
Or, v = ![\dfrac{\textrm s}{\textrm t}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20s%7D%7B%5Ctextrm%20t%7D)
Since here displacement is function of time
So , v = ![\frac{\partial s(t)}{\partial t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20s%28t%29%7D%7B%5Cpartial%20t%7D)
Or, v = ![\frac{\partial (t³ - 2 t² + 3)}{\partial t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20%28t%C2%B3%20-%202%20t%C2%B2%20%2B%203%29%7D%7B%5Cpartial%20t%7D)
Or, v = 3 t² - 4 t + 3
So, velocity is the function of time = v = 3 t² - 4 t + 3 meter per minutes
Now, Again
Acceleration = a = ![\frac{\partial v}{\partial t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20v%7D%7B%5Cpartial%20t%7D)
Or, a = ![\frac{\partial (3 t² - 4 t + 3)}{\partial t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20%283%20t%C2%B2%20-%204%20t%20%2B%203%29%7D%7B%5Cpartial%20t%7D)
Or, a = 6 t - 4
∴ Acceleration is the function of time = a = 6 t - 4
Now, Acceleration of bike after 3 minutes
So, at t = 3 min
i.e a = 6 t - 4
Or, a = 6 × 3 - 4
Or, a = 18 - 4
∴ a = 14 meter² per minutes
Hence, The Acceleration of bike after 3 minutes of ride is 14 meter² per minutes . Answer
2.25t+5=13.5t+14
5-14=13.5t-2.25t
-9=11.25t
t=-9/11.25
t= -0.8