Answer: 4 hours. (Note, it said "return journey"!! Could throw others off)
How-To: Mr. Ramos went at 80km/h the way there, on the return it said he was 20km/h faster, so on the return journey he was going 100km/h. He was traveling 400km, so (400km)/(100km/h)=4h
Are you looking for a acute angle?
Answer:
37.8 metre
Step-by-step explanation:
CHECK THE COMPLETE QUESTION BELOW;
Linda shoots an arrow at a target in an archery competition. The arc of the arrow can be modeled by the equation y= -0.02x to the power of 2 + 0.65+4 where x is the horizontal distance (in meters) from Linda and y is the height (in meters) of the arrow. How far from Linda does the arrow hit the ground? Round to the nearest tenth.
From the question, we are told that the equation that modelled the arc is
y=-0.02x²+0.65x+4
From the question, "x" in the equation=
the horizontal distance (in meters
While "y" in the equation = the height (in meters) of the arrow.
We can find the value of x and y by equating to zero(since arrow hits the ground when its height (y) is zero) then solve the quadratic equation using quadratic formula
y=-0.02x²+0.65x+4=0
We have, x=37.79 or -5.29
The negative x= -5.29 can be described as been at the back of Linda,
But the distance is of positive value, therefore, the arrow hit the ground at 37.8 metre from Linda after Rounded to the nearest tenth.
Answer:
K(-4,8) is the ortho center.
Step-by-step explanation:
In a right angled triangle, The vertex of the right angle is the ortho center.
Here we are given
J(-4,-1), K(-4,8) & L(2,8)
Using distance formula we get
![JK^{2}= (-4+4)^{2}+ (8+1)^{2}=0+81=81](https://tex.z-dn.net/?f=JK%5E%7B2%7D%3D%20%28-4%2B4%29%5E%7B2%7D%2B%20%288%2B1%29%5E%7B2%7D%3D0%2B81%3D81)
![KL^{2}= (-4-2)^{2}+ (8+-8)^{2}=36+0=36](https://tex.z-dn.net/?f=KL%5E%7B2%7D%3D%20%28-4-2%29%5E%7B2%7D%2B%20%288%2B-8%29%5E%7B2%7D%3D36%2B0%3D36)
![JL^{2}= (-4-2)^{2}+ (8+1)^{2}=36+81=117](https://tex.z-dn.net/?f=JL%5E%7B2%7D%3D%20%28-4-2%29%5E%7B2%7D%2B%20%288%2B1%29%5E%7B2%7D%3D36%2B81%3D117)
So we can say that
![JK^2 + KL^2=JL^2](https://tex.z-dn.net/?f=JK%5E2%20%2B%20KL%5E2%3DJL%5E2)
By converse of pythagorean theorem we get
![](https://tex.z-dn.net/?f=%3CK%20%3D%2090%C2%B0)
Hence the Vertex of the right angle is K(-4,8)
K(-4,8) is the ortho center.