Using proportions, it is found that:
- Peter is walking at a rate of 3 km/h.
- MJ is biking at a rate of 9 km/h.
---------------------------
- Peter is walking at a rate of x km/h.
- MJ is biking 6 km/h faster than Peter, thus 6 + x km/h.
- Opposite directions, thus, their distance increases at a rate of (6 + 2x) km each hour, as
.
6 + 2x km each hour, 18 km after 1.5 hours, thus, the rule of three is:
1h - (6 + 2x) km
1.5h - 18 km
Applying cross multiplication:
Then:
- Peter is walking at a rate of 3 km/h.
- MJ is biking at a rate of 9 km/h.
A similar problem is given at brainly.com/question/24112433
Hello Friend,here is the solution for your question
<span>so the given function is </span>
y= √(-2cos²x+3cosx-1)
i.e = √[-2(cos²x-3/2+1/2)]
i.e = √[-2(cosx-3/4)²-9/16+1/2]
i.e. = √[-2(cos-3/4)²-1/16]
i.e. = √[1/8-3(cosx=3/4)²]-----------(1)
Now here in this equation is this quantity :-
<span>(cosx=3/4)²----------------(2) is to it's minimum value then the whole equation </span>
<span>i.e. = √[1/8-3(cosx=3/4)²] will be maximum and vice versa </span>
And we know that cosx-3/4 will be minimum if cosx=3/4
<span>therefore put this in (1) we get </span>
(cosx=3/4)²=0 [ cosx=3/4]
<span>hence the minimum value of the quantity (cosx=3/4)² is 0 </span>
<span>put this in equation (1) </span>
we get ,
i.e. = √[1/8-3(cosx=3/4)²]
=√[1/8-3(0)] [ because minimum value of of the quantity (cosx=3/4)² is 0 ]
=√1/8
=1/(2√2)
<span>this is the maximum value now to find the minimum value </span>
<span>since this is function of root so the value of y will always be ≥0 </span>
<span>hence the minimum value of the function y is 0 </span>
<span>Therefore, the range of function </span>y is [0,1/(2√2)]
__Well,I have explained explained each and every step,do tell me if you don't understand any step._
In 8, 9, 10, all the triangles are similar, meaning corresponding sides have the same ratio.
8. hypotenuse / (short side) = 25/x = x/9
x² = 25*9 = 5²×3²
x = √(5²×3²) = 5*3 = 15
9. (long side) / (short side) = x/7 = 9/x
x² = 7*9
x = √(9*7) = 3√7
10. (short side) / (long side) = x/48 = 48/64
x = 48²/64 = 36
Answer:
Step-by-step explanation:
The fox is faster. Because he is a fox.
Also because he can (assuming he doesn't fatigue or get caught by hounds in the second half of the hour) run 42 miles in 1 hour.
The rabbit runs 35 miler per hour.
Velocity = Distance/time
Fox velocity = 21 miles/0.5 hour
Dividing by 0.5 is the same as multiplying by 2, so...
Fox velocity = 42 miles/hour
