Ratios are used to relate two or more quantities
The number of motor bikes that pass the intersection is 14
The given parameters are:
![Cars: Bikes =7 : 2](https://tex.z-dn.net/?f=Cars%3A%20Bikes%20%3D7%20%3A%202)
![Total = 63](https://tex.z-dn.net/?f=Total%20%3D%2063)
The number of motor bikes is calculated using:
![Bikes = \frac{Bikes\ ratio}{Car\ ratio + Bike\ ratio} \times Total](https://tex.z-dn.net/?f=Bikes%20%3D%20%5Cfrac%7BBikes%5C%20ratio%7D%7BCar%5C%20ratio%20%2B%20Bike%5C%20ratio%7D%20%5Ctimes%20Total)
This gives
![Bikes = \frac{2}{7 + 2} \times 63](https://tex.z-dn.net/?f=Bikes%20%3D%20%5Cfrac%7B2%7D%7B7%20%2B%202%7D%20%5Ctimes%2063)
![Bikes = \frac{2}{9} \times 63](https://tex.z-dn.net/?f=Bikes%20%3D%20%5Cfrac%7B2%7D%7B9%7D%20%5Ctimes%2063)
Divide 63 by 9
![Bikes = 2 \times 7](https://tex.z-dn.net/?f=Bikes%20%3D%202%20%5Ctimes%207)
![Bikes = 14](https://tex.z-dn.net/?f=Bikes%20%3D%2014)
Hence, the number of motor bikes that pass the intersection is 14
Read more about ratios at:
brainly.com/question/22692485
Slope-intercept form y = mx + b
where m------> slope
b-------> y-intercept
m= (y1-y2)/(x1-x2)
P1(-3,5) (x1,y1)
P2(2,10) (x2,y2)
m= (5-10)/(-3-2)
m= (-5)/(-5)
m=1
Until now, the equation is y=mx+b
y=1.x+b
y=x+b
But, whe can plug the point P2(2,10) in y =x+b
10 =2 + b
10 - 2 = b
b= 8
Then, the equation is y=mx+b
y= x+8 <-------------------Solution
Verification P1(-3,5) y = x+8 5=-3+8 Ok
P2(2,10) y = x +8 10 = 2+8 Ok
Answer: The length of the base of the triangle is 16 inches.
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula
Area of a triangle (A) = base x height x 1/2
Replacing with the values given:
42 = b (5 1/4) 1/2
Solving for b (lenght of the base)
42 / (5 1/4) 1/2 = b
16 in = b
The length of the base of the triangle is 16 inches.
Feel free to ask for more if needed or if you did not understand something.
Answer:
(2x,2y) .
Step-by-step explanation:
coordinate increases by times 2.
Answer:
The rate at which both of them are moving apart is 4.9761 ft/sec.
Step-by-step explanation:
Given:
Rate at which the woman is walking,
= 3 ft/sec
Rate at which the man is walking,
= 2 ft/sec
Collective rate of both,
= 5 ft/sec
Woman starts walking after 5 mins so we have to consider total time traveled by man as (5+15) min = 20 min
Now,
Distance traveled by man and woman are
and
ft respectively.
⇒ ![m=2\ ft/sec=2\times \frac{60}{min} \times 20\ min =2400\ ft](https://tex.z-dn.net/?f=m%3D2%5C%20ft%2Fsec%3D2%5Ctimes%20%5Cfrac%7B60%7D%7Bmin%7D%20%5Ctimes%2020%5C%20min%20%3D2400%5C%20ft)
⇒ ![w=3\ ft/sec = 3\times \frac{60}{min} \times 15\ min =2700\ ft](https://tex.z-dn.net/?f=w%3D3%5C%20ft%2Fsec%20%3D%203%5Ctimes%20%5Cfrac%7B60%7D%7Bmin%7D%20%5Ctimes%2015%5C%20min%20%3D2700%5C%20%20ft)
As we see in the diagram (attachment) that it forms a right angled triangle and we have to calculate
.
Lets calculate h.
Applying Pythagoras formula.
⇒
⇒ ![h=\sqrt{(2400+2700)^2+500^2} = 5124.45](https://tex.z-dn.net/?f=h%3D%5Csqrt%7B%282400%2B2700%29%5E2%2B500%5E2%7D%20%3D%205124.45)
Now differentiating the Pythagoras formula we can calculate the rate at which both of them are moving apart.
Differentiating with respect to time.
⇒ ![h^2=(m+w)^2+500^2](https://tex.z-dn.net/?f=h%5E2%3D%28m%2Bw%29%5E2%2B500%5E2)
⇒ ![2h\frac{d(h)}{dt}=2(m+w)\frac{d(m+w)}{dt} + \frac{d(500)}{dt}](https://tex.z-dn.net/?f=2h%5Cfrac%7Bd%28h%29%7D%7Bdt%7D%3D2%28m%2Bw%29%5Cfrac%7Bd%28m%2Bw%29%7D%7Bdt%7D%20%20%2B%20%5Cfrac%7Bd%28500%29%7D%7Bdt%7D)
⇒
...as ![\frac{d(500)}{dt}= 0](https://tex.z-dn.net/?f=%5Cfrac%7Bd%28500%29%7D%7Bdt%7D%3D%200)
⇒ Plugging the values.
⇒
...as
ft/sec
⇒
ft/sec
So the rate from which man and woman moving apart is 4.9761 ft/sec.