Answer:
9.56 ft/sec
Step-by-step explanation:
We are told that a 5.8-ft-tall person walks away from a 9-ft lamppost at a constant rate of 3.4 ft/sec.
I've attached an image showing triangle that depicts this;
Thus; dx/dt = 3.4 ft/sec
From the attached image and using principle of similar triangles, we can say that;
9/y = 5.8/(y - x)
9(y - x) = 5.8y
9y - 9x = 5.8y
9y - 5.8y = 9x
3.2y = 9x
y = 9x/3.2
dy/dx = 9/3.2
Now, to find how fast the tip of the shadow is moving away from the lamp post, it is;
dy/dt = dy/dx × dx/dt
dy/dt = (9/3.2) × 3.4
dy/dt = 9.5625 ft/s ≈ 9.56 ft/sec
Its important to know how to estimate quotients so when you have a quotient that doesn't divide easy or is a little long. You get get to a number that is easier.
Answer:
Its (5 x 7) x 4
Step-by-step explanation:
5 x (7 x 4)
5 x (28)
140
------------
(5 x 7) x 4
(35) x 4
140
Answer:
871.5
Step-by-step explanation:
directly proportional
y = kx
y = 12 when x = 14
12 = k(14)
k = 12/14
k = 6/7
--------------------------
what is the value of x when y = 747
747 = (6/7) * x
Multiply both sides by 7/6
747 * 7/6 = x
871.5 = x
A 36 year old male will pay $4.55 per $1,000 for a 10 year policy,
He bought a $150,000 policy:
150,000 / 1000 = 150
Multiply the rate per 1000 by 150:
4.55 x 150 = 682.50
His annual premium is $682.50
