An object is sold for a price with a 7% tax. The final price is then $21.40. What was the original price
2 answers:
Answer:
The original price of object is $20
Step-by-step explanation:
Given : An object is sold for a price with a 7% tax. The final price is then $21.40.
We have to find the original price.
Since the final price includes the original price and tax paid.
So $ 21.40 includes original price and tax paid.
Let original price is x, then
Tax paid is 7% of original price that is
Thus,
Simplify, for x,
we have,
Divide both side by 1.07 . we have,
x = 20
Thus, the original price of object is $20
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Answer:
The diagonal is increasing at the rate of 119/104cm/min of the given rectangle.
Step-by-step explanation:
Dimensions of the rectangle
Height = 5cm
Rate of base = 3/2 cm/min
Area = 60cm^2
We know the area of a rectangle of given by = base* Height
b*h = 60
b*5 = 60
b = 12cm
Applying Pythagoras theorem while drawing a diagonal to the rectangle
so our diagonal will be 13cm
Upon differentiating the area of the rectangle we get
b*h = A=60cm^2
using the chain rule of differentiation
h*db/dt + b*dh/dt = 0
b*dh/dt = -h*db/dt
12*dh/dt = -5*3/2
dh/dt = -5/8 cm//min
so the height of the rectangle is decreasing at the rate of -5/8cm/min
now we have all the measurements we need
b = 12 , db/dt = 3/2cm/min
h = 5 , dh/dt = -5/8 cm/min
Upon differentiating we get
2b*db/dt + 2h*dh/dt = 2D*dD/dt
b*db/dt + h*dh/dt = D*dD/dt
12*3/2 + 5*(-5/8) = 13*dD/dt
18 -25/8 = 13*dD/dt
= 13*dD/dt
dD/dt =
Therefore the diagonal is increasing at the rate of 119/104cm/min of the given rectangle.