Recall that
where is the angle between the vectors
whose magnitudes are
, respectively.
We have
the beginning balance of the monthly bank statement for Ignatius' checking account was 124.82, and the ending balance was 659.27
1 answer:
Answer:
C.) he had $534.45 more in credit than in debits
Step-by-step explanation:
Let's call C the amount in credit that Ignatius had, and D the amount in debits that Ignatius had during the month.
We know that the initial amount in his account was 124.82, while the final balance was 659.27. The final amount is equal to the initial amount plus the amount of credits minus the amount of debits; in formula:
Re-arranging the equation, we find:
Which means that Ignatius had $534.45 more in credit than in debits, which corresponds to option C.
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Given:
The area of the squares are given.
To find:
The exact side length or estimate side length of the square.
Solution:
We know that, the area of a square is
Where, a is the side length of the square.
Area of the square is 100 square units. So, the side length is:
Therefore, the side length is 10 units.
Area of the square is 95 square units. So, the side length is:
It is not exact. We know that .
Therefore, the side length is between 9 and 10.
Area of the square is 36 square units. So, the side length is:
Therefore, the side length is 6 units.
Area of the square is 30 square units. So, the side length is:
It is not exact. We know that .
Therefore, the side length is between 5 and 6.
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.