A = LW
A = 72
L = W + 1
72 = W(W + 1)
72 = W^2 + W
W^2 + W - 72 = 0
(W + 9)(W - 8) = 0
W + 9 = 0
W = -9......extraneous solution...does not work here
W - 8 = 0
W = 8 <==
L = W + 1
L = 8 + 1
L = 9
so the width (W) is 8 ft and the Length is 9 ft
Answer:
amount is 1000 × 
$40762.20 balance of Donna's account will be 1 million dollars when she retires in 40 years
rate 14.97 % when Donna's account will have a balance of 1 million dollars in 40 years when principal is $2500
Step-by-step explanation:
principal = $1000
rate = 8 % = 0.08
to find out
the future value, S(t)
principal when Donna's account will be 1 million dollars when she retires in 40 year
at what rate Donna's account will have a balance of 1 million dollars in 40 years
solution
we know compounded continuously formula i.e.
amount = principal × 
..................1
put the value principal and rate in equation 1 to find amount any time
amount = principal ×
amount = 1000 ×
in 2nd part we have time 40 year and amount 1 million so put rate amount and time in equation 1 to find principal
rt = 0.08 × 40 = 3.2
amount = principal ×
1000000 = principal × 
principal = 1000000 /
principal = 1000000 / 24.5325302
principal = 40762.20397
so $40762.20 balance of Donna's account will be 1 million dollars when she retires in 40 years
in 3rd part we have amount 1 million and principal $2500 and time 40 year put all these in equation 1 to find rate
amount = principal ×
1000000 = 2500 × 
take ln both side
ln = ln (1000000 / 2500 )
40 r = ln 400
r = ln (400) / 40
r = 0.149787
so rate 14.97 % when Donna's account will have a balance of 1 million dollars in 40 years when principal is $2500
P = 2a + b
10= 2a + 3
2a = 10-3
a = 7/2 = 3.5
Therefore, numerical value of a is 3.5
Answer:
In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. The equality between A and B is written A = B, and pronounced A equals B.[1][2] The symbol "=" is called an "equals sign". Two objects that are not equal are said to be distinct.
Step-by-step explanation:
For example:
{\displaystyle x=y}x=y means that x and y denote the same object.[3]
The identity {\displaystyle (x+1)^{2}=x^{2}+2x+1}{\displaystyle (x+1)^{2}=x^{2}+2x+1} means that if x is any number, then the two expressions have the same value. This may also be interpreted as saying that the two sides of the equals sign represent the same function.
{\displaystyle \{x\mid P(x)\}=\{x\mid Q(x)\}}{\displaystyle \{x\mid P(x)\}=\{x\mid Q(x)\}} if and only if {\displaystyle P(x)\Leftrightarrow Q(x).}{\displaystyle P(x)\Leftrightarrow Q(x).} This assertion, which uses set-builder notation, means that if the elements satisfying the property {\displaystyle P(x)}P(x) are the same as the elements satisfying {\displaystyle Q(x),}{\displaystyle Q(x),} then the two uses of the set-builder notation define the same set. This property is often expressed as "two sets that have the same elements are equal." It is one of the usual axioms of set theory, called axiom of extensionality.[4]
Answer:
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Step-by-step explanation:
