Let
x------> the length side of the square base of the box
y-------> the height of the box
we know that
volume of the box=b²*h
b=x
h=y
volume=256 cm³
so
256=x²*y------>y=256/x²--------> equation 1
<span>The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.</span>
surface area of the cardboard=area of the base+perimeter of base*height
area of the base=x²
perimeter of the base=4*x
height=y
surface area=x²+4x*y-----> equation 2
substitute equation 1 in equation 2
SA=x²+4x*[256/x²]-----> SA=x²+1024/x
step 1
find the first derivative of SA and equate to zero
2x+1024*(-1)/x²=0------> 2x=1024/x²----> x³=512--------> x=8 cm
y=256/x²------> y=256/8²-----> y=4 cm
the answer is
the length side of the square base of the box is 8 cm
the height of the box is 4 cm
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:
a = $31.23 per month
b = $20.83 per month
c = 249.98 = $249.98 interest charges
= $624-249.98 = 374.02 profit part decrease 8% inc.
d = 35.35%
e = Answer is in the name; basic payment is a contract which means whilst account remains open charges are requested without fail. Should balance be less or on zero, charges are still applied.
Step-by-step explanation:
2500 x 1.2499 = interest only for start month 13 =3124.75
3124.75/ 100 x 1.08 = 8% of this = 249.98 each year.
We only have to divide each by 12 to work out monthly individual charges and subtract to find out payments.
3124.75 - 249.98 = 2874.77 = Total after charges each year.
249.98/12 = 20.83 = monthly charges.
3124.75- 2500 = 624.75 payments each year
624.75/12 = 52.06 month 1 payment before charge
52.06-20.83 =31.23 total minimum payment
2500 + 249.98
Percentage = 200:600 = 1/3 33% + (comparing to ratio 10:25 closer to 40%)
We find ratio 200:600= 33.33 + 49.995/24.75 = 2.02
33+2.02 = 35.35%
notice, that, pure juice is 100% juice, dohhh, thus 100/100 = 1.00
50% is 50/100 or 0.50 in decimal format
so..... whatever those two quantities amount to, that is, the 50% and pure juice, or (4)(0.50) + (x)(1.00)
they will equal the mixture desired 60% juice, or 0.60, namely (4+x)(0.60)
thus (4)(0.50) + (x)(1.00) = (4+x)(0.60)
solve for "x"
