Answer:
He makes $735.
Step-by-step explanation:
Multiply 22x40 and subtract 145.
Answer:
x = 8,49 ft
y = 4,24 ft
Step-by-step explanation:
Let x be the longer side of rectangle and y the shorter
Area of rectangle = 36 ft² 36 = x* y ⇒ y =36/x
Perimeter of rectangle:
P = 2x + 2y for convinience we will write it as P = ( 2x + y ) + y
C(x,y) = 1 * ( 2x + y ) + 3* y
The cost equation as function of x is:
C(x) = 2x + 36/x + 108/x
C(x) = 2x + 144/x
Taking derivatives on both sides of the equation
C´(x) = 2 - 144/x²
C´(x) = 0 2 - 144/x² = 0 ⇒ 2x² -144 = 0 ⇒ x² = 72
x = 8,49 ft y = 36/8.49 y = 4,24 ft
How can we be sure that value will give us a minimun
We get second derivative
C´(x) = 2 - 144/x² ⇒C´´(x) = 2x (144)/ x⁴
so C´´(x) > 0
condition for a minimum
3x/8 divided by 7y/4
you can not divide fractions, so you must multiply by the reciprocal.
3x/8 x 4/7y now you can simplify the 4 and 8
3x/2 x 1/7y now multiply across
3x/2(7y)
3x/14y should be your answer
Answer: 12 students
Step-by-step explanation:
Let X and Y stand for the number of students in each respective class.
We know:
X/Y = 2/5, and
Y = X+24
We want to find the number of students, x, that when transferred from Y to X, will make the classes equal in size. We can express this as:
(Y-x)/(X+x) = 1
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We can rearrange X/Y = 2/5 to:
X = 2Y/5
The use this value of X in the second equation:
Y = X+24
Y =2Y/5+24
5Y = 2Y + 120
3Y = 120
Y = 40
Since Y = X+24
40 = X + 24
X = 16
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Now we want x, the number of students transferring from Class Y to Class X, to be a value such that X = Y:
(Y-x)=(X+x)
(40-x)=(16+x)
24 = 2x
x = 12
12 students must transfer to the more difficult, very early morning, class.
Answer:
7.56 km²
Step-by-step explanation:
Given data:
Width of the fjord, w = 6.3 km
Retreated terminus of the glacier between may 2001 and June 2005, d = 7.5 km
thus, the length lost , y = 7.5 - 6.3 = 1.2 km
now, the area is given as:
A = Length × width
on substituting the values, we get
A = 1.2 × 6.3
or
A = 7.56 km²
Hence, the surface area lost by the glacier in the fjord is 7.56 km²