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
Answer:
11.4
Step-by-step explanation:
40% of 38 is 15.2, 38-15.2=22.8. 22.8/2=11.4 (since there's two people)
Answer:
A liter is 1000 mL so half of 1000 = 500
500 mL is the answer!Step-by-step explanation:
Answer:
A person must get an IQ score of at least 138.885 to qualify.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
(a). [7pts] What IQ score must a person get to qualify
Top 8%, so at least the 100-8 = 92th percentile.
Scores of X and higher, in which X is found when Z has a pvalue of 0.92. So X when Z = 1.405.
A person must get an IQ score of at least 138.885 to qualify.
Answer:
see explanation
Step-by-step explanation:
The Remainder theorem states that if f(x) is divided by (x - h) then
f(h) is the remainder, thus
division by (x - 1) then h = 1
f(1) = 4(1)³ - 7(1)² - 2(1) + 6
= 4 - 7 - 2 + 6 = 1 ← remainder
The factor theorem states that if (x - h) is a factor of f(x), then f(h) = 0
Here f(1) = 1
Hence (x - 1) is not a factor of f(x)
