Part A.
Using the Pythagorean theorem,
PR² = PQ² +QR²
PR² = (14 ft)² +(6 ft)² = 196 ft² +36 ft² . . . . substitute the given numbers
PR² = 232 ft² . . . . . . . . . . . . . . . . . . . . . . . .find the sum
PR = √(232 ft²) ≈ 15.23 ft . . . . . . . . . . . . . take the square root
The length of rod PR is 15.23 ft.
Part B.
Using the Pythagorean theorem,
PR² = PQ² +QR²
(16 ft)² = (14 ft)² +QR² . . . . . . . substitute the given numbers
256 ft² -196 ft² = QR² . . . . . .. subtract 14²
60 ft² = QR² . . . . . . . . . . . . . . find the sum
√(60 ft²) = QR ≈ 7.75 ft . . . . . take the square root
The new height QR is about 7.75 ft.
8; 20/5=4, 4*2=8 so therefore it's 8 pounds
9514 1404 393
Answer:
split the number into equal pieces
Step-by-step explanation:
Assuming "splitting any number" means identifying parts that have the number as their sum, the maximum product of the parts will be found where the parts all have equal values.
We have to assume that the number being split is positive and all of the parts are positive.
<h3>2 parts</h3>
If we divide number n into parts x and (n -x), their product is the quadratic function x(n -x). The graph of this function opens downward and has zeros at x=0 and x=n. The vertex (maximum product) is halfway between the zeros, at x = (0 + n)/2 = n/2.
<h3>3 parts</h3>
Similarly, we can look at how to divide a (positive) number into 3 parts that have the largest product. Let's assume that one part is x. Then the other two parts will have a maximum product when they are equal. Their values will be (n-x)/2, and their product will be ((n -x)/2)^2. Then the product of the three numbers is ...
p = x(x^2 -2nx +n^2)/4 = (x^3 -2nx^2 +xn^2)/4
This will be maximized where its derivative is zero:
p' = (1/4)(3x^2 -4nx +n^2) = 0
(3x -n)(x -n) = 0 . . . . . . . . . . . . . factor
x = n/3 or n
We know that x=n will give a minimum product (0), so the maximum product is obtained when x = n/3.
<h3>more parts</h3>
A similar development can prove by induction that the parts must all be equal.
Answer:
Step-by-step explanation:
Answer:
100
Step-by-step explanation:
Because if 50 percent of x is 50 than x = 100
