Answer:
<h3>36 and 12</h3>
Step-by-step explanation:
Let the two positive integers be x and y.
If their product is 432, then
xy = 432 ......... 1
Also if the sum of the first plus three times the second is a minimum, then;
p(x) = x + 3y
From 1;
y = 432/x ..... 3
Substitute 3 into 2;
p(x) = x+3y
p(x)= x + 3(432/x)
p(x) = x + 1296/x
Since the expression is at minimum when dp(x)/dx = 0
dp/dx = 1 + (-1296)/x²
dp/dx = 1 -1296/x²
0 = 1 -1296/x²
0 = (x²-1296)/x²
cross multiply
0 = x²-1296
x² = 1296
x = √1296
x = 36
Since xy = 432
36y = 432
y = 432/36
y = 12
Hence the two positive numbers are 36 and 12
Answer:
10.24
Step-by-step explanation:
Area of a circle=sides²
Area of a circle=(3.2)²=3.2(3.2)=10.24
To find the fraction inbetween,
1. Add up the 2 fractions
2 Divide it by 2
Step (!) Add them up:
2/3 + 1 1/3 = 2
Step (2) Divide the answer by 2:
2÷ 2 = 1
Answer: The number between 2/3 and 1 1/3 is 1.
<span>n = 11<span>.
Explanation:
Let m be the number of boxes Mark sells and a be the number of boxes Ann sells.
Since Mark sells 10 less than n, m = n-10. Since Ann sells 2 less than n, a = n-2.
Together, they sold n-10+n-2=2n-12 boxes.
We know that they sold less than n boxes, so our inequality would be
2n-12<n.
To solve this, subtract n from both sides:
2n-12-n<n-n; n-12<0.
Add 12 to both sides:
n-12+12<0+12; n<12.
This means there were less than 12 boxes. The next number down is 11; this woks because Mark sold 10 less than n; 11-10=1. Mark sold at least 1 box.
If n=10, however, 10-10=0; this doesn't work, because Mark did sell at least 1 box. </span></span>
Answer:
40 passes
Step-by-step explanation:
we know that
Bobby catches 8 passes in 3 football games
so
using proportion
Find out how many passes does he catch in 15 games
