Answer:
Mark has 13 marbles
Don has 40 marbles
Step-by-step explanation:
Let the number of Mark's Marbles = M
Let the number of Don's Marble = D
D = 1 + 3M - - - - (1) (Don has 1 more than 3 times the number of marbles Mark has)
D + M = 53 - - - - - (2) (total number of marbles is 53)
puttin the value of D from equation (1) into equation (2)
(1 + 3M) + M = 53
1 + 3M + M = 53
1 + 4M = 53
4M = 53 - 1 = 52
4M = 52
M = 52 ÷ 4
M = 13
finding D by putting the value of M (M = 13) into equation 1
D = 1 + 3M - - - - (1)
D = 1 + 3 (13)
D = 1 + 39
D = 40
∴ Mark has 13 marbles
Don has 40 marbles
Let, the numbers are: x, (24-x)
Let, P(x) denote their products. Then, we have:
P(x) = x(24-x) = 24x - x²
P'(x) = 24-2x
P''(x) = -2
Now, P'(x) = 0 ⇒ x = 12
Also,
P''(12) = -2 < 0
So, By second derivative test, x = 12 is the point of local maxima of p. Hence the product of the numbers is the maximum when the numbers are 12 and (24-12) = 12
So, In short that numbers would be 12,12
Hope this helps!
Answer:
last option
Step-by-step explanation:
Sin A: opp/hyp (opposite/hypotenuse)
opposite of A is 24 and the hypotenuse is 30
write that as a fraction: 24/30
simplify and it is: 4/5
Cos A: adj/hyp (adjacent/hypotenuse)
adjacent side of A is 18 and the hypotenuse if 30
write that as a fraction: 18/30
simplify and it is: 3/5
If you scroll up I answered a previous question like this in the same subject
Answer: 50.27
Step-by-step explanation:
Area = pi r^2
= pi x 16
