14x45=630
43×2=86
(14×45)-(43×2)= 630-86=544
there would be 544 pens left
Answer:
C.
Step-by-step explanation:
First finding height using Pythagoras theorem
(H)²=(B)²+(P)²
8.2²=5.4²+P²
P² = 67.24 - 29.16
P² = 38.08
P = 6.2
Now
Volume of cone = (1/3)πr²h
= (1/3)(3.14)(5.4)²(6.2)
= (1/3)(567.9)
= 189.2 cm³
X + y = 6
x - 6y = -9
Subtract the equations, you get:
y - (-6y) = 6 - (-9)
7y = 15
y = 15/7
x + 15/7 = 6
x + 15/7 = 42/7
x = (42-15)/7
x = 27/15
None of your answer choices are correct, since the solution to the systems of equation is (27/15, 15/7)
Answer:
x = 10 cm, y = 5 cm gives a minimum area of 300 cm^2.
Step-by-step explanation:
V= x^2y = 500
Surface area A = x^2 + 4xy.
From the first equation y = 500/x^2
So substituting for y in the equation for the surface area:
A = x^2 + 4x * 500/x^2
A = x^2 + 2000/x
Finding the derivative:
dA/dx = 2x - 2000x^-2
dA/dx = 2x - 2000/x^2
This = 0 for a minimum/maximum value of A, so
2x - 2000/x^2 = 0
2x^3 - 2000 = 0
x^3 = 2000/ 2 = 1000
x = 10
Second derivative is 2 + 4000/x^3
when x = 10 this is positive so x = 10 gives a minimum value of A.
So y = 500/x^2
= 500/100
= 5.
Hi there! The answer is C.
We can find the slope of this line by making y the subject of the equation.
Now we can see that the slope of this line (which is positioned in front of x) is 3/4. Therefore, the slope of any line parallel to this one is 3/4 as well. The answer is C.
