Let x = the length of the rectangle
Let w= the width
Two sections are required, hence 2w of fence required
2x+3w=500
this can be written as:
3w=1500-2x
w=(1500-2x)/3
Area=x*w
replacing w with our expression:
A=x(1500-2x)/3
A=(500x-2x^2)/3
This is a quadratic equation, if we find the axis of symmetry we will know what value of x gives maximum area:
Axis of symmetry: x=-b/2a
From our equation we get:
a=-2/3; b=1500/3
thus
x=(1500/3)/(-(-2/3))
x=750
thus the maximum area will be given by length of 750
Answer:
<em>c=6, d=2</em>
Step-by-step explanation:
<em>Equations
</em>
We must find the values of c and d that make the below equation be true
![\sqrt[3]{162x^cy^5}=3x^2y \sqrt[3]{6y^d}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B162x%5Ecy%5E5%7D%3D3x%5E2y%20%5Csqrt%5B3%5D%7B6y%5Ed%7D)
Let's cube both sides of the equation:
![\left (\sqrt[3]{162x^cy^5}\right )^3=\left (3x^2y \sqrt[3]{6y^d}\right)^3](https://tex.z-dn.net/?f=%5Cleft%20%28%5Csqrt%5B3%5D%7B162x%5Ecy%5E5%7D%5Cright%20%29%5E3%3D%5Cleft%20%283x%5E2y%20%5Csqrt%5B3%5D%7B6y%5Ed%7D%5Cright%29%5E3)
The left side just simplifies the cubic root with the cube:
![162x^cy^5=\left (3x^2y \sqrt[3]{6y^d}\right)^3](https://tex.z-dn.net/?f=162x%5Ecy%5E5%3D%5Cleft%20%283x%5E2y%20%5Csqrt%5B3%5D%7B6y%5Ed%7D%5Cright%29%5E3)
On the right side, we'll simplify the cubic root where possible and power what's outside of the root:

Simplifying

Equating the powers of x and y separately we find
c=6
5=3+d
d=2
The values are

Answer:
option (C) the same
Step-by-step explanation:
In the given question , it is mentioned that the ball of mass 0.2 kilograms is thrown with the velocity of 4 m/s in the horizontal direction
and, the 0.4 kilogram green ball is thrown in the horizontal direction with the velocity of 8 m/s
Here in both the cases no component of velocity in the vertical direction is provided.
Hence, it will be a case of free fall in the vertical direction.
Now,
from Newton's equation of motion, we have
here,
s is the distance
a is the acceleration
t is the time
in the above equation, mass has no role and the value of acceleration i.e acceleration due to gravity and distance of fall in the vertical direction is same.
Hence, the time taken for both the balls will be same.
Hence,
The correct answer is option (C) the same
I agree with Marita, that the angles could have the same measure. This can be proven if you set the two amounts equal and solve for x.
9x - 25 + x = x + 50 + 2x - 12
To begin, we should combine like terms on both sides of the equation to start simplifying the equation.
10x - 25 = 3x + 38
Next, we should subtract 3x from both sides and add 25 to both sides to get the variable x alone on the left side of the equation.
7x = 63
Finally, we should divide both sides by 7, to get rid of the coefficient of x.
x = 9
If you plug in 9 for x in our first equation, you get that both of the angle measurements equal 65 degrees. This means that Marita is correct, because if x = 9, then the angles would have the same measure.
The answer would be 6 (This is just to get 20 caracters NOT PART OF ANSWER)