Let x =lenght, y = width, and z =height
<span>The volume of the box is equal to V = xyz </span>
<span>Subject to the surface area </span>
<span>S = 2xy + 2xz + 2yz = 64 </span>
<span>= 2(xy + xz + yz) </span>
<span>= 2[xy + x(64/xy) + y(64/xy)] </span>
<span>S(x,y)= 2(xy + 64/y + 64/x) </span>
<span>Then </span>
<span>Mx(x, y) = y = 64/x^2 </span>
<span>My(x, y) = x = 64/y^2 </span>
<span>y^2 = 64/x </span>
<span>(64/x^2)^2 = 64 </span>
<span>4096/x^4 = 64/x </span>
<span>x^3 = 4096/64 </span>
<span>x^3 = 64 </span>
<span>x = 4 </span>
<span>y = 64/x^2 </span>
<span>y = 4 </span>
<span>z= 64/yx </span>
<span>z= 64/16 </span>
<span>z = 4 </span>
<span>Therefor the dimensions are cube 4.</span>
Answer:
Step-by-step explanation:
Use Pythagorean theorem.
c^2 = a^2+b^2
c^2 = 4^2+6^2
c^2 = 16+36
c^2 = 52
c = √52 = 7.21
Answer:
Charlotte has 23 of her book left to read. She can read 29 of it each day.
Step-by-step explanation:
Answer:
$104
Step-by-step explanation:
- First, find the employee’s hourly rate. You can do this by dividing the total amount earned by the total hours worked.
- Now that you know that the employee’s hourly rate is $13 per hour, you can multiply the hourly rate by the number of hours.
Here the base angle given is 51°.
The side opposite to 51° is y
The hypotenuse is given as 12.
The trigonometric ratio associating opposite & hypotenuse is sin
We know sin = Opposite/ Hypotenuse
Substituting the values of angle , opposite & hypotenuse
We have
y/12 = sin 51°
Multiplying both sides by 12 we get
y=12 × sin 51°
y = 9.326
Rounding to the nearest hundredths we get
y = 9.33
