Surface area of a sphere = <span>4π<span>r2</span></span>
the volume of a sphere= <span><span>43</span>π<span>r3</span></span>
so <span>5000π=<span>4/3</span><span>πr3
</span></span><span>> r^3 = 5000 x 3 / 4
=>
r^3 = 3750
</span>taking cube root on both sides
r=15.53616
hope it helps
For this problem, I think there is no need for the details of 12 inches width and 4 inches length. This is because an equation is already given. It was clearly specified that A as a function of θ represents the area of the opening. Then, we are asked to find exactly that: the area of opening. Moreover, the value of θ was also given. Therefore, I am quite sure that the initial details given are for the purpose of red herring only.
So, all we have to do is substitute θ=45° to the function given.
A = 16 sin 45° ⋅ (cos 45° + 1)
The angle 45° is a special angle in trigonometry. So, it would be easy to remember trigonometric functions of this angle. Sine of 45° is equal to √2/2 while cosine of 45° is also √2/2.
A = 16(√2/2) ⋅ (√2/2 + 1)
A = 8+8√2
A = 19.31 square inches
A) He wanted to create zero pairs on the left side of the equation to get a positive coefficient of x on the right side
Answer:
50.24 yards
Step-by-step explanation:
We will use the pythagorean theorem to find hypotenuse of each of the 4 triangles.
Pythagorean Theorem is 
For Spinach area, two of the legs are 8 and 6. Solving for hypotenuse:
For watermelon area, two of the legs are 12 and 8. Solving for hypotenuse:
in red peppers area, the hypotenuse is already given as 15. But we need to find one leg since that will be the leg of the triangle in tomatoes area. Hypotenuse is 15 and one leg is 12, so the other leg is:
So, in tomatoes area, we have one leg 9 and another leg 6. Solving for hypotenuse:
Adding all the four hypotenuses, we get the length of the walkway:
Length of Walkway = 
yards
Answer: The required system of equations are
y = 30x
13x + y = 258
Step-by-step explanation:
Let x represent the number of hours
that the driver worked.
Let y represent the number of miles that the truck drove.
For every truck that goes out, Mason must pay the driver $13 per hour of driving and also has an expense of $1 per mile driven for gas and maintenance. If on a particular day, his total expenses for the driver, gas and truck maintenance were $258, it means that
13x + y = 258
On that particular day, the driver drove an average of 30 miles per hour.
Speed = distance/time
It means that
y/x = 30
y = 30x
