step 1 :
Because soccer ball is in the shape of sphere, we can use the formula of volume of a sphere to find volume of the soccer ball.
Write the formula to find volume of a sphere.
V = <span>4/3 · ∏r</span>³ ----- (1)
Step 2 :
To find the volume, we need the radius of the sphere. But, the diameter is given, that is 24 cm. So, find the radius.
r = diameter / 2
r = 24/2
r = 12
Step 3 :
Plug ∏ ≈ 3.14 and r = 12 in (1).
<span>V ≈ 4/3 </span>· 3.14 · 12³
Simplify.
<span>V ≈ 4/3 </span>· 3.14 · 1728
<span>V ≈ 7,234.6</span>
<span>Hence, the volume of the soccer ball is about 7,234.6 cubic cm. </span>
Answer:
Yes, at positive x-coordinates.
Step-by-step explanation:
Finding the equation for g(x):
Slope = (3-6)/ (1-0) = -3
y-intercept = y value when x = 0 = 6.
So g(x) = -3x + 6
Solve them simultaneously:
x^2 + y^2 = 16
g(x) : y = -3x + 6
Substitute for y in the first equation:
x^2 + (-3x + 6)^2 = 16
x^2 + ( 9x^2 - 36x + 36) = 16
10x^2 - 36x + 20 = 0
5x^2 - 18x + 10 = 0
x = [-(-18) +/- sqrt ( (-18)^2 - 4 * -18 * 10)] / (5*2)
= ( 18 +/- sqrt 124 )/ 10
= (1.8) +/- 1,114
These 2 roots are both positive.
Answer:
$192
Step-by-step explanation:
The cost function is given as:
C(x)=18x+240
The price function is given as:
p(x)= 90 - 3x
The revenue R(x) is the product of the price and the number of products. It is given by:
R(x) = xp(x) = x(90 - 3x) = 90x - 3x²
The profit P(x) is the difference between the revenue and the cost of production. Therefore:
P(x) = R(x) - C(x) = 90x - 3x² - (18x + 240) = 90x - 3x² - 18x - 240
P(x) = -3x² + 72x - 240
The standard equation of a quadratic equation is ax² + bx + c. The function has a maximum value at x = -b/2a
Since P(x) = -3x² + 72x - 240, the maximum profit is at:
x = -72/2(-3) = 12
at x = 12, the profit is:
P(12) = -3(12)² + 72(12) - 240 = -432 + 864 - 240 = $192
The correct answer is x^2 + 5.