Answer:
d = 2(40.11 cm) = 80.22 cm
Step-by-step explanation:
The formula for volume of a sphere is V = (4/3)πr³
and here V = (4/3)πr³ = 2145 cm³
Let's simplify this equation by multiplying both sides by (3/4); this will cause (4/3) to disappear:
(3/4)(4/3)πr³ = (3/4)2145 cm³, or
r³ = 1608.75 cm³
Taking the cube root of both sides, we get:
r = 40.11 cm
Remembering that diameter = 2 times radius, we calculate the diameter:
d = 2(40.11 cm) = 80.22 cm
Answer:
D. 5
Step-by-step explanation:
The trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ
<h3>
How to solve the trigonometric identity?</h3>
Since (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]
Using the identity a² - b² = (a + b)(a - b), we have
(cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]
= (cos²θ - sin²θ)(cos²θ + sin²θ)/[(1 - tan²θ)(1 + tan²θ)] =
= (cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] (since (cos²θ + sin²θ) = 1 and 1 + tan²θ = sec²θ)
Also, Using the identity a² - b² = (a + b)(a - b), we have
(cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] = (cosθ - sinθ)(cosθ + sinθ)/[(1 - tanθ)(1 + tanθ)sec²θ]
= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)/cosθ × (cosθ + sinθ)/cosθ × sec²θ]
= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)(cosθ + sinθ)/cos²θ × 1/cos²θ]
= (cosθ - sinθ)(cosθ + sinθ)cos⁴θ/[(cosθ - sinθ)(cosθ + sinθ)]
= 1 × cos⁴θ
= cos⁴θ
So, the trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ
Learn more about trigonometric identities here:
brainly.com/question/27990864
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Independent variable: hours (t)
dependent variable: distance (h)
Answer:
200(50) is for the original revenue, and (200 - 10(50 + 5)) is if they increase it once.