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Home » Given \( 3w^2 = 192 \). - jntua results

Given \( 3w^2 = 192 \). - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 The ratio of the number of apples to oranges in a basket is 5:3. If there are 40 apples, how many oranges are there?

📌 Let the number of oranges be \( x \). The ratio equation is \( \frac{40}{x} = \frac{5}{3} \).

📌 Cross-multiply: \( 5x = 3 \times 40 \).

📌 Solve for \( x \): \( 5x = 120 \).

📌 Divide by 5: \( x = 24 \).

📌 Therefore, there are 24 oranges.

📌 Find the derivative of the function \( f(x) = 3x^3 - 5x^2 + 2x - 7 \).

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Solution: Convert to Cartesian coordinates using $\rho = \sqrt{x^2 + y...
\rho^2 = 2\rho \sin\phi \cos\theta \implies x^2 + y^2 + z^2 = 2x.
Rearranging:
x^2 - 2x + y^2 + z^2 = 0 \implies (x^2 - 2x + 1) + y^2 + z^2 = 1 \impl...
This is a sphere centered at $(1, 0, 0)$ with radius 1.
\boxed{\text{A sphere of radius 1 centered at } (1, 0, 0)}
Question: Find the maximum value of $\left(\sin x + \csc x\right)^2 +...
Solution: Expand the expression:
Simplify using $\sin^2 x + \cos^2 x = 1$ and $\csc^2 x = 1 + \cot^2 x$...
+ 2 + 2 + \cot^2 x + \tan^2 x = 5 + \cot^2 x + \tan^2 x.

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