To express the amount “one lakh thirty thousand” in numerical form, you break it down into two parts: One lakh: In the Indian numbering system, ‘lakh’ refers to one hundred thousand (100,000). Thirty thousand: This is simply represented as 30,000. Now, when you combine these two values, you get: 100,000 (for one lakh) 30,000 (for … Read more
To calculate 60 percent of 90, you can follow a simple mathematical formula. Percentages are a way to express a number as a fraction of 100, so 60 percent can be written as 60/100 or simply 0.6 in decimal form. Here is how you can do the calculation: Convert the percentage to decimal: 60% = … Read more
To express the remainder as a fraction when dividing 64 by 30, we start by performing the division. When you divide 64 by 30, it goes 2 times (because 30 x 2 = 60), leaving a remainder. To find the remainder, you subtract: Remainder = 64 – 60 = 4 Now, we can express the … Read more
To solve the equation 3x + 5 = 35 – x + 8 + x – 5 + 2x + 10, we first need to simplify both sides of the equation. 1. **Simplify the right-hand side:** Combine like terms on the right side: Start with the constants: 35 + 8 – 5 + 10 = … Read more
The expression 5x² + 18x + 8 can be factored using a systematic approach. To factor a quadratic expression of the form ax² + bx + c, we look for two numbers that multiply to give ac (the product of a and c) and that add up to b. In this case, we have: a … Read more
To understand why cos(90) * sin(x) and sin(90) * cos(x) yield specific results, we first need to look at the trigonometric values of the angles involved. 1. **Trigonometric Values**: The cosine of 90 degrees is zero, while the sine of 90 degrees is one: cos(90) = 0 sin(90) = 1 2. **Calculating the Expressions**: – … Read more
To determine the probability of not being dealt a heart from a standard 52-card deck, we first need to understand the composition of the deck. A standard deck consists of 52 cards, divided into four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards. Since there are 13 hearts in the deck, this … Read more
To simplify the expression 1 + tan²(x), we can utilize a well-known identity from trigonometry. The identity states: 1 + tan²(x) = sec²(x) Here’s the step-by-step explanation: Recall that the tangent function is defined as: tan(x) = sin(x) / cos(x) Using this definition, we know: tan²(x) = (sin²(x) / cos²(x)) Substituting this into the expression: … Read more
A polynomial is considered prime (or irreducible) if it cannot be factored into the product of two non-constant polynomials over the given field. In simpler terms, a prime polynomial is one that cannot be broken down into simpler polynomial factors. To determine if the polynomial x⁴ + 3x² + x² + 3 is prime, we … Read more
To understand the relationship between the cosine of 30 degrees and the sine of 60 degrees, we can draw upon fundamental trigonometric identities and properties of the angles in a right triangle. We start with the given information: the cosine of 30 degrees is indeed √3/2. This is a well-known value in trigonometry that comes … Read more