What is the largest 2-digit multiple of 17?

[ad_1] What is the largest 2-digit multiple of 17? A multiple is a product that we get when one number is multiplied by another number. Answer: The largest 2-digit multiple of 17 is 85. Let’s find the largest 2-digit multiple of 17 Explanation: Let us look at the 17 times table and list all the 2 … Read more

Find the gcf of the terms of the polynomial. 44×5 + 16×3

[ad_1] Find the gcf of the terms of the polynomial. 44×5 + 16×3 Solution: Given polynomial 44×5 + 16×3 The steps involved are Find the GCF for the numerical part 44, 16 Find the GCF for the variable part x5, x3 Multiply the values together The factors of 44 are 1, 2, 4, 11, 22, … Read more

Find dy/dx. x = t sin(t), y = t2 + 7t

[ad_1] Find dy/dx. x = t sin(t), y = t2 + 7t Solution: Given are the parametric functions. x = t sin(t) y = t2 + 7t We know that differentiation of parametric functions is given by: dy/dx = dy/dt . dt/dx dx/dt = sin(t)dt/dt + td(sin(t))/dt = sin(t) + tcos(t) dy/dt = d(t2) /dt … Read more

Show that 0.2353535… = \(0.2\overline{35}\) can be expressed in the form of p/q, where p and q are integers and q is not equal to zero.

[ad_1] Show that 0.2353535… = \(0.2\overline{35}\) can be expressed in the form of p/q, where p and q are integers and q is not equal to zero. The problem is based on the conversion of decimal numbers to a rational form. Answer: 0.2353535… = \(0.2\overline{35}\) can be expressed as 233/990 i.e., in the form of … Read more

Find the derivative of y = log_10(x)

[ad_1] Find the derivative of y = log_10(x) We define log functions as the inverses of exponentials. Answer: The derivative of log\(_{10}\)(x) = 1/ (x ln 10) Let see, how we can find the derivative of y = log\(_{10}\)(x). Explanation:  We have to find the derivative of log10 x y = ln(x) ⇔ x=ey y = log\(_{10}\)(x) … Read more

Classify -2×4 – x3 + 8×2 = 12 by degree.

[ad_1] Classify -2×4 – x3 + 8×2 = 12 by degree. Solution: A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by … Read more

What is the factored form of 5×2 – 18x – 8?

[ad_1] What is the factored form of 5×2 – 18x – 8? Solution: The given equation is a quadratic equation that can be factored by splitting the middle term. On finding the factors of 5 × 8 i.e. 40. The factors of 40 are 1, 2, 4, 5, 8, 10, and 20. We will use … Read more

Simplify the expression: cot x sin x – sin + cos x

[ad_1] Simplify the expression: cot x sin x – sin + cos x Solution: Given expression is cot x sin x – sinx + cos x We know by the trigonometric ratio that cotx = cosx/sinx = cosx/sinx . sinx – sinx + cosx = cosx – sinx + cosx = 2cosx – sinx Therefore,the … Read more

Evaluate lim h → 0 [√(9 + h) – 3] / h.

[ad_1] Evaluate lim h → 0 [√(9 + h) – 3] / h. We will use the concepts of limit in order to find the required answer. Answer: The value of the lim h → 0 [√(9 + h) – 3] / h is 1/6 Let us see how we will use the concept of limit in … Read more

Any polygon with two pairs of parallel opposite sides is a parallelogram. True or False?

[ad_1] Any polygon with two pairs of parallel opposite sides is a parallelogram. True or False? Parallelograms are interesting shapes with many interesting properties. Even the shape rectangle is a type of parallelogram. They have an immensely large number of applications across many fields including engineering and science. They are one of the most steady … Read more

Evaluate 1 5/8

[ad_1] Evaluate 1 5/8 1 5/8 is a mixed fraction. We will convert to an improper fraction and find its decimal value. Answer: 1 5/8 is equal to 13/8 as an improper fraction and 1.625 as a decimal. Follow the steps mentioned below to find 1 5/8. Explanation: Step 1: Multiply the denominator with the whole number. So, 1 × … Read more

If c(x) = 4x – 2 and d(x) = x2 + 5x, what is c(d(x))?

[ad_1] If c(x) = 4x – 2 and d(x) = x2 + 5x, what is c(d(x))? Solution: A function that depends on any other function is called a composite function. A composite function is created by composing one function within another function. Given, c(x) = 4x – 2 d(x) = x2 + 5x We have … Read more

What is an integer that is not a whole number?

[ad_1] What is an integer that is not a whole number? An integer is a number with no decimal or fractional part. Integers include natural numbers, negatives of natural numbers and zero. Answer: A negative integer is an integer that is not a whole number. An integer is negative if it is less than zero. Explanation: Any … Read more

Find the value of each of the following:(i) tan-1 (1/√3)(ii) tan-1 (-1/√3)(iii) tan-1 (cos (π /2) )(iv) tan-1 (2 cos (2π /3) )

[ad_1] Find the value of each of the following: (i) tan-1 (1/√3) (ii) tan-1 (-1/√3) (iii) tan-1 (cos (π /2) ) (iv) tan-1 (2 cos (2π /3) ) To find the values of the above inverse trigonometric ratios, we will use trigonometric identities. Answer: The value of inverse tan ratios are (i) is π / 6, (ii) is … Read more

Find the surface area of a sphere with a radius of 7 inches?

[ad_1] Find the surface area of a sphere with a radius of 7 inches? Solution: The surface area of a sphere is the area occupied by the curved surface of the sphere. Circular shapes take the shape of a sphere when observed as three-dimensional structures.  The surface area of the sphere of radius r is given by … Read more

If 3t – 7 = 5t , then 6t =

[ad_1] If 3t – 7 = 5t , then 6t = Solution: A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = … Read more

The measure of central angle ABC is π/2 radians. What is the area of the shaded sector? 6π units2, 9π units2, 18π units2, 36π units2

[ad_1] The measure of central angle ABC is π/2 radians. What is the area of the shaded sector? 6π units2, 9π units2, 18π units2, 36π units2 Solution: The measure of central angle ABC is π/2 radians (Given) Shaded sector = 1/4 of the area of the circle We know that  Area of a circle = πr2 = π × … Read more