# Math

## What is the proton’s speed as it passes through point P?

Problem 21.63 A proton follows the path shown in (Figure 1). Its initial speed is v0 = 1.4 x 10^6 m/s. Part A What is the proton’s speed as it passes through point P? Express your answer to two significant figures and include the appropriate units.

## At what point does the curve have maximum curvature? y = 9ln x?

at what points does this curve has max curvature? Answer 1 we are given y=9ln(x) we can use formula k(x)=frac{|y”|}{(1+(y’)^2)^{3/2}} y’=frac{9}{x} y”=-frac{9}{x^2} now, we can plug it and we get k(x)=frac{frac{9}{x^2}}{[1+(frac{9}{x})^2]^{frac{3}{2}}} k(x)=frac{9x}{left(x^2+81right)^{frac{3}{2}}} now, we can find derivative k'(x)=frac{d}{dx}left(frac{9x}{left(x^2+81right)^{frac{3}{2}}}right) =9cdot frac{frac{d}{dx}left(xright)left(x^2+81right)^{frac{3}{2}}-frac{d}{dx}left(left(x^2+81right)^{frac{3}{2}}right)x}{left(left(x^2+81right)^{frac{3}{2}}right)^2} =9cdot frac{1cdot left(x^2+81right)^{frac{3}{2}}-3xsqrt{x^2+81}x}{left(left(x^2+81right)^{frac{3}{2}}right)^2} k'(x)=frac{9left(-2x^2+81right)}{left(x^2+81right)^{frac{5}{2}}} now, we can set it to 0 and then we can […]

## At what point does the curve have maximum curvature? y = 9ln x?

at what points does this curve has max curvature? Answer 1 we are given y=9ln(x) we can use formula k(x)=frac{|y”|}{(1+(y’)^2)^{3/2}} y’=frac{9}{x} y”=-frac{9}{x^2} now, we can plug it and we get k(x)=frac{frac{9}{x^2}}{[1+(frac{9}{x})^2]^{frac{3}{2}}} k(x)=frac{9x}{left(x^2+81right)^{frac{3}{2}}} now, we can find derivative k'(x)=frac{d}{dx}left(frac{9x}{left(x^2+81right)^{frac{3}{2}}}right) =9cdot frac{frac{d}{dx}left(xright)left(x^2+81right)^{frac{3}{2}}-frac{d}{dx}left(left(x^2+81right)^{frac{3}{2}}right)x}{left(left(x^2+81right)^{frac{3}{2}}right)^2} =9cdot frac{1cdot left(x^2+81right)^{frac{3}{2}}-3xsqrt{x^2+81}x}{left(left(x^2+81right)^{frac{3}{2}}right)^2} k'(x)=frac{9left(-2x^2+81right)}{left(x^2+81right)^{frac{5}{2}}} now, we can set it to 0 and then we can […]

## The graph of f(x) = x6 – 2×4 – 5×2 + 6 is shown below. How many roots of f(x) are rational numbers?

The graph of f(x) = x6 – 2×4 – 5×2 + 6 is shown below. How many roots of f(x) are rational numbers? Answer 1 Two rational roots: 1 and -1 Step-by-step explanation: See the images for an explanation! Answer 2 1,-1 are rational numbers Step-by-step explanation: Given equation: Roots of f(x) are : ⇒ […]

## In triangle trs, vz = 6 inches. what is rz?

In triangle trs, vz = 6 inches. what is rz? 3 inches 6 inches 12 inches 18 inches Answer 1 we know that In a triangle, a median is created by a vertex connected to the midpoint of the opposite side. Where all three lines intersect is the centroid, which is also the “center of […]

## In circle y, what is m∠szt?

In circle y, what is m∠szt? 86° 94° 108° 128° Answer 1 First, you need to solve for the angle TZU. The formula for it is_mTZU= 0.5(arcTU+arcSR)mTZu= 0.5(72°+100°) = 86° Vertical angles, as you should know, are congruent. Always. mTZU is a vertical angle to mSZR. This means mSZR is also 86° Now, the sum […]

## Which shows the image of ΔRST after the rotation (x, y) → (y, –x)?

Which shows the image of ΔRST after the rotation (x, y) → (y, –x)? Answer 1 On a coordinate plane, a triangle has points R prime (1, 2), S prime (3, negative 1), T prime (7, 1) Step-by-step explanation: We assume that the coordinates of the vertices of the given triangle are supposed to be […]

## Express the complex number in trigonometric form. -4i my answer = 4(cos 180° + i sin 180°)

Express the complex number in trigonometric form. -4i my answer = 4(cos 180° + i sin 180°) Answer 1 So you put in the answer that when you revert it into complex again, it would be -4. The correct answer would be 4(cos 270 + i sin 270) Answer 2 -4i =  4(cos 270 +i […]

## What do the letters clu stand for in relation to an insurance agent?

What do the letters clu stand for in relation to an insurance agent? a. chartered legal underwriter b. certified legal underwriter c. certified licensed underwriter d. chartered life underwriter Answer 1 Chartered life underwriter Answer 2 In insurance, the letters CLU indicates the title of Chartered Life Underwriter, one of the most respected and prestigious […]

## What’s the correct letter name for ð1 below?

What’s the correct letter name for ð1 below? Answer 1 D. 1 is in angle ABC Answer 2 D. ∠ABC Step-by-step explanation: We are given a figure consisting of rays AB, CB and DB having a common end point B. It is required to find the value of 1 marked in the figure. As, we […]

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