
Every point (x,y) on the curve y=log(3x)/log2 is transferred to a new point by the following translation (x′,y′)=(x−m,y−n), where m and n are integers. The set of (x′,y′) form the curve y=log(12x−96)/log2. What is the value of m+n? ...

Every point (x,y) on the curve y=log23x is transferred to a new point by the following translation (x′,y′)=(x+m,y+n), where m and n are integers. The set of (x′,y′) form the curve y=log2(12x−96). What is the value of m+n?

Every point (x,y) on the curve y = \log_{2}{3x} is transferred to a new point by the following translation (x',y') =(x+m,y+n), where m and n are integers. The set of (x',y') form the curve y = \log_{2}{(12x96)} . What is the value of m + n ?

1. a.) Find an equation for the line perpendicular to the tangent curve y=x^3  9x + 5 at the point (3,5) [* for a. the answer that I obtained was y5 = 1/18 (x3) ] b.) What is the smallest slope on the curve? At what point on the curve does the curve have this slope? c.) ...

The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (4, 1) is a point on the curve? x2 − y2 = 15 x2 + y2 = 15 x + y = 15 < my answer xy = 15


A curve passes through the point (1,11) and it's gradient at any point is ax^2 + b, where a and b are constants. The tangent to the curve at the point (2,16) is parallel to the xaxis. Find i) the values of a and b ii) the equation of the curve

The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (4, 1) is a point on the curve? x2 − y2 = 15 x2 + y2 = 15 x + y = 15 xy = 15

The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (3, 1) is a point on the curve?

The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (2, 1) is a point on the curve?

Consider the curve deﬁned by the equation y = 4x^3 +3x. Set up an integral that represents the length of curve from the point (0,0) to the point (4,268).

The slope of the tangent to a curve at any point (x, y) on the curve is x/y . Find the equation of the curve if the point (3,4) on the curve.

1. Given the curve a. Find an expression for the slope of the curve at any point (x, y) on the curve. b. Write an equation for the line tangent to the curve at the point (2, 1) c. Find the coordinates of all other points on this curve with slope equal to the slope at (2, 1)

Given that x²cos ysin y=0 ,(0,π): a)verfiy that given point is on the curve. b)use implicit differentiation to find the slope of the above curve at the given point. c)find the equation for tangent and normal to the curve at that point.

consider the curve defined by the equation y=a(x^2)+bx+c. Take a point(h,k) on the curve. use Wallis's method of tangents to show that the slope of the line tangent to this curve at the point(h,k) will be m= 2ah+b. have to prove this for tow cases: a>0 and a<0. Thank you

the tangent yo the curve y=x^2 +5x 2 @ the point (1,4)intersect the normal to the same curve @ the point (3,8) at the point P.Find the coordinates of point P.[ans: 1/3,16/3] just give me some hint to calculate this solution.


Find an equation of the tangent to the curve at the given point. y=4(sinx)^2 point: pi/6,1) So I took the derivative of the original function to get: y' = 8cosx*sinx I then chose a point to plug in to find a point for the slope. i picked pi/6 because i thought it would be ...

A certain density curve looks like an interverted letter V. The first segment goes fro the point (0,0.6) to the point (0.5,1.4). The segment goes from (0.5.1.44) to (1,0.6). (a) Sketch the curve. Verify that the area under the curve is 1, so that it is a valid density.  Okay...

A curve passes through the point (0, 2) and has the property that the slope of the curve at every point P is three times the ycoordinate of P. Find an equation of the curve. dy/dp = 3y or ∫ (3/y) dy = ∫ dp or 3 ln(y) = p + c or @ (0,2) ln(2) = 0 + c or c = ln(2) 3...

The equation of a curve is y = 2x^3 + 3x^2 Find: xintercept of the curve yintercept of the curve b) Determine the stationery point of the curve. i) for each point in(b) above, determine whether it is a maximum or a minimum

given the curve x + xy + 2y^2 = 6... a. find an expression for the slope of the curve. i got (1y)/(x + 4y) as my answer. b. write an equation for the line tangent to the curve at the point (2,1). i got y = (1/3)x + (5/3). but i didn't any answer for c! c. find the ...

for the parametric curve defined by x=32t^2 and y=52t ...sketch the curve using the parametric equation to plot of the point. use an arrow to indicate the direction of the curve for o<t<1. Find an equation for the line tangent to the curve at the point where t=1. x=3...

How should i do this question?? it says: find the equation of the tangent to the curve y=(x2)^3 at the point (3,1). calculate the coordinates of the point where this tangent meets the curve again. I know how to get the first part, if i'm not wrong, it's y = 3x  8 but no ...

a curve ahs parametric equations x=t^2 and y= 11/2t for t>0. i)find the coordinates of the point P where the curve cuts the xaxis which i found to be P(1/4, 0) the next part i cant do ii) find the gradient of the curve at this point. So far, I have the gradient to be: 2...

A curve passes through the point (7,6) and has the property that the slope of the curve at every point P is 4 times the ycoordinate of P. What is the equation of the curve? Simplify the equation as much as possible.

how to solve for radius of horizontal curve with coordinates(NE) for points A,B, C on the curve Point A : N1405.4018 E1256.7569 Point B : N1283.3703 E1294.7027 Point C : N1225.9373 E1286.6137


how to solve for radius of horizontal curve with coordinates(NE) for points A,B, C on the curve Point A : N1405.4018 E1256.7569 Point B : N1283.3703 E1294.7027 Point C : N1225.9373 E1286.6137

A vertical parabolic sag curve is to be designed to connect a downgradient of 1 in 20 with an upgradient of 1 in 15, the chainage and reduced level of the intersection point of the two gradients being 797.7 m and 83.544 m respectively. In order to allow for necessary ...

If the equation of the tangent line to the curve y=9cosx at the point on the curve with xcoordinate 3pi/4 is written in the form y=mx+b then m=? and b=?

A vertical parabolic sag curve is to be designed to connect a downgradient of 1 in 20 with an upgradient of 1 in 15, the chainage and reduced level of the intersection point of the two gradients being 797.7 m and 83.544 m respectively. In order to allow for necessary ...

When looking at a titration curve, I have to determine which is not true and I have it narrowed down to two options: The initial starting point on the titration curve is where pH depends only on [HA]0 or The finial point on a titration curve the pH depends only on [A] I would...

A curve has implicit equation x^22xy+4y^2=12 a)find the expression for dy/dx in terms of y and x. hence determine the coordinates of the point where the tangents to the curve are parallel to the xaxis. b)Find the equation of the normal to the curve at the point (2sqrt3,sqrt3).

Consider the curve defined by 2y^3+6X^2(y) 12x^2 +6y=1 . a. Show that dy/dx= (4x2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope 1 is tangent to the curve at point P. Find the x – and y – ...

The line that is normal to the curve x^2=2xy3y^2=0 at(1,1) intersects the curve at what other point? Please help. Thanks in advance. We have x2=2xy  3y2 = 0 Are there supposed to be 2 equal signs in this expression or is it x2 + 2xy  3y2 = 0 ? I'll suppose it's the second ...

Consider the curve given by the equation y^3+3x^2y+13=0 a.find dy/dx b. Write an equation for the line tangent to the curve at the point (2,1) c. Find the minimum ycoordinate of any point on the curve. the work for these would be appreciated i don't need the answers.

Consider the paraboloid z=x^2+y^2. The plane 3x2y+z7=0 cuts the paraboloid, its intersection being a curve. What is the "the natural" parametrization of this curve? Hint: The curve which is cut lies above a circle in the xyplane which you should parametrize as a function of...


Consider the paraboloid z=x^2+y^2. The plane 3x2y+z7=0 cuts the paraboloid, its intersection being a curve. What is the "the natural" parametrization of this curve? Hint: The curve which is cut lies above a circle in the xyplane which you should parametrize as a function of...

Consider the curve given by x^2+4y^2=7+3xy a) Show that dy/dx=(3y2x)/(8y3x) b) Show that there is a point P with xcoordinate 3 at which the line tangent to the curve at P is horizontal. Find the ycoordinate of P. c) Find the value of d^2y/dx^2 (second derivative) at the ...

The curve y = x/(sqrt(5 x^2)) is called a bulletnose curve. Find an equation of the tangent line to this curve at the point (2, 2)

Image with a flat horizontal line with a curve on top (beg curve: X, top middle curve: Y, End bottom curve: Z) Describe how the vertical component of the velocity of the water varies form point X to point Z? Mark scheme Answer: decreases from x to y DON’T GET I thought it ...

a curve is such that dy/dx=4x+7. the line y=2x meets the curve at point 'P'. Given that the gradient of the curve at P is 5. State the coordinates of P.

The length of a curve for 0 <= x <= 20 is given by the integral from 0 to 20 of √(1 + 84x^4) dx. If this curve contains the point (1,11), what is the equation of the curve? My answer is 3x^3 + 8.

a curve is such that dy/dx=4x+7. the line y=2x meets the curve at point 'P'. Given that the gradient of the curve at P is 5. State the coordinates of P.

The gradient of a curve is defined by dy/dx = 3x^(1/2)  6 Given the point (9, 2) lies on the curve, find the equation of the curve

The curve y =x/(sqrt(5−x^2)) is called a bulletnose curve. Find an equation of the tangent line to this curve at the point (2,2).

Linear approximation: Consider the curve defined by 8x^2 + 5xy + y^3 = 149 a. find dy/dx b. write an equation for the tangent line to the curve at the point (4,1) c. There is a number k so that the point (4.2,k) is on the curve. Using the tangent line found in part (b), ...


Can I still use the equation that I generated from my curve when doing the experiment even if the number I want to calculate is bigger than the last point in my curve ( ps the curve is a best fit line) would my answer be accurate??

sketch the curve using the parametric equation to plot the points. use an arrow to indicate the direction the curve is traced as t increases. Find the lenghth of the curve for o<t<1. Find an equation for the line tangent to the curve at the point where t=t. the equation...

A curve is traced by a point P(x,y) which moves such that its distance from the point A(1,1) is three times the distance from the point B(2,1). Find the equation of the curve and identity.

How do I make a graph of f'(1) = f'(1) = 0, f'(x) > 0 on (1,1), f'(x) < 0 for x < 1, f'(x) > 0 for x >1 Thanks. if the derivative is postive on 1 to 1, you have a curve that shope upward as x increases. If the derivative is zero at 1, and 1, thekn at 1 the...

find the eqt. of tangent to the curve y=x^2+2x10 @ the point where the curve cuts the yaxis.[ans:y=2x10] how do i do this because they didn't give me the point...?

Given the curve x^2xy+y^2=9 A) write a general expression for the slope of the curve. B) find the coordinates of the points on the curve where the tangents are vertical C) at the point (0,3) find the rate of change in the slope of the curve with respect to x I don't even know...

find the coordinates of the point where the tangent to the curve y=x^3 +x +2 at the point (1,4) meets the curve again. [ans:2,8] pls help me i don't understand the question....

Find the xyequation of the curve that passes through (2, 2) and whose slope at any point on the curve is equal to 5 times the xcoordinate of that point

In each case, sketch the two speciﬁed normal curves on the same set of axes: a A normal curve with m 20 and s 3, and a normal curve with m 20 and s 6. b A normal curve with m 20 and s 3, and a normal curve with m 30 and s 3. c A normal curve with m 100 and s 10, and a ...

Determine the equation of a curve in the xyplane that passes through the point (0, 1) and has the slope x2 sin 4x at any point (x, y) on the curve.


Find the coordinates of a point on the curve y=6x^2 at which the tangent of the curve at the point is perpendicular to the line y=1/4x+1.

The tangent to the curve 2y= 2x^2 5x +4 at the point where x=1 is parallel to the normal to the curve y= ax^2 + bx +10 at the point (2,2). Calculate the values of a and b. The answers are a=1, b=6

A curve is traced by a point P(x,y) which moves such that its distance from the point A(1,1) is three times the distance from the point B(2,1). Find the equation of the curve and identity.

When looking at a titration curve, I have to determine which is false and I have it narrowed down to two options: The initial starting point on the titration curve is where pH depends only on [HA]0 or The finial point on a titration curve the pH depends only on [A] I would ...

Show that the tangent line to the curve y=x^3 at the point x=a also hits the curve at the point x=2a. Any help?! PLEASE!

The slope of a curve is at the point (x,y) is 4x3. Find the curve if it is required to pass through the point (1,1). Work... 4(1)3=1 y1=1(x1) y=x

Suppose that f(x) is an invertible function (that is, has an inverse function), and that the slope of the tangent line to the curve y = f(x) at the point (2, –4) is –0.2. Then: (Points : 1) A) The slope of the tangent line to the curve y = f –1(x) at the point (–4, 2) ...

A racecar is initially travelling at 75 mph at point A as it enters the Scurve shown. In order to successfully traverse the curve, the racecar driver applies his brakes and decelerates uniformly between point A and B. Point B is located 750 ft down the track from point A. ...

A racecar is initially travelling at 75 mph at point A as it enters the Scurve shown. In order to successfully traverse the curve, the racecar driver applies his brakes and decelerates uniformly between point A and B. Point B is located 750 ft down the track from point A. ...

Could someone please help me with these tangent line problems? 1) Find the equation of the line tangent to the given curve at the indicated point: 3y^3 + 2x^2 = 5 at a point in the first quadrant where y=1. 2) Show that there is no point on the graph of x^2  3xy + y^2 = 1 ...


If a tangent line is drawn to the parabola y = 3  x^2 at any point on the curve in the first quadrant, a triangle is formed with the axes. At what point on the curve should the tangent be drawn to form a triangle of least area?

What is the value of the zscores if the area of the curve to this point is 0.887? How much of this are is between the peak of the curve and this point?

Describe how the vertical component of the velocity of the water varies form point X to point Z? Image with a flat horizontal line with a curve on top (beg curve: X, top middle curve: Y, End bottom curve: Z) Mark scheme Answer: decreases from x to y DON’T GET I thought it ...

If a tangent line is drawn to the parabola y = 3  x^2 at any point on the curve in the first quadrant, a triangle is formed with the axes. At what point on the curve should the tangent be drawn to form a triangle of least are?

The demand curve for a monopoly is: 1. the MR curve above the AVC curve. 2.above the MR curve. 3.the MR curve above the horizontal axis. 4. the entire MR curve.

Find the line which passes through the point (0, 1/4) and is tangent to the curve y=x^3 at some point. So I found the derivative which is 3x^2. Let (a, a3) be the point of tangency. 3x^2 = (a3  1/4)/(a0) I'm not sure how to solve for a. Yes, the point is (0,1/4) but it's not...

. Given that x²cos y_sin y=0,(0,π). A. Verify that the given points on the curve. B.use implicit differention to find the slope of the above curve at the given point. C.find the equation of tangent and normal to the curve at that.

label a point f inside the curve. why is this an inefficient point? label a point g outside the curve. why is this point unattainable? why are pointS A THROUGH E ALL EDDICIENT POINTS?

label a point f inside the curve. why is this an inefficient point? label a point g outside the curve. why is this point unattainable? why are pointS A THROUGH E ALL EFFICIENT POINTS?

I'm desperate! Find the point where the curve r(t)=(12sint)i  12(cost)j+ 5tk is at a distance 13pi units along the curve from the point (0,12,0) in the direction opposite to the direction of increasing arc length. Thanks for any advice...


there are two tangents lines to the curve f(x) = 3x^2 that pass through the point p =0,1 find the x coordinates of the point where the tangents line intersect the curve

Notice that the curve given by the parametric equations x=25−t^2 y=t^3−16t is symmetric about the xaxis. (If t gives us the point (x,y),then −t will give (x,−y)). At which x value is the tangent to this curve horizontal? x = ? At which t value is the tangent to this ...

Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2 + 1 and connect the tangent point to the xaxis. If the tangent point is close to the yaxis, the line segment is long. If the tangent point is far from the yaxis, the line ...

I'm working on logarithmic equations and I'm stuck on how my book arrives at the next step. First, they use the change of base formula on, log(sqrt(2))(x^3  2) (sqrt(2)) is the base,changing to base 2 log(sqrt(2))(x^3  2)= log2(x^3  2)/(log2(sqrt(2)) I understand that part...

original curve: 2y^3+6(x^2)y12x^2+6y=1 dy/dx=(4x2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point P.

original curve: 2y^3+6(x^2)y12x^2+6y=1 dy/dx=(4x2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point P.

Consider the closed curve in the day plane: 2x^22xy+y^3=14 a) show that dy/dx=2y4x/3y^22x (I got this part) b) find equation lines to the curve when y=2 c) if the point (2.5, k) is on the curve, use part b to find the best approximation of the value of k

A curve is defined by the parametric equations: x = t2 – t and y = t3 – 3t Find the coordinates of the point(s) on the curve for which the normal to the curve is parallel to the yaxis. You must use calculus and clearly show your working, including any derivatives you need...

1. The sequence log2 32, log2 y, log2 128, ... forms an arithmetic sequence. What is the value of y? 2. If log a^2 b^3 = x and log (a/b) = y, what are the values of log a and log b?

1. Sketch the curves y=e^x and y=e^2x, using the same axes. The line y=4 intersects the first curve at A and the second curve at B. Calculate the length AB to two decimal places. 2. Find the coordinates of the turning point on the curve y=2e^3x+8e^3x and determine the nature...


Point P in the curve y=x^3 has coordinates (3,27) and PQ is the tangent to the curve at P.Point Q touches the xaxis.Find the area of the region enclosed between the curve, PQ and the xaxis. My answer: I used differenttiation to find the gradient of the tangent: dy/dx=3x^2. ...

1. At what point does the normal line to the curve x^2  XY + Y^2 = 3 at the point (1,1) intersect the curve again? 2. Find the constants A, B so that if Y=A*sin X + B cos X, then Y satisfies the differential equation Y" + 2Y = 0. 3. Find the points on he graph of Y = e^x  e...

a circle of radius 1 rolls around the outside of a circle of radius 2 without slipping. the curve traced by a point on the circumfarence of the smaller circle is callled an epicycloid. use the angle theta to find a set of parametric equations for this curve.

a circle of radius 1 rolls around the outside of a circle of radius 2 without slipping. the curve traced by a point on the circumfarence of the smaller circle is callled an epicycloid. use the angle theta to find a set of parametric equations for this curve.

1. At what point does the normal line to the curve x^2  XY + Y^2 = 3 at the point (1,1) intersect the curve again? 2. Find the constants A, B so that if Y = Asin X = B cos X, then Y satisfies the differential equation Y" + 2Y = 0. 3. Find the points om he graph of Y  e^x  e...

1. At what point does the normal line to the curve x^2  XY + Y^2 = 3 at the point (1,1) intersect the curve again? 2. Find the constants A, B so that if Y=A*sin X + B cos X, then Y satisfies the differential equation Y" + 2Y = 0. 3. Find the points on he graph of Y = e^x  e...

The point P(2,1) lies on the curve y=1/(1x) If Q is the point (x, 1/(1x) find slope of secant line. these are the points 2, 1 1.5,2 1.9,1.111111 1.99,1.010101 1.999,001001 2.5,0.666667 2.1,0.909091 2.01,0.990099 2.001,0.999001 using the results from the points guess the ...

In this problem we consider drawing some straight lines which form a nice pattern. Consider joining the point (0.1,0) to the point (0,0.9) by a line segment; then joining (0.2,0) to (0,0.8) by a line segment; and so on. In general, consider joining the points (a,0) and (0,b) ...

Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x1)e^x. For which value of x is the slope of the tangent line to f positive? Negative? Zero? 2) Find an equation of the tangent line to the oven curve at the specified point. Sketch the curve and the...

The slope of the tangent to the curve y=f(x) is given by (1/9)(x^2)(y^2). The curve passes through the point (3,1). Find the value of y when x=3*cubedroot(3).


Find the point on the curve y=1 x2+14 x such that the tangent line to the curve is parallel to 2 x + 10 y = 23

A vector parallel to the tangent to the curve x=3t^(4/3) y=2t^3 1 z= 2/(t^2) at the point (3,3,2) on the curve is: the answer is <2,3,2> how do you get this??

Use a formula for slope of a line tangent to a parametric curve to find dy/dx for the curve c(s) = (s^(1)6s, 7s^3) at the point with s=4

Use the formula for slope of a line tangent to a parametric curve to find dy/dx for the curve c(s) = (s^16s, 7s^3) at the point with s=4

For the curve given by 4x^2+y^2=48+2xy, show that there is a point P with xcoordinate 2 at which the line tangent to the curve at P is horizontal.
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