Parabola and directrix

A parabola has a focus(0,2) and a directrix line y=1 . Describe what happens to this parabola if the directrix line moves up vertically and moves farther away from the focus.Describe what happens... more

limit of summation notation of (i^4/n^5+i/n^2) when n goes to infinity on interval[0,1]

evaluate limit by recognizing it as a Riemann sum for a function f(x) on the interval [0,1],and then using integrationlimit(n to inf) sigma(i^4/n^5+i/n^2) ,,(i from 1 to inf)my teacher said that we... more

True/False: Let b ∈ R, b>0 and let B:={x^2 | x ∈ (−b,0)}. We then have that inf(B) = 0 and sup(B) = b^2

Statement: "Let b ∈ R, b>0 and let B:={x^2 | x ∈ (−b,0)}. We then have that inf(B) = 0 and sup(B) = b^2"I'm not sure where to start with this question. Can anyone help?

Find the area of the region bounded by following

Sketch the region enclosed by the given curves and decide whether to integrate with respect to x or y. Find the area of the region bounded by:2y=5sqrtxy=32y+4x=9

14d

If y= Find dy/dx

y= (4x-5)^3 (4x+2)^3 find dy/dx how do i solve this problem to find dy/dx?

Height of a Statue

A statue is mounted on top of a 42 foot hill. From the base of the hill to where you are standing is 73 feet and the statue subtends an angle of 10.3° to where you are standing. Find the height of... more

Think book answer may be wrong

Hi, Our school course book is Understanding Pure Mathematics by Sadler and Thorning and we are asked to solve cot(2x) = -2/5 for which the book gives four answers: 55.9, 145.9, 235.9, and 325.9.... more

07/15/19

Derive equation y=kx that cuts through a given circle. Which value is k?

Derive the equation y = kx for a straight line which cuts a 90 degrees arc of the circlex2 + y2 - 6x - 2y + 5 = 0The line goes through the origin.What is the value of k? The answer should have at... more

06/29/19

Find the sum of the infinite series (-1 + (-3)^n) / 4^n from n =2 to infinity

Find the sum of the infinite series (-1 + (-3)n) / 4n starting from n = 2 all the way to infinity. I figured it would be a geometric series, but I am having trouble finding the ratio in order to... more

IMPOSSIBLE QUESTION!!! I have the question in the link below.

https://docs.google.com/document/d/1-7UkQpvidcO4-gMiuDlPSLCV7AUchLWHWAt2D1P2xwM

Geometry I NEED Help

Write the equation of the tangent line to the circle ( x - 2 )2 + ( y + 3 )2 = 25 at ( 6,0 )

05/03/19

What are the maximum and minimum values of f(x) = x^2 e ^x + 4xe^x + 16?

1. Let f(x) = x 2 e x + 4xex + 16. (a) Determine the maximum and minimum values of f(x) and determine whether they are local or global max/mins. It may help to know that limx→∞ f(x) = ∞ and lim... more

what numbers make 14 and when you subtract them make 6?

I am 9 and i have gotten alot of "which numbers make this number but when you subtract make this number" questions.

What is the range of the function defined by f(x)=x+2/x

What is the range of the function defined by f(x)=x+2/x :a) [2,+∞)b) (-∞,-2√2)∪(2√2,+∞)c) (-∞,+∞)d)( -∞,1)∪(1,+∞)please explain how to find range

finding circumference

How can I find the circumference of a circle with an area of 66.5 in squared?
1 3 4 5 6 7 16

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