The angle of a sector of a cone is 135, and the slant height is 20 centimeters. What is the diameter of the cone?

An isosceles trapezoid ABCD with height 2 units has all its vertices on the parabola y=a(x+1)(x−5). What is the value of a, if p

horrorfan [7]

Answer:

a = -0.3575

Step-by-step explanation:

The points A and D lie on the x-axis, this means that they are the x-intercepts of the parabola, and therefore we can find their location.

The points A and B are located where

$y=a(x+1)(x-5)=0$

This gives

$x=-1$

$y=5$

Now given the coordinates of A, we are in position to find the coordinates of the point B. Point B must have y coordinate of y=2 (because the base of the trapezoid is at y=0), and the x coordinate of B, looking at the figure, must be x coordinate of A plus horizontal distance between A and B, i.e

$B_x=A_x+\frac{2}{tan(60)} =-1+\frac{2\sqrt{3} }{3}$

Thus the coordinates of B are:

$B=(-1+\frac{2\sqrt{3} }{3},2)$

Now this point B lies on the parabola, and therefore it must satisfy the equation $y=a(x+1)(x-5).$

Thus

$2=a((-1+\frac{2\sqrt{3} }{3})+1)((-1+\frac{2\sqrt{3} }{3})-5)$

Therefore

$a=\frac{2}{((-1+\frac{2\sqrt{3} }{3})+1)((-1+\frac{2\sqrt{3} }{3})-5)}$

$\boxed{a=-0.3575}$

8 0

3 years ago

W(x) = 3x; find (-3x)

Mashutka [201]

So this means W(-3x) = 3x. So it's equal to 3(-3x), which simplifies to be -9x. Whenever you have a function, it looks like f(x). f doesn't have to be the letter, it can be a, b, c, or like in this case, W. It just means the output of what W(x) is if x equals the number in the parentheses, which is -3x in this case.

7 0

3 years ago

A science teacher has 0.4 of seawater she gives each of her 22 tune in a container or a 5ml spoon she asked as soon as you put t

lidiya [134]

Answer:

the photo is the answer