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3 years ago

Determine between which consecutive integers the real zeros of each function are located f(x) = 3x3 – 10x2 + 22x – 4

1 answer:

7 0

we have to find which consective integer the real zero is present so for this we will assume
x=0:
f(0)= 3*0-10*0+22*0-4 = -4
now

 for: x=1:
f(1)=3*1-10*1+22*1-4=3-10+22-4=11
now it means that the real zero lies between 0 and 1

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5.6×10⁴ in standard notation

Gnoma [55]

56,000 in standard notation

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3 years ago

3x2 - 5x + 6) + (9 - 8x - 4x2)

Ksju [112]

Answer:

13-13x

Step-by-step explanation:

3*2=6

(6-5x+6) + (9-8x-8)

Combine Like Terms

(12-5x) + (1-8x)

Put x on one side and numbers on the other.

(12+1) + (-5x+ (-8x))

13-13x

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3 years ago

A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) rep

prohojiy [21]

The sketch of the parabola is attached below

We have the focus $(a,b) = (2, -0.5)$
The point $P(x,y)$
The directrix, c at $y=-1.5$

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; $(2, -0.5)$ and $(x,y)$ .
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$

Step 2
Find the distance between the point P to the directrix $c$ . It is a vertical distance between y and c, expressed as $y-c$

Step 3
The equation of parabola is then given as
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$ = $y-c$
$(x-a)^{2}+ (y-b)^{2}= (y-c)^{2}$ ⇒ substituting a, b and c
$(x-2)^{2}+ (y--0.5)^{2} = (y--1.5)^{2}$
$(x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2}$ ⇒Rearranging and making $y$ the subject gives

$y= \frac{ x^{2} }{2} -2x+1$

7 0

3 years ago

How do you find surface area of a triangular prism ?

RSB [31]

The formula to find the surface area of a triangular prism is basically finding out the area of one of the faces of a traingle, which is:

 $(base)*(height)/2$

So, basically you take the face of the triangle that your trying to find the surface area of and plug in your values for the base length and height, multiply them together, hen divide that product by 2 to find your surface area :)

Thank you for the question! I hope this helped! Have an amazing day!! :D

5 0

3 years ago

Which of the following best describes a cylinder?

alexandr1967 [171]

Hey there!

The shape being described in letter A is a prism. A prism has two polygonal shapes on either end that can be any shape consisting of three or more sides. This won't be your answer, since cylinders have circular bases on either side.

The shape being described in letter B is a cylinder. Not sure why they needed to throw in the plane part, but this is the only answer that describes the bases as being circular (or, as they put it, discs).

The shape being described in letter C is a pyramid. If a shape has a polygonal base and meets at a point at the other end, it will be a pyramid. Obviously, a pyramid only has one end, meaning that this isn't your answer.

The shape being described in letter D is a cone. Again, if a shape has a base and meets at a point, it will be a pyramid. However, in the case of a cone, the base will be circular and the other side will meet at a point. The entire shape will be rounded where a pyramid would have edges. Again, not your answer.

Your answer will be B. Hope this helped you out! :-)

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3 years ago