Which of the following best describes the relationship between the focus and directrix of a parabolaA. The focus is half the distance from the parabola as the directrix
B. The focus is twice the distance from the parabola as the directrix
C. They are Equidistant from the parabola
D. They both lie on the graph of the parabola

Answers

Answer 1

Answer:

Answer:

C)They are Equidistant from the parabola

Step-by-step explanation:

Focus of parabola : The focus of a parabola is a fixed point on the interior of a parabola

Directrix of parabola : A parabola is set of all points in a plane which are at equal distance away from a given point and given line. The given line is called the directrix. The given point is Focus

So, The vertex of the parabola is at equidistant between focus and the directrix.

So, They are Equidistant from the parabola

Hence Option C is correct.

Answer 2

Answer: they are equidistant from the parabola
that is how a parabola is constructed

C is answer

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PLEASE HELP !!!!!!!!!

D (t)=16t□2+96t+112 where t represents time in seconds

Answers

a.
the starting point is where t=0
d(0)=-16(0)^2+96(0)+112
D(0)=112
started from 112 feet

b. max height is vertex
for
y=ax^2+bx+c
the x value of the vertex is -b/2a

so
D(t)=-16t^2+96t+112
t value of vertex is -96/(2*-16)=3
it reaches after 3 seconds

C. simpliy evaluate D(t) for t=3
D(3)=-16(3)^2+96(3)+112
D(3)=-16(9)+288+112
D(3)=-144+400
D(3)=256
max height is 256ft

What does the expression l∙w represent

Answers

It represents Length times width

Which group of numbers is listed from least to greatest?-6, -7, -8, 0, 2
9, 7, 5, -4, -9
-8, -6, -1, 5, 8
-4, 5, -6, 7, -8

Answers

Group 3 Is. Notice what would be bigger as a positive is smaller as a negative. You can find this on a number line if you need more resources. Hope this helps!

This Is Quite Simple. The Greater The Negative, The Smaller The Number.
So, -6, -7, -8, 0, 2 Is Incorrect. 9,7,5,-4,-9, Is Greatest To Least, So Incorrect. -8, -6, -1, 5, 8 Is Correct, -4, -5, -6, 7, -8 Is Obviously Incorrect, So C. :D

The sides of a square are 2^4/9 inches long. what is the area of the square?A. 2^16/81 square inches
B. 4^16/81 square inches
C. 2^8/9 square inches
D. 4^8/9 square inches

Answers

The area of a square is the length of a side times itself:
2_4/9 * 2_4/9
Mixed numbers cannot be multiplied, so first convert to improper fractions:
(9*2)+4 = 18+4 = 22/9
22/9 * 22/9
Multiply straight across:
(22*22)/(9*9) = 484/81
Now turn this into a mixed number:
81 goes into 484 five times with 79 left over:
5_79/81 square inches
Since this is not one of the answer choices, I'm wondering if the given length of the side of the square is incorrect?

Whats the formula of an rectangle

Answers

Answer:

Perimeter: 2l+2w

Area: lw

Step-by-step explanation:

Let l=length, and w=width

Answer:

For Perimeter its 2times length + 2times width

and for Area its: length times width

Hope this helps :)

I found this question in the Sample Assessment Material of the iGCSE Further Pure Maths.The volume of a right circular cone is increasing at the rate of 45 cm3 s–1. The height of the cone is always three times the radius of the base of the cone. Find the rate of increase of the radius of the base, in cms–1, when the radius of the cone is 4 cm. Give your answer correct to 3 significant figures.

Answers

Hello,

Thinking further,

V(R,h)=f(R) for h=3R

V=πR²*3R/2=πR^3

dV/dt=45
but dV/dt=dV/dR* dR/dt==>45=3πR²*dR/dt
==>dR/dt=45/(3πR² )
If R=4 then dR/dt=15/(π*16)=0.2984155...≈0.298

Without any certainty!!!

Final answer:

The rate of increase of the radius when the radius of the cone is 4 cm is approximately 0.299 cm/s. This was calculated by using the derivative of the volume of a cone with respect to its radius, with the height of the cone always being three times the radius.

Explanation:

The subject of this question relates to the rate of change in the context of the volume and radius of a cone. The volume of a right circular cone is given by the formula V = 1/3πr²h. Given that the height is always three times the radius, we can substitute h = 3r into the formula, which gives V = 1/3πr³ * 3 = πr³.

The rate of change of the volume with respect to time (dV/dt) is given as 45 cm³/s. We can set up an equation using the derivative of the volume with respect to the radius and the relation dV/dt = (dV/dr)(dr/dt). Calculating the derivative of the volume with respect to the radius, we find that dV/dr = 3πr². Substituting the provided values into our relation gives us 45 = 3π(4)²*dr/dt. Solving for dr/dt, we find the rate of change of the radius to be approximately 0.299 cm/s to 3 significant figures.

Learn more about Rate of Change here:

brainly.com/question/20816247

#SPJ2

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