MATHEMATICS HIGH SCHOOL

A square has a perimeter of 12 cn. What is its area

Answers

Answer 1

Answer:

Answer:

The area of the square is 9 inches

Step-by-step explanation:

12/4=3 to get the length of one side of the square.

Multiply it by itselfto find the area.

Answer 2

Answer:

Answer:

Step-by-step explanation:

Hope it helped

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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:

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2.) Consider the following equations:−x − y = 1
y = x + 3

If the two equations are graphed, at what point do the lines representing the two equations intersect?
(−1, 2) - answer?
(−2, 1)
(1, −2)
(2, −1)

Answers

Hello,
let's try by elimination

x+y=-1
y=x+3
We put the value of y into the first equation

x+(x+3)=-1
==>2x=-4
==>x=-2
So with the second equation, y= -2+3=1

Answer is B (-2,1)

Which of the following is not a correct description of the graph of the function y = -2x - 7?(A) The graph of the function contains the point (−2, −3), and when the value of x increases by 1 unit, the value of y decreases by 2 units.
(B) The graph of the function contains the points (−1, −5), (2, −11), and (4, −15).
(C) The graph of the function is a line that passes through the point (0, −7) with a slope of −2.
(D) The graph of the function contains the points (0, −7), (1, −9), and (3, −1).

Answers

Try graphing the function and go over each answer to see whether or not its true

To the nearest tenth, what is the length of the hypotenuse of a right triangle if one side measures 4.5 meters and the other side measures 9 meters?1) 10.1 meters
2) 20.3 meters
3) 101.3 meters
4) 202.6 meters

Answers

C squared= a squared + b squared
C squared = 4.5 squared + 9 squared
C squared = 20.25 + 81
C squared = 101.25
Square root 101.25 you get 10.06 round up and you get the answer to be number 1

the answer is 1) 10.1 meters

According to the pythagora theorum,

h² = a² + b²

h² = 4.5² + 9²

= 20.25 + 81

thus, h² = 101.25

thus, h = √101.25

thus, h = 10.06230589 units, or 10.1 rounded to the nearest tenth

Plz help i will mark brainliest

Answers

the answer is 5.5x10^-5

Emily needs to buy fabric to make curtain panels for her windows. Each panel will be 4 feet long and 1/2 foot wide. Each piece of fabric that she can buy is 4 feet long and 2 feet wide . How many panels can she make from i piece of fabric?

Answers

Each panel is 4 ft long and 1/2 ft wide

The piece of fabric is 4 ft long and 2 ft wide

So she can therefore fit 4 panels into this. We can calculate this by area
4*1/2=2ft^2

4x2=8ft^2

So 4*2 =8

The pieces of fabric are already the correct length, so it is just a matter of how many panels will fit into one piece of fabric. 2/(1/2) = 4, so she can make 4 panels from 1 piece of fabric.

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