can anyone help with these questions

[knightrider]

1)The object and image positions for a lens of focal length f are related by the formula 1/u+1/v=1/f where u is the distance of the object from the lens and v is the distance of the image from the lens.
a)Make f the subject of the equation
b)Make u the subject of the equation.
c)How far from the lens is the image when an object is 30 cm in front of a lens of focal length 25 cm?

2)The volume of a cone is given by the rule V=1/3pie*R^2*h, where r is the radius of the widest part of the cone and h is the vertical height of the cone. Given that the volume of a cone is 100 cm3 and its radius at the widest point is sqrt12 cm, find the height of the cone, expressing your answer in terms of pie.

[RKTR]

1 a)(v+u)/(uv) =1/f
       f=(uv)/(u+v)
   
   b) 1/u = (v-f)/(fv)
       u= (fv)/ (v-f)
   
   c) 30= (25v)/(v-25)
       30v-750=25v
        5v=750
         v=150cm

2. 100= (1/3)(pie)(12)h
      100=4pie h
       h= 25/ pie 
 

[knightrider]

thankyou for your help

can you help with this

The length of a side of a right-angled triangle can be found using Pythagoras' theorem: c2 = a2 + b2, where c is the length of the longest side, and a and b are the lengths of the two shorter sides. Find the value of b in the triangle above.
a=2root3
c=4

[T-Infinite]

thankyou for your help

can you help with this

The length of a side of a right-angled triangle can be found using Pythagoras' theorem: c2 = a2 + b2, where c is the length of the longest side, and a and b are the lengths of the two shorter sides. Find the value of b in the triangle above.
a=2root3
c=4

Most of these questions just require you to sub in the given information.
So you're given, a and given c, just put it in the given equation:

[Only Cheating Yourself]

1)The object and image positions for a lens of focal length f are related by the formula 1/u+1/v=1/f where u is the distance of the object from the lens and v is the distance of the image from the lens.
a)Make f the subject of the equation
b)Make u the subject of the equation.
c)How far from the lens is the image when an object is 30 cm in front of a lens of focal length 25 cm?

2)The volume of a cone is given by the rule V=1/3pie*R^2*h, where r is the radius of the widest part of the cone and h is the vertical height of the cone. Given that the volume of a cone is 100 cm3 and its radius at the widest point is sqrt12 cm, find the height of the cone, expressing your answer in terms of pie.

a.) I see f as a denominator and we need to be the subject.  I see two fractions on the other side, i want to make f the numerator so i form a reporical but i can't do that because these two separate fractions so i need to make 1 fraction, so i cross multiply which is gong to make v+u as the numerator and so make the denominators same by multiplying so its     v+u/vu=1/f now i can flip them so slip everything vu/v+u=f/1, now i have 1 as the denominator now to get rid of it i multiply both sides by 1 so its now 1 but you don't have to write it so vu/v+u=f and now F is the subject

b.)So we want u the subject, so let 1/u stay as it is and we'll move 1/v to the right side so, 1/u=1/f- 1/v, now we have 1/u by its self we need to make u the numerator as its easier to make it the subject, so again we cross multiply so we can combine the fractions into 1, so 1/u=v-f/vf   now we flip them to make u the numerator so u/1=v-f/vf, so get rid of the 1 we multiply both sides but again we don't need to write the 1 as 1 times anything just stays the same so the answer is   u=v-f/vf

c.)  I had trouble with this one as well!  So  the questions asking how far from the lens is the image  which is what v stands for so we need to make v the subject.  So get 1/v on one side so move 1/u to the other side so
1/v=1/f-1/u now cross multiply to make it 1 fraction so 1/v=u-f/fu, now flip it to make v the numerator so flip both sides  v/1=fu/u-f , multiply 1 to both sides so now we have made v the subject.  v=fu/u-f, now plug in the information provided so 30*25/30-25=150cm the answer is 150cm

[knightrider]

thx what about this question

For safety considerations, wheelchair
ramps are constructed under regulated
specifications. One regulation requires
that the maximum gradient of a ramp
exceeding 1200 mm in length is 1/14

a)Does a ramp 25 cm high with a
horizontal length of 210 cm meet
the requirements?

b)Does a ramp with gradient 1/18 meet the specifications?
c)A 16 cm high ramp needs to be
built. Find the horizontal length
of the ramp required to meet the
specifications.

[Phy124]

thx what about this question

For safety considerations, wheelchair
ramps are constructed under regulated
specifications. One regulation requires
that the maximum gradient of a ramp
exceeding 1200 mm in length is 1/14

a)Does a ramp 25 cm high with a
horizontal length of 210 cm meet
the requirements?

The length is 210cm or 2100mm therefore it exceeds a length of 1200mm and hence needs a gradient less than 1/14.

The gradient is given by the rise/run which is 25/210 = 5/42

1/14 is equal to 3/42 so we know it does not meet the requirements as 5/42 > 3/42

b)Does a ramp with gradient 1/18 meet the specifications?

1/18 < 1/14, so yes.

c)A 16 cm high ramp needs to be
built. Find the horizontal length
of the ramp required to meet the
specifications.

If the horizontal length is less than 1200mm then the gradient could be anything, so we can just assume to start with the horizontal length will be greater than 1200mm and hence is restricted by a gradient of 1/14.

rise/run = 16/horizontal length = 1/14

Therefore the horizontal length is equal to 14*16 = 224cm

[knightrider]

thx for your help and also i have a multiple choice question that says
Which of the following lines has a
gradient of −2?
Which of the following lines has a
gradient of 3?

how would i do this?

[Phy124]

Remember that the gradient is the rise over the run.

If a line goes right and upwards it has a positive rise and a positive run +/+ = +, hence positive gradient.

If a line goes left and upwards it has a positive rise and a negative run +/- = -, hence negative gradient.

If a line goes right and downwards it has a negative rise and a positive run -/+ = -, hence negative gradient.

If a line goes  left and downwards it has a negative rise and a negative run -/- = +, hence positive gradient.



The first one (6a) is easy because you are looking for a line with a negative gradient and there is only one line (B) which has this property.

A and D have positive gradients, E has a 0 gradient and C has an undefined gradient.



For the second one (6b) we are looking for a line with positive gradient, this means it can be on of B, C, D and E (A has an undefined gradient).

To find the value of the gradient take two points (x₁, y₁) and (x₂, y₂) and use the formula:



You'll find that if you look at line E and take the points (x₁, y₁) = (4,1) and (x₂, y₂) = (2,-5) that it has gradient 3.

[knightrider]

what about these questions using simultaneous equations

5)The sum of two whole numbers, x and y, is 41. The difference between them is 3. Write two equations involving x and y and solve them to find the numbers.

6)A farmer counts emus and sheep in a paddock, and notes there are 57 animals and 196 feet. Assuming no animal amputees, how many of each animal are there?

7)A sports store supplies 24 basketballs and 16 cricket balls to one school for $275.60, and delivers 12 basketballs and 32 cricket balls to another school for $211. If delivery is free, how much did the supplier charge for each type of ball?

8)A businessperson hires a stretch limousine for 2 days and a sedan for 3 days while on an interstate trip. If the total car hire cost of the trip was $675, and the limousine cost triple the price of the sedan, find the cost per day of the limousine.

9)this is mulitple choice

A manufacturing plant produces square and circular metal panels in fixed sizes. If the mass of a square panel is 13 kg and that of a circular panel is 22 kg, how many of each panel are there in a truck loaded with 65 panels of total mass 1205 kg? The equations to solve are:
a)13s + 22c = 1205, s + c = 65

b)22s + 13c = 1205, s + c = 65

c)13s + 22c = 65, s + c = 1205

d)22s + 13c = 65, s + c = 1205

e)13s + 22c = 1205, s + c = 35

plz show full working out for questions thx

[Phy124]

what about these questions using simultaneous equations

5)The sum of two whole numbers, x and y, is 41. The difference between them is 3. Write two equations involving x and y and solve them to find the numbers.

Let x equal the higher number and y equal the lower number.

You can derive one equation by noting that the sum of the two numbers is 41 and another by noting that the difference (higher number minus lower number is 3)

Spoiler

6)A farmer counts emus and sheep in a paddock, and notes there are 57 animals and 196 feet. Assuming no animal amputees, how many of each animal are there?

Let x = emus and y = sheep

Emus have 2 feet and sheep have 4.

The total amount of animals will be the sum of the emus (x) and sheep (y) and this is equal to 57, this is our first equation.

Next, total number of feet is the sum of the number of emus (x) multiplied by the number of feet on each emu (2) and the number of sheep (y) multiplied by the number of feet on each sheep (4), this is equal to 196, so we have our second equation.

Spoiler

Therefore we have 16 emus and 41 sheep.

7)A sports store supplies 24 basketballs and 16 cricket balls to one school for $275.60, and delivers 12 basketballs and 32 cricket balls to another school for $211. If delivery is free, how much did the supplier charge for each type of ball?

Let x = price of basketball and y = price of cricket ball

The store supplies 24 basketballs at $x and 16 cricket balls at $y for a total price of $275.60, this forms our first equation.

The store then supplies 12 basketballs at $x and 32 cricket balls at $y for a total price of $211, this forms our second equation.

Spoiler

Therefore basketballs cost $9.45 and cricket balls cost $3.05[/tex]

I'll leave the last two for you to do but I'll give you some hints.

8)A businessperson hires a stretch limousine for 2 days and a sedan for 3 days while on an interstate trip. If the total car hire cost of the trip was $675, and the limousine cost triple the price of the sedan, find the cost per day of the limousine.

Spoiler

Let x = the cost of the limousine per day and y = the cost of the sedan per day.

You are looking for the cost per day of the vehicles and thus you need to form two equations relating the number of days each vehicle was hired and the amount it costs per day. (e.g. if a vehicle clost $z per day and was hired for 5 days it would cost a total price of 5z over the 5 days).

Do this for both vehicles and sum them to equal the total price.

Note that you also have a relationship that the limousine costs three times as much as the sedan, therefore x = 3y, this is your second equation.

9)this is mulitple choice

A manufacturing plant produces square and circular metal panels in fixed sizes. If the mass of a square panel is 13 kg and that of a circular panel is 22 kg, how many of each panel are there in a truck loaded with 65 panels of total mass 1205 kg? The equations to solve are:
a)13s + 22c = 1205, s + c = 65

b)22s + 13c = 1205, s + c = 65

c)13s + 22c = 65, s + c = 1205

d)22s + 13c = 65, s + c = 1205

e)13s + 22c = 1205, s + c = 35

plz show full working out for questions thx

Spoiler

Let s = the number of square panels and c = the number of circular panels

The total weight will be given by the number of square panels (s) multiplied by the weight of a square panel (13) added to the number of circular panels (c) multiplied by the weight of a circular panel (22), this weight is given by 1205. This forms your first equation.

The second equation is simply the number of square panels (s) added to the number of circular panels (c) to equal the number of total panels (65).

[Butterscotch]

what about these questions using simultaneous equations

5)The sum of two whole numbers, x and y, is 41. The difference between them is 3. Write two equations involving x and y and solve them to find the numbers.

Picture attached:

Edit: Beaten by Phy124.

[knightrider]

how would you find the equations for these graphs

[LOLs99]

how would you find the equations for these graphs

Hint: use the general equation for linear y= mx+c and sub in coordinates/x or y int.

[Phy124]

how would you find the equations for these graphs

Because you are shown the y-intercept it is easiest to put it straight in the form where is the gradient given by and is the y-intercept of the line.

Let's do question a.

We can see from the graph that the y-intercept is 2 and hence .

Now to find the gradient we take any two points. I'll use and