How can you determine if two ratios are equivalent

Answers

Answer 1

Answer: You can set the two ratios to have the same denominator. The ratios will be equivalent if and only if the numerators are ALSO the same.

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QI - The sum of the distance of a movingpoint from the points (c,0) and (-c,0) is
always 2a units. Find the equation to the locus
of the moving point.

Answers

Answer:

$(x^2)/(a^2)+(y^2)/(a^2-c^2)=1$

Step-by-step explanation:

Let P be the moving point and the given points be A (c,0) and B (-c, 0). If (h, k) be the co-ordinates of any position of P on its locus then:

PA + PB = 2a

PA = 2a - PB

PA² = 4a² + PB² – 4a ∙ PB

PA² – PB² = 4a² – 4a ∙ PB

[(h - c)² +(k - 0)²] - [(h + c)² +(k - 0)²] = 4a² – 4a. PB

-4hc = 4a² – 4a∙PB

a ∙ PB = a² + hc

Taking square

a² ∙ PB² = (a² + hc)²

a² [(h + c)² + (k - 0)²] = (a² + hc)²

a² [h² + c² + 2hc + k²] = a⁴ + 2a²hc + h²c²

a²h² – h²c² + a²k² = a⁴ – a²c²

(a² – c²)h² + a²k² = a² (a² – c²)

h²/a² + k²/(a² – c²) = 1

Therefore, the required equation to the locus of P is

$(x^2)/(a^2)+(y^2)/(a^2-c^2)=1$

Macy has some ropes, each 2 feet long. Nellie has some ropes, each 3 feet long. Oscar has some ropes, each 5 feet long. What is the length of each line of ropes when they are of the same length?

Answers

they should be altogether for 10 feet long

Ron and Pam each have 20 pennies. Ron will put his pennies into 4 group.pam will put her pennies into 5 groups. Who will have more pennies in each group? Explain.

Answers

Hi there,

So lets look at this problem. Ron has 20 pennies. Pam has 20 pennies. If Ron has 4 groups each group will have 5 pennies to add up to 20. Pam will have 5 groups and each group will have 4 pennies to add up to 20.

Therefore Ron will have more pennies in his group.

I need help solving this 8

Answers

Answer:

whats the question?

Step-by-step explanation:

8 < x+3 = 8-3 < x =5X+3< 12 = x<12-3 = x<9

A dump truck is unloading sand that falls into a conical pile. Find the height of the cone when the diameter of the pile is 16 ft and the volume of the sand is 550 ft3. Round your answer to the nearest tenth.

Answers

Answer:

8.21

Step-by-step explanation:

formula is:

V= 3 $(volume)/(pie(diameter))$

you plug everything in but when you go to plug in your diameter you need to use the radius. the radius is always half of the diameter.

A blueprint scale is 1/4 in = 1 ft. If the blueprint measurement is 3 in in x 3 in, what should you cut?

Answers

I should cut out a 12 ft by 12 foot

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