The surface area of two similar figures are 25 in ^2 and 36 in ^2 if the volume of the smaller figure is 250 in ^3 then what is the volume of the larger figure?

432 in^3

Step-by-step explanation:

The ratio of linear dimensions is the square root of the ratio of the areas, so is ...

scale factor = √(36/25) = 6/5

The ratio of volumes is the cube of the ratio of linear dimensions, so is ...

volume ratio = (scale factor)^3 = (6/5)^3 = 216/125

Then the volume of the larger figure is ...

larger volume = (250 in^3)·(216/125) = 432 in^3

step-by-step explanation:

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places