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According to the information given in the problem....we have a^2*b^3=y, y is a random constant.

Thus, we have 7^2*3^3=1323.

a^2*6^3=1323, 

a=6.125

agree with ElectricPavlov !

Sorry I don't know if it's just me, but please check your formatting when you post a question. I can't see any values or numbers that are supposed to be in the problem.

Thanks!

Surface Area of a sphere =4*pi*r^2

SA of Earth =4 * 3.141592 x 6,371^2 =5.1 * 10^8 km^2

5.1E8 * 29.2%[percentage of land on Earth] =148,938,826 km^2 -SA of Mars(approx.)

148,938,826 /[4*pi] =11,852,175 km^2  - Take the square root of this.

Sqrt(11,852,175) =~ 3,443 km (approx) -the radius of Mars.

3443 / 6371 [This is Earth's radius] =~54% of Earth's radius is Mars's radius.

First the problem states that nadia and olivia can clean a horse stable in 8 hours. That means that every hour, they complete 1/8 of the cleaning required for the stable. Next, the problem tells us that if Nadia cleans it herself, it would've taken her 12 hours to do it, meaning every hour, she completes 1/12 of the stable. From here on out, we can get how long olivia takes to clean the stable if we subtract the work efficiency of their combined cleaning and Nadia's cleaning alone. This is just 1/8 - 1/12, which is equal to 1/24. This means that every hour, Olivia cleans 1/24 of the stable, meaning she takes 24 hours to clean the stable by herself. (wow that's a lot of time)

Varies inversly  means   a² ~ 1/b³     or more correctly    a² = k/b³    where k is a 'proportionality constant'

Sub in the values given to find the value of 'k'

  (7)^2 = k/(3^3)

49 = k/27

k = 1323

So    a^2 = 1323/b^3     now sub in the question numbers to find a^2

         a^2 = 1323/(6^3)    = 6.125

Let's name the angle corresponding to one of the isosceles sides "x". With this, we have 2 base angles of "x" degrees(on the side of length 40), and a third angle of measurement 180-2x degrees. By dropping an altitude to side AC, we form two right triangles, both of which are congruent to each other AAS. Since the problem asks for the sin of ACB, we need only the opposite side of the right triangle, which is the altitude, divided by the hypotenuse. Because the two right triangles formed are congruent, the base of 40 is split into two halves of length 20. We then realize that this forms a 3 - 4 -5 triangle with a scale factor of 5:

Meaning that the length of the altitude of AC is 15 (3 * 5). Now that we have the opposite side, sine is just opposite / hypotenuse, which is 15 / 25 giving us our final answer of 3/5

Triangle ABC is isosceles.  Picture a line perpendicular to AC and half way along, going from AC to B .  It will have a height given by sqrt(25² - 20²) by Pythagoras.  Hence the sin(ACB) = sqrt(25² - 20²)/25 = sqrt(5*45)/25 = 15/25 = 3/5

Because x - 1 is of first degree, f(x) must be one degree less than the degree of the polynomial on the RHS. i.e. f is of degree 3.

Thank you!

thank u so much

Since the growth is doubling, the graph will not have a proportional relationship.

Therefore, the answer would be D: Nonlinear.

Hope this helped!

We cannot find the height of the prism if we do not know the base.

Thank you!

This is a very simple way to solve it:

We know that the x^2 terms come from:  (-4)*(-7)+2t+(-5)*1

                                                                 28 + 2t -5

                                                                 23 + 2t

If we want this equal to zero, we must have 23+2t = 0 

                                                                      t = -11.5

Hope this helped!

geno... I think you had a mistake.

The formula for inverse proportion is x= k/y.

From the x and y values we were given, we can find out that 2=k/4.

We can figure out that k=8.

Now the equation: Since we know k, we can plug in k as x, and y as 1 from the given value.

x=8/1.

Therefore, x will be equal to 8.

Yeah --I messed up -- I used the formula for the area of a circle instead of the formula for the circumference of the circle:

Correcting:

  Circumference  =  2·pi·radius

  (1/8)·2·pi·6  =  answer #1

  (1/8)·2·pi·3  =  answer #2

Now, subtract answer #2 from answer #1.

Sorry ...

2.355" ....  calculations at the link

This was posted here: https://web2.0calc.com/questions/3d-geometry_3 

Hope this helped!

By the way, here are ALL the combinations that sum up to 9 for 3 dice:

126  135  144  153  162  216  225  234  243  252  261  315  324  333  342  351  414  423  432  441  513  522  531  612  621  Total =  25

This is the difference in length of a 45^o arc of a circle with a radius of 6" and the length of a 45^o arc of a circle with a radius of 3". 

The circumference of a circle with radius 6" is 2 • 6 • 3.14 = 37.68 .... in other words, pi times diameter 

Since 45^o is 1/8 of the way around the circumference, the length of the first arc is (1/8) • 37.68 = 4.710 

The circumference of a circle with radius 3" is 2 • 3 • 3.14 = 18.84 .... in other words, pi times diameter 

Since 45^o is 1/8 of the way around the circumference, the length of the first arc is (1/8) • 18.84 = 2.355 

Longer arc minus shorter arc is 4.710 – 2.355 = 2.355 .... since the units were inches the answer is 2.355" 

_.

y varies inversely as sqrt(x)     --->     y = k / sqrt(x)

x = 2, y = 4                              --->      4  =  k / sqrt(2)     --->     4·sqrt(2)  =  k

x = ?, y = 1                              --->     1  =  4·sqrt(2) / sqrt(x)   

                                     --->     1·sqrt(x)  =  4·sqrt(2)

                                     --->         sqrt(x)  =  4·sqrt(2)

                                     --->    [ sqrt(x) ]²  =  [ 4·sqrt(2) ]²

                                     --->                  x  =  32