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Correct, so 7+15=22.

First, change the 10 feet and 14 feet into inches-10(12)=120 inches and 14(12)=168 inches, respectively.

Now, we know that 120/8=15, so we have 168/15=11.2 inches long.

\(2\tan^2(x) = 3\tan(x)+1\\ 2\tan^2(x) - 3\tan(x)-1 = 0\\ u = \tan(x)\\ 2u^2 - 3u-1 = 0\\ u = \dfrac{3\pm\sqrt{9+8}}{4} = \dfrac{3\pm \sqrt{17}}{4}\)

\(x = \arctan\left(\dfrac{3+\sqrt{17}}{4}\right),~\arctan\left(\dfrac{3-\sqrt{17}}{4}\right)\\ x \approx 1.05913,~-0.273729\)

I believe that would be you CUMULATIVE GPA.....which takes in to account all of you semesters' grades.....

ye that way seems more efficient, thank you

thanks

\(\text{why not just do}\\ p=\left(x, \dfrac{12-3x}{4}\right)\\ |p|^2 =\dfrac{25 x^2}{16}-\dfrac{9 x}{2}+9= \dfrac{25}{4}\\ 25x^2 - 72x+144= 100\\ 25x^2 - 72x+44 = 0 \\ x = \dfrac{22}{25},~2\\ \vec{OB} = \dfrac{22}{25}\hat{i} + \dfrac{117}{50}\hat{j}\\ \vec{OB} = 2\hat{i} + \dfrac 3 2 \hat{j}\)

OHHHH ok my intuition was so wrong lol

thanks very much

Perhaps this will help:

Thanks!

Lol, K.

It actually is

Let the first term be 3

Let the common ratio = 2

So....the first five terms are

3, 6, 12, 24, 48

The nth term is given by

3 (2)^{(n - 1)}

1. A right circular cone is inscribed in a right circular cylinder. The volume of the cylinder is $72\pi$ cubic centimeters. What is the number of cubic centimeters in the space inside the cylinder but outside the cone? Express your answer in terms of $\pi$.

The cone will have a volume of 1/3 of the cylinder....so....the space between them is

]72 pi - 24pi ] cm^3  =    48 pi cm^3

2. Can't be answered since we don't know the vertices of the original triangle

Well...I don't know how "fast" this is

Let   B = (0, 0)   A = (0, 2)    E = (0, 1)   F = (1,0)  D = (2, 2)

We can find the equation of the line containing AF as   y = -2x + 2

And the equation  of the line containing  BD is  y =  1x

So we can find the x coordinate of H as

x = -2x + 2

3x = 2

x = 2/3

And y = 2/3

So...the area of triangle BHF =  (1/2) (BF)(2/3)  = (1/2) (1) (2/3) = 1/3

And the equation of the line containing ED is (1/2)x + 1

So....the x coordinate of I can be found as  

(1/2)x + 1 = -2x+ 2

(5/2)x = 1

x = 2/5

And the y coordinate = (1/2)(2/5) + 1 =  1/5 + 1 = 6/5

Now....the area of triangle ADE = (1/2)(AE)( AD)  = (1/2)((1) (2) =   1

And the area of triangle ADI = (1/2)(height) (AD) =  (1/2) (2 - 6/5) (2)  =  (1/2)(4/5)(2)  = 4/5

So...the area  of triangle AEI = area of  ADE - area of ADI =   1 - 4/5 = 1/5

And the area of triangle ABF = (1/2)(BF)(AB) = (1/2)( 1) (2) =  1

So...the area of BEIH =  area of ABF - area of AEI - area of BHF =

1 - (1/5) - (1/3)  =

1 - 3/15 - 5/15 =

1 - 8/15 =

7 / 15

We can set this up as a ratio:

253.1ft / 42.9ft     =     x ft / 6.2 ft        x = 6.2 *  253.1/42.9   = 36.6 ft shadow of woman 

Ten years ago, the sum of the ages of Ted and his twin brother Todd was 22. How old is Ted now?

Ted and Todd are twins, thus they are the same age. 

When the sum of their ages was 22, each brother was 11. 

Move forward ten years (i.e., 11 + 10), and Ted is now 21.  So is Todd, if it matters. 

...

Maybe Stacy should consult with Marty......or CPhill !

https://web2.0calc.com/questions/geometry-help_77

B.  

Since MRT is a central angle =  147°.....then MAT is an inscribed angle subtending the same arc...so it measures (1/2)147  =   73.5°

But what are the measures of the angles listed?