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You misunderstood the question, Synth got it right

EDIT: link to the site synth took the answer from (The latex there is readable)

2k = 2 x 2 = 4 perfect square. k=2^1 - the exponent =1

3k = 3 x 9 =27 perfect cube. k=3^2 - the exponent = 2

5k =5 x 625 =3,125 perfect 5th power. k= 5^4 - the exponent =4

Sum of the exponents of k =1 + 2 + 4 = 7

can you ecplain that modulo part

Thanks, guys! 

Please help with this geometry question

In rectangle \(ADEH\), points B and C trisect \(\overline{AD}\),
and points G and F trisect \(\overline{HE}\).
In addition, \(\overline{AH}=\overline{AC}=2\).
What is the area of quadrilateral \(WXYZ\) ?

\(\text{Let $\overline{AH}=\overline{AC}=2$ } \\ \text{Let $\overline{AB}=\overline{BC}=\dfrac{\overline{AC}}{2} = 1$ } \\ \text{Let $\overline{AB}=\overline{XZ} = 1$ } \\ \text{Let $\overline{BX}=\dfrac{\overline{AH}}{2} = 1$ } \)

\(\text{Let triangle $XWZ = $ triangle $BYC$ } \)

\(\begin{array}{|rcll|} \hline \mathbf{A_{\text{quadrilateral } WXYZ}} &\mathbf{=} & \mathbf{ A_{XWZ} + A_{XYZ} } \quad | \quad A_{XWZ} = A_{BYC} \\\\ &=& A_{BYC} + A_{XYZ} \quad | \quad A_{BYC} =\dfrac{\overline{BC}\cdot x}{2} \quad A_{XYZ} =\dfrac{\overline{XZ}\cdot (1-x)}{2} \\\\ &=& \dfrac{\overline{BC}\cdot x}{2} + \dfrac{\overline{XZ}\cdot (1-x)}{2} \quad | \quad \overline{BC}=\overline{XZ}=1 \quad \\\\ &=& \dfrac{x}{2} + \dfrac{1-x}{2} \\\\ &=& \dfrac{x+1-x}{2} \\\\ &\mathbf{=} & \mathbf{ \dfrac{1}{2} } \\ \hline \end{array}\)

Lightning, if someone responds to your question it is polite for you to respond.

A thank you and also a point is always appreciated but if you do not understand or you need more help, or even if you think the answer is wrong, then please interact with the answerer!!

In triangle HAC, using Pythagoras's Theorem, the hypotenuse HC =Sqrt(8)

In triangle AHX, using Pythagoras's Theorem, HX=Sqrt(2)

In triangle BCY, using Pythagoras's Theorem, CY=1/sqrt(2)

Therefore, XY =HC - HX - CY =XY =sqrt(8) - sqrt(2) - 1/sqrt(2) =1/sqrt(2) =WZ

By similar reasoning, XW=YZ = 1/sqrt(2)

Therefore, the area of the quadrilateral WXYZ =[1/sqrt(2)]^2 =1/2

Mathematica 11 Home Edition gives the following 2  values:
solve ceiling({y}) floor({y}) = 42 for y

-7 < y < -6          and        6 < y < 7

If \(y>0\), find the range of all possible values of  \(y\)  such that  \(\lceil{y}\rceil\cdot\lfloor{y}\rfloor=42.\)

\lceil{y}\rceil\cdot\lfloor{y}\rfloor=42. 

Express your answer using interval notation.

\(6 \lt y \lt 7\)

Source:

If the surface area of a cylinder with radius of 4 feet is 48pi square feet,

what is its volume?

\(\text{Let $V$ the volume of a cylinder.} \\ \text{Let $r$ the radius of a cylinder.} \\ \text{Let $h$ the height of a cylinder.} \\ \text{Let $S$ the surface area of a cylinder.}\)

\(\begin{array}{|lrcll|} \hline (1) & V &=& \pi r^2h \\ \\ \hline \\ & S &=& 2\pi r^2 + 2\pi rh \quad & | \quad -2\pi r^2 \\ (2) & S-2\pi r^2 &=& 2\pi rh \\ \\ \hline \\ \dfrac{(1)}{(2)} & \dfrac{V}{S-2\pi r^2} &=& \dfrac{\pi r^{2}h}{2\pi rh} \\\\ & \dfrac{V}{S-2\pi r^2} &=& \dfrac{\not{\pi} r^{\not{2}}\not{h}}{2\not{\pi} \not{r}\not{h}} \\\\ & \dfrac{V}{S-2\pi r^2} &=& \dfrac{r}{2} \quad & | \quad \cdot \left( S-2\pi r^2 \right) \\\\ & V &=& \dfrac{r}{2}\cdot \left(S-2\pi r^2 \right) \quad & | \quad S=48\pi,\quad r=4 \\\\ & V &=& \dfrac{4}{2}\cdot \left(48\pi-2\pi 4^2 \right) \\\\ & V &=& 2\cdot \left(48\pi-32\pi \right) \\\\ & V &=& 2\cdot \left(16\pi \right) \\\\ & \mathbf{V} &\mathbf{=}& \mathbf{32\pi \ feet^3 } \\ \hline \end{array}\)

delete

Why did you post this question again? I gave you a hint and you completely ignored it. Stop reposting questions again and again after they have been answered.

Heureka PLEASE do not answer

That's a really good answer!

6% compounded monthly =[1 + 0.06/12]^12 =1.005^12=1.061678 - 1 x 100 =6.1678% Effective annual rate, which is equivalent to the rate of "r" compounded annually. In other words, 6% compounded monthly = 6.17%, or bank's rate of "r" compounded annually.

i) There are ways to choose a school for a persidency meeting.

ii) There are ways for the host school to send representatives and each of the other two schools sends  representative.

70  -  65 =5 mph faster - car's speed per hour compared to the bus.

5  x  8 hours =40 miles farther that the car will have travelled in 8 hours.

19  -  15 = 4 feet - extra space that garage has

4 / 2      = 2 feet - her front wheels need to be from the entrance of the garage.

$50,000 x 1.04^2 =

$50,000 x 1.0816  = $54,080 - Jose's investment after 2 years.

$50,000 x (1 + .04/4]^(2*4) = 

$50,000 x       1.01^8               =

$50,000 x        1.0828567056280801 =$54,143 - Patricia's investment after 2 years.

$54,143  -  $54,080 =$63 - extra interest that Patricia earned on her investment.

Hint: substitute 1 for y and 1 for z to find r, then substitute 1 for x and 1 for z to find s, and then substitute 1 for x and 1 for y to find t.