heureka

Eric jogged

3 1/4 miles on Monday,

5 5/8 miles on Tuesday, and

8 miles on Wednesday.

Suppose he continues the pattern for the remainder of the week.

How far will Eric jog on Friday?

$\begin{array}{lrrll} \text{Monday} & 3 & \frac{2}{8} & \text{ miles} \\ &&&& +2\frac{3}{8}\\ \text{Tuesday} & 5 & \frac{5}{8} & \text{ miles} \\ &&&& +2\frac{3}{8}\\ \text{Wednesday} & 7 & \frac{8}{8} & \text{ miles} \\ &&&& +2\frac{3}{8}\\ \text{Tursday} & 9 & \frac{11}{8} & \text{ miles} \\ &&&& +2\frac{3}{8}\\ \text{Friday} & 11 & \frac{14}{8} & \text{ miles} \\ \end{array}$

Eric will jog on Friday $11\frac74 \ \text{miles}$

Find sin A if cos A =7/25

I. Quadrant:

$\sin{(A)} = + \sqrt{1-\cos^2{(A)}}\\ \sin{(A)} = + \sqrt{1-(\frac{7}{25})^2}\\ \sin{(A)} = + \sqrt{1-\frac{7^2}{25^2}}\\ \sin{(A)} = + \sqrt{ \frac{25^2-7^2}{25^2}}\\ \sin{(A)} = + \frac{ \sqrt{ 25^2-7^2 } } {25}\\ \sin{(A)} = + \frac{24} {25}\\ \sin{(A)} = 0.96$

IV. Quadrant:

$\sin{(A)} = - \sqrt{1-\cos^2{(A)}}\\ \sin{(A)} = -\sqrt{1-(\frac{7}{25})^2}\\ \sin{(A)} = - \sqrt{1-\frac{7^2}{25^2}}\\ \sin{(A)} = - \sqrt{ \frac{25^2-7^2}{25^2}}\\ \sin{(A)} = - \frac{ \sqrt{ 25^2-7^2 } } {25}\\ \sin{(A)} = - \frac{24} {25}\\ \sin{(A)} = -0.96$

Find sin A if cos A = 0.4

I. Quadrant:

$\sin{(A)} = + \sqrt{1-\cos^2{(A)}}\\ \sin{(A)} = + \sqrt{1-0.4^2}\\ \sin{(A)} = 0.91651513899$

IV. Quadrant:

$\sin{(A)} = - \sqrt{1-\cos^2{(A)}}\\ \sin{(A)} = - \sqrt{1-0.4^2}\\ \sin{(A)} = -0.91651513899$

what is the next 3 terms in this geometric sequence?... 32, 48, 72, 108

Geometric Sequence ... 32, 48, 72, 108, ...

The common ratio r is 1.5

$r = 1.5\\ r = \frac{48}{32} = \frac{72}{48} = \frac{108}{72}$

The  geometric sequence is $a,\ a\cdot r,\ a\cdot r^2,\ a\cdot r^3,\ a\cdot r^4,\ \dots$

$\begin{array}{rcll} a_{n+1} &=& a_n \cdot r \\ \end{array}$

32,

32*1.5 = 48

48 *1.5 = 72

72 * 1.5 = 108

108 * 1.5 = 162

162 * 1.5 = 243

243 * 1.5 = 364.5

The next 3 terms in this geometric sequence 162, 243, 364.5

9.296e+7 i need this writen out with zeros

$\begin{array}{rcll} 9.296\cdot 10^7 &=& 92960000 \end{array}$

what is 5/16 - 1/16

$\begin{array}{rcll} \frac{5}{16} - \frac{1}{16} &=& \frac{5-1}{16} \\ &=& \frac{4}{16} \\ &=& \frac{4}{4\cdot 4} \\ &=& \frac{\not{4}}{\not{4}\cdot 4} \\ &=& \frac{1}{4} \\ \end{array}$

What is square root of 583

The square root of 583 is 24.1453929353

(4^3X^6YZ^3)(5^2X^2Y^3Z^2)

$\begin{array}{rcll} (4^3x^6yz^3)\cdot (5^2x^2y^3z^2) &=& 4^3x^6yz^3 5^2x^2y^3z^2 \\ &=& 4^35^2x^6x^2yy^3z^3z^2\\ &=& 4^35^2x^{6+2}y^{1+3}z^{3+2}\\ &=& 4^35^2x^{8}y^{4}z^{5}\\ \end{array}$

Find the mass of Planet X, given that its radius is 3.39e6m and that the acceleration due to gravity on its surface is 3.73m/s2.

$\begin{array}{rcll} \text{ The mass of Planet X } &=& M \\ r &=& 3.39\cdot 10^6\ m \\ a &=& 3.73\cdot \frac{m}{s^2} \\\\ \text{Newton }\\ F &=& G \cdot \frac{ M\cdot m }{r^2} \qquad & G = 6.67\cdot 10^{-11} \cdot \frac{m^3}{kg\cdot s^2}\\ F &=& m \cdot a \\\\ F = G \cdot \frac{ M\cdot m }{r^2} &=& m \cdot a \\ G \cdot \frac{ M\cdot m }{r^2} &=& m \cdot a \\ G \cdot \frac{ M }{r^2} &=& a \\ \mathbf{M} &\mathbf{=}& \mathbf{\frac {a\cdot r^2}{G} } \\\\ M & =& \frac { 3.73\cdot \frac{m}{s^2}\cdot (3.39\cdot 10^6\ m)^2}{6.67\cdot 10^{-11} \cdot \frac{m^3}{kg\cdot s^2}} \\ M & =& \frac { 3.73\cdot \frac{m}{s^2}\cdot 3.39^2\cdot 10^{12}\ m^2}{6.67\cdot 10^{-11} \cdot \frac{m^3}{kg\cdot s^2}} \\ M & =& \frac { 3.73\cdot 3.39^2\cdot 10^{12} }{6.67\cdot 10^{-11} } \cdot \frac{m\cdot m^2\cdot kg\cdot s^2}{m^3\cdot s^2} \\ M & =& \frac { 3.73\cdot 3.39^2\cdot 10^{12}\cdot 10^{11} }{6.67} \cdot \ kg \\ M & =& \frac { 3.73\cdot 3.39^2\cdot 10^{23} }{6.67} \cdot \ kg \\ \mathbf{M} &\mathbf{=}& \mathbf{6.42661664168\cdot 10^{23} \cdot \ kg }\\ \end{array}$

Find the circumcenter of a triangle that has these points

A=(4,5)

B=(-8,-6)

C=(4,-6)

find the midd point between A and B

The circumcenter of a right triangle is the midd point between A and B (Thales' theorem).

M is the midd point between A and B.

$\begin{array}{rcll} \vec{M} &=& \frac12\cdot \left[ \vec{A} + \vec{B} \right]\\ \vec{M} &=& \frac12\cdot \left[ \binom{4}{5} + \binom{-8}{-6} \right]\\ \vec{M} &=& \frac12\cdot \left[ \binom{4-8}{5-6} \right]\\ \vec{M} &=& \frac12\cdot \left[ \binom{-4}{-1}\right]\\ \vec{M} &=& \dbinom{ -\frac{4}{2} } {-\frac{1}{2} }\\ \vec{M} &=& \binom{-2}{-0.5} \\ \end{array}$

The circumcenter of a right triangle is (-2, -0.5)