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sin = -12/13

sec = 1/cos       if sec <0 then cos < 0

sin²    + cos²  = 1    yields    cos = - 5/13

Tan = sin / cos   

csc = 1/sin

sec = 1/cos

cot = cos/sin            plug in the values of sin and cos to compute these trig values....

1/3 of the distance = 700 km     remaining distance = 1400 km

distance / rate = time

700 km / 760 km/h    +   1400 km / 800 km/ hr   =   .........   hr

Q1     T = 2pi sqrt (L/g)

               so gravity is inversely proprtional to  T period

           L/(T/2pi)²  = g      so  g is in direct proprtional to L

Q2      net g will be   Earth - moon  g    which will affect T (the period)   Moon g will be very small....

Amount invested at 7% = S

Amount invested at 5% =150,000 - S

0.07S  +  0.05*[150,000 - S] =10,000, solve for S

S =$125,000 amount invested at 7%

$150,000 - $125,000 =$25,000 amount invested at 5%

The ratios of the 3 investors is: 2 : 3 : 10

Sum of the ratios =2 + 3 + 10 = 15

[2 / 15] x $30,000,000 = $4,000,000 share of the smallest investor

[3 / 15] x $30,000,000 = $6,000,000 share of the 2nd investor

[10 / 15] x $30,000,000 =$20,000,000 share of the biggest investor.

Children's tickets = C

Adult tickets          =300 - C

5C  +  9*(300 - C) =2340, solve for C

C =90 Children's tickets sold

300 - 90 = 210 Adult tickets sold.

Solve for r:
A = 2 π h r + 2 π r^2

A = 2 h π r + 2 π r^2 is equivalent to 2 h π r + 2 π r^2 = A:
2 π h r + 2 π r^2 = A

Divide both sides by 2 π:
r^2 + h r = A/(2 π)

Add h^2/4 to both sides:
r^2 + h r + h^2/4 = h^2/4 + A/(2 π)

Write the left hand side as a square:
(r + h/2)^2 = h^2/4 + A/(2 π)

Take the square root of both sides:
r + h/2 = sqrt(h^2/4 + A/(2 π)) or r + h/2 = -sqrt(h^2/4 + A/(2 π))

Subtract h/2 from both sides:
r = sqrt((h^2)/4 + A/(2 π)) - h/2 or r + h/2 = -sqrt(h^2/4 + A/(2 π))

Subtract h/2 from both sides:

r = sqrt((h^2)/4 + A/(2 π)) - h/2 

The answer is 7.

Please look at the explanation on this website: https://brainly.com/question/17238542

Thank oy so much hectictar!!!!

See a very clear solution here: https://socratic.org/questions/582476bab72cff56d798b941#:~:text=1%20Answer&text=By%20the%20sum%20and%20difference,B%E2%88%92sinAsinB%20.&text=Use%20the%20identity%20sin2,%3D1%E2%88%92cos2%CE%B8%20.&text=This%20identity%20has%20been%20proved!

1.

Remember:       distance   =   rate * time

Since he was going at two different rates for each part of the trip, lets first calculate the distance he flew during the first part of the trip and then we can calculate the distance he flew during the second part of the trip. The total distance traveled will be the sum of these two distances.

distance₁   =   rate₁ * time₁   =   680 mi/hr  *  (3.8 / 2) hr   =   680 mi/hr   *   1.9 hr   =   1292 mi

distance₂   =   rate₂ * time₂   =   740 mi/hr  *  (3.8 / 2) hr   =   740 mi/hr   *   1.9 hr   =   1406 mi

total distance   =   distance₁  +  distance₂   =   1292 mi  +  1406 mi   =   ?

2.

By solving the first formula for time,  we get:       time   =   distance / rate

Again let's split this into two parts for each part of the trip.

For the 1st part..... the distance is one third of the total distance, and the rate is 1032 km/hr.

For the 2nd part.... the distance is two thirds of the total distance, and the rate is 696 km/hr.

\(\text{time}_1\ =\ \dfrac{\text{distance}_1}{\text{rate}_1}\ =\ \dfrac{\frac13\cdot1860\ \text{km}}{1032\ \frac{\text{km}}{\text{hr}} } \ =\ \dfrac{620\ \text{km}}{1032\ \frac{\text{km}}{\text{hr}} }\ =\ \dfrac{620}{1032}\ \text{hr}\)

\(\text{time}_2\ =\ \dfrac{\text{distance}_2}{\text{rate}_2}\ =\ \dfrac{\frac23\cdot1860\ \text{km}}{696\ \frac{\text{km}}{\text{hr}} }\ =\ \dfrac{1240\ \text{km}}{696\ \frac{\text{km}}{\text{hr}} }\ =\ \dfrac{1240}{696}\ \text{hr}\)

\(\text{total time}\ =\ \text{time}_1+\text{time}_2 \ =\ \dfrac{620}{1032}\ \text{hr}\ +\ \dfrac{1240}{696}\ \text{hr}\ =\ \Big( \dfrac{620}{1032}\ +\ \dfrac{1240}{696}\Big)\ \text{hr}\ \approx\ 2.38\ \text{hr} \) _

помогите !!!!!!! пожалуйста

х * (- 6 + х) = - 8

x² - 6x + 8 = 0

Use the quadratic formula to solve this

x = 4,  x = 2

thank you so much! i understand it a lot better now!!!

Remember that raising a number to the power of  -1  "flips" it so the numerator becomes the denominator and vice versa.

Like this:          ( a / b )^-1   =   b / a          and          ( a )^-1   =   ( a / 1 )^-1   =   1 / a

\((i-i^{-1})^{-1}\\~\\ =\quad(i-\frac1i)^{-1}\)

                                     Get a common denominator between  \(i\)  and  \(\frac1i\)  by multiplying the first term by  \(\frac{i}{i}\)

\(=\quad(i\cdot\frac{i}{i}-\frac1i)^{-1}\\~\\ =\quad(\frac{i^2}{i}-\frac1i)^{-1}\\~\\ =\quad(\frac{i^2-1}{i})^{-1}\)

                                     Replace  \(i^2\)  with  -1

\(=\quad(\frac{-1-1}{i})^{-1}\\~\\ =\quad(\frac{-2}{i})^{-1}\\~\\ =\quad\frac{i}{-2}\\~\\ =\quad-\frac{1}{2}i\)

Since vertical angles are congruent, we can make the following equation:

(4x + 7)°   =   (7x - 35)°

                                           We can remove the degree signs and parenthesees from both sides of the equation.

4x + 7   =   7x - 35

                                           Subtract 4x from both sides, add  35  to both sides.

7 + 35   =   7x - 4x

                                           Combine like terms.

42   =   3x

                                           Divide both sides of the equation by  3

?   =   x

Alternate approach:

Since a  180°  angle forms a straight line, we can make the following equation:

(4x + 7)°  +  (10x - 23)°   =   180°

                                                       Remove the degree signs from every term, then we can drop the two

                                                       sets of parenthesees because there is only addition between them

4x + 7  +  10x - 23   =   180

                                                       Simplify the left side by combining like terms.

14x  -  16   =   180

                                                       Add  16  to both sides.

14x   =   196

                                                       Divide both sides of the equation by  14

x   =   ?

x < 7.

1. Domain = (-inf,inf), Range = (-inf,inf)

2. a + b = 14.

y = -2/15*x + 8/15.

wow tysm! that really helped! :)

I see no square. Maybe try again?

Hint: to calculate the third side, use the law of cosines and quadratic equation.

To find the angle you're looking for, use the law of cosines.

Good luck!

Solve for x:
x^4 - 3 x^3 + 5 x^2 - 27 x - 36 = 0

The left hand side factors into a product with three terms:
(x - 4) (x + 1) (x^2 + 9) = 0

Split into three equations:
x - 4 = 0 or x + 1 = 0 or x^2 + 9 = 0

Add 4 to both sides:
x = 4 or x + 1 = 0 or x^2 + 9 = 0

Subtract 1 from both sides:
x = 4 or x = -1 or x^2 + 9 = 0

Subtract 9 from both sides:
x = 4 or x = -1 or x^2 = -9

Take the square root of both sides:

x = 4    or    x = -1    or    x = 3 i    or    x = -3 i

I can't really tell what fraction that is... please fix the latex! :)

The two segments HI and IJ must add up to the length of the HJ. So we have the equation:

3x-5+(x-1)=7x-27

4x-6=7x-27

3x=21

x=7

The length of HJ equals the total of its two segments. 

(3x – 5) + (x – 1)  =  7x – 27 

                 4x – 6  =  7x – 27  

                       3x  =  21  

                         x  =  7 

_.