Search 75,900 tutors

1+ Sec^2 X. Sin^2 X = 1 + 1/(cos^2 X). Sin^2 X = 1 + Sin^2 X/cos^2 X = 1+ tan^2 X =Sec^2 X

# What is the equation of the line that passes through the points (2, 5) and (1, 2)? (answer)

We know that the general equation of a line passing through two points (x1, y1) and ( x2, y2) is, (x-x1)/(x1-x2) = (y-y1)/(y1-y2) substituting the values of x1, y1, x2, y2,  (x-2)/(2-1)= (y-5)/(5-2) or, x-2 = (y-5)/3  or, 3x-6 = y-5 or 3x-y=1    So the...

vu-4u+2vu-u = vu+2vu-4u-u =3vu-5u =u(3v-5)

If 'h' is the height of the building, and X is the distance, then h/x =  tan 35  therefore, x/h= 1/tan35     .....(1) When he moves  100 feet toward the building the angle changes to 400 so h/x-100 = tan 40 therefore ( x-100) /h = 1/tan 40 So x/h-100/h...

# For a show adult tickets are \$8.75 and children's tickets are \$3.50. 460 tickets were sold for a total of 3143 how many adults tickets were sold? (answer)

If x and y are the number of adult and child tickets then 8.75 x + 3.5 y= 3143....... (1) and, x + y = 460.......(2) Multiplying  both sides of the equation with 3.5 we get, 3.5 x + 3.5 y = 3.5 x 460 = 1610.....(3) Subtracting (3) from (1) we have, 8.75 x-3.5 x =...

It will be easier to visualize once you draw a figure.  If h is the elevation  of the baloon, then,  (h-75)/(300)= Tan 200 Therefore, h-75= 300 tan 200 So,  h= 75 + 300 x tan200

# (Sec theata+ Csc theata)(cos theata+ sin theata) (answer)

(Sec x + Csc x)(cos x+ sinx) ..... I used x instead of theata = [1/cos x + 1/sinx] (cosx +sinx) = [(sinx+ cosx)/cosxsinx]/ (cosx+sinx) = 1/cosxsinx =(1/cosx)x(1/sinx)= Secx Cosecx   Now you can replace theata for x.

# how do you factor -x^2-1 (answer)

-x2 -1 = -1-x2 = i2 - x2 = (i + x) (i - x )

(8.1x 104 )/(1.8 x10-4) = ( 8.1/1.8)x 104-(-4) = 4.5x108

# A certain mountain has an elevation of 19,570 feet. (answer)

In 96 years total loss is 9 acres.  Therefore yearly loss= 9/96 Acres/year =  0.09375 acres/year If  Loss of acreage is L in time "t"  years, then L= 0.09375t.  So the Equation is A= A0 - 0.09375t where A0 is the initial acreage and A is the acreage after...

Int  dx/(sinx+cosx)=  Int  (cosx-Sinx)dx/(Cos2x-sin2x)= Int  cosx dx/ (1-2Sin2x) - Int sinx dx/ (2cos2x-1) ..(.1) Let  1-2sin2x =u   and 2cos2x-1 =v so, du= -2 (2)cosx dx =-4cosx dx, thus cosx dx = -1/4 du........(2) and dv= -2 (2) sinx dx = -4sin...

# What are the two points to this system of equations solved by the substitution method? (answer)

The equations are, 7y=x+2.........(1) and 4x-8y=12......... (2) If we multiply each sides of (1) with 4, we get 28 y= 4x+8, Rearranging, we get 4x-28y  = -8   ......(3) Subtracting (3) from  (2) we have  -8y-(-28y)= 12-(-8) Thus, -8y+28y = 12+8 So...

# Remove Parenthess and Simplify expression. 1/2(7y-2)+1/4(2y+9) (answer)

1/2(7y-2)+1/4(2y+9) = 7y/2 - 1 +y/2 + 9/4 = (7y+y)/2 +9/4-1 = 8y/2 + (9-4)/4 = 4y +5/4

# I want to cut 56 each pieces of steel out of a sheet of steel, the pieces are 3" x 2.5", what size sheet would I need, did not want much waste (answer)

The total amount needed would be 56 X 3 X 2.5 Sq inch =420 sq in =12" X 35" So the minimum size of the metal sheet required is 1ft X 3 ft = 3 Sq ft  You can easily cut out 14 strips of 1 ft length. Each of the strips can be cut to make 4 of 3" pieces, thus making a total...

(x-4)² + (x-2)² + (x-3)² = x2 -8x+16 + x2 -4x +4 + x2-6x +9 = 3x2-18x +29

x6-64= (x3)2 - (8)2  = (x3+8) (x3-8) =(x+2)(x2 -2x+4) (x-2)(x2 +2x+4)

(2r + 1 )( r -2 ) = - (3r -6 ) 2r2+ r-4r-2 = -3r+6 2r2-3r-2=-3r+6 2r2=8 r2=4 Thus r= +2 or -2