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F ind all values of x in the range 0° <= x <= 180° satisfying tan(x+45°)= 8tan(x)

tan(x)+tan(45)/1-tan(x)tan(45) = 8tan(x)

8tan²(x)-7tan(x)+1=0

tan(x)=0.6952 or 0.1798

x = arctan(0.6952) = 34.8070 deg and arctan(0.1798) = 10.1932 deg

Answered by Tomos M. • Maths tutor

6158 Views

Solve integral [3x^2 (x^3 + 1)^6] dx

Using the substitution u = x³+1 the answer can be found

(x³+1)⁷/7 + C

Answered by Kathryn S. • Maths tutor

7318 Views

Find the values of k for which the equation (2k-3)x^2 - kx + (k-1) = 0

A quadratic equation has two equal roots when its discriminant is equal to 0. Calculating the discriminant of the given equation: D = k² - 4(k-1)(2k-3) = k² - 8k²+20k-12...

Answered by Katerina P. • Maths tutor

4566 Views

A curve C has the following equation: x^3 + 3y - 4(x^3)*(y^3) a) Show that (1,1) lies on C b) Find dy/dx

a) Substituting the coordinate (1,1) into the left hand side of the equation for C we obtain: (1³) + 3*1 - 4(1³)(1³) = 1 + 3 - 4 = 0 = The right hand side of the equation,...

Answered by Harry W. • Maths tutor

3137 Views

show that tan(x)/sec2(x) = (1/2)sin(2x)

tan(x)/sec²(x) Sec(x) = 1/cos(x), therefore 1/sec(x) = cos(x). also tan(x) = sin(x)/cos(x).using substitution, tan(x)/sec²(x) = (sin(x)/cos(x)) * cos²(x) = sin(x)cos(x). s...

Answered by Olaitan O. • Maths tutor

4718 Views