Matematik Ödev Yardımı
Matematik öğrenmesi heyecan verici bir derstir. Düzenli çalışmamızda anlamadığımız karmaşık problemlerle karşılaştığımızda ne yapmalıyız? Artık matematik ödevi yardım aracıyla problemleri aramaya başlayabilir ve hızlı bir şekilde çözüme ulaşabilirsiniz.
Bu bir fotoğraf çözme eğitim platformudur. İstediğiniz yanıtları, yalnızca sonuçları değil, aynı zamanda çok akıllı çözümleri de aramak için yalnızca 10 saniyeye ihtiyacınız var. Mevcut en hızlı ve en doğru fotoğraf çözme aracıdır! Aynı zamanda bu AI matematik problemi çözücü, ilkokul, ortaokul ve lisedeki her türlü ders kitabının soru bankasının %90‘ını içerir ve her türlü matematik ödevi problemini ortadan kaldırır!
- SECTION B (20 MARKS) 2. a. A line passes through points A(2,-1,5) and B(3,6,-4) i. Write a vector equation of the line. (5marks) ii. Write parametric equations for the line. (5marks) iii Determine if the point C (0,-15,9) lies on the line. (5marks) b. Find the foci,vertices and asymptotes of a hyperbola with equation ((x+2)^2)/(9)=1+((y-1)^2)/(4) (5marks) 3. a. Find the axis, vertex ,focus and directrix of the parabola 2y^2+16x-12y+2=0 (6 mark) b. Let z_(1)=2+2sqrt (3i) and z_(2)=-1-sqrt (3i) Evaluate 3(z_(1)z_(2)) (4 marks) c. Given that overrightarrow (A)=i-3j+2k and overrightarrow (B)=2i+6j find i. overrightarrow (A)X3overrightarrow (B) (5 marks) ii. overrightarrow (B)Xoverrightarrow (A) (5 marks) 4. a. Check if the two line 3x-5=2y and 4x+5y=1 are parallel (4 marks) b. Find the foci vertices and asymptotes of a hyperbola with equation ((x+2)^2)/(9)-1=-((y-1)^2)/(4) (6 marks) c. Find a unit vector that is perpendicular to both overrightarrow (A)=2i-2j-k and overrightarrow (B)=i+j+k What is the area of the parallelogram with overrightarrow (A) and overrightarrow (B) as its sides? (5 marks) d. Find the axis.vertex,focus and directrix of the parabola y^2+8x-6y+1=0 (5 marks) 5. a. Write the equation of the circle 6x^2+6y^2-24x+36y+30=0 in standard form (4 marks) b. Derive the equation of an ellipse and use it to find the foci and vertices of the ellipse (x^2)/(16)=1-(y^2)/(25) (10 marks) c. Given overrightarrow (A)=3i-2j-5k and overrightarrow (B)=2i+j+k Find; Vert -7AVert (2 marks) ii Vert 2overrightarrow (A)-overrightarrow (3BVert ) (2 marks) ii,overrightarrow (A),overrightarrow (B) (2 marks)
- 1. Find Lagrange polynomials that approximate f(x)=x^3 (a) Find the linear interpolation polynomial P_(1)(x) using the nodes x_(0)=-1 and x_(1)=0. (b) Find the quadratic interpolation polynomial P_(2)(x) using the nodes x_(0)=-1 x_(1)=0 and x_(2)=1 (c) Find the cubic interpolation polynomial P_(3)(x) using the nodes x_(0)=-1,x_(1)=0 x_(2)=1 and x_(3)=2 (d) Find the linear interpolation polynomial P_(1)(x) using the nodes x_(0)=1 and x_(1)=2 (e) Find the quadratic interpolation polynomial P_(2)(x) using the nodes x_(0)=0, x_(1)=1 and x_(2)=2
- Exercises for Introduction to Interpolation 1. Consider P(x)=-0.02x^3+0.1x^2-0.2x+1.66 which passes through the four points (1,1.54),(2,1.5),(3,1.42) and (5,0.66) (a) Find P(4) (b) Find P'(4) (c) Find the definite integral of P(x) taken over [1,4] (d) Find the extrapolated value P(5.5) (e) Show how to find the coefficients of P(x)
- Theta between them. (6 marks) c. Simplify (4+3i)^3 (3 marks) d. Differentiate between standard and general forms of a circle (4 marks) e. Express r=1-3cosTheta in rectangular coordinates (3 marks) f. Find the polar equation of the circle whose Cartesian equation is 2x^2+2y^2=8x (6 marks) g. Find the equation of hyperbola having foci at F1(-5,0) and F2(5,0) and the difference of the total radii 6. (4 marks)
- Exercises for Taylor Series and Calculation of Functions 1. Let f(x)=sin(x) and apply Theorem 4.1 (a) Use x_(0)=0 and find F_(5)(x),P_(7)(x) and P_(9)(x) (b) Show that if vert xvert leqslant 1 then the approximation sin(x)approx x-(x^3)/(3!)+(x^5)/(5!)-(x^7)/(7!)+(x^9)/(9!) has the error bound vert E_(9)(x)vert lt 1/10!leqslant 2.75574times 10^-7 (c) Use x_(0)=pi /4 and find P_(5)(x) , which involves powers of (x-pi /4)