The diagram below shows a sketch of the line y = 16 – x² and y = x² – 4x intersecting at point A and...

The diagram below shows a sketch of the line y = 16 – x² and y = x² – 4x intersecting at point A and B.

a)Find the coordinates of A and B.
b)Calculate the area bounded by the curve y = 16 – x² the y-axis and the x-axis.
c)Calculate the area of the shaded region that lies below the x – axis.
d)Calculate the area of the region enclosed by the curves y = 16 – x², y = x² – 4x and the y – axis.

---

---

Kavungya answered the question on September 17, 2019 at 05:43

Exams With Marking Schemes

• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Grade 8
• Grade 9
• PP1
• PP2
• Playgroup
• Form 1
• Form 2
• Form 3
• Form 4

Related Questions

---

• Towns P(36⁰N, 49⁰E) and town Q(36⁰N, 131⁰W) are on the earth surface. a)Find the difference between P and Q along the parallel of latitude... (Solved)
  

  Towns P(36⁰N, 49⁰E) and town Q(36⁰N, 131⁰W) are on the earth surface.
  a)Find the difference between P and Q along the parallel of latitude given that the radius of the earth is 6370km. (Give your answer to the nearest km.)
  b)Another town R, is 840km East of town Q and on the same latitude, find the position of R.
  c)If the local time at town Q is 12:30am on Monday, what is the local time of town R?
  

  Date posted: September 17, 2019 .    Answers (1)

• The table below shows the values of x and y for the curve represented by; (Solved)
  

  The table below shows the values of x and y for the curve represented by;
  

  Date posted: September 17, 2019 .    Answers (1)

• A mixed school can accommodate a maximum of 440 students. The number of girls must be at least 120 while the number of boys must... (Solved)
  

  A mixed school can accommodate a maximum of 440 students. The number of girls must be at least 120 while the number of boys must exceed 150.
  Taking x to represent the number of boys and y the number of girls, write down all the inequalities representing the information above.
  

  Date posted: September 16, 2019 .    Answers (1)

• The points with coordinates (5,5) and (-3, -1) are the ends of a diameter of a circle centre A. Determine; a)The coordinates of A. b)The equation of... (Solved)
  

  The points with coordinates (5,5) and (-3, -1) are the ends of a diameter of a circle centre A. Determine;
  a)The coordinates of A.
  b)The equation of a circle, expressing it inform of x² + y² + ax + by + c = 0 where a, b and c are constants

  Date posted: September 16, 2019 .    Answers (1)

• Using trapezoidal rule of 5 strips determine the area under the curve y=3x² – 20 between the line x=1 and x=6. (Solved)
  

  Using trapezoidal rule of 5 strips determine the area under the curve y=3x² – 20 between the line x=1 and x=6.

  Date posted: September 16, 2019 .    Answers (1)

• A farmer bought a tractor at Kshs.210,000 and sold at Kshs.52,500, after using it for five years. Calculate the annual rate of depreciation of the... (Solved)
  

  A farmer bought a tractor at Kshs.210,000 and sold at Kshs.52,500, after using it for five years. Calculate the annual rate of depreciation of the tractor.

  Date posted: September 16, 2019 .    Answers (1)

• Two chords PQ and RS of a circle meet a point X outside the circle. If PX = 6cm, QX = 3.5 cm and XS... (Solved)
  

  Two chords PQ and RS of a circle meet a point X outside the circle. If PX = 6cm, QX = 3.5 cm and
  XS = 3 cm, find the length of the chord RS.
  

  Date posted: September 16, 2019 .    Answers (1)

• Triangle ABC is the image of triangle XYZ when transformed under the matrix . If the area of triangle ABC is 770cm², find the... (Solved)
  

  Triangle ABC is the image of triangle XYZ when transformed under the matrix . If the area of triangle ABC is 770cm², find the area of triangle XYZ.

  Date posted: September 16, 2019 .    Answers (1)

• The probability that Christine qualifies for a job as a marketing manager depends on whether she passes or fails in mathematics. The probability that she... (Solved)
  

  The probability that Christine qualifies for a job as a marketing manager depends on whether she passes or fails in mathematics. The probability that she fails in mathematics is ⅓. If she passes the probability that she qualifies for the job is ¾. If she fail there is a probability of 1/6 that she qualifies for the job. What is the probability that she qualifies for the job.

  Date posted: September 16, 2019 .    Answers (1)

• Solve the equation (Solved)
  

  Solve the equation
  

  Date posted: September 16, 2019 .    Answers (1)

• The length and the breadth of a rectangular floor were measured and found to be 4.1m and 2.2m respectively. If a possible error of 0.01m... (Solved)
  

  The length and the breadth of a rectangular floor were measured and found to be 4.1m and 2.2m respectively. If a possible error of 0.01m was made in each measurement. Calculate the percentage error in the area of the floor.

  Date posted: September 16, 2019 .    Answers (1)

• Make y the subject of the formula. (Solved)
  

  Make y the subject of the formula.
  

  Date posted: September 16, 2019 .    Answers (1)

• Use logarithms, correct to 4 decimal places to evaluate (Solved)
  

  Use logarithms, correct to 4 decimal places to evaluate
  

  Date posted: September 16, 2019 .    Answers (1)

• The figure below shows cuboids ABCDEFGH. Given that AB=12 cm, BC= 8 cm and BF=4 cm. (a)State the projection of AG on the plane EFGH. (b)Determine the... (Solved)
  

  The figure below shows cuboids ABCDEFGH. Given that AB=12 cm, BC= 8 cm and BF=4 cm.
  
  (a)State the projection of AG on the plane EFGH.
  (b)Determine the angle between the line AG and the Plane EFGH.
  (c)Given that L! M and N are the mid points DC, FG and AB respectively, determine the angle between the planes ADM and NLM.
  (d)Find the angle between the skew lines AG and BC.
  

  Date posted: September 16, 2019 .    Answers (1)

• Two variables A and B are believed to be related by a law of the form A=mn^B + 1.1 where m andn are constants. The... (Solved)
  

  Two variables A and B are believed to be related by a law of the form A=mn^B + 1.1 where m and n are constants. The table below shows corresponding values of A and B as obtained from an experiment.
  
  By drawing a suitable straight line graph estimate the values of m and n.
  

  Date posted: September 16, 2019 .    Answers (1)

• (a)Bag A contains 4 red balls and 5 white balls while bag B contains 6 red balls and 4 white ones. (i)A bag is picked at... (Solved)
  

  (a)Bag A contains 4 red balls and 5 white balls while bag B contains 6 red balls and 4 white ones.
  (i)A bag is picked at random and a ball is picked, find the probability that the ball is
  white.
  (ii)A ball is removed from A and placed in bag B. Two balls are then picked from B at random one at a time without replacement; find the probability that the two balls are of the same colour.
  (b)Three boys and three girls sit in a row of six seats. Find the probability that:-
  (i)Three girls sit together.
  (ii)The girls and boys sit in alternative seats.
  

  Date posted: September 16, 2019 .    Answers (1)

• A¹B¹C¹D¹ is the image of ABCD under a shear parallel to x – axis D(2,4) is mapped onto D¹(1,4) while A(-1,1) is mapped onto A¹(1,1).... (Solved)
  

  A¹B¹C¹D¹ is the image of ABCD under a shear parallel to x – axis D(2,4) is mapped onto D¹(1,4) while A(-1,1) is mapped onto A¹(1,1). If the co – ordinates of A,B,C and D are (-1,1), (0,1), (3,4) and (2,4) respectively:-
  (a)Draw ABCD and A¹ B¹C¹ and D¹ under the shear on the grid provided and state
  Co-ordinates of B¹ and C¹.
  (b)State the invariant line.
  (c)A¹ B¹C¹ and D¹ undergoes a stretch parallel to y – axis with scale factor -2 and invariant line y =3. On the same grid, draw A//B//C//D// the image of A¹ B¹C¹ D¹ under the stretch
  (d)Describe completely the transformation that maps A//B//C//D// onto ABCD.
  

  Date posted: September 16, 2019 .    Answers (1)

• Use a ruler and compass ONLY for all constructions in this question. (a)Construct a triangle ABC in which AB=6 cm, BC= 7 cm and angle ABC... (Solved)
  

  Use a ruler and compass ONLY for all constructions in this question.
  (a)Construct a triangle ABC in which AB=6 cm, BC= 7 cm and angle ABC = 75⁰.
  (b)Measure
  (i)the length of AC
  (ii)the angle ACB
  (c)(i)Construct the locus of p such that BP = PC
  (ii)Construct the locus of Q such that Q is on the opposite side of BC as A and angle
  BCQ = 30⁰.
  (d)(i)the locus of P and Q meet at X, mark X .
  (ii)Construct the locus of R in which angle BRC = 120⁰.
  

  Date posted: September 16, 2019 .    Answers (1)

• The table below shows taxation rates in Kenya. A civil servant is provided with a house and pays a nominal rent of Ksh. 6260 per Month.... (Solved)
  

  The table below shows taxation rates in Kenya.
  
  A civil servant is provided with a house and pays a nominal rent of Ksh. 6260 per Month. In addition the government gives him a medical allowance of Kshs. 7,000 p.m, entertainment allowance of Kshs. 3,000 p.m. He is entitled to a personal relief of Ksh. 1700 p.m. If the civil servants net tax is Kshs. 6,900 p.m.
  Determine his :-
  (a)Gross tax p.m
  (b)Taxable income p.m
  (c)Basic salary p.m
  

  Date posted: September 16, 2019 .    Answers (1)

• During a charity walk to raise funds for displaced Kenyans in the election violence, Otieno, Omollo and David decided to walk from Kisumu to kisii... (Solved)
  

  During a charity walk to raise funds for displaced Kenyans in the election violence, Otieno, Omollo and David decided to walk from Kisumu to kisii a distance of 250km, at an average speed of 4 km/hr. Each day they begin their walk at 6.00 a.m and after walking 4 hrs, take a break of 30 minutes then walk for the next 3 hrs after which they have a lunch break for 1 ½ hrs. Their final leg for the day last 3 hours.
  (a)Find the time:-
  (i)When their first break ends.
  (ii)When their lunch time begins.
  (iii)When their day ends.
  (b)Find the number of days they will take to complete the journey.
  
  

  Date posted: September 16, 2019 .    Answers (1)