Two places P and Q are on the parallel of latitude 26°N. The two points lie on 10°W and 30°E longitudes respectively.

Two places P and Q are on the parallel of latitude 26°N. The two points lie on 10°W and 30°E longitudes respectively.
(a) Find the distance between P and Q along their parallel of latitude in
(i) km (Taking R = 6370km and pi = 3.142)
(ii) nm
(b) Find in km the distance between points P and Q along a great circle.
(c) Two planes X and Y left P for Q at an average speed of 1200 knots and 5000 knots respectively. If X flew along the
great circle and Y along the parallel of latitude, which one arrived earlier and by how much time?

---

---

sharon kalunda answered the question on May 9, 2019 at 10:36

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

---

• The diagram below shows two intersecting circles with centres X and Y. HG is a tangent to the circle centre X at C. (Solved)
  

  The diagram below shows two intersecting circles with centres X and Y. HG is a tangent to the circle centre X at C.
  
  (a) Determine:
  (i) Angle DXE
  (ii) Length DE
  (b) Hence, calculate the area of the shaded region.

  Date posted: May 9, 2019 .    Answers (1)

• Given that OA = 3i + 2j - 4k and OB = 4i + 5j - 2k. P divides AB externally in the ratio 3:... (Solved)
  

  Given that OA = 3i + 2j - 4k and OB = 4i + 5j - 2k. P divides AB externally in the ratio 3: -2. Determine the position
  vector of P in terms of i, j and k.

  Date posted: May 9, 2019 .    Answers (1)

• P and Q are the points on the ends of the diameter of the circle below. (Solved)
  

  P and Q are the points on the ends of the diameter of the circle below.
  
  (a) Write down in terms of x and y the equation of the circle in the form;
  ax² + by² + x + y + c = 0
  (b) Find the equation of the tangent at Q in the form ax + by + c = 0.

  Date posted: May 9, 2019 .    Answers (1)

• (a) Given matrices P and Q below,Find PQ. (Solved)
  

  (a) Given matrices P and Q below,Find PQ.
  
  (b) Hence, find the point of intersection of the lines 4x + y = 9 and 3y =2x -1

  Date posted: May 9, 2019 .    Answers (1)

• A glass is in the shape of a frustum of a cone. (Solved)
  

  A glass is in the shape of a frustum of a cone.
  
  The bottom of the glass is a curve of radius 2cm. A father pours water into the glass to a height of 9cm, while the
  surface of the water is a circle of radius 6cm.
  (a) Calculate the volume of the water in the glass.
  (b) The son who is playing with marbles drops two spherical balls into the water. The water level in the glass rises by
  1.5cm as a result.
  Calculate:
  (i) the volume of one marble.
  (ii) the radius of a marble.

  Date posted: May 9, 2019 .    Answers (1)

• The angle of elevation of the top of a flag post from a point A on the level ground is 12°. The angle of elevation... (Solved)
  

  The angle of elevation of the top of a flag post from a point A on the level ground is 12°. The angle of elevation of the top
  of the flag post from another point B nearer to the flag post and 98m away from A is 34°. B is in between A and the
  bottom of the flag post and the three points are collinear. Find the height of the flag post to the nearest metre.

  Date posted: May 9, 2019 .    Answers (1)

• The interior angles of an irregular polygon are 70° and 110° and the rest are each 144°. Determine the number of sides of the polygon. (Solved)
  

  The interior angles of an irregular polygon are 70° and 110° and the rest are each 144°. Determine the number of sides
  of the polygon.

  Date posted: May 9, 2019 .    Answers (1)

• The sketch below shows curve y = 2x² + 4x + 3 and a straight line intersecting the curve at points A and B. (Solved)
  

  The sketch below shows curve y = 2x² + 4x + 3 and a straight line intersecting the curve at points A and B.
  
  If the x-intercepts is -3.5 and the y-intercept is 7, find :
  a) the equation of the straight line.
  b) the coordinates of A and B
  c) the area of the shaded region

  Date posted: May 9, 2019 .    Answers (1)

• Mrs Mureithi has 20 acres of land. She intends to grow maize and beans. She requires sh.2000 to plant an acre of maize and sh.4000 for... (Solved)
  

  Mrs Mureithi has 20 acres of land. She intends to grow maize and beans. She requires sh.2000 to plant an acre of maize
  and sh.4000 for an acre of beans. Twice the area to be planted with maize should not be less than one of beans. The
  total capital available is sh.60000. The estimated profit is sh.5000 for an acre of maize and sh.7000 for an acre of
  beans.
  By letting x and y to represent the area to be planted with maize and beans respectively.
  a) Find the inequalities to represent the information.
  b) On the grid provided, represent the inequalities and show the region which satisfy the condition.
  c) Determine the expected maximum profit.

  Date posted: May 9, 2019 .    Answers (1)

• A triangle PQR whose vertices are P(2, 2), Q(5, 3) and R(4, 1) is mapped onto triangle P1Q1R1 by a transformation whose matrix is (Solved)
  

  A triangle PQR whose vertices are P(2, 2), Q(5, 3) and R(4, 1) is mapped onto triangle P1Q1R1 by a transformation
  whose matrix is
  
  a) On the grid provided below, draw triangle PQR and triangle P1Q1R1
  b) Triangle P1Q1R1 is mapped onto a triangle whose vertices are P11(-2, -2), Q11(-5, -3) and R11(-4, -1)
  i) Draw triangle P11Q11R11 on the same grid.
  ii) Find the matrix representing transformation that maps triangle P1Q1R1 onto triangle P11Q11R11
  c) Describe the transformation that maps PQR onto triangle P11Q11R11

  Date posted: May 9, 2019 .    Answers (1)

• In the figure below, AB is a diameter of the circle. Chord PQ intersects AB at N. BR which is a tangent to the circle... (Solved)
  

  In the figure below, AB is a diameter of the circle. Chord PQ intersects AB at N. BR which is a tangent to the circle at B
  meets PQ produced at R.
  
  Given that PN = 14cm, NB = 5cm and BR = 6.5cm.
  Calculate :
  a) NR
  b) AN

  Date posted: May 9, 2019 .    Answers (1)

• PQRS is a trapezium where PQ is parallel to SR. PR and SQ intersect at X, so that SX = kSQ and PX = hPR... (Solved)
  

  PQRS is a trapezium where PQ is parallel to SR. PR and SQ intersect at X, so that SX = kSQ and PX = hPR where k and h
  are constants.
  Vectors PQ = 3q and PS = s, SR = q
  a) Show this information on a diagram.
  b) Express vector SQ in terms of s and q
  c) Express SX in terms of k, q and s
  d) Express SX in terms of h, q and s
  e) Obtain h and k
  f) In what ratio does X divide SQ ?

  Date posted: May 9, 2019 .    Answers (1)

• A certain number of people agreed to contribute equally to buy books worth shs.1200 for a school library. Five people pulled out and so that others... (Solved)
  

  A certain number of people agreed to contribute equally to buy books worth shs.1200 for a school library. Five people
  pulled out and so that others agreed to contribute an extra sh.40 each. Their contribution enabled them to raise the
  sh.1200 expected.
  a) If the original number of people was x, write an expression of how much each was originally going to contribute.
  b) Write down the expression of how much each contributed after the five people pulled out.
  c) Calculate how many people made the contribution.
  d) If the prices of books before buying went up in the ratio 5 : 4 how much extra did each contributor give.

  Date posted: May 9, 2019 .    Answers (1)

• Three ships P, Q and R are at sea such that ship Q is 400km on a bearing of 030o from ship P. Ship R... (Solved)
  

  Three ships P, Q and R are at sea such that ship Q is 400km on a bearing of 030o from ship P. Ship R is 750km from
  ship Q and on a bearing of S60oE from ship Q. Ship Q is 1000km and to the north of an enemy ship S.
  a) Taking a scale of 1cm to represent 100km, locate the position of ships P, Q, R and S.
  b) Find the compass bearing of :
  i) ship P from ship S
  ii) ship S from ship R
  c) Use the scale drawing to determine
  i) the distance of S from P
  ii) the distance of R from S
  d) Find the bearing of :
  i) Q from R
  ii) P from R

  Date posted: May 9, 2019 .    Answers (1)

• Write down the three inequalities which define the region R. (Solved)
  

  Write down the three inequalities which define the region R.
  
  

  Date posted: May 9, 2019 .    Answers (1)

• The figure below represents a swimming pool. Calculate the volume of the swimming pool in litres. (Solved)
  

  The figure below represents a swimming pool. Calculate the volume of the swimming pool in litres.
  
  

  Date posted: May 9, 2019 .    Answers (1)

• The first, the 7^th and the 25^th terms of an arithmetic progression are the first three consecutive terms of a geometrical progression. The 20^th term... (Solved)
  

  The first, the 7^th and the 25^th terms of an arithmetic progression are the first three consecutive terms of a geometrical progression. The 20^th term of the arithmetic progression is 22. Find:
  a) i) The first term and common difference of the arithmetic progression.
  ii) The sum of the first 40 terms of the arithmetic progression.
  b) i) The 10th term of the geometric progression.
  ii) The sum of the first 10 terms of the geometric progression.

  Date posted: May 9, 2019 .    Answers (1)

• Find the percentage error in calculating the volume of the cuboid whose dimensions are 8.2cm by 6.2cm by 5.7cm (Solved)
  

  Find the percentage error in calculating the volume of the cuboid whose dimensions are 8.2cm by 6.2cm by 5.7cm

  Date posted: May 9, 2019 .    Answers (1)

• OA = 2i + 3j + 4k while OB = 5i + 9j - 2k. P divides AP externally in the ratio 2 : 1.... (Solved)
  

  OA = 2i + 3j + 4k while OB = 5i + 9j - 2k. P divides AP externally in the ratio 2 : 1. Find he coordinates of P.

  Date posted: May 9, 2019 .    Answers (1)

• Find the value of k if 4x² + 25x + 5 + k is a perfect square. (Solved)
  

  Find the value of k if 4x² + 25x + 5 + k is a perfect square.

  Date posted: May 9, 2019 .    Answers (1)