Questions asked by siera ♠️

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• Please solve 16^(1-x)=(1)/(8)? Thank You
  
• R = r#sqrt((A+B)/(A-B))#. Make A the subject of the formula?
  
• Solve #x^2-x-2=0# graphically, by first sketching #y=x^2#?
  
• Solve #4^(3x)=8^(x-2)#? Thank You.
  
• Erin goes off on a long bike ride, averaging 10 km/h. One hour later her brother Alistair starts chasing after her at 16 km/h. How long will it take Alistair to catch up to Erin?
  
• Two ancient armies are 1 km apart and begin walking toward, each other. The Vikons walk at a pace of 3 km/h and the Mohicas walk at a pace of 4 km/h. For how long will they walk before the battle begins?
  
• A river is flowing downstream at a rate of 2 metres per second. Brendan, who has an average swimming speed of 3 metres per second, decides to go for a swim in the river. He dives into the river and swims downstream to a certain point, then swims back...?
  
• A square hut with side lengths of 5 m is to be surrounded by a veranda of width x metres. Find the width of the veranda if its area is to be 24 m^2?
  
• Find the exact perimeter of this triangle?
  
• The ratio between the areas of two similar prisms is 4:9. If the mass of the smaller prism is 48 kilograms, what is the mass of the larger prism?
  
• A certain square pyramid has a volume of #100 cm^3#. A similar but smaller pyramid has a surface area equal to one fifth of the larger. What is the volume of the smaller pyramid?
  
• If the volume of a sphere is increased by 25%, what is the percentage increase in the surface area, correct to the nearest whole?
  
• I deposited $600 in an account which pays 1% interest per month. Two months later, I deposited another $600 in the same account. How much would be in the account after a further two months?
  
• Solve #(3^x - 1)(2^(2x) - 1/16) = 0# for x?
  
• Sketch the graph #{(x,y)|(y<=2^x)nn(y>=0)nn(x>=-2)}# ?
  
• If *log4 = 0.602*, evaluate *log2.5*?
  
• If #log(a)3 = 0.477#, evaluate #log(a)sqrt(3)#?
  
• Given that #log(a)2 = x#, find #log(a)2a# in terms of #x#?
  
• If #x = log2# and #y = log3#, express #log75# in terms of #x# and #y#?
  
• If #y = ae^(4t)#, express #t# in terms of #a# and #y#?
  
• Solve #(logx^2)^2 - logx^3 - 10 = 0# for #x#?
  
• #A(x)# is a polynomial of degree 4 and #B(x)# is a polynomial of degree 3. What is the degree of #A(4)# x #B(4)#?
  
• Find the coordinates of the intersection of the graphs of these equations? 1. #(x-1)^2+y^2=4# and #y=2x#
  
• For the circle #x^2+y^2=4# and the line #y=mx+4#, determine the exact values of the gradient, #m#, so that the line: #a)# is a tangent to the circle? #b)# intersects the circle in 2 places? #c)# does not intersect the circle?
  
• A tennis ball is lobbed from ground level and must cover a horizontal distance of 22m if it is to land just inside the opposite end of the court.? -->
  
• How do you find the inverse function of: #y=x^2+2x-15# for #x>=-1#?
  
• Solve #x^3+x^2-7x+2=0# by first factorising the LHS?
  
• How do you prove that AMON is cyclic?
  
• How do you prove that DCPQ is cyclic?
  
• Find the length of #x#?
  
• #AC# is a tangent to the circle at #B# and #AE# is a tangent to the circle at #F#. Using the information on the diagram, how do you find the values of #x# and #y#?
  
• What is the area of the annulus shown in the diagram, given that the length of #AB# is #14cm#?
  
• Two similar glasses have diameters of 6 cm and 8 cm respectively. The smaller glass holds 108 milliliters. How do you find the capacity of the larger glass?
  
• A rhombus has sides #8 cm# in length and its shortest diagonal is #10 cm# in length. What is the area of the rhombus to the nearest #cm^2#?
  
• In the diagram, two circles intersect at #B# and #E#. #ABC# is a line parallel to the #FED#. How do you prove that #ACDF# is a parallelogram?
  
• A rally car drives #85km# along a road from #A# and #B#, on a bearing #029degreesT#. The car then travels #58km# along a road to #C# on a bearing #153degreesT#?
  
• How do you find the area of the shaded region in the diagram below?
  
• A belt is fitted tightly around two wheels of radii #20 cm# & #5 cm# which are #5 cm# apart. How do you show that the length of the belt is #30(pi + sqrt3) cm#?
  
• The real numbers #a, b# and #c# satisfy the equation: #3a^2 + 4b^2 + 18c^2 - 4ab - 12ac = 0#. By forming perfect squares, how do you prove that #a=2b=c#?
  
• Solve for x if |x+2|=|2x+1| ?
  
• How do you solve #x^3 -|x|=0#?
  
• What values of #c# in the equation #|2x+1|=x+c# give exactly two solutions?
  
• How do you solve #2sinpix = 1# graphically and algebraically?
  
• A hemispherical bowl is 18cm in diameter and contains water to a depth of 7cm when level. How far can the bowl roll before the water pours out?
  
• How do you prove that #(cos3theta)/sintheta +(sin3theta)/costheta = 2cot2theta#?
  
• How do you prove #tan(pi/4 + theta) - tan(pi/4 - theta) = 2tan2theta#?
  
• How do you prove: #sin(alpha-beta)/(sinalphasinbeta) + sin(beta - gamma)/(sinbetasingamma) + sin(gamma-alpha)/(singammasinalpha) = 0#?
  
• How do you prove #tan(A+B+C) = (tanA+tanB+tanC-tanAtanBtanC)/(1-tanAtanB-tanBtanC-tanCtanA)#?
  
• Each rectangle is 6cm long and 3cm wide, they share a common diagonal of PQ. How do you show that #tanalpha = 3/4#?
  
• The quadrilateral ABCD is a parallelogram with diagonal AC perpendicular to CD. The two diagonals intersect at E. How do you show that #DE^2 + 3EA^2 = AD^2#?
  
• A rhombus with 20 cm sides has a 12 cm diagonal. How long is the other diagonal?
  
• How do you prove that EF || AB ?
  
• How do you find m in terms of n, supposing that angle CEF is the interior angle of another regular polygon with m sides?
  
• How do you evaluate #lim_(theta->0)# #((sin2thetatan3theta)/theta^2)#?
  
• How do you find #lim_(theta->0)# #((1-cos^2 theta)/theta ^2)#?
  
• How do you evaluate #lim_(x->0)# #(cosax-cosbx)/x^2#?
  
• How do you prove that #cos^2theta - cos^2 3theta = sin4thetasin2theta#?
  
• How do you express #2costheta + 2cos(theta + pi/3)# in the form #Rcos(theta + alpha)#, where #R>0# and #0< alpha <pi/2#?
  
• How do you solve the equation #3sin2theta - 2cos2theta = 2# for #0 <= theta <= 2pi#, using the substitution #t=tantheta#?
  
• How do you find the general solution to the equation #6cos^2x-cosxsinx-sin^2x=0#?
  
• How do you calculate the mass of ethanol that must be burnt to increase the temperature of #210 g# of water by #65^@#, if exactly half of the heat released by this combustion is lost to the surroundings?
  
• If the heat of combustion of ethanol is #1367kJmol^-1#, how would you calculate the theoretical mass of ethanol required to heat #200mL# of water from #21.0^@# to #45.0^@#?
  
• 2.08 grams of anhydrous barium chloride was dissolved in water to make 50.00mL of solution and then added to 50.00mL of an aqueous solution containing 2.84 g of anhydrous sodium sulfate. A white precipitate of barium sulfate formed. How do you...?
  
• How do you write the nuclear equation of the 'annihilation of beta particles to form radiation'?