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'?