Questions asked by siera ♠️
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Please solve 16^(1x)=(1)/(8)?
Thank You

R = r#sqrt((A+B)/(AB))#. Make A the subject of the formula?

Solve #x^2x2=0# graphically, by first sketching #y=x^2#?

Solve #4^(3x)=8^(x2)#?
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. #(x1)^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+2x15# for #x>=1#?

Solve #x^3+x^27x+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(alphabeta)/(sinalphasinbeta) + sin(beta  gamma)/(sinbetasingamma) + sin(gammaalpha)/(singammasinalpha) = 0#?

How do you prove #tan(A+B+C) = (tanA+tanB+tanCtanAtanBtanC)/(1tanAtanBtanBtanCtanCtanA)#?

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)# #((1cos^2 theta)/theta ^2)#?

How do you evaluate #lim_(x>0)# #(cosaxcosbx)/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^2xcosxsinxsin^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'?