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In a geometric series, the first and fourth terms are 2048 and 256 respectively. Calculate r, the common ratio of the terms. The sum of the first n terms is 4092. Calculate the value of n.

A geometric series S always follows the same pattern: S = a + ar + ar^2 + ar^3 ... Here i've labelled the first term a, and the common ratio r. The next term in a geometric series is always the preceding ter...
SW
Answered by Sam W. • Maths tutor
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The quadratic equation (k+1)x^2+12x+(k-4)=0 has real roots. (a) Show that k^2-3k-40<=0. (b) Hence find the possible values of k.

(a) There is a quadratic equation which should e solved using the delta andthe roots formulas. delta=a 2 -4ab delta=144-4(k+1)(k-4) delta=-4k 2 +12k+160 Because the problem tells us that the roots are real, ...
AB
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Háblame de las lenguas de España y cómo contribuyen a la identidad española

En España existen algunas lenguas diferentes, no solo el castellano. El catalán, de Cataluña y las islas baleares, es bien conocido por la gente fuera de España, también el euskera, idioma de los vascos. Ade...
CM
Answered by Charlie M. • Spanish tutor
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A rocket travels with constant velocity in a straight line in deep space. A ball is thrown from the back to the front (ie from the thrusters to the nose). Describe the path of the ball. Describe the path if the rocket were accelerating along this line.

Consider first what happens when the rocket travels with constant velocity. Constant velocity implies that there are balanced forces (or indeed no forces) acting on the rocket. This is Newtons 1st Law. We kn...
SW
Answered by Sam W. • Physics tutor
5800 Views

Express 3cos(theta) + 5sin(theta) in the form Rcos(theta - alpha) where R and alpha are constants, R>0 and 0<alpha<90. Give the exact value of R and the value of alpha to 2dp.

Write out identity: Rcos(theta - alpha) = Rcos(theta)cos(alpha) + Rsin(theta)sin(alpha) from formula booklet Write out in form of question so it's easier to compare: 3cos(theta) + 5sin(theta) = R[cos(alpha)c...
OS
Answered by Olivia S. • Maths tutor
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