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A curve C is mapped by the equation ( 1+x)(4-x). The curve intersects the x-axis at x = –1 and x = 4. A region R is bounded by C and the x-axis. Use calculus to find the exact area of R.

First draw the curve. Figure out and write the integration problem. Integral 4 -1 (1+x)(4-x) dx.Expand integral 4 -1 4 + 3x - x 2 dx.= 4 -1 [4x + 3x 2 /2) -x 2 ] = 16 + 30 - 64/3 - (-4 + 3/2 + 1/3)= 125/6
VD
Answered by Vishesh D. • Maths tutor
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Describe and explain the change in the shape of the graph y=x^2 and y=x^2 + 2.

The graph is translated by two in the positive y-axis direction. For example, for the equation y=x 2 , taking the x-axis values of 0,1,2 and 3, y= 0 2 ,1 2 , 2 2 and 3 2 respectively: These values being 0,1,...
MS
Answered by Matthew S. • Maths tutor
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Describe the conduction system of the heart and explain how the atria and ventricles contract sequentially.

The heart consists of four chambers, two atria and two ventricle. The conduction system of the heart mediates synchronised contraction of the chambers to allow the heart to effectively pump blood. The conduc...
CS
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Explain the bonding in and the shape of a benzene molecule.

Stage 1 -Bonding 1a) Each C has three (covalent) bonds 1b) Spare electrons (in a p orbital) overlap (to form a pi cloud) 1c) delocalisation Stage 2 -Shape 2a) Planar 2b) Hexagon/6 carbon ring/120o bond angle...
YC
Answered by Yousif C. • Chemistry tutor
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Escribe sobre tus últimas vacaciones. Debes incluir: dónde se alojabas, lo que hacías y lo qué más te gustaba .

En mis últimas vacaciones, fui a españa con mi familia. Anteayer , volvimos del piso en el que nos alojabamos. Todos los días nos relajábamos en la playa. Lo que más disfruté fue la tranquilidad. Si pudiera ...
MB
Answered by Michael B. • Spanish tutor
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