Math Answers

Find the polynomial of degree 4 whose graph goes through the points (−3,−296),(−2,−60),(−2,−60), (0,4), (2,4) and (3,−110).

Two buildings are 25 m apart. From the top of the shorter
building, the angles of elevation and depression of the top and bottom
of the taller building are 31° and 48° respectively. What is the height
of the taller building? Give your answer to the nearest metre.

5. Given that vectors
a→=5i^−2j^+3k^
b→=3i^+j^−2k^
c→=i^−3j^+4k^
, calculate the scalar triple product
a⃗ ⋅(b⃗ ×c⃗ )

6. Given that vectors
a→=5i^−2j^+3k^,
b→=3i^+j^−2k^
and
c→=i^−3j^+4k^
, calculate the vector triple product
a⃗ ×(b⃗ ×c⃗ )

Model the Earth as a sphere, and take the diameter of the Earth as 12740 km.

Calculate the circumference of the Earth.

Calculate the surface area of the Earth, and give your answer in scientific notation.

Find the point of intersection of the following two lines:

x + 4y = 9,

7x − 3y = 1

Find the values of x where the line y = −2x + 20 intersects the parabola y = 2x^2 + 3x − 22.

Integrate with respect to x :
∫41x+1x√dx

1. Integrate with respect to x :
∫2−1x2(x3+4)2dx

2. Integrate with respect to x :
∫2−1x2(x3+4)2dx

3. Integrate with respect to x :
∫3−1x7+x2−−−−−√dx

2 Evaluate the value of
f(x−2)
f(x−2)
, if
f(x)=x2+5x+5

Solve the following equations, giving answers as integers, surds or fractions in their simplest form.

14x − 3 = 2x + 21

1/4 (9 + x) + 10 = −3 + 1/2x

__x___ _ 2 _
x − 4 + x + 3 = 1