Can someone help with any of these math questions?

15.

Mass = T tonnes = ? kg (use formula shown)

Density = 2.5g/cm³ = 2.5g/cm³ * (1kg/1000g) * (100cm/m)³ = ?? kg/m³

Density = Mass/Volume

Volume = Mass/Density = (? kg) / (?? kg/m³) = ??? m³

13.

a₁ = a

a₄ = a + 3d = ka

a₇ = a + 6d = 9a

Solve for k

Hint: a₇−a₄ = 3d = a₄−a₁ → 9a−ka = ka−a

23.

Draw a line from O to top of circle, and from O to point where circle and rectangle intersect.

You now have 3 shapes:

• 1/4 circle with radius = 10 cm

• Right triangle with hypotenuse = 10 cm, base = 8 cm → height = 6 cm

　α = angle in right triangle at O → cosα = 8/10 = 4/5

• Sector with central angle θ, where sinθ = 4/5

18.

a)

Drop perpendicular from B to AD at point E

AD = AE + ED = AE + 7.3

To find AE, use right angle ABE:

cos(58) = AE/4.7

b)

There are a number of ways to do this

Since BC||AD, then ∠ACB = ∠CAD

sin(58) = BE/4.7 = CD/4.7 → CD = ?

tan(∠ACB) = tan(∠CAD) = CD/AD → ∠ACB = ?

or

Using law of cosines in △ABC, we get:

AC² = AB² + BC² - 2(AB)(BC) cos(∠ABC)

　Note: you can easily find ∠ABC since you already know 3 of the

　angles of the trapezium.

Using law of sines in △ABC, we get:

sin(∠ACB)/AB = sin(∠ABC)/AC → ∠ACB = ?

21.

a)

Probe by AAA

b)

Since Area(BCDE) = Area(ABE), then Area(ACD) = 2 * Area(ABE)

Since ratio of areas of similar triangles = 2, then ratio of sides = √2

AC/AB = √2

(AB+BC)/AB = √2

(AB+3)/AB = √2

AB = ?