Bethany used the steps below in an attempt to solve for angle B in triangle ABC.
4.1 cm
2.7 cm
4.5 cm
[Not drawn to scale]
4.12 - 4.52+2.72 -2(4.5)(2.7)cos B
4.1=4.5+2.7-24.3cos B
-3.1--24 3cOSB
0.1276= COS B

Given that,

The area parameters are

A = 2.7 cm, B = 4.1 cm C = 4.5 cm

We want to find the angle extended by B.

Using cosine Rule

b² = a² + c² - 2ac•Cosθ

4.1² = 2.7² + 4.5² - 2 × 2.7 × 4.5• Cosθ

16.81 = 7.29 + 20.25 - 24.3•Cosθ

16.81 - 7.29 - 20.25 = -24.3•Cosθ

-10.73 = -24.3•Cosθ

Cosθ = -10.73 / -24.3

Cosθ = 0.4416

θ = Cos~1 (0.4416)

θ = 63.8°

The angle B is 63.8°

unpaid balance is : $149.99-$50 = $99.99 new balance = 149.99+2.62-50 = $102.61 finance charge = 99.99- 0.21/12= $1.75 new balance = 99.99+1.75 = $101.74 average daily balance method average daily balance= 3399.70/30 = $113.32 finance charge = $ 0.21/12ă—113.32 = $1.98 new balance = $149.99-50+1.98 = $101.97

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.