Round 5.955 to the nearest tenth.
2 answers:
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Answer:
θ = 0.896 and 2.246.
Step-by-step explanation:
We will use the identity
sin²θ + cos²θ = 1
and the double angle formula
cos2θ = cos²θ - sin²θ = (1 - sin²θ) - sin²θ = 1 - 2sin²θ
1. Convert the equation to a more solvable form.
2. Solve the quadratic
a = 2; b = 1; c = -2
(a) Set up the equation.
(b) Evaluate the roots
3. Solve for θ
(a) The negative root
u = sinθ = -1.281
sinθ cannot be less than -1. No solution.
(b) The positive root
If sin(x) = a, then
x = arcsin(x) + 2πn and
x = π - arcsin(a) + 2πn
(i) Case 1
u = sinθ = 0.7808
θ = arcsin(0.7808) + 2πn
θ = 0.8959 ± 2πn
If n = 0,
θ = 0.8959
(ii) Case 2
θ = π - 0.8959 + 2πn
If n = 0,
θ = π - 0.8959 = 2.246
The solutions are θ = 0.8959 and θ = 2.246
The diagram below shows the graph of f(θ) with its roots at 0.896 and 2.246.
The right answer is option B. 138.7
Step-by-step explanation:
Given function is:
To find h(-7), we have to put -7 in place of x
The value of function at -7 is 138.7.
Hence,
The right answer is option B. 138.7
Keywords; Functions, Operations
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Answer:
y = 9x - 11
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 3, - 38) and (x₂, y₂ ) = (8, 61)
m = =
= 9, thus
y = 9x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (8, 61), then
61 = 72 + c ⇒ c = 61 - 72 = - 11
y = 9x - 11 ← equation of trend line