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1 year ago

(35 POINTS!!) Based on the graph of the trigonometric functions f (θ) = 4sin θ + 1 and g (θ) = cos 2θ, at

Mathematics

1 answer:

Mashcka [7]1 year ago

7 0

The values on the interval [0, 2π) that makes f (θ) equal to g(θ) is; A: 0, π

<h3>How to solve Trigonometric Functions?</h3>

We are given the trigonometric functions;

f(θ) = 4sin θ + 1

g(θ) = cos 2θ

We know from trigonometric identities that;

cos 2θ = 1 - 2sin²θ

At f(θ) = g(θ), we have;

4sin θ + 1 = 1 - 2sin²θ

2sin²θ + 4sin θ = 0

2sinθ(sin θ + 2) = 0

2sinθ = 0

θ = sin⁻¹(0/2)

θ = 0, π

Read more about Trigonometric Functions at; brainly.com/question/6904750

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Two children own two-way radios that have a maximum range of 3 miles. One leaves a certain point at 1:00 P.M., walking due north

Grace [21]

Answer:

The answer is 21 minutes

Step-by-step explanation:

We use the equation Xf = Xo + vt

1) At 1:00 PM, child one leaves the starting point heading north at a constant velocity of 6 mi/hr or .1 [mi/min] (divide by 60 to convert from [mi/hr] to [mi/min])

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3) Now, child 2 starts walking and we know that when the range reaches 3 miles, they won´t be able to communicate. So the sum of the final position of child 1 and child 2 must be 3[mi]

Child 1 final position => $x_{1f} = x_{1f1} +v_{1} t\\x_{1f} =1.5+v_{1} t$
Child 2 final position => $x_{2f} =0+v_{2} t$

4) Sum the equations and equate to 3

$x_{1f} +x_{2f} =3$

5) Substitute the values we already know

$1.5+v_{1} t+v_{2}t=3\\ 1.5+.1t+.15t=3\\1.5+.25t=3\\t=\frac{3-1.5}{.25} \\t=6 [min]$

6) in 15 + 6 minutes they will be 3miles apart

7) In 21 minutes they will still be able to communicate with one another.

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3 years ago

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Mamont248 [21]

Answer:

D.1767.1 in³

Step-by-step explanation:

volume of a sphere=4/3πr³

where r=radius of the sphere

Given diemeter= 15in

so radius=15/2=7.5in

volume=4/3×π×(7.5)³

=4/3×22/7×(7.5)³

=1767.1in³

hope it helps...

have a great day!!

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2 years ago

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Solution

The input value for which the statement f(x) = g(x) is true, is the value of "x" where the graph of the two functions intersect. Accordind with the graph, the two functions f(x) and g(x) intersect at x between 1 and 2, approximately at x=1.5

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