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sergejj [24]
2 years ago
5

Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = 3 cos2(x) − 6 sin(x), 0 ≤ x ≤ 2π (a) Find the inte

rval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local minimum and maximum values of f. local minimum value local maximum value (c) Find the inflection points. (x, y) = (smaller x-value) (x, y) = (larger x-value) Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down. (Enter your answer using interval notation.) Need Help? Read It Watch It

Mathematics
1 answer:
marta [7]2 years ago
7 0

Answer:

f(x) = 3 cos2(x) − 6 sin(x), 0 ≤ x ≤ 2π

We plot the function using a graphing calculator (See attached image below)

a) 1. Find the interval on which f is increasing.

f(x) increases for

x ∈ [π/2 , 7π/6] ∪ [3π/2, 11π/6]

2. Find the interval on which f is decreasing

f(x) decreases for

x ∈ [0 , π/2) ∪ (7π/6, 3π/2) ∪ (11π/6, 2π]

(b) Find the local minimum and maximum values of f

Local minimum.      f = -9

Local maximum.      f = 4.5

(c) 1. Find the inflection points

Please see second image attached

Points,

(x,y) = (2.50673, -2.66882)

(x,y) = (4.14456, 3.79382)

(x,y) = (5.28022, 3.79382)

2. Find the interval on which f is concave up.

x ∈ [0 , 2.50673] ∪ [4.14456, 5.28022]

3. Find the interval on which f is concave down.

x ∈ (2.50673, 4.14456) ∪ (5.28022, 2π]

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malfutka [58]

Answer:

y = -34

Step-by-step explanation:

Step 1

1/4 y + 9 = 1/2

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7 0
3 years ago
Determine a pair of angles (one positive and one negative) in degree measure coterminal to the angle 117°.​
andre [41]

Answer:

Option B.

Step-by-step explanation:

When we have an angle A, in degrees, the coterminal angles are all the angles that can be written as:

B = A + n*360°

Where n is a positive or a negative integer (if n = 0, then B = A, which means that A is coterminal with itself, which is trivial).

Now we want to find two coterminal angles to 117°, such that one is positive and the other negative.

Then we can do:

for the positive one, use n = 1.

B = 117° + 1*360° = 477°

For the negative one, use n = -1

B = 117° - 1*360° = -243°

Then the two angles are 477° and -243°

The correct option is B.

4 0
2 years ago
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A right triangle has legs measuring 4.5 meters and 1.5 meters. The lenghts of the legs of a second triangle are proportional to
Eduardwww [97]
We know that
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then
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so
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</span>case B) 8 m and 5 m ------> ratio=8/5---->1.6
so
the legs of a second triangle are not proportional to the lengths of the legs of the first triangle

case C) 7 m and 3.5 mm ------> ratio=7/3.5---->2
so
the legs of a second triangle are not proportional to the lengths of the legs of the first triangle


case D) 10 m and 2.5 m ------> ratio=10/2.5---->4
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the legs of a second triangle are not proportional to the lengths of the legs of the first triangle

case E) 11.25 m and 3.75 m ------> ratio=11.25/3.75---->3
so
the legs of a second triangle are  proportional to the lengths of the legs of the first triangle

the answer is
A) 6 m and 2 m
E) 11.25 m and 3.75 m




4 0
3 years ago
Victoria deposited $3,000 into an IRA that grew to $6,000 at her retirement. If Victoria is currently in the 15% bracket and is
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