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11Alexandr11 [23.1K]
3 years ago
15

Solve 2cos^2x+5cosx+2=0

Mathematics
1 answer:
Nuetrik [128]3 years ago
6 0
2cos^2x+5cosx+2=0\\
x\in\\
\Delta=b^2-4ac\\
\Delta=9\\
\sqrt{\Delta}=3\\
cosx=1\\
or\\
cosx=-6\\
-6\notin\\

Then using trygonometric table or a graph we read that:
cosx=1\Leftrightarrow(x)=0

Period of cosinus function = 2π
So the last answer is x=0+2k\pi\\
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Exercise 3.5. For each of the following functions determine the inverse image of T = {x ∈ R : 0 ≤ [x^2 − 25}.
masya89 [10]

a. The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

b. The inverse image of g(x) is g^{-1}(x) = e^{x}

c. The inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

<h3 /><h3>The domain of T</h3>

Since T = {x ∈ R : 0 ≤ [x^2 − 25} ⇒ x² - 25 ≥ 0

⇒ x² ≥ 25

⇒ x ≥ ±5

⇒ -5 ≤ x ≤ 5.

<h3>Inverse image of f(x)</h3>

The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

f : R → R defined by f(x) = 3x³

Let f(x) = y.

So, y = 3x³

Dividing through by 3, we have

y/3 = x³

Taking cube root of both sides, we have

x = ∛(y/3)

Replacing y with x we have

y = ∛(x/3)

Replacing y with f⁻¹(x), we have

So,  the inverse image of f(x) is f⁻¹(x) = ∛(x/3)

<h3>Inverse image of g(x)</h3>

The inverse image of g(x) is g^{-1}(x) = e^{x}

g : R+ → R defined by g(x) = ln(x).

Let g(x) = y

y =  ln(x)

Taking exponents of both sides, we have

e^{y} = e^{lnx} \\e^{y} = x

Replacing x with y, we have

y = e^{x}

Replacing y with g⁻¹(x), we have

So, the inverse image of g(x) is g^{-1}(x) = e^{x}

<h3>Inverse image of h(x)</h3>

The inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

h : R → R defined by h(x) = x − 9

Let y = h(x)

y = x - 9

Adding 9 to both sides, we have

y + 9 = x

Replacing x with y, we have

x + 9 = y

Replacing y with h⁻¹(x), we have

So, the inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

Learn more about inverse image of a function here:

brainly.com/question/9028678

5 0
2 years ago
What is the area of triangle ABC?
erica [24]

Answer:

what is the area of triangle ABC choices

35 square unit

4 0
2 years ago
The ages of several trees on school property are shown below: 3 years, 8 years, 10 years, 14 years, 11 years What is the mean ag
almond37 [142]
3+8+10+14+11= 46 
46/(how many trees) 5= 9.2
9.2 years is your answer. 
5 0
3 years ago
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Joey bought 10 cupcakes and has four friends. He wants to have nothing left, but he wants everyone including him to have the sam
Roman55 [17]

we use divsion, 10 divided by 5 is 2, everyone get 2 yumy cupcakes.

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3 years ago
Melanie invested $5,500 in an account paying an interest rate of 6.9% compounded continuously. Assuming no deposits or withdrawa
Phantasy [73]

Answer:

A=\$11,748.76

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

A=P(e)^{rt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

t=11\ years\\ P=\$5,500\\ r=6.9\%=6.9/100=0.069  

substitute in the formula above

A=5,500(e)^{0.069*11}  

A=5,500(e)^{0.759}  

A=\$11,748.76

7 0
3 years ago
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