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d1i1m1o1n [39]
3 years ago
12

What is the maximum value of Sinx+cosx

Mathematics
1 answer:
Harrizon [31]3 years ago
6 0

The answer is 2 since both

\sin(x),\cos(x)\in[0,1]

The maximum value of \sin(x) is 1 and the same for cosine. The sum becomes 1 + 1 which evaluates to 2.

Hope this helps.

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The net worthw(t) of a company is growing at a rate of′(t) = 2000−121t2dollarsper year, wheretis in years since 1990.(a) If the
stiv31 [10]

Answer:

The worth of the company in 2000 is $56,000.

Step-by-step explanation:

The growth rate of the company is:

f'(t)=2000-12t^{2}

To determine the worth of the company in 2000, first compute the change in the net worth during the period 1990 (<em>t</em> = 0) to 2000 (<em>t</em> = 10) as follows:

\int\limits^{10}_{0} {2000-12t^{2}} \, dt =\int\limits^{10}_{0} {2000} \, dt-12\int\limits^{10}_{0} {t^{2}} \, dt=2000 |t|^{10}_{0}-12|\frac{t^{3}}{3}|^{10}_{0}\\=(2000\times10)-(4\times10^{3})\\=20000-4000\\=16000

The increase in the company's net worth from 1990 to 2000 is $16,000.

If the company's worth was $40,000 in 1990 then the worth of the company in 2000 is:

Worth in 2000 = Worth in 1990 + Net increase in company's worth

                        =40000+16000\\=56000

Thus, the worth of the company in 2000 is $56,000.

4 0
3 years ago
An expression is shown: martha evaluates the expression using these steps: step 1: step 2: step 3:
earnstyle [38]

Answer:Answer: D Step 3 ; f²k³

Explanation:

(k⁻¹)⁻³ = k³

Step-by-step explanation:

8 0
4 years ago
A rectangular prism has a length of 13 feet, a height of 2 feet, and a width of 4 feet. what is its volume, to the nearest, in c
ioda

Answer:104ft^3

Step-by-step explanation:

volume=length x width x height

Volume=13 x 4 x 2

Volume=104ft^3

5 0
3 years ago
-2(x-2)=-16 answer.
REY [17]

Answer:

-2x+4=-16

-2x = -16-4

-2x = -20

x = -20/-2

x = 10

3 0
3 years ago
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What is the equation of the line that contains the two points (0,-1) and (-1,-3)?
Nady [450]
The answer is in this picture

4 0
3 years ago
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