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4 years ago

Express cos5mcos(-3m) as a sum or difference.

Mathematics

1 answer:

balandron [24]4 years ago

7 0

Answer:

Step-by-step explanation:

Using the product to sum formula

• 2cosAcosB = cos(A+B) + cos(A - B)

note that cos(- 3m) = cos 3m, hence

cos5m cos(- 3m)

= cos 5m cos3m ← A = 5m and B = 3m

= $\frac{1}{2}$ ( 5m + 3m) + cos(5m - 3m) ]

= $\frac{1}{2}$ cos 8m + $\frac{1}{2}$ cos 2m

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The annual net income of a company for the period 2007–2011 could be approximated by P(t) = 1.6t2 − 11t + 44 billion dollars (2

son4ous [18]

Answer:

$P'(t) = 3.2 t -11$

And we can set equal this derivate to 0 in order to find the critical point and we got:

$3.2 t-11= 0$

$t = \frac{11}{3.2}= 3.4375$

And we can calculate the second derivate and we got:

$P''(t) = 3.2 >0$

So then w can conclude that the value of t = 3.4375 represent the minimum value for the function and we can replace in the original function and we got:

$P(3.4375) = 1.6(3.4375)^2 - (11*3.4375) +44 = 25.094$

So then the minimum annual income occurs at t = 3.43 (between 2008 and 2009) and the value is 25.094

Step-by-step explanation:

For this case we have the following function:

$P(t) = 1.6 t^2 -11t +44$

Where P represent the annual net income for the period 2007-2011 and $2 \leq t \leq 7$

And t represent the time in years since the start of 2005

In order to find the lowet income we need to use the derivate, given by:

$P'(t) = 3.2 t -11$

And we can set equal this derivate to 0 in order to find the critical point and we got:

$3.2 t-11= 0$

$t = \frac{11}{3.2}= 3.4375$

And we can calculate the second derivate and we got:

$P''(t) = 3.2 >0$

So then w can conclude that the value of t = 3.4375 represent the minimum value for the function and we can replace in the original function and we got:

$P(3.4375) = 1.6(3.4375)^2 - (11*3.4375) +44 = 25.094$

So then the minimum annual income occurs at t = 3.43 (between 2008 and 2009) and the value is 25.094

5 0

3 years ago

PLEASE HELP FAST.....WILL MARK AS BRAINLIEST IF GIVEN GOOD ANSWER

Lady bird [3.3K]

Answer:

False, the dilation factor is 2.

Step-by-step explanation:

Notice how each measure of the segments for the red quadrilateral is 2x the amount of the segments for the blue triangle? That right there is the dilation factor.

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4 years ago

Can someone simply explain how to find the area of a triangular prism ? step by step ^^;

Vika [28.1K]

The formula:
A = bh + L (s1 + s2 + s3)

A: area
b: base
h: height
L: length
s1: side 1 (cross-sectional area)
s2: side 2 (cross-sectional area)
s3: side 3 (cross-sectional area)

Here’s an example (see attached image)

A = (4 x 6) + (12 x [7 + 7 + 4])
A = (24) + (12 x 18)
A = 24 + 216
A = 240cm^2

I hope this helped? Comment if you need more explanation or anything!

8 0

3 years ago

Let x be an even integer. What is the product of the next two consecutive even integers?

Ymorist [56]

X represents the even integerx + 2 represents the next even integerx + 4 represents the next even integer The product of the next two even integers(x + 2)(x + 4)x2 + 6x + 8 FOIL

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4 years ago

Sheng ran 2 2/3 miles and walked 1 mile. How much farther did Sheng run than walk

nadezda [96]

Answer: 1 2/3 more

Step-by-step explanation:

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3 years ago