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3 years ago

The expression cos 4xcos 3x +sin 4r sin 3x is equivalent to

Mathematics

1 answer:

iris [78.8K]3 years ago

8 0

Answer:

Step-by-step explanation:

cos 4x cos 3x+ sin 4x sin 3x=cos(4x-3x)=cos x

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The game commission observes the fish population in a stream and notices that the number of trout increases by a factor of 1.5 e

just olya [345]

Answer:

A - $f(t)=80(1.5)^t$

B - Graph given below

C - Number of trouts in 5th week are 607.2

D - Population of trouts will exceed 500 on the 5th week.

Step-by-step explanation:

We are given that,

The number of trout increases by a factor of 1.5 each week and the initial population of the trout is observed to be 80.

Part A: So, the explicit formula representing the situation is,

$f(t)=80(1.5)^t$ , where f(t) represents the population of trouts after 't' weeks.

Part B: The graph of the function can be seen below.

It can be seen that the function is an exponential function.

Part C: It is required to find the number of trouts in the 5th week.

So, we have,

$f(5)=80(1.5)^5$

i.e. $f(5)=80\times 7.59$

i.e. f(5) = 607.2

Thus, the number of trouts in 5th week are 607.2

Part D: We are given that the trout population exceeds 500.

It is required to find the week in which this happens.

So, we have,

$50$

i.e. $(1.5)^t>\frac{500}{80}$

i.e. $(1.5)^t>6.25$

i.e. $t\log 1.5>\log 6.25$

i.e. $t\times 0.1761>0.7959$

i.e. $t>\frac{0.7959}{0.1761}$

i.e. t > 4.5

As, t represents the number of weeks. So, to nearest whole, t = 5.

Thus, the population of trouts will exceed 500 on the 5th week.

7 0

3 years ago

The table below shows a proportional relationship. True or False?

lana66690 [7]

According to the image, the table shows a relationship that is not proportional. First of all, you cannot multiply a number by 0 and get something other than 0. Anything multiplied by 0 is always 0.

Second, the rule is different for each row.

2x5=10

4x4=16

6x3.6=22

A proportional relationship must increase by the same amount, and this does not, which means it is not proportional.

6 0

3 years ago

E: 84:62 <br> help me please

vfiekz [6]

I pretty sure you times it by 3 and then you get 21:18

7 0

4 years ago

Read 2 more answers

To determine whether the pipe welds in a nuclear power plant meet specifications, a random sample of welds is selected, and test

klasskru [66]

Transmutation is the process of changing the substance, tangible or not, from one form to the other. It means the transformation of one element in the periodic table into another by one or a series of nuclear decays or reactions. One type of transmutation is nuclear transmutation. Nuclear transmutation is the conversion of one chemical element or isotope into another though nuclear reactions or nuclear decay. Second type of transmutation is artificial transmutation. Artificial transmutation occur in machinery that uses nough energy to cause changes in the nuclear structure of the elements.

6 0

3 years ago

I NEED HELP ASAP NOW I WILL MARK YOU BRAINLIST PLEASE

fenix001 [56]

Answer:

Mark the Mariana's Trench as 2 nick to the left of -5 and Mount Everest in the middle of positive 5 and 6.

Then, the absolute value equation is: |-6.9|+|5.5|

8 0

4 years ago