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Ghella [55]
3 years ago
13

Find a possible solution to the equation sin(3x+13)=cos(4x)

Mathematics
1 answer:
olga2289 [7]3 years ago
6 0
Recall that sine and cosine are co-functions. That means they satisfy the equation

\sin x = \cos(90-x)

For example, sin 30° = cos 60°. Now, using this property, we have

\sin(3x + 13) = \cos[90 - (3x + 13)]

As can be seen from the equation provided, it shows that sin(3x + 13) = cos(4x). This means that the left-hand side of the equations are equivalent. Thus, we have

90 - (3x + 13) = 4x
90 - 3x - 13 = 4x
77 = 7x
x = 11

We now have the value of x. We can also check if we got the right answer by substituting the value into the original equation.

Answer: 11
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Dennis can walk 2.833 miles each hour . About how far can he walk in 3 hours and 15 minutes
Bezzdna [24]

well, let's split the hours in minutes, so since 1 hr is 60 minutes, so he can walk 2.833 miles in 60 minutes, well, 3 hrs is 3*60 = 180 minutes, then we add 15 minutes, that's 195 minutes.

if he can walk 2.833 miles in 60 minutes, how long will it be for 195 minutes?

\bf \begin{array}{ccll} miles&minutes\\ \cline{1-2} 2.833&60\\ x&195 \end{array}\implies \cfrac{2.833}{x}=\cfrac{60}{195}\implies \cfrac{2.833}{x}=\cfrac{4}{13} \\\\\\ 36.829=4x\implies \cfrac{36.829}{4}=x\implies 9.20725 = x

4 0
3 years ago
What is the volume of the composite figure below? (formula for volume of a prism is 1/3 Bh where B is the area of the base.)
arsen [322]

Answer:

Last Option; 84 cu. mm

Step-by-step explanation:

We know that;

Volume = 1/3(Bh)

And that this is figure has a square base, therefore B that represents the area of the base will be: 6 * 6 = 36

And height = 7mm

Therefore we can say;

Volume = (1/3)*(6 x 6)*(7)

Volume = (1/3)*(36)*(7)

Volume = (12)*(7)

<u>Volume = 84</u>

Hope this helps!

6 0
3 years ago
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