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3 years ago

1. find the exact value of cos2θ if sin 2θ=3/4 and θ is between 0° and 90°

Mathematics

1 answer:

musickatia [10]3 years ago

5 0

Answer:

<u>Identities used:</u>

sin²θ + cos²θ = 1
cos2θ = cos²θ - sin²θ

sin2θ = 3/4, and θ in the first quadrant
cos²2θ = 1 - sin²2θ
cos2θ = √(1 - sin²2θ) = √(1 - 9/16) = √(7/16) = √7 / 4

sinθ(cos²θ - cos2θ) =
sinθ(cos²θ - (cos²θ - sin²θ) =
sinθ(sin²θ) =
sin³θ

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charle [14.2K]

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Step-by-step explanation:

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2 years ago

Write a linear equation to represent this

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3 years ago

Explain the error a student is asked to find when the value of an investment of $5200 is an account that earns 4.2% annual inter

zloy xaker [14]

We are given the following information

Investment = $5200

Annual interest rate = 4.2% = 0.042

Final amount = $16,500

Number of years = 27.7 years

Number of compoudings = quartely = 4

The student uses the following model

$V(t)=5200(1.014)^{3t}$

The general formula for compound interest is given by

$V(t)=P(1+\frac{r}{n})^{nt}$

As you can see, the number of compoundings is incorrect (3 vs 4)

The interest rate is also incorrect.

Let us substitute the given values into the above formula

$\begin{gathered} V(t)=P(1+\frac{r}{n})^{nt} \\ V(t)=5200(1+\frac{0.042}{4})^{4\cdot27.7} \\ V(t)=5200(1+0.0105)^{110.8} \\ V(t)=5200(1.0105)^{110.8} \\ V(t)=\$16543.5^{} \end{gathered}$

Therefore, the final amount is approximately $16,543.5

5 0

1 year ago

The equation of a circle is ( x - 3) 2 + ( y + 2) 2 = 25. The point (8, -2) is on the circle.

Shtirlitz [24]

Answer:

x =8 is the equation of the tangent.

Step-by-step explanation:

Here the equation of the given circle is: $(x-3)^{2} + (y+2)^{2} = 25$

Now, comparing it with the general equation of circle: $(x-h)^{2} + (y -k)^{2} = r^2$

we get the central coordinates (h,k) = (3,-2)

So, the slope of the line joining center and (8, -2) = $\frac{-2 -(-2)}{8-3} = \frac{0}{5} = 0$

Since the slope of line = 0, line is parallel to x axis.

Now, as tangent and the line is perpendicular to each other

⇒Slope of the tangent = -1/ slope of the line = $\frac{-1}{0}$

Now, by point slope formula: the equation of the tangent is

(y-y0) = m (x-x0)

or, $(y +2) = \frac{-1}{0} (x -8)$

or x =8 is the equation of the tangent.

8 0

3 years ago

How many days will it take for a sum of $4,000 to earn $80 interest if it is deposited in a bank paying ordinary simple interest

Maksim231197 [3]

Answer:

It will take 146 days to earn an interest of $80.

Step-by-step explanation:

The simple interest formula is:

$I=\frac{P\times r\times t}{100}$

It is provided that:

I = $80

P = $4,000

r = 5% p.a.

Compute the time required as follows:

$I=\frac{P\times r\times t}{100}$

$t=\frac{I\times 100}{P\times r}$

$=\frac{80\times 100}{4000\times 5}\\\\=0.4\ \years\\\\=0.4\times 365\ days\\\\=146\ days$

Thus, it will take 146 days to earn an interest of $80.

4 0

2 years ago