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3 years ago

Select all the correct answers.

Mathematics

2 answers:

Arada [10]3 years ago

7 0

Answer:

5.43 × 1014

Step-by-step explanation

Cloud [144]3 years ago

3 0

Answer:

45.25

Step-by-step explanation:

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If cos 0=sin b then which of the following must be true?

miv72 [106K]

Rgtef erggreedg wrrevgerv erevt

7 0

4 years ago

Fit a trigonometric function of the form f(t)=c0+c1sin(t)+c2cos(t)f(t)=c0+c1sin⁡(t)+c2cos⁡(t) to the data points (0,5.5)(0,5.5),

larisa86 [58]

Answer

$f(t)=-0.2+4.1sin(t)+4cos(t)$

Step-By-Step Explanation

Given the function $f(t)=c_0+c_1sin(t)+c_2cos(t)$ .

For each pair (t, f(t)) in the data points (0,5.5), (π/2,0.5), (π,−2.5), (3π/2,−7.5)

$f(0)=c_0+0c_1+c_2=5.5$ .

$f(\pi /2)=c_0+c_1+0c_2=0.5$ .

$f(\pi)=c_0+0sin(t)-c_2=-2.5$ .

$f(3\pi /2)=c_0-c_1+0c_2=-7.5$ .

Expressing this as a system of linear equations in matrix form AX=B

$\left(\begin{array}{ccc} 1 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & -1 \\ 0 & -1 & 0 \end{array} \right)\left( \begin{array}{c} c_{0} \\ c_{1} \\ c_{2}\\ \end{array} \right)=\left(\begin{array}{c} 5.5 \\ 0.5 \\ -2.5 \\ -7.5 \end{array} \right)$

Where

$A=\left(\begin{array}{ccc} 1 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & -1 \\ 0 & -1 & 0 \end{array} \right)$ ,

$B=\left(\begin{array}{c}5.5\\0.5\\-2.5\\-7.5\end{array} \right)$

$X=\left(\begin{array}{c}c_0\\c_1\\c_2\end{array}\right)$

To determine the values of X, we use the expression

$X=(A^{T}A)^{-1}A^{T}B$

$A^{T}A= \left(\begin{array}{ccc} 3 & 1 & 0 \\ 1 & 2 & 0 \\ 0 & 0 & 2 \end{array} \right)$

$(A^{T}A)^{-1}= \left(\begin{array}{ccc} 0.4 & -0.2 & 0 \\ -0.2 & 0.6 & 0 \\ 0 & 0 & 0.5 \end{array} \right)$

$A^{T}B=\left(\begin{array}{c} 3.5 \\ 8 \\ 8 \end{array} \right)$

Therefore:

$X=\left(\begin{array}{ccc} 0.4 & -0.2 & 0 \\ -0.2 & 0.6 & 0 \\ 0 & 0 & 0.5 \end{array} \right)\left( \begin{array}{c} 3.5 \\ 8 \\ 8 \end{array} \right)$

$X=\left(\begin{array}{c}c_0\\c_1\\c_2\end{array}\right)=\left(\begin{array}{c} -0.2 \\4.1\\4\end{array}\right)$

Therefore, the trigonometric function which fits to the given data is:

$f(t)=-0.2+4.1sin(t)+4cos(t)$

8 0

3 years ago

Can someone help me with this

ivann1987 [24]

Answer:

56x

Step-by-step explanation:

Think of it an a triangle and a rectangle. The area of the rectangle is obviously 13 x 4x, which is 52x

for triangle, the hypotenuse is C, Right hand side is B and the side that is in the shape is B.

Area of triangle = (bh) / 2

B = 13 - 9, so B = 4

A = 6x - 4x, so A = 2x

the area is 2x x 4, which is 8x.

8x / 2 = 4x

The area is 4x + 52x, so the final answer is 56x

8 0

2 years ago

What is 10 +10×2÷8+5

Anna [14]

Answer:

just use a calculator next time 17.5

Step-by-step explanation:

its 17.5 my dude

7 0

4 years ago

Read 2 more answers

1.08t can be written as (1.081/12)12t to give the approximate equivalent monthly interest rate based on an annual rate of 8%. Us

kobusy [5.1K]

Because t is given in years and 1.08 = 1 + 0.08, the annual percent increase
is 8%.
To find the monthly percent increase that gives an 8% annual increase,
use the fact that
t = $\frac{1}{12} * 12 t$ 
and the properties of exponents to rewrite the
model in a form that reveals the monthly growth rate.

$1.08^{t} 
= 1.08^{(1/12)(12t)} 
= (1.08^{1/12}) ^{12t} 
= 1.0064634^{12t}$

6 0

3 years ago

Read 2 more answers