What are the missing values?

Mathematics

1 answer:

nata0808 [166]2 years ago

5 0

The missing values of question #2 are- 26, 27, 28, 29, 30, 31, 32, 33.

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The functions f (theta) and g (theta) are sine functions, where f (0) equals g (0) equals 0.The amplitude of f (theta) is twice

777dan777 [17]

If period of $f(\theta)$ is one-half the period of $g(\theta)$ and
 $g(\theta)$ has a period of 2π, then $T_{g} =2T_{f}=2 \pi$ and $T_{f}= \pi$ .

To find the period of sine function $f(\theta)=asin(b\theta+c)$ we use the rule $T_{f}= \frac{2\pi}{b}$ .

f is sine function where f (0)=0, then c=0; with period $\pi$ , then $f(\theta)=asin 2\theta$ , because $T_{f}= \frac{2 \pi }{2} = \pi$ .

To find a we consider the condition $f( \frac{ \pi }{4} )=4$ , from where $asin2* \frac{\pi}{4} =a*sin \frac{ \pi }{2} =a=4$ .

If the amplitude of $f(\theta)$ is twice the amplitude of $g(\theta)$ , then $g(\theta)$ has a product factor twice smaller than $f(\theta)$ and while period of $g(\theta)$ is 2π and g(0)=0, we can write $g(\theta)=2sin\theta$ .

8 0

2 years ago

Equation of a straight line (see attached)

Viefleur [7K]

Answer:

y = 2x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$