Using the fact that i=−1‾‾‾√:

Write the equation of the trigonometric graph.

prisoha [69]

Answer:

$f(x)= \sin(6x)+3$

Step-by-step explanation:

The parent function of this graph is: y = sin(x)

The sine function is periodic, meaning it repeats forever.

Standard form of a sine function:

$f(x) = \sf A \sin (B(x + C)) + D$

A = amplitude (height from the mid-line to the peak)
2π/B = period (horizontal distance between consecutive peaks)
C = phase shift (horizontal shift - positive is to the left)
D = vertical shift

The parent function y = sin(x) has the following:

Amplitude (A) = 1
Period = 2π
Phase shift (C) = 0
Vertical shift (D) = 0
Mid-line: y = 0

From inspection of the given graph:

Amplitude (A) = 1
$\sf Period=\dfrac{\pi}{12}-\dfrac{-\pi}{4}=\dfrac{\pi}{3}$
Phase shift (C) = 0
Vertical shift (D) = +3 (as mid-line is y = 3)

$\sf If\:Period=\dfrac{\pi}{3} \implies \dfrac{2 \pi}{B}=\dfrac{\pi}{3}\implies B=6$

Substituting the values into the standard form:

$\implies f(x) =1 \sin (6(x + 0)) + 3$

$\implies f(x) = \sin (6x) + 3$

Therefore, the equation of the given trigonometric graph is:

$f(x)= \sin(6x)+3$

6 0

2 years ago

Question text Natalie bought six ice cream cones at $1.69 each. She had to pay a tax of 3%. What was the total cost of her treat

alexira [117]

Answer: $13

Step-by-step explanation:

6 icecream cones at 1.69 per one= 6×$1.69

=$10.14

30% tax= 30/100=0.3

30% of icecream cost

0.3 × $10.14

=$3.042

Total cost of her treat= cost of icecream + tax rate

= $10.14 + $3.042

=$13.18

Rounded to the nearest cent= $13

7 0

3 years ago

A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 34.5 ft3. what dimensions

____ [38]

Answer:

$l \approx 3.3\,ft$ , $x = 3.2\,ft$

Step-by-step explanation:

The equations of volume and surface area are presented below:

$34.5 = l^{2}\cdot x$

$A_{s} = 2\cdot l^{2} + 4\cdot l \cdot x$

The length of the tank is:

$x = \frac{34.5}{l^{2}}$

The expression fo the surface area is therefore simplified into an univariable form:

$A_{s} = 2\cdot l^{2} + 4\cdot \left(\frac{34.5}{l} \right)$

$A_{s} = 2\cdot l^{2} + \frac{138}{l}$

The first and second derivatives of the expression are, respectively:

$A_{s}' = 4\cdot l -\frac{138}{l^{2}}$

$A_{s}'' = 4 +\frac{276}{l^{3}}$

The first derivative is equalized to zero and length of the square side is now found:

$4\cdot l -\frac{138}{l^{2}} = 0$

$4\cdot l^{3}-138 = 0$

$l^{3} = \frac{138}{4}$

$l = \sqrt[3]{\frac{138}{4} }$

$l \approx 3.3\,ft$

Now, the second derivative offers a criteria to determine if solution leads to an absolute minimum:

$A_{s}'' = 4 + \frac{276}{(3.3\,ft)^{3}}$

$A_{s}'' = 11.7$ (Absolute minimum)

The depth of the tank is:

$x = \frac{34.5\,ft^{3}}{(3.3\,ft)^{2}}$

$x = 3.2\,ft$

6 0

3 years ago

Please help me please help me if you don't know gently move your hand

Firdavs [7]

Answer:

Assuming that d=diameter, then

C=43.96cm

Step-by-step explanation:

Diameter=14cm

14x3.14=43.96cm

5 0

3 years ago

Given: ΔKLM, KL = LM = 13in, KM = 10in. Find: The area of ΔKLM.

KengaRu [80]

Answer:

$60 in^{2}$

Step-by-step explanation:

We are given a ΔKLM, in which KL=LM=13 in and KM=10 in which means two sides of the given triangle are same and thus is an isosceles triangle.

Its median drawn from L to the KM will be altitude. Therefore, ΔKLN and ΔLMN are right triangles.

In ΔKLN, using the pythagoras property, we have

$13^{2}=5^{2}+LN^{2}$

$169-25=LN^{2}$

$\sqrt{144} =LN$

$12=LN$

Now, Area of triangle= 1/2×base×height

=1/2×10×12

=60 squared inches.

4 0

3 years ago