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3 years ago

A block is set in motion hanging from a spring and oscillates about its resting position

Mathematics

2 answers:

coldgirl [10]3 years ago

8 0

Answer:

t = 1.277 sec and t = 2.848 sec

Step-by-step explanation:

This problem is much more easily done by graphing it than by computing it using algebra.

The values of t we're looking for are the ones that make x = 0, so we want the solutions of $0.6sin(2t)+0.4cos(2t)=0$ on the interval [0, 3].

According to the graph, this is true when t = 1.277 seconds and t = 2.848 seconds.

Paha777 [63]3 years ago

6 0

Answer:

t = 1.28, 2.85

Step-by-step explanation:

x = 0.6sin(2t)+0.4cos(2t)

x = 0, so

0.6sin(2t)+0.4cos(2t) = 0

0.6sin(2t) = -0.4cos(2t)

Convert into tan(2t) by dividing both sides by 0.6cos(2t):

tan(2t) = -0.4/0.6

tan(2t) =-2/3

Since t lies in [0,3] ,

2t lies in [0,6]

tan(2t) =-2/3

Basic angle:

0.5880026035

Tan is negative is second and fourth quadrants

2t = 2.553590005, 5.695182704

t = 1.276795025, 2.847591352

You might be interested in

The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y + 7 = (x – 10). What is the stan

torisob [31]

The point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ is $\fbox{\begin\\\ \math 2x+5y=-15\\\end{minispace}}$ i.e., $\fbox{\begin\\\ \bf option C\\\end{minispace}}$ .

Further explanation:

It is given that line passes through the points $(-5,-1)$ and $(10,-7)$ .

The objective is to determine the point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ .

The options given are as follows:

Option A: 2x-5y=-15

Option B: 2x-5y=-17

Option C: 2x+5y=-15

Option D: 2x+5y=-17

Consider the point $(-5,-1)$ as $(x_{1},y_{1})$ and $(10,-7)$ as $(x_{2},y_{2})$ .

Slope of a curve is defined as the change in the value of $y$ with respect to change in value of $x$ .

The slope of the line is calculated as follows:

$\fbox{\begin\\\ \math m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\end{minispace}}$

To obtain the value of slope substitute the value of $x_{1},y_{1},x_{2},y_{2}$ in the above equation.

$\begin{aligned}m&=\dfrac{-7-(-1)}{10-(-5)}\\&=\dfrac{-6}{15}\\&=\dfrac{-2}{5}\end{aligned}$

Therefore, the slope of the line is $\fbox{\begin\\\ \math m=\dfrac{-2}{5}\\\end{minispace}}$

The general way to express the equation of a line in its point slope form is as follows:

$\fbox{\begin\\\ \math (y-y_{1})=m(x-x_{1})\\\end{minispace}}$

To obtain the point slope form of the equation of the line substitute the value of $m$ , $x_{1}$ and $y_{1}$ in the above equation.

$\begin{aligned}(y-(-1))&=\dfrac{-2}{5}(x-(-5))\\(y+1)&=\dfrac{-2}{5}(x+5)\\5y+5&=-2x-10\\5y+2x&=-15\end{aligned}$

From the above calculation it is concluded that the point slope form the equation of a line is $\fbox{\begin\\\ \math 5y+2x=-15\\\end{minispace}}$

Figure 1 (attached in the end) represents the graph of the function $5y+2x=-15$ .

This implies that the correct option for the point slope form of the line is option C.

Therefore, the point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ is $2x+5y=-15$ i.e., option C.

Learn more:

1. A problem to complete the square of quadratic function brainly.com/question/12992613

2. A problem to determine the slope intercept form of a line brainly.com/question/1473992

3. Inverse function brainly.com/question/1632445.

Answer details

Grade: High school

Subject: Mathematics

Chapter: Linear equation

Keywords: Equation, linear equation, slope, intercept, x-intercept, y-intercept, intersect, graph, curve, slope intercept form, line, y=3x/2-3, standard form, point slope form.

6 0

3 years ago

Read 2 more answers

There were 5 people with a Pi-Day shirt on in class with 27 not wearing such a fun

ANTONII [103]

Answer:

377

Step-by-step explanation:

5 / 32 = 59 / x

x = 377.6

6 0

3 years ago

The minimum point on the graph of the equation y = f(x) is (-1, -3). What is the minimum point

vladimir1956 [14]

Answer:

(4, -3)

Step-by-step explanation:

the equation f(x-5) is a translation of the equation f(x) by 5 units to the right.

So, if all points of the equation f(x) are shifted 5 units to the right, the minimum point of the graph is also shifted 5 units to the right, so to find the minimum point of y = f(x - 5), we just need to sum 5 units to the x-coordinate:

Minimum point = (-1 + 5, -3) = (4, -3)

So the minimum point of y = f(x - 5) is (4, -3).

7 0

3 years ago

I need help on both, I don’t understand. It’s dealing with similar triangles

11111nata11111 [884]

Answer:

11. MN = 4 m

12. LK = 8 m

Step-by-step explanation:

11. Apply pythagorean theorem to find MN:

MN = √(5² - 3²) = √(25 - 9) = √16

MN = 4 m

12. Recall: The ratio of the corresponding side lengths of any two given similar triangles are equal.

MN corresponds to LK

MO corresponds to KO

Therefore:

LK/MN = KO/MO

LK/4 = 10/5

LK/4 = 2

Multiply both sides by 4

LK = 2*4

LK = 8 m

4 0

3 years ago

Can I have some help

VARVARA [1.3K]

Sure what do you need help with

6 0

3 years ago

Read 2 more answers