A carpenter bought 850 nails. Each nail
has a mass of 5.2 x 10-3 kg. What is the total
mass, in kilograms, of the nails the carpenter
bought. Express your answer as a decimal.

Answer:

its a rectangle

Step-by-step explanation:

Answer:

Hence, the [tex]y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t))\end{array}[/tex] and approximately value of [tex]y(t)[/tex] is [tex]-0.844[/tex].

Given :

 [tex]my''+cy'+ky=F(t), y(0)=0, y'(0)=0,[/tex]

Where  [tex]m=2[/tex] kilograms

           [tex]c=8[/tex] kilograms per second

           [tex]k=80[/tex] Newtons per meter

          [tex]F(t)=20\sin (6t)[/tex] Newtons

Explanation :

(1)

Solve the initial value problem. [tex]y(t)[/tex]

   [tex]my''+cy'+ky=F(t), y(0)=0, y'(0)=0,[/tex]

[tex]\Rightarrow 2y''+8y'+80y=20\sin (6t)[/tex]

[tex]\Rightarrow y''+4y'+40y=10\sin (6t)[/tex]

Auxilary equations :[tex]F(t)=0[/tex]

[tex]\Rightarrow r^2+4r+40=0[/tex]

[tex]\Rightarrow r=\frac{-4\pm\sqrt{4^2-4\times 1\times 40}}{2\times 1}[/tex]

[tex]\Rightarrow r=\frac{-4\pm\sqrt{16-160}}{2}[/tex]

[tex]\Rightarrow r=\frac{-4\pm\sqrt{-144}}{2}[/tex]

[tex]\Rightarrow r=\frac{-4\pm12i}{2}[/tex]

[tex]\Rightarrow r=-2\pm6i[/tex]

The complementary solution is [tex]y_c=e^{-2t}\left(c_1\cos 6t+c_2\sin 6t\right)[/tex]

The particular Integral, [tex]y_p=\frac{1}{f(D)}F(t)[/tex]

[tex]y_{y} &=\frac{1}{D^{2}+4 D+40} 25 \sin (6 t) \\\\ y_{y} &=\frac{25}{-6^{2}+4 D+40} \sin (6 t) \quad\left(D^{2} \text { is replaced with }-6^{2}=-36\right) \\\\y_{y} &=\frac{25}{4 D+4} \sin (6 t) \\\\y_{y} &=\frac{25}{4(D+1)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4(D+1)(D-1)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4\left(D^{2}-1\right)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4(-36-1)} \sin (6 t) \\\\y_{y} &=-\frac{25}{148}(D-1) \sin (6 t) \\y_{y} &=-\frac{25}{148}\left(\frac{d}{d t} \sin (6 t)-\sin (6[/tex]

Hence the general solution is :[tex]y=y_c+y_p=e^{-2t}(c_1\cos 6t+c_2\sin 6t)-\frac{25}{148}(6\cos 6t-\sin 6t)[/tex]

Now we use given initial condition.

[tex]y(t) &=e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\\y(0) &=e^{-\alpha 0)}\left(c_{1} \cos (0)+c_{2} \sin (0)\right)-\frac{25}{148}(6 \cos (0)-\sin (0)) \\\\0 &=\left(c_{1}\right)-\frac{25}{148}(6) \\\\c_{1} &=\frac{75}{74} \\\\y(t) &=e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\[/tex]

[tex]y^{\prime}(t)=-2 e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)+e^{-2 t}\left(-6 c_{1} \sin 6 t+6 c_{2} \cos 6 t\right)-\frac{25}{148}(-36 \sin (6 t)-6 \cos (6 t)) \\\\y^{\prime}(0)=-2 e^{0}\left(c_{1} \cos 0+c_{2} \sin 0\right)+e^{0}\left(-6 c_{1} \sin 0+6 c_{2} \cos 0\right)-\frac{25}{148}(-36 \sin 0-6 \cos 0) \\\\0=-2\left(c_{1}\right)+\left(6 c_{2}\right)-\frac{25}{148}(-6) \\\\0=-2 c_{1}+6 c_{2}+\frac{75}{74} \\\\0=-2\left(\frac{75}{74}\right)+6 c_{2}+\frac{75}{74} \\\\[/tex][tex]\begin{array}{l}0=-\frac{150}{74}+6 c_{2}+\frac{75}{74} \\\\\frac{150}{74}-\frac{75}{74}=6 c_{2}\end{array}[/tex]

[tex]\begin{array}{l}c_{2}=\frac{25}{148}\\\\\text { Substitute } c_{1} \text { and } c_{2} \text { in } y(t) \text { . Then }\\\\y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t))\end{array}[/tex]

(2)

[tex]y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\y(t)=\left(\frac{75}{74} e^{-2 t} \cos 6 t+\frac{75}{148} e^{-2 t} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\y(t)=\frac{75}{74}\left(e^{-2 t}-1\right) \cos 6 t+\frac{25}{148}\left(3 e^{-2 t}+1\right) \sin 6 t \\\\|y(t)| \leq \frac{75}{74} e^{-2 t}-1|\cos 6 t|+\frac{25}{148}\left|3 e^{-2 t}+1\right||\sin 6 t| \\\\[/tex]

[tex]|y(t)| \leq \frac{75}{74}\left|e^{-2 t}-1\right|+\frac{25}{148}\left|3 e^{-2 t}+1\right| \\\\\lim _{t \rightarrow \infty} y(t) \leq \lim _{t \rightarrow \infty}\left\{\frac{75}{74}\left|e^{-2 t}-1\right|+\frac{25}{148}\left|3 e^{-2 t}+1\right|\right\} \\\\\lim _{t \rightarrow \infty} y(t)=\left\{\frac{75}{74}\left|\lim _{t \rightarrow \infty}\left(e^{-2 t}-1\right)\right|+\frac{25}{148}\left|\lim _{t \rightarrow \infty}\left(3 e^{-2 t}+1\right)\right|\right\} \\[/tex]

[tex]\lim _{t \rightarrow \infty} y(t)=\left\{\frac{75}{74}(-1)+\frac{25}{148}(1)\right\}=-\frac{75}{74}+\frac{25}{148}=-\frac{-150+25}{148}=-\frac{125}{148} \approx-0.844[/tex]

Answer:

oh no

Step-by-step explanation:

sorry about that I guess

Using the sine rule,

[tex] \frac{a}{sin(a)} = \frac{b}{sin(b)} = \frac{c}{sin(c)} [/tex]

Here we are going to use the values of A and C,

[tex] \frac{12}{sin(a)} = \frac{14}{sin(90)} \\ \frac{12}{sin(a)} = \frac{14}{1} \\ sin(a) = 12 \div 14 \\ sin(a) = 0.8571[/tex]

So sin(A) = 12/14 = 6/7 = 0.8571, but since the question says in its simplest radical form, I think the closest answer to it should be

[tex] \frac{ \sqrt{3} }{2} [/tex]

Answer: Hello the scatter plot related to your question is missing attached below is the scatter plot

answer :  The model fails to capture the relationship between the variables accurately, and there may exist nonlinear relationship ( C )

Step-by-step explanation:

The conclusion that can be drawn based upon the scatter chart is that The model fails to capture the relationship between the variables accurately, and there may exist nonlinear relationship

A scatter plot helps in observing the relationship within different numeric variables but the scatter plot attached fails in the showing the actual relationship

Answer:

t = -100

Step-by-step explanation:

Simplify to isolate t:

[tex]\frac{t}{2}+10-10=-40-10[/tex]

[tex]\frac{t}{2} * \frac{2}{1} = -50 * 2[/tex]

[tex]t = -100[/tex]

Answer:

26 customers

Step-by-step explanation:

First:  determine the z score from standard normal probability table with an indicative area of 0.1

Z-score from probability table  = - 1.28

mean   = 3.5 minutes

std  = 3 minutes

next determine the Z-score based on the information given in the question

Z = ( std -  mean )  / processing time

  = ( 3 - 3.5 ) / 2 = -0.25

Finally determine the number of customers

N = [tex](\frac{-1.28}{-0.25} )^2[/tex]  = 1.6384 / 0.0625 = 26.21 ≈ 26 customers  

Answer:

1/12

Step-by-step explanation:

To find experimental probability you have to solve the Number of times an event occurs / Total number of trials. So since the 5 only appears once and there are 12 numbers, it would be 1/12. Did this help?

The experimental probability of rolling 5 will be 0.18.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences. Then the probability is given as,

P = (Favorable event) / (Total event)

The table is given below:

Number      Total

    1                12

   2                16

   3                21

   4                23

   5                18

   6                10

The experimental probability of rolling a 5 is calculated as,

P = 18 / (12 + 16 + 21 + 23 + 18 + 10)

P = 18 / 100

P = 0.18

Thus, the probability is 0.18.

More about the probability link is given below.

https://brainly.com/question/795909

#SPJ2

Answer:

[tex]h(x) = (\frac{f}{g})(x)[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 3x^3 + 9x^2 -12x[/tex]

[tex]g(x) = x - 1[/tex]

[tex]h(x) = 3x^2 + 12x[/tex]

Required

What defines h(x)

Looking at the degree of f(x), g(x) and h(x), we have:

[tex]h(x) = (\frac{f}{g})(x)[/tex]

See proof

[tex]h(x) = (\frac{f}{g})(x)[/tex]

This gives:

[tex]h(x) = \frac{f(x)}{g(x)}[/tex]

[tex]h(x) = \frac{3x^3 + 9x^2 -12x}{x - 1}[/tex]

Factorize

[tex]h(x) = \frac{(3x^2 + 12x)(x - 1)}{x - 1}\\[/tex]

[tex]h(x) = 3x^2 + 12x[/tex]

Slope : -2

y - intercept : 3

Equation : y = -2x+3

Answer:

Step-by-step explanation:

Slope: -0.5

Y-Intercept: 3

y = -0.5x+3

Answer:

P=34ft

Step-by-step explanation:

Solution

P=2(l+w)=2·(12+5)=34ft

Answer:

[tex]\frac{8x^{18} }{y^{2} }[/tex]

Step-by-step explanation:

Answer:

609 m²

Step-by-step explanation:

Area of unshaded:

(6 x 18) + ((13-6) x 7) = 157

Area of overall rectangle:

36 x 28 = 1008

Area of the chunck of rectangle not included:

11 x 22 = 242

Area of shaded:

1008 - 157 - 242 = 609

Answer:

B Center: (-4, 8) Radius = 4

Step-by-step explanation:

Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

3 [tex]\frac{3}{4}[/tex] x [tex]\frac{2}{5}[/tex]

[tex]\frac{15}{4}[/tex] x [tex]\frac{2}{5}[/tex]

[tex]\frac{30}{20}[/tex] = [tex]\frac{3}{2}[/tex]

or another way

[tex]\frac{15}{4}[/tex] x [tex]\frac{2}{5}[/tex]

[tex]\frac{3}{2}[/tex] x [tex]\frac{1}{1}[/tex] = [tex]\frac{3}{2}[/tex]

Answer:

1/20

Step-by-step explanation:

According to G0ogle 5 percent equals 1/20 in lowest terms.

Answer:

5% equals 5/100 which is 1/20 in lowest terms.

Step-by-step explanation:

5% is basically equivalent to 5/100. 5/100 in lowest terms is 1/20 since you divide the numerator and denominator by 5.

I hope this helps, have a nice day.

Answer:

I think it depends how far bill wants to hike..

Step-by-step explanation:

Answer:

C) 56

Step-by-step explanation:

DEG and FEG are on a straight line forming 180 degree.

Set your formula up as

180 = (3x+31)+(2x-6)

180 = 3x +2x +31 - 6

180 - 31 + 6 = 5x

155 = 5x

155/5 = x

31 = x

Now substitute 31 in place of x

FEG = (2*31-6)

FEG = 56

Answer:

the answer is 6.

Step-by-step explanation:

Answer:

6.

Step-by-step explanation:

3+3=6 = 2×3=6

you can do draw 3 circles 2 times and add it all together.

Answer:

A.) The aircraft rose quickly into the air at takeoff, and then continued at a constant altitude.:)

Answer:

Omg, thank u so much I am on this question rn on Edulatic and I have 100 Q's and I'm only on Q 45, This Question rly helped me a lot bc it came with the answer. God Bless you!!

Answer:

54 square ft

Step-by-step explanation:

Find missing sides:

8+6 = 14

9-6 = 3

Find area of full rectangle:

9×8 = 72

Find the area of the missing part of the full rectangle

3×6 = 18

Find the area of the actual shape:

72-18 = 54

Area = 54 square ft

Answer: 7500

Step-by-step explanation:

multiply 150 by 50

Answer:

d. 63%

Step-by-step explanation:

percent, will be white?

A41% b50% c59% d63%

The probability of white = P (w) = 41/65= 0.63

The  probability of yellow = P (y)= 24/65= 0.369=0.37

The probability of choosing white is 0.63 . When rounded to  nearest percent gives

0.63*100/100

=0.63*100 percent

= 63 percent

= 63%

the probability of getting   the next marble white is the same as the probability of getting a white.

Answer: (b)

Step-by-step explanation:

Given

The function is given as

[tex]f(x)=\dfrac{x^2-12x+20}{x-2}[/tex]

Solving the function

[tex]f(x)=\dfrac{x^2-2x-10x+20}{x-2}\\\\f(x)=\dfrac{(x-2)(x-10)}{(x-2)}\\\\f(x)=x-10[/tex]

for [tex]x=2[/tex]

[tex]f(2)=2-10\\f(2)=-8[/tex]

The function is continuous at [tex]x=2[/tex] because [tex]\lim_{x \to 2} f(x)[/tex] exists.

If the limit exists at a point, then the function is continuous.  

Answer:

on edge its fs not b or c

Step-by-step explanation:

Answer:

A. Right 6, Down 5

Step-by-step explanation:

I don't know how to explain this

Answer:

2

Step-by-step explanation:

your dog doesn't love you because it saw what you did. it knows. be cautious around your dog from now on. it knows more than you think and sees all. I'm warning you

Answer:

The probability that they will meet is 0.4375

Step-by-step explanation:

Let A and B be two friends who choose to meet  the same one-hour period.Since there are 60 minutes in an hour therefore n= 60

A can wait for 15 minutes

So the probability of A to meet is given by P(A)=  (15/60)= 1/4

Similarly

B can wait for 15 minutes

So the probability of B to meet is given by P(B)=  (15/60)= 1/4

The  probability  that A cannot meet is given by 1- P(A)=  1-1/4= 3/4

Similarly

The  probability  that B cannot meet is given by 1- P(B)=  1-1/4= 3/4

And

The  probability  that both  A  and B cannot meet is given by = 3/4*3/4= 9/16

So the probability that both will meet = 1- 9/16= 7/16= 0.4375

Answer:

look at the picture i have sent

Answer:

The cities are 35 cm apart in map.

The scale on a map is 5 cm : 8 km.

Step-by-step explanation:

mrk me brainliest please