(b) Notice that x=0.5 meter when θ = 45o. By approximately how many radians should you increase θ if you want the x coordinate of the point R to decrease to x = 0.45 meters? Use the tangent line approximation.

Answers

Answer 1

The angle is increased in approximately 0.095 radians (5.443°) for [tex]x = 0.45\,m[/tex].

Based on the statement we construct the geometric diagram, by definition of tangent we have expressions for the initial and final angles ([tex]\theta_{1}[/tex], [tex]\theta_{2}[/tex]), in radians, of the figure:

Initial triangle

[tex]\tan \theta_{1} = \frac{y_{1}}{x_{1}}[/tex] (1)

Final triangle

[tex]\tan \theta_{2} = \frac{y_{2}}{x_{2}}[/tex] (2)

By using (2), the equivalence [tex]\theta_{2} = \theta_{1}+\Delta \theta[/tex] and trigonometric identities we have the following expression:

[tex]\frac{y_{2}}{x_{2}} = \frac{\tan \theta_{1}+\tan \theta_{2}}{1-\tan \theta_{1}\cdot \tan \theta_{2}}[/tex] (3)

By (1), we simplify the expression:

[tex]\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}} + \tan \Delta \theta}{1-\frac{y_{1}}{x_{1}}\cdot \tan \Delta \theta}[/tex] (3b)

If [tex]0 \le \Delta \theta \le \frac{\pi}{6}[/tex], then we can use the following approximation:

[tex]\tan \Delta\theta \approx \Delta \theta[/tex] (4)

Then, we reduce (3b) into an entirely algebraic expression:

[tex]\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}}+\Delta \theta }{1-\frac{y_{1}}{x_{1}}\cdot \Delta \theta }[/tex] (3c)

Where [tex]y_{2} = \sqrt{r^{2}-x_{2}^{2}}[/tex].

Now we clear [tex]\Delta \theta[/tex] within the formula:

[tex]\Delta \theta = \frac{\frac{y_{2}}{x_{2}}-\frac{y_{1}}{x_{1}}}{\frac{y_{1}}{x_{1}}\cdot \left(1+\frac{y_{2}}{x_{2}} \right) }[/tex]  (5)

If we know that [tex]x_{1} = y_{1} = 0.5[/tex], [tex]r = 0.707[/tex] and [tex]x_{2} = 0.45[/tex], then we estimate the angle change:

[tex]y_{2} = \sqrt{0.707^{2}-0.45^{2}}[/tex]

[tex]y_{2} \approx 0.545[/tex]

[tex]\Delta \theta = \frac{\frac{0.545}{0.45}-1 }{1\cdot \left(1+\frac{0.545}{0.45} \right)}[/tex]

[tex]\Delta \theta = 0.095[/tex]

As [tex]\Delta \theta < \frac{\pi}{6}[/tex], then the result seems to be reasonable. The angle is increased in approximately 0.095 radians (5.443°) for [tex]x = 0.45\,m[/tex].

We kindly invite to check this question on trigonometric identities: https://brainly.com/question/24836845

(b) Notice That X=0.5 Meter When = 45o. By Approximately How Many Radians Should You Increase If You

Related Questions

HELP
The perimeter of a rectangular pool is 740 yd. If the length is 30 yd less than four times the width, find the length and width.


The length of the rectangular pool is __ yd.

Answers

The length of the rectangle is 12 yd

Mr. Levy has a budget of $18,000. Uniforms for the marching band cost $315 each, and he needs 62 uniforms. He says, "Since 60x$300=$18,000, I can stay within the budget." Do you agree? Explain.​

Answers

Answer:

No. See explanation  below.

Step-by-step explanation:

No.

Since 60 × $300 = $18,000, he would be exactly at budget if he needed 60 uniforms and if each uniform cost $300, but he needs more than 60 uniforms, and each uniform costs more than $315, so the total cost is definitely more than $18,000.

No, Mr. Levy would not be staying within budget.

Sure, 60 · $300 is $18,00, but he didn't take in the other $15 or the 2 extra uniforms.

If he were to do the math correctly, he should have done 62 · $315, which would be $19,530.

If Mr. Levy were to buy all the uniforms and not worry about it because "60 · $300 is $18,000," he would go over the budget by $1,530.

Have a luvely day!

Identify the kind of sample that is described
The student government association at a certain college chooses three classes, at random, being taught during a given semester
and samples all students in those classes to ask about a new grading policy.

Answers

Answer:

Cluster sampling

Step-by-step explanation:

Choosing groups and sampling whole group.

4 lbs of tomato’s cost $14 complete the double number line so that it shows how much it will cost for up to 8 lbs of tomato’s

Answers

Answer:

the answer is 28$ because since the lbs get doubled so ypu also have to double the cost

Use the ALEKS calculator to write
13
24
as a decimal rounded to the nearest tenth.
Enter your search term

Answers

Answer:

0.13

0.24

Step-by-step explanation:

please mark as brainlist

Answer:

0.13

0.24

Step-by-step explanation:

What type of correlation does the data set display?
х
y
2
13
5 11
7 10
9
8
11
2
A. Negative
O B. No correlation
C. Positive

Answers

Answer:

B-NO CORRELATION.....

A ladybug crawls around the outside of a rectangle that measures 7.5 cm by 8.5 cm. The ladybug stays exactly 3.9 cm from the rectangle at all times to form a larger figure. What is the area of the new rectangle bound by the path of the bug?

Answers

Answer:

185.64 [tex]cm^{2}[/tex]

Step-by-step explanation:

Width =7.5+3.9*2 = 15.3 cm

Length = 8.5+3.9*2=16.3 cm

Big Area = 15.3*16.3 = 249.39 [tex]cm^{2}[/tex]

Small Area = 7.5*8.5 = 63.75 1 [tex]cm^{2}[/tex]

area bounded by the path of the bug = 249.39-63.75 = 185.64 [tex]cm^{2}[/tex]

NO LINKS..... There are 39 people on a city bus. The ratio of adults to children is 10:3. At the next stop, 3 adults get off the bus. What is the new ratio of adults to children on the bus? A. 3:1 B. 9:2 C. 7:3 D. 12:1

Answers

Since the ratio is 10:3 we can find the total number of children and adults by finding how many times 13 (10+3) goes into 39. 39 / 13 = 3 so we can take the original 10:3 ratio and just scale it up to fit the whole group 10:3 * 3 -> 30:9:

From here it gets a little easier we know three adults of the 30 get off at the next stop bringing us to 27. So now our ratio is 27:9 we can simplify that down to 3:1 to get our final answer. Hope that helps!

shola earns #750 every month. if she spends 4/5 of her salary and saves the rest, how much does she save every month?​

Answers

Answer:

250

Step-by-step explanation:

Amount she earns = 750

amount she spend = ⅘ of 750 = ⅘×750= 600

amount she saves = 750-600

Shola saves $150 every month.

What is multiplication?

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is multiplied by 3, or 2 is added 3 times.

Given:

Shola earns $750 every month.

She spends 4/5 of her salary.

That means,

4/5 of $750.

And 4/5 of $750 = 4/5 x 750

                            = 4 x 150

                            = 600

She spends $650 per month.

Saved amount,

= $750 - $600

= $150

Therefore, $150 is her monthly savings.

To learn more about the multiplication;

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Luisa buys a plane ticket that has an original price of $\$240$ . She uses a coupon code to get a $30\%$ discount off of the original price. She is then charged a $7\%$ tax on the discounted price.

What is the final cost for Luisa's plane ticket?

Answers

Answer:

c

Step-by-step explanation:

Answer:

179.76

Step-by-step explanation:

If there are 240 dollars then minus 30%240-30%=168.00Then, plus the 7% 168+7%= 179.76I hope this helps!

The current / in an electric circuit varies inversely with the resistance R. If a current of 60 amperes is produced by a resistance of 9 ohms, what current will be produced by a resistance of 6 ohms?


A resistance of 6 ohms will produce a current of
amperes

Answers

Answer:

Step-by-step explanation:

E = IR

E = 60(9)

E = 540 V

540 = I(6)

I = 540/6

I = 90 Amperes

Danielle's text messaging plan costs $8 for the first 550 messages and 15¢ for each additional text message. If she owes $8.60 for text messaging in the month of October, how many text messages did she send that month?

Answers

Answer:

Danielle sent 554 text messages that month.

Step-by-step explanation:

In Oct she owed: $8 + 60¢

Because 15¢ = 1 additional message => 60¢ = 4 additional messages

So Danielle sent 550 messages (=$8) and 4 additional messages (=  60¢)

=> She sent: 550 messages + 4 additional messages = 554 messages

Hope this helps!

Bài 4: 350 Cho tam giác ABC nhọn, hai đường cao BD, CE cắt nhau tại H. M là trung điểm của BC. K đối xứng với H qua M. a) Chứng minh tứ giác BHCKlà hình bình hành b) Chứng minh BK LAB và CK AC. c) Gọi 0 là trung điểm của AK. Chứng minh OM IBC d) Gọi N là điểm đối xứng với H qua BC. Chứng minh BNKC là hình thang cần​

Answers

no sabo la respuesta jajaja

What is (- 2g-6)-(g-10)

Answers

Answer:

-3g + 4

Step-by-step explanation:

Answer:

Step-by-step explanation

(-2g-6)-\left(g-10\right)

(−2g−6)−(g−10)

thanks ill mark brainliest​

Answers

If I'm watching Gossip Girl, then it is Monday.

Hope this helps you!

Answer:

if i am watching Gossip   Girl then it is monday

Step-by-step explanation:

that is the common sense that everyone should know

hope this helps everyone and have a great summer!

Investing $10,000 in a savings account at 3% annual interest compounded monthly will result in approximately how much money after
10 years?
formula: A = P(1 + r/m)^mt

O $10, 564.68
O $13, 439.16
O $13, 493.54
O $13,000.00

Answers

Answer:

$13,493.54

Step-by-step explanation:

We are gonna use the provided formula: A = P(1 + r/m)^mt

A = Final amount (?)

P = Starting amount (10,000)

r = rate (0.03)

m = times applied (12 since it is compounded monthly)

t = years (10)

A = 10,000(1 + 0.03/12)^12·10

I would suggest using a calculator, but let's try to get a little far with this

A = 10,000(1 + 0.0025)^12·10

A = 10,000(1.0025)^120

A = 13,493.535471908333

First round 0.69 to the nearest tenth.

Answers

Answer:

0.69 rounded to the nearest tenth is 0.7

0.7 is the answer because you round the 69 round to 70.

100 points, Please help!

Answers

Answer:

Look if you say 100 points. Give a hundred points. If you want an answer be honest~ and say fifty points

Step-by-step explanation:

1=17

2=97

Answered:

1 = 17

2 = 97

The labor cost for a certain dish is $40 per hour. If it takes 45 minutes to make the dish, what is the labor cost for this particular dish?

Answers

30 dollars …………………………….

A company makes a profit of $y (in thousand dollars) when it produces x computers,
where y is given by the formula y = a(x - 100)(x - 200) for x 20 If 120
computers are produced, the profit will be $3,200,000.
a) Find the value of a.

b) What is the maximum profit the company can make? At this profit, how many
computers should be produced?

c) If the company targets to make at least $4,800,000, what is the range of the
number of computers to be produced?


Answers

Using quadratic function concepts, it is found that:

a) The value of a is -2000.

b) The maximum profit the company can make is of $5,000,000, when 150 computers should be produced.

c) Between 140 and 160 computers need to be produced.

The profit is modeled by:

[tex]y = a(x - 100)(x - 200)[/tex]

Item a:

If 120  computers are produced, the profit will be $3,200,000, hence when [tex]x = 120, y = 3200000[/tex], and this is used to find a.

[tex]y = a(x - 100)(x - 200)[/tex]

[tex]3200000 = a(120 - 100)(120 - 200)[/tex]

[tex]-1600a = 3200000[/tex]

[tex]a = -\frac{3200000}{1600}[/tex]

[tex]a = -2000[/tex]

The value of a is -2000.

Item b:

We first place the quadratic function into standard form, thus:

[tex]y = -2000(x - 100)(x - 200)[/tex]

[tex]y = -2000(x^2 - 300x + 20000)[/tex]

[tex]y = -2000x^2 + 600000x - 40000000[/tex]

Which has coefficients [tex]a = -2000, b = 600000, c = -40000000[/tex].

Then, we have to find the vertex:

[tex]x_V = -\frac{b}{2a} = -\frac{600000}{2(-2000)} = 150[/tex]

[tex]\Delta = b^2 - 4ac = (600000)^2 - 4(-2000)(-40000000) = 40000000000 [/tex]

[tex]y_V = -\frac{\Delta}{4a} = -\frac{40000000000 }{4(-2000)} = 5000000[/tex]

The maximum profit the company can make is of $5,000,000, when 150 computers should be produced.

Item c:

We are working with a concave down parabola, hence the range is between the roots of:

[tex]y = -200x^2 + 600000x - 40000000[/tex]

[tex]4800000 = -200x^2 + 600000x - 40000000[/tex]

[tex]-200x^2 + 600000x - 44800000 = 0[/tex]

The coefficients are [tex]a = -200, b = 600000, c = -44800000[/tex].

Then:

[tex]\Delta = b^2 - 4ac = (600000)^2 - 4(-2000)(-44800000) = 1600000000[/tex]

[tex]x_1 = \frac{-b - \sqrt{Delta}}{2a} = \frac{-600000 - \sqrt{1600000000}}{2(-2000)} = 160[/tex]

[tex]x_2 = \frac{-b + \sqrt{Delta}}{2a} = \frac{-600000 + \sqrt{1600000000}}{2(-2000)} = 140[/tex]

Between 140 and 160 computers need to be produced.

A similar problem is given at https://brainly.com/question/24705734

Use point-slope form to write the equation of a line that passes through the point (19,-17) with slop -5/3

Answers

Answer:

  y +17 = -5/3(x -19)

Step-by-step explanation:

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

You want a line with slope -5/3 through point (19, -17). Its equation is ...

  y -(-17) = -5/3(x -19) . . . . . substitute the given values

  y +17 = -5/3(x -19) . . . . . simplify

Help me poeaseeeeeeeeeeee

Answers

Answer:

C. Hope It's Help :)))))

Answer:

4.5

Step-by-step explanation:

∛100 = ?

100 = 2 x 2 x 5 x 5

∛100

= ∛ ( 2 x 2 x 5 x 5 )

= 4.642

4.642 ~ 4.5

The approximation 4.642 can also be written as 4.5

Therefore,

∛100 = 4.5

What is the value of x? Midsegments of triangles

Answers

Hi how u doin ?

[tex] \frac{16}{x + 4} = \frac{1}{2} \\ [/tex]

inverse both sides

[tex] \frac{x + 4}{16} = \frac{2}{1} \\ [/tex]

Multiply both sides by 16

[tex]16 \times \frac{x + 4}{16} = 16 \times 2 \\ [/tex]

[tex]x + 4 = 32[/tex]

Subtract both sides 4

[tex]x + 4 - 4 = 32 - 4[/tex]

[tex]x = 28[/tex]

There u go..... Have a great day ❤

this is just and addition to the great posting below, just supplementing.

keeping in mind that the midsegment of a triangle is half the length of the parallel base/side, Check the picture below.

Bradley is 27 years older than Madison seven years go, the sum of their ages was 59?

Answers

Answer:

how old is Madison right then I can't really help u solve it with that little info

What is the z-score of x, when x = 1 and X ~ N (12,3)? Must Show Working

Answers

Answer:

=1−12/3≈−3.67

Step-by-step explanation:

The z-score of x = 1, when x ~ N(12, 3), is approximately -3.6667.

To find the z-score of x when x = 1, we'll use the formula for z-score:

z = (x - μ) / σ

Given:

x = 1

μ (mean) = 12

σ (standard deviation) = 3

Substituting these values into the formula, we get:

z = (1 - 12) / 3

Calculating the numerator:

1 - 12 = -11

Dividing the numerator by the denominator:

-11 / 3 ≈ -3.6667

Therefore, the z-score of x = 1, when x follows a normal distribution with a mean of 12 and a standard deviation of 3, is approximately -3.6667.

To know more about z-score, refer here:

https://brainly.com/question/31871890

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QUIEN MONDA ME AYUDA A SOLUCIONA'
f(x)=(3x-4x)(-8x² + 3x)
POR FAVOR

Answers

Answer:

- x(- 8x^2 + 3x)

8x^3 - 3x^2


5. Hamza chopped up
pineapple and gave į to his
mum. He also ate half himself.
How much was left to give to
his dad?

Answers

Answer:

depends how much he chopped up

Step-by-step explanation:

Answer:

Nothing

Step-by-step explanation:

"5. Hamza chopped up

pineapple and gave ½ to his

mum. He also ate half himself.

How much was left to give to

his dad?"

1 - 1/2 - 1/2 = 2/2 - 1/2 - 1/2 = 1/2 - 1/2 = 0

Answer: There was nothing left for him.

In the 7th grade, 30% of students wear a medium size shirt. If 93 students wear a medium, how many total students are there in the 7th grade?

Answers

Answer:

310

Step-by-step explanation:

Answer:

310

Step-by-step explanation:

is/of = % / 100

[tex]93/x = 30/100[/tex]

93 * 100=9300

9300/30 = 310

An airline with two types of airplanes, P1 and P2, has contracted with a tour group to provide transportation for a minimum of 400 first class, 900 tourist class, and 1500 economy class passengers. For a certain trip, airplane P1 costs $10,000 to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane P2 costs $8500 to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

Answers

The relationship between airplane 1 and airplane 2 is an illustration of objective function

14 of airplane 1 and 7 of airplane 2 should be used to minimize the operation cost

How to determine the number of each type of airplane?

Represent P1 and P2 with x and y, respectively.

From the question, we ave have the following parameters:

                    x             y           Minimum

First class   20          18                400

Tourist        50          30               900

Economy    110          44              1500

Cost        10000      85000

So, the objective cost function to minimize would be:

C = 10000x + 8500y

And the constraints are:

20x + 18y ≥ 400

50x + 30y ≥ 900

110x + 44y ≥ 1500

x, y ≥ 0

Next, we plot the graphs of the constraints

From the graph (see attachment), we have the following feasible solutions

(x,y) = {(4.9,21.8), (8.5,12.7), (14,6.7)}

Substitute these values in the objective function.

C(5,22) = 10000 * 5 + 8500 * 22 = 237000

C(9,13) = 10000 * 9 + 8500 * 13 = 200500

C(14,7) = 10000 * 14 + 8500 * 7 = 199500

The minimum value is:

C(14,7) = 199500

Hence, 14 of airplane 1 and 7 of airplane 2 should be used to minimize the operation cost

Read more about objective function at:

https://brainly.com/question/16826001

Can someone answer this

Answers

Answer:

Step-by-step explanation:

multiply by 6

4-24x+21=-54x+5

54x-24x=5-4-21

30x=-20

x=-20/30=-2/3

X= -2/3 is this the answer you’re looking for?
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