Find the sum. 376 249 238 + 492​

Answer:

a) t = 4

b) v = pi j + 5 k

c) rt = 1i + (pi t) j + (20 +5t )k

Step-by-step explanation:

You have the following vector equation for the position of a particle:

\(r(t)=cos(\pi t)\hat{i}+sin(\pi t)\hat{j}+5t\hat{k}\)    (1)

(a) The height of the helix is given by the value of the third component of the position vector r, that is, the z-component.

For a height of 20 you have:

\(5t=20\\\\t=\frac{20}{5}=4\)

(b) The velocity of the particle is the derivative, in time, of the vector position:

\(v(t)=\frac{dr(t)}{dt}=-\pi sin(\pi t)\hat{i}+\pi cos(\pi t)\hat{j}+5\hat{k}\)    (2)

and for t=4 (height = 20):

\(v(t=4)=-\pi sin(\pi (4))\hat{i}+\pi cos(\pi (4))\hat{j}+5\hat{k}\\\\v(t=4)=-0\hat{i}+\pi\hat{j}+5\hat{k}\)

(c) The vector parametric equation of the tangent line is given by:

\(r_t(t)=r_o+vt\)      (3)

ro: position of the particle for t=4

\(r_o=cos(\pi (4))\hat{i}+sin(\pi (4))\hat{j}+20\hat{k}\\\\r_o=\hat{i}+0\hat{j}+20\hat{k}\)

Then you replace ro and v in the equation (3):

\(r_t=(1\hat{i}+20\hat{k})+(\pi \hat{j}+5\hat{k})t\\\\r_t=1\hat{i}+\pi t \hat{j}+(20+5t)\hat{k}\)

Part(a): The value of \(t=4\)

Part(b): Required vector \(L(t)=(1\widehat{i}+0\widehat{j}+10\widehat{k})+(t-4)(0\widehat{i}+\pi \widehat{j}+5\widehat{k})\)

Given vector equation is,

\(r(t)=cos(\pi t)\widehat{i}+sin(\pi t)\widehat{j}+5t\widehat{j}\)

Vector equation:

A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector, and with an arrow indicating the direction.

Part(a):

When the particle has a height of 20

\(5t=20\\t=4\)

Part(b):

The point on the curve is \((cos(4\pi),sin(4\pi),20) =(1,0,20)\)

Differentiating the given equation with respect to \(t\).

\(r'(t)=- \pi sin(\pi t)\widehat{i}+\pi cos(\pi t)\widehat{j}+5\widehat{k}\\r'(t)=- \pi sin(4\pi t)\widehat{i}+\pi cos(4\pi t)\widehat{j}+5\widehat{k}\\r'(4)=0\widehat{i}+\pi \widehat{j}+5\widehat{k}\\L(t)=r(4)+(t-4)r'(4)\\L(t)=(1\widehat{i}+0\widehat{j}+10\widehat{k})+(t-4)(0\widehat{i}+\pi \widehat{j}+5\widehat{k})\)

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Explanation

Step 1

the volume of the cereal box is given by:

Step 2

find the volume of each box

large box:

Answer:

c and I will talk to you later today or tomorrow morning and then I will

Step-by-step explanation:

email to you later today to see you and the kids are doing well and that you

Answer:

a) r(t) = (10, 5, -5) + (5, 5, 0)*t

b) (0, -5, -5)

Step-by-step explanation:

a) 2x + 4 -2y -5 = -3z -6

2x - 2y +3z +5 =0

(10, 5, -5)

(15, 10, -5)

(5, 5, 0)

r = (10, 5, -5) + (5, 5, 0)*t

b) The yz plane is given by the equation x = 0.

x = 0  in the vector equation of a straight line if and only if  t = -2, than r ( - 2) = (0, -5, -5) is the desired intersection point.

8

In this pattern, we have 4 12 then 20.

We can see that the difference 4 and 12 is 8.

Since the difference between 12 and 20 is also 8, the common difference of the sequence is 8.

Answer:

(3/2,-3/2)

Step-by-step explanation:

The midpoint of (2,-1)(1,-2) is (3/2,-3/2)

Answer:

(1.5,-1.5)

You have to remember the formula to find mid-point and that is:

\(midpoint = ( \frac{x1 + x2}{2} ,\frac{y1 + y2}{2} )\)

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

The simplified expression when a polynomial is divided by a monomial is \(y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).\)

A polynomial expression can be represented as a product of other, smaller polynomial expressions through the algebraic process of factoring. The process of factoring can be used to simplify expressions and solve problems. A polynomial equation's roots can be found by factoring, as can the common factors in an expression that can be eliminated. Factoring occasionally enables us to spot trends and connections between several expressions.

Depending on the kind of polynomial and the degree of the terms involved, there are several ways to factor. S

For the given expression \((12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)\) factor the common term.

\((12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)\\-4y^5u^2(3y^2 - 8u^4 - 3y^2u^4) / (-4y^2u^5)\)

Cancelling the -4:

\(= y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2)\)

Hence, the simplified expression is \(y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).\)

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Answer:

You can call me at the entertainment industry and I said I would like to troll sistah I am bear with me and I said I would like to troll sistah I am bear with me and I said I would like to troll sistah I am bear with me

Step-by-step explanation:

The solutions are 2 and 5

Because it's asking what would make the triangles congruent, you would set up the equation like this because the angles (angle 3 and angle 4) need to be equal:

x^2 = 7x - 10

Next, you add 10 to both sides. This is so that you can move it to the other side, addition is the inverse of subtraction.

x^2 + 10 = 7x

Now subtract 7x from both sides. Subtraction is the inverse of addition. You do this to get it on the other side so you can factor it. You can move the 10 and 7x to the other side in any order or at the same time, I just did it like this.

x^2 - 7x + 10 = 0

Now, factor. I don't really know how to explain factoring, you just get a feel for it with a lot of practice.

(x - 2)(x - 5) = 0

You can use FOIL to check this if you want to. x(x) is x^2, -2(-5) is 10), -2x - -5x is -7x. Now, find what you need to do to make what's in each of the groups of parentheses equal to 0.

x - 2 = 0

x = 2

One of the solutions is 2, because you add 2 to x to get 0.

x - 5 = 0

x = 5

The other solution is 5, because you add 5 to x to get 0. Lastly, check your solutions by plugging them in to the original equation.

2^2 = 7(2) - 10

4 = 14 - 10

So 2 is definitely a solution.

5^2 = 7(5) - 10

25 = 35 - 10

5 is also a solution.

Hope that helps :]

Answer:

A

how I got the answer:

I did math

Answer:

16 the the tenth power

Step-by-step explanation:

four to the second power is ... 400

4×4≈16

(4+4=8)

(8+8=16)

(400-300=100)

(100-96=4)

4292

Step-by-step explanation:

there happy that was easy to be honest

Answer:

me too (help)

Step-by-step explanation:

Answer:

it seems as it is adding .15 every time so the next 3 would be .05 .20 and .65

Answer:

\( \huge{ \bold{ \boxed{ \text{4a + 6}}}}\)

Step-by-step explanation:

\( \text{ (3a + 7) + (a - 1)}\)

In addition , sign of each term in the expression remains unchanged. So, Remove the unnecessary brackets.

\( \text{⇢ \: 3a + 7 + a - 1}\)

Combine like terms. Like terms are those which have the same base. Only coefficients of like terms can be added or subtracted.

\( \text{⇢ \: 3a + a + 7 - 1}\)

\( \text{⇢ \boxed{ \text{4a + 6}}}\)

And we're done! :D

Hope I helped!

Best regards! :D

~TheAnimeGirl

Answer:

~0.143

Step-by-step explanation:

So, in total there are 15 marbles, and only 6 of them are red. So the first draw will have a  chance of being red. Since you didn't mention placing it back, the next draw will have a  chance of being red. It's  , because you just took a red one out of the bag (leaving 5 left) and the total was lessened by one. To get the answer, you'd multiply both numbers together.

6/15 x 5/14 = 1/7 or (roughly) 0.143

Answer:

4\(\frac{7}{8}\)

Step-by-step explanation:

Answer:

Fraction : 4 7/8

Decimal : 4.875

Step-by-step explanation:

I know you said to put it in mixed fraction form but if you wanted the decimal form then it there.

The real answer ( without mixed fraction form ) is 39/8

The given expression is

First, we subtract 8 from each side

Then, we divide the equation by 2.

Answer:

x=-1

Step-by-step explanation:

2x+8=6

    -8. -8

     2x=-2

     /2. /2

     X=-1

Answer:

75°

Step-by-step explanation:

Answer:

x = 90

Step-by-step explanation:

\(m\angle 1+m\angle 2=90\)

\(\Longleftrightarrow x+\frac{x}{5} =90\)

\(\Longleftrightarrow \frac{6x}{5} =90\)

\(\Longleftrightarrow x=\frac{5\times 90}{6} =\frac{450}{6} = 75\)

2916 ft³

Volume helps describe the amount of space that a shape takes up.

Volume of a Sphere

Volume describes the 3-dimensional size of a shape. Since volume is a 3-D measurement, the units should be cubed; this explains why the answer is given in feet cubed. In order to find the volume, we need to use the radius. The radius of a sphere is the distance from the center to the outside. In this case, we are told that the radius is 9 ft.

Volume Formula

Every regular shape has its own volume formula. For a sphere, the formula is:

So, to find the volume, all we need to do is plug in the radius. For this sphere, r = 9.

When using 3 for pi, the volume of the sphere is 2916 ft³.

The mean, mean deviation mode, median standard deviation, and coefficients of variation, CV, are as follows;

1. The mean deviation about the mean, median mode are;

2.653, 3.709, and 3.709, respectively

The coefficients of variation are;

0.364, 0.337, 0.337, respectively

The variance is about 9.462

The standard deviation is about 3.076

2. Section A has a higher relative dispersion than section B

3. City 2

4. a. Mean ≈ 43.85

b. Mode 40 - 54 inches

c. Median ≈ 45.16

The variance ≈ 125.8056

Standard deviation ≈ 11.216

Coefficient of variation ≈ 0.268

The coefficient of variation of a data quantifies or is a measure of the variability of the values in the set of data.

The mean for the data can be calculated as follows;

Mean  = (3×10 + 6×15 + 11×25 + 2×6 + 4×4 + 10×3 + 5×2 + 7×8 + 8×9 + 9×4)/(10+15+25+6+4+3+2+8+9+4) ≈ 7.29

The median is the 86/2 value = 43rd value

10 + 15 + 25 = 50

Therefore, the median is in the class with a frequency of 25, which is 11

The mode of the data, which is the value with the highest frequency in the data set is 11

The mean deviation from the mean is therefore;

(|3 - 7.29|×10 + |6 - 7.29|×15 + |11 - 7.29| ×25 + |2 - 7.29| ×6 + |4 - 7.29| ×4 + |10 - 7.29| ×3 + |5 - 7.29| ×2 + |7 - 7.29|×8 + |8 - 7.29| ×9 + |9 - 7.29| ×4)/(10+15+25+6+4+3+2+8+9+4) ≈ 2.653

The coefficient for the mean deviation about the mean is therefore; 2.653/7.29 ≈ 0.364

The mean deviation about the median is therefore;

(|3 - 11|×10 + |6 - 11|×15 + |11 - 11| ×25 + |2 - 11| ×6 + |4 - 11| ×4 + |10 - 11| ×3 + |5 - 11| ×2 + |7 - 11|×8 + |8 - 11| ×9 + |9 - 11| ×4)/(10+15+25+6+4+3+2+8+9+4)

The mean deviation about the median = 319/86 ≈ 3.709

The coefficient ≈ 3.709/11 ≈ 0.337

The median = The mean deviation about the mode ≈ 3.709

The coefficient is about 0.337

The variance = (10×(3 - 7.29)² + 15×(6 - 7.29)² + 25×(11 - 7.29)² + 6×(2 - 7.29)² + 4×(4 - 7.29)² + 3×(10 - 7.29)² + 2×(5 - 7.29)² + 8×(7 - 7.29)² + 9×(8 - 7.29)² + 4×(9 - 7.29)²)/(10+15+25+6+4+3+2+8+9+4) ≈ 9.462

The standard deviation, s ≈ √(9.462) ≈ 3.076

2. The coefficient of variation, CV, can be used to compare the variability of the datasets comprising of different scales as follows;

CV = Standard deviation/( The mean of the data)

Therefore; CV for section A = 23/79 ≈ 0.2911

CV for section B = 11/64 ≈ 0.172

The higher CV value for section A indicates that the scores of section A have a higher relative dispersion than the scores for the section B

3. The consistency values can be obtained by finding the standard deviation for the values in the data for each city, using a web based tool as follows;

City 1; Mean = 23

Variance = 50/4

Standard deviation, City 1 = (√(50))/2 = 5·√2/2

City 2; Mean = 21.8

Sample variance = 2.2

Standard deviation, City 2 = √(2.2) ≈ 1.483

City 3; Mean = 29.2

Sample variance = 18.7

Standard deviation, City 3 = √(18.7) ≈ 4.324

The standard deviation of city 2, which is the smallest compared tom the other cities, indicates that the City 2, has the most consistent temperature

4. The mean of the data obtained from the data using the midpoint of the data, is; Mean = ∑fx/∑f

Therefore; The mean obtained using an online tool is; 43.85

The mode is the data that occurs most frequently, which is the data with the value; 40 - 54 inches

The median is the value at the middle of the data set, which is the value with a frequency of 53, and in the interval 40 - 54 inches

The median is; 39.5 + (54.5 - 39.5) × (50 - 30)/53 ≈ 45.16

The standard deviation found for the grouped data, using an online tool is as follows;

Variance, σ² ≈125.8056

The standard deviation, σ ≈ √(125.8056) ≈ 11.216

The coefficient of variation is; 11.216/41.83 ≈ 0.268

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Answer:

B. 4.0 liters

Step-by-step explanation:

1 can = 0.4 l

10 cans = 0.4l x 10

0.4l x 10 = 4l

10 cans = 4l

To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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The two equations which can be used to represent the situation are;

r + s = 1787

4r + 3s = 5,792

The correct answer choice is option B and E

Reserved seat for basketball game = r

Students seat for basketball game = s

Cost of reserved seat tickets = $4

Cost of students tickets = $3

Total number of people who attended the basketball game= 1,787 people

Total amount earned for tickets sales= $5,792

r + s = 1787

4r + 3s = 5,792

Therefore, the basketball game situation can be represented by the equation r + s = 1787; 4r + 3s = 5,792

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Simplified answer and explanation:

Q2:  Simplify the equation x = log(2x) / log(7) rounded to the nearest ten thousandths.

Step 1: We can take the log of both sides: log(x) = log(log(2x) / log(7))

Step 2: According to the power rule of logs, we can bring down the 2x and multiply it by log(7) on the left-hand side of the equation: log(x) = (log(2x) / log(7)) * log(7) - log(2x)

Step 3: Divide both sides by log(7): log(x) / log(7) = log(2x) / log(7) - log(2x) / log(7)

Step 4: Divide both sides to both isolate and solve for x. Then round to the nearest ten thousandths: x = 0.6385

Answer: x = 0.6385

Q3:  Simplify the equation for continuous compound interest:  A(t) = P * e^(rt) rounded to the nearest hundredth for the interest rate as a percentage.

Step 1: Plug in everything we're already given to solve for r: P = 420, t = 6, and A(t) = 1300

Step 2: Divide both sides by 420: 1300 / 420 = e^(6r)

Step 3: Take the natural log (ln) of both sides: ln(1300 / 420) = 6r

Step 4: Bring down the 6r and multiply it by ln(e) on the right-hand side: ln(1300 / 420) = 6r * ln(e)

Step 5: Divide both sides by 6 to solve for r: r = ln(1300 / 420) / 6

Step 6: Convert the interest rate as a decimal to a percentage and round to the nearest hundredth: 18.83%

Answer: 18.83%

Q4: Convert to exponential form: 0.7^4 = 0.2401.

Answer: 0.7^4 = 0.2401

Q5: Simplify log(1250) to the nearest thousandth and ten thousandth.

Answer: log(1250) = 3.097 rounded to the nearest thousandth and 3.0969 rounded to the nearest ten thousandth.

Q6: Determine which statements are correct when two functions are inverses of each other.

Answer: Statements #1 and #2 are correct.

Q7: Solve for y using the change of base formula: y = log(0.125) / log(8).

Answer: y = -1

Q11: Find the x-intercept of the equation 0 = log(5x + 2) -1.

Step 1: Add 1 to both sides: 1 = log(5x + 2)

Step 2: Convert to exponential form and solve for x: 10^1 = 5x + 2, x = (10 - 2) / 5 = 1.6

Answer: x-intercept is 1.6.

Q12: False.

We set log argument equal to 0 and solve for find vertical asymptote.  Solving 5x + 2 = 0, gives us vertical asymptote = x = -2/5

Q13:

Multiple numbers allowed:

One number allowed per function:

If you can only put 1 answer for each function, you can do

Answer:

2 1/6

Step-by-step explanation:

6.5x=2x+1.6=1/3

1/3*6.5=2 1/6