MATHEMATICS COLLEGE

HELP ME PLZ THXxx u

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Answer 1

Answer:

Answer:

1. Line g

2. Line j (not sure)

3. Plane S

4. 3 ( QT, QR, TR )

Step-by-step explanation:

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6/8 reduced to the lowest term

(1 point) For the given position vectors r(t)r(t), compute the (tangent) velocity vector r′(t)r′(t) for the given value of tt . A) Let r(t)=(cos4t,sin4t)Let r(t)=(cos⁡4t,sin⁡4t). Then r′(π4)r′(π4)= ( , )? B) Let r(t)=(t2,t3)Let r(t)=(t2,t3). Then r′(5)r′(5)= ( , )? C) Let r(t)=e4ti+e−5tj+tkLet r(t)=e4ti+e−5tj+tk. Then r′(−5)r′(−5)= i+i+ j+j+ kk ?

Answers

Answer:

(a)

$r'(\frac \pi 4) =(0.-4)$

(b)

r'(5)= (10,75)

(c)

$r'(-5) =4 e^(-20)\hat i-5e^(25)\hat j+\hat k$

Step-by-step explanation:

(a)

Give that,the position vector is

r(t) = (cos 4t, sin 4t)

Differentiating with respect to t

r'(t) = (-4sin 4t, 4 cos 4t) [ $(d)/(dt) cos mt = -m \ sin \ mt$ and $(d)/(dt) sin mt = m \ cos \ mt$ ]

To find the $r'(\frac\pi 4)$ , we put $t=\frac \pi4$

$r'(\frac\pi 4) = (-4sin (4.\frac \pi 4), 4 cos (4.\frac \pi 4))$

=(0, -4)

(b)

Give that,the position vector is

r(t) = (t²,t³)

Differentiating with respect to t

r'(t) = (2t, 3t²)

To find r'(5) , we put t=5

r'(5) = (2.5,3.5²)

= (10,75)

(c)

Given position vector is

$r(t) = e^(4t)\hat i+e^(-5t)\hat j+t\hat k$

Differentiating with respect to t

$r'(t) =4 e^(4t)\hat i+(-5)e^(-5t)\hat j+\hat k$

$\Rightarrow r'(t) =4 e^(4t)\hat i-5e^(-5t)\hat j+\hat k$

To find r'(-5) , we put t= - 5 in the above equation

$r'(-5) =4 e^(4.(-5))\hat i-5e^(-5.(-5))\hat j+\hat k$

$\Rightarrow r'(-5) =4 e^(-20)\hat i-5e^(25)\hat j+\hat k$

For the given position vectors r(t)r(t), compute the (tangent) velocity vector r′(t)r′(t) for the given value of tt are:

$A) r' (\pi /4) = (0, -4) \nB) r'(5) = (10, 75)\nC) r'(-5) = (4e^(-20), -5e^(25), 1)$

To compute the velocity vector, we need to find the derivative of the position vector with respect to time (t). This will give us the tangent velocity vector.

A) Let r(t) = (cos⁡4t, sin⁡4t).

To find r'(t), we take the derivative of each component with respect to t:

r'(t) = (d/dt (cos⁡4t), d/dt (sin⁡4t))

r'(t) = (-4sin⁡4t, 4cos⁡4t)

To find r'(π/4), we substitute t = π/4 into r'(t):

r'(π/4) = (-4sin⁡(4(π/4)), 4cos⁡(4(π/4)))

r'(π/4) = (-4sin⁡π, 4cos⁡π)

r'(π/4) = (0, -4)

B) $Let \ r(t) = (t^2, t^3).$

To find r'(t), we take the derivative of each component with respect to t:

$r'(t) = (d/dt (t^2), d/dt (t^3))\nr'(t) = (2t, 3t^2)$

To find r'(5), we substitute t = 5 into r'(t):

$r'(5) = (2(5), 3(5)^2)\nr'(5) = (10, 75)$

C) Let $r(t) = e^(4t)i + e^(-5t)j + tk.$

To find r'(t), we take the derivative of each component with respect to t:

$r'(t) = (d/dt (e^(4t)), d/dt (e^(-5t)), d/dt (t))]\n\nr'(t) = (4e^(4t)), -5e^(-5t), 1)$

To find r'(-5), we substitute t = -5 into r'(t):

$r'(-5) = (4e^(4{-5}), -5e^(-5(-5)), 1) \n\nr'(-5) = (4e^(-20), -5e^(25), 1)$

So, the answers are:

$A) r' (\pi /4) = (0, -4) \nB) r'(5) = (10, 75)\nC) r'(-5) = (4e^(-20), -5e^(25), 1)$

To know more about vectors:

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The following dot plot shows the number of cavities each of Dr. Vance's 63 patients had last month. Each dot represents a different patient. Which of the following is a typical number of cavities one patient had?

Answers

Answer:

$The$ $answer$ $is$ $2$

Step-by-step explanation:

There are lots of ways we can think about the typical number of cavities.

What was the most common number of cavities?

If we split the cavities evenly among all the patients, how many cavities would each patient have?

What would be the balance point of the data?

What is the middlemost number of cavities?

The most patients had 0cavities.

If we split the cavities evenly, each patient would have 2 or 3 cavities.

If we put our dot plot on a balance scale, it would balance when the pivot was between 2 and 3 cavities.

The scale would tip if, for example, we put the pivot at 5 cavities.

There are 8 patients with 2 cavities each. About half of the rest of the patients have fewer than 2 cavities and about half have more than 2 cavities.

Of the choices, it is reasonable to say that a patient typically had about 2 cavities.

$Thank$ $you$ $for$ $reading$ , $stay$ $safe!!!$ -Written in $2/4/2021$

Final answer:

The 'typical' number of cavities one patient had can be determined by finding the mode (most common number) in the data set, which should be represented in the dot plot. To do this, one would count the number of dots at each value on the dot plot. The value with the most dots would be the 'typical' number of cavities.

Explanation:

The question is asking for a 'typical' number of cavities one patient had out of Dr. Vance's 63 patients. In statistics, a typical, or 'common', value can be shown by calculating the mode, which is the number that appears most frequently in a data set.

Unfortunately, the dot plot is missing from the information provided. However, to find the mode (or typical value) using a dot plot, you would typically count how many dots are at each value on the plot. The value with the most dots (indicating the most patients with that number of cavities) is the mode. This would be the 'typical' number of cavities a patient of Dr. Vance had last month.

Let's create a hypothetical scenario. If your dot plot looked like this:

0 cavities: 10 patients
1 cavity: 15 patients
2 cavities: 24 patients
3 cavities: 8 patients
4 cavities: 6 patients

The mode would be 2 cavities because 24 patients had this amount, more than any other amount. Therefore, the 'typical' number of cavities one patient had would be 2.

Learn more about Dot Plot & Mode here:

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Tina makes 480 sandwiches

Answers

Why is Tina making so many sandwiches?

I´ll go find if there is the rest of the question

I believe if this is the correct question then this would be the rest

Tina makes 480 sandwiches she only makes tuna sandwiches, beef sandwiches, hand sandwiches and cheese sandwiches. 3/8 of the sandwiches are tuna. 35% of the sandwiches are beef. the ratio of the number of ham sandwiches to the number of cheese sandwiched is 5 : 6. work out the number of ham sandwiches that Tina makes

3 / 8 ×480 + 35 /100× 480 + 5x + 6x = 480

180 + 24 × 7 + 11x = 480

180 + 168 + 11x = 480

348 + 11x = 480

11x = 480 - 348

= 132

x = 132 / 11

= 12

no of ham sandwiches = 5x

= 5 ×12

= 60

therefore , the # of ham sandwiches = 60

HOPe tHIS HELPS

17
Σ (15 – 9n)
η = 4

Answers

Answer:

-1113

Step-by-step explanation:

You apparently want the sum of the 14-term arithmetic sequence ...

-21, -30, -39, ..., -138

The average term is ...

(-21 -138)/2 = -79.5

so the sum of the 14 terms is ...

(14)(-79.5) = -1113

17

Σ (15 – 9n) = -1113

η = 4

nth term

aₙ = 15 - 9n

a₄ = 15-9*4 = 15-36= -21

a₁₇ = 15 - 9(17) = -138

Sum;

S = (a₁ + aₙ)*n/2

n = 14

a₁ = a₄= -21

aₙ = a₁₇ = -138

S = (-21 - 138)*14/2

S = -1113

The distance d of a particle moving in a straight line is given by d(t) = 2t3 + 5t – 2, where t is given in seconds and d is measured in meters. Find an expression for the instantaneous velocity v(t) of the particle at any given point in time.

Answers

Answer:

6t^2 + 5

Step-by-step explanation:

i took the test and somehow got it correct:)

Answer:

Step-by-step explanation:

hello,

$v(t)=(d(t))/(t)=2t^2+5-(2)/(t)$

hope this helps

Please answer correctly!

Graphing the equation y-3=1/3(x+4)

Thank you.

Answers

Answer:

X intercept (-13,0)

y intercept (0,13/3)

Step-by-step explanation:

slope intercept form

y=1/3x+13/3

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