40 points! Help (Vectors)

Answer:

  7.1 cm

Step-by-step explanation:

You want the height of a cylinder of radius 8.2 cm and volume 1500 cm³.

  V = πr²h . . . . . formula for the volume of a cylinder

  h = V/(πr²) . . . formula solved to give h

  h = (1500 cm³)/(π·(8.2 cm)²) ≈ 7.1 cm

The depth of the water is about 7.1 cm.

Answer:

Step-by-step explanation:

I will ASSUME that your equation is

s(t) = 3t⁴ - 40t³ + 126t² - 9

1) velocity is the derivative of position

v(t) = s'(t) = 12t³ - 120t² + 252t

2) changing what? position? velocity? acceleration? gender? color?

position No   the plot is continuous

velocity Yes  both magnitude and direction. Zeros at t = 0, 3, and 7 s

acceleration Yes, both magnitude and direction. Zeros at approx. t = 1.306 and 5.361 s

gender? who knows

color? probably.

3) velocity is positive (moving to the right on a standard number line) for

0 < t < 3 and t > 7

Moves to the left for

t < 0 and 3 < t < 7

1. the velocity of the object at any time "t" is v(t) = 12t³ - 120t² + 252t.

2. the object stops changing at t = 6 and t = 3.5.

3. the object is moving to the right in the interval 0 < t < 3.5 and moving to the left in the interval t > 6.

To determine the velocity of the object at any time "t," we need to find the derivative of the position function "s(t)" with respect to "t."

1. Velocity of the object at any time "t":

The velocity is the rate of change of position with respect to time, which is given by the derivative of the position function, s(t).

s(t) = 3t⁴ - 40t³ + 126t² - 9

To find the velocity function, we take the derivative of s(t) with respect to t:

v(t) = d/dt (3t⁴ - 40t³ + 126t²- 9)

v(t) = 12t³ - 120t² + 252t

So, the velocity of the object at any time "t" is v(t) = 12t³ - 120t² + 252t.

2. Does the object ever stop changing?

The object stops changing when its velocity becomes zero. To find when the velocity is zero, we need to solve the equation v(t) = 0.

12t³ - 120t² + 252t = 0

Now, we can factor out common terms:

t(12t² - 120t + 252) = 0

Now, set each factor equal to zero and solve for "t":

1st factor: t = 0

2nd factor: 12t² - 120t + 252 = 0

To solve the quadratic equation, we can either factor it further or use the quadratic formula. Factoring the quadratic equation gives us:

(t - 6)(12t - 42) = 0

Setting each factor to zero:

1. t - 6 = 0

t = 6

2. 12t - 42 = 0

12t = 42

t = 3.5

So, the object stops changing at t = 6 and t = 3.5.

3. When is the object moving to the right and when is the object moving to the left?

The object is moving to the right when its velocity (v(t)) is positive, and it is moving to the left when its velocity (v(t)) is negative.

Let's analyze the velocity function

v(t) = 12t³ - 120t² + 252t

To find the intervals where the object is moving to the right or left, we need to determine when v(t) is positive or negative.

1. Find critical points by setting v(t) = 0 and solving for "t":

12t³ - 120t² + 252t = 0

As we already found earlier, the critical points are t = 6 and t = 3.5.

2. Test each interval created by these critical points using test points to determine the sign of v(t) in those intervals.

Pick a value of "t" in each of these intervals:

- When t < 3.5 (e.g., t = 0),

- When 3.5 < t < 6 (e.g., t = 4),

- When t > 6 (e.g., t = 7).

Now, substitute these test values into the velocity function v(t):

- v(0) = 12(0)³ - 120(0)² + 252(0) = 0

- v(4) = 12(4)³ - 120(4)² + 252(4) = 192

- v(7) = 12(7)³ - 120(7)² + 252(7) = -588

Based on the test points, we can conclude:

- The object is moving to the right when 0 < t < 3.5 (positive velocity).

- The object is moving to the left when t > 6 (negative velocity).

Therefore, the object is moving to the right in the interval 0 < t < 3.5 and moving to the left in the interval t > 6.

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Answer:

Y=76x

Step-by-step explanation:

if you divide 3 and 228 it is 76. if you divide 5 and 380 it is 76.if you divide 532 and 7 it is 76. and if you divide 11 and 836 it is 76.

Answer:

Step-by-step explanation:

The trick is to get rid of b in y = mx + b. The way to do that is to take 2 values and subtract them

(380 - 228) / (5 - 3) = 152/2 = 76

Not all problems work out this nicely.

The answer is

y = 76x

In this case you can be a little more direct. m = 380 ÷ 5 = 76, but not all equations are this well behaved and doing it the long way is the best way.

Answer/Step-by-step explanation:

To find the answer subtract 2 1/4 by 1/3

Step-by-step explanation:

............no.................

Answer:

the whole number 5 goes to the left of the decimal

Step-by-step explanation:

so think about it this way...

I have  10 dots   ..........  that is 1.0 but if I only have 5 of the 10 I have 0.5. if you have anymore questions just ask and ill help

[tex] \: \: \: \: [/tex]

[tex]6x - 30 - 3x = - 12[/tex]

[tex]6x - 30 = - 12[/tex]

[tex] 3x = - 18[/tex]

[tex]x = 3[/tex]

[tex] \: \: \: \: \: [/tex]

[tex]\sf \longmapsto6(x−5)=3x−12[/tex]

[tex]\sf \longmapsto(6)(x)+(6)(−5)=3x+−12[/tex]

[tex]\sf \longmapsto6x+−30=3x+−12[/tex]

[tex]\sf \longmapsto \: 6x - 30 = 3x - 12[/tex]

[tex]\sf \longmapsto \: 6x−30−3x=3x−12−3x[/tex]

[tex]\sf \longmapsto3x−30=−12[/tex]

[tex]\sf \longmapsto3x−30+30=−12+30[/tex]

[tex]\sf \longmapsto3x=18[/tex]

[tex]\sf \longmapsto \: \dfrac{3x}{3} = \dfrac{18}{3} [/tex]

[tex]\sf \longmapsto \: x = 6[/tex]

[tex] \boxed{\sf \: x = 6 }[/tex]

9514 1404 393

Answer:

  31°

Step-by-step explanation:

One way to find the difference angle is to look at the angle of the quotient. We can use complex numbers to represent the vectors for the purpose of that math. The magnitude is not important in this problem, so we do not have to finish the division.

  (8 -2i)/(5 -5i) = (8 -2i)(5 +5i)/((5 -5i)(5 +5i)) = (40 -10i +40i +10)/( )

The numerator is 50 +30i, which has an angle of ...

  arctan(30/50) ≈ 30.96° ≈ 31°

_____

Additional comment

Effectively, we have found the angle as the angle of the product of one vector with the conjugate of the other, when written as complex numbers. In vector terms, you might use the definition of the dot product. That seems to take a lot more math.

  u·v = |u|×|v|×cos(θ)

  θ = arccos(u·v/(|u|×|v|))

  θ = arccos((8·5 +(-2)(-5))/√((8² +(-2)²)(5² +(-5)²))) = arccos(50/√3400)

For me, it helps to ask this question: Does it make sense to apply the midpoint? If it doesn't make sense, then the data is discrete. Otherwise, the data is continuous.

Here's an example:

Let's say we are counting the number of people buying a movie ticket. So the numbers we care about are positive whole numbers 1,2,3,... It doesn't make sense to apply the midpoint to the values 1 and 2 to get 1.5; you can't sell half a ticket. Therefore the variable "number of movie tickets sold" is a discrete variable. There are gaps in the data.

On the other hand, if we were measuring the weight of various coins, then this variable is continuous. It's possible to have any positive number decimal number weight (eg: 2.275 grams perhaps). It makes sense to apply the midpoint to any two weights and get some other weight. We don't have to worry about sticking to whole numbers only. Unlike before, there aren't any gaps and we consider this number set to be dense.

One way you could remember the two is to keep this in mind: If you count it, then it's likely discrete. If you can measure it, then it's continuous.

There are probably exceptions to that rule, but for the most part it holds up I think.

1.

[tex]y=\frac{5}{3} x-2[/tex]

2.

[tex]y=-2x+2[/tex]

3.

[tex]y=x+5[/tex]

4.

[tex]y=\frac{1}{4}x[/tex]

Answer:

Step-by-step explanation:

The number of miles driven is sometimes written as a mixed number, and thus is a continuous variable (whereas the number of pencils purchased is not continuous (it's a whole number).

The domain of the continuous function are [0, n), where n represents the number of miles driven and is rarely over about 500 miles per day; the range is [$22, r), where r is ($0.10/mile)(number of miles driven), or approximately $50.  If the renter drove 600 miles the upper end of the range would be $60.  And so on.

Answer:

ratio of long-sleeved shirts to short-sleeved shirts is 1:2 this is my answer that I thought of if you don't feel comfortable believing me just wait for another person to answer and see what they say.

Step-by-step explanation:

Answer:

1875

Step-by-step explanation:

Step-by-step explanation:

30-(12-7)= red pens

30-19

11

Probability=

11/30

8V+3=105

clt

8v=105-3

=102

divide both sides by 8v

8v=102/8v

V=12.75

Answer: Yes

Step-by-step explanation: They are similar because it the same kind of triangle just ones smaller and the other is bigger.

9514 1404 393

Answer:

  (c)  ΔTRS

Step-by-step explanation:

Perhaps the easiest way to find corresponding vertices is to look at the angle markings:

  1 mark: angles J and T

  2 marks: angles K and R

  3 marks: angles I and S

Then, in order of corresponding angles, we have ...

  ΔJKI ≅ ΔTRS

Answer: 10

Explanation:

(30)-(30)= 0

Singular matrices must equal 0

(Correct on my quiz)

The value of x would make the following matrix singular is 10

For a matrix to be singular, the determinant of the matrix must be zero.

For the given 2 by 2 matrix, for the matrix to be a singular matrix then, its determinant must be zero as shown;

(5* 6) - (3 * x) = 0

30 - 3x = 0

3x = 30

x = 10

Hence the value of x would make the following matrix singular is 10

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Answer:

1/27

Step-by-step explanation: I took the quiz and the right answer is 1/27

The value of the given expression would be 0.25 which is simplified by using the PEMDAS rule in the expression.

The Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction rule is abbreviated as PEMDAS. This rule is used to answer the problem correctly and properly.

The given expression would be below as:

⇒ [(1 1/4−3/4)⋅(−2/3)3]÷(−4)

Using the PEMDAS rule in the above expression,

⇒ [(5/4−3/4)⋅(−2/3)3]÷(−4)

Apply the subtraction operation,

⇒ [(2/4)⋅(−6/3)]÷(−4)

Reduce the fractions, and we get

⇒ [(1/2)⋅(−2)]÷(−4)

Cancel out the terms of 2 to each other

⇒ (−1)÷(−4)

Cancel out the negative sign to each other

⇒ 1 / 4

Apply the division operation to get

⇒ 0.25

Therefore, the value of the given expression would be 0.25 which is evaluated.

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Answer: A) y = x + 3

Step-by-step explanation:

Use two points given in the table and plug them into slope-intercept form y = mx + b.

In order to solve for m, the slope, by plugging them into  [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex].

(0, 3) (2, 5)

[tex]\frac{5-3}{2-0}[/tex] = [tex]\frac{2}{2}[/tex] = 1

Use one of the points and plug it into the slope-intercept form y = mx + b.

3 = 1(0) + b

3 = 0 + b

3 = b

The linear equation to the table would be y = x + 3.

Answer: a) 250

b) I don’t understand

Step-by-step explanation: I’m not sure if it’s correct or not

Step-by-step explanation:

a⟩. a = (5x²)/2 = {5(10)²}/2 = {5(10*10)}/2 = {5(100)}/2 = 500/2 = 250Ans.

b⟩. b = {2x²(x - 5)}/10x = [2(10)²{10²-5}]/10(10)² = [2(10*10){10*10 - 5}]/10(10*10) = [2(100){100 - 5}/10(100) = [200 {95}]/1000 = 19000/1000 = 19 Ans.

Hope this helps!!

Answer:

w= -2. Solve for w: (w-5) (w+2) = w^2-4. Expand out terms of the left hand side: w^2-3 w-10 = w^2-4. Subtract w^2-4 from both sides

Step-by-step explanation:

Answer:

The answer is 37.68 or 37.7

Step-by-step explanation:

What you have to do first is find the diameter. So you have to multiply the radius (r) by 2 to get the diameter. 6 times 2 is 12. After that you, will multiply 12 by pi, or 3.14 to get 37.68

Answer:

The second and third equations are the correct ones.

Step-by-step explanation:

You don't need one, if you want one, do the problem yourself.

Answer: B. 8⋅7/2−12=22−2⋅3 and C. 48 ÷ 8 + 2³ = 5 + 3²

Answer:

option B is correct answer.

Step-by-step explanation:

(200-75)/2 = 62.5 miles per hour.

Answer:

75,388

Step-by-step explanation:

Long Multiplication form

[tex]\mathrm{Mutliply\:the\:bold\:numbers}[/tex]

[tex]\frac{\begin{matrix}\space\space&8&0&\textbf{2}\\ \times \:&\space\space&9&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&\space\space&\space\space&8\end{matrix}}[/tex]

[tex]\frac{\begin{matrix}\space\space&8&\textbf{0}&2\\ \times \:&\space\space&9&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&\space\space&0&8\end{matrix}}[/tex]

[tex]\mathrm{Multiply}\\\\8\cdot \:4=32[/tex]

[tex]\mathrm{Carry\:}3\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}2\mathrm{\:in\:the\:result\:line}[/tex]

[tex]\frac{\begin{matrix}\space\space&3&\space\space&\space\space&\space\space\\ \space\space&\space\space&\textbf{8}&0&2\\ \times \:&\space\space&\space\space&9&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&\space\space&2&0&8\end{matrix}}[/tex]

[tex]\mathrm{Add\:the\:carried\:digit,\:}3\mathrm{,\:to\:the\:result}[/tex]

[tex]\frac{\begin{matrix}\space\space&3&\space\space&\space\space&\space\space\\ \space\space&\space\space&8&0&2\\ \times \:&\space\space&\space\space&9&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\end{matrix}}[/tex]

[tex]\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}[/tex]

[tex]\frac{\begin{matrix}\space\space&\space\space&\textbf{8}&\textbf{0}&\textbf{2}\\ \space\space&\times \:&\space\space&\textbf{9}&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\end{matrix}}[/tex]

[tex]\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:2\cdot \:9=18[/tex]

[tex]\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}8\mathrm{\:in\:the\:result\:line}[/tex]

[tex]\frac{\begin{matrix}\space\space&\space\space&\space\space&1&\space\space\\ \space\space&\space\space&8&0&\textbf{2}\\ \space\space&\times \:&\space\space&\textbf{9}&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\\ \space\space&\space\space&\space\space&8&\space\space\end{matrix}}[/tex]

[tex]\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:1+0\cdot \:9=1[/tex]

[tex]\frac{\begin{matrix}\space\space&\space\space&\space\space&\textbf{1}&\space\space\\ \space\space&\space\space&8&\textbf{0}&2\\ \space\space&\times \:&\space\space&\textbf{9}&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\\ \space\space&\space\space&1&8&\space\space\end{matrix}}[/tex]

[tex]\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:8\cdot \:9=72[/tex]

[tex]\mathrm{Carry\:}7\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}2\mathrm{\:in\:the\:result\:line}[/tex]

[tex]\frac{\begin{matrix}\space\space&7&\space\space&1&\space\space\\ \space\space&\space\space&\textbf{8}&0&2\\ \times \:&\space\space&\space\space&\textbf{9}&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\\ \space\space&2&1&8&\space\space\end{matrix}}[/tex]

[tex]\mathrm{Add\:the\:carried\:digit,\:}7\mathrm{,\:to\:the\:result}[/tex]

[tex]\frac{\begin{matrix}\space\space&7&\space\space&1&\space\space\\ \space\space&\space\space&8&0&2\\ \times \:&\space\space&\space\space&9&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\\ 7&2&1&8&\space\space\end{matrix}}[/tex]

[tex]\mathrm{Add\:the\:rows\:to\:get\:the\:answer.\:\:\:Fill\:in\:trailing\:zeros\:\:(not\:required)}[/tex]

[tex]\frac{\begin{matrix}\space\space&\space\space&8&0&2\\ \space\space&\times \:&\space\space&9&4\end{matrix}}{\begin{matrix}0&3&2&0&8\\ 7&2&1&8&0\end{matrix}}[/tex]     [tex]=75,388[/tex]

See Image for the addition:

The expected value of the game is the mean value of the game

The expected value of the game is $9

For the first spinner;

For the second spinner;

So, the probability of spinning a 2 and a vowel is:

[tex]\mathbf{P(2\ and\ vowel) = \frac 14 \times \frac 14 = \frac{1}{16}}[/tex]

The earning for spinning a 2 and a vowel is $39.

So, the expected earning is:

[tex]\mathbf{Expected = 39 \times \frac{1}{16} = 2.4375}[/tex]

So, the probability of spinning a 2 and a consonant is:

[tex]\mathbf{P(2\ and\ consonant) = \frac 14 \times \frac 34 = \frac{3}{16}}[/tex]

The earning for spinning a 2 and a consonant is $26.

So, the expected earning is:

[tex]\mathbf{Expected = 26 \times \frac{3}{16} = 4.875}[/tex]

So, the probability of spinning a 1 and a vowel is:

[tex]\mathbf{P(1\ and\ vowel) = \frac 34 \times \frac 14 = \frac{3}{16}}[/tex]

The earning for spinning a 1 and a vowel is $9.

So, the expected earning is:

[tex]\mathbf{Expected = 9 \times \frac{3}{16} = 1.6875}[/tex]

So, the expected value of the game is:

[tex]\mathbf{Game =2.4375+ 4.875 + 1.6875}[/tex]

[tex]\mathbf{Game =9}[/tex]

Hence, the expected value of the game is $9

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Answer: 5:30

Step-by-step explanation: there are 5 apples and 30 total fruits.

Answer:

5:30 or simplified 1:6

Step-by-step explanation:

There are 30 fruits including the apples, and the apples only make up 5 of the fruits.

Answer:

12hrs and 32 minutes

Step-by-step explanation:

because the same am time to pm time is exactly 12 hrs and 11:34am is 26 minutes away from 12am so you can 26 minutes to get to 12am then 12am is 12hrs away from 12pm so you add 12hrs and now you are at 12pm at 12pm you add 6 minutes to get to 12:06pm which is a total of 12hrs and 32 minutes

The length of the vegetable garden is 11.7 ft.

The dimension of the garden are 3 section long and 2 section wide.

let

each section length = x

Therefore,

length of garden = 3x

width of garden = 2x

Area of the vegetable garden = 91.26 ft²

3x(2x) = 91.26 ft²

6x² = 91.26

x² = 91.26 / 6

x² = 15.21

x = √15.21

x = 3.9

length of the vegetable garden = 3(3.9) = 11.7 ft

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