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2 years ago

Subtract vector v = <2, -3> from vector u = <5, 2>.

Mathematics

2 answers:

Law Incorporation [45]2 years ago

4 0

Step-by-step explanation:

<5, 2> - <2, -3> = <5 - 2, 2 - (-3)> = <3, 5>

enot [183]2 years ago

3 0

Answer:

<3,5>

Step-by-step explanation:

We are subtracting vector v from vector u

u-v

<5, 2>- <2, -3>

< 5-2, 2--3>

<3, 2+3>

<3,5>

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2 years ago

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Find the product. (2p + 7)(3p - 9)

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3 years ago

During which time period does Landon's elevation change the fastest? Explain how you know?

bogdanovich [222]

<h3>1. How many inches per minute does London's elevation change between 4 minutes and 8 minutes. </h3>

The question actually asks for the slope of the line that stands for the points $(4,3) \ and \ (8,6)$ why? because the questions tells us that London's elevation changes between 4 minutes and 8 minutes here. Hence, to find the slope of this line we have to use the following formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ But: \\ \\ P(x_{1},y_{1})=P(4,3) \\ P(x_{2},y_{2})=P(8,6)$

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ But: \\ \\ P(x_{1},y_{1})=P(4,3) \\ P(x_{2},y_{2})=P(8,6) \\ \\ So: \\ \\ m=\frac{6-3}{8-4}=0.75in/min$

<em>So London's elevation changes 0.75 inches per minute</em>

<h3>2. During which time period does London's elevation change the fastest?</h3>

The greater the absolute value of the slope of the line the faster London's elevation changes. Since this is a Piecewise function, we must analyze each period.

FIRST:

→ Between 0 minutes and 4 minutes the function is constant, so there is no any change here.

→ Between 10 minutes and 14 minutes the function is constant, so there is no any change here.

→ Between 18 minutes and 22 minutes the function is constant, so there is no any change here.

So the solution is not in these parts of the function.

SECOND:

→ Between 4 minutes and 10 minutes the function has a positive slope, so there is change here.

In the previous item we calculated the slope between 4 and 8 minutes that is the same slope between 4 and 8 minutes and equals 0.75.

→ Between 14 minutes and 18 minutes the function has a positive slope, so there is change here.

Let's take two points here, say, $(16,5) \ and \ (18,3)$

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ But: \\ \\ P(x_{1},y_{1})=P(16,5) \\ P(x_{2},y_{2})=P(18,3) \\ \\ So: \\ \\ m=\frac{3-5}{18-16}=-1 in/min$

As you can see, the absolute value here is 1 that is greater than 0.75.

<em>In conclusion, London's elevation changes the fastest between 14 and 18 minutes</em>

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3 years ago

The Social Justice Club is going to rent a mammoth barbeque to cook the hot dogs for the hot dog sale After contacting three ren

zimovet [89]

Answer:

(A)Cost of Rental A, C= 15x

Cost of Rental B, C=5x+50

Cost of Rental C, C=9x+20

(B)

i. Rental C ii. Rental A iii. Rental B

Step-by-step explanation:

Let x be the number of hours of the barbeque use by the club.

Rental A: $15/h

Cost of Rental A, C= 15hx

Rental B: $5/h + 50

Cost of Rental B, C=5x+50

Rental C: $9/h + 20

Cost of Rental C, C=9x+20

The graph of the three models is attached below

If the barbecue's usage hour is from 11.05 to 4.30 when the football match ends.

Number of Hours between 11.05am and 4.30pm=4 hours 25 Minutes = 4.42 Hours

Cost of Rental A, C= 15x=15(4.42)=$66.30

Cost of Rental B, C=5x+50 =5(4.42)+50=$72.10

Cost of Rental C, C=9x+20=9(4.42)+20=$59.78

Rental C should be chosen as it offers the lowest cost.

Number of Hours = 12.30 -11.05 =1 hour 25 Minutes = 1.42 Hours

Cost of Rental A, C= 15x=15(1.42)=$21.30 Cost of Rental B, C=5x+50 =5(4.42)+50=$57.10 Cost of Rental C, C=9x+20=9(4.42)+20=$32.78

Rental A should be chosen since it offers the lowest cost.

If the barbecue is returned the next day, say after 24 hours

Cost of Rental A, C= 15x=15(24)=$360 Cost of Rental B, C=5x+50 =5(24)+50=$170 Cost of Rental C, C=9x+20=9(24)+20=$236

Rental B should be chosen as it offers the lowest cost.

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3 years ago

Create the f(x) function based on the table. Your answer should be in function notation. X f(x) - 10 -6 -9 -5 1-8 -4 -7 1-3 5 9

Minchanka [31]

Answer:

$f(x) = x + 4$

Step-by-step explanation:

First create an equation in slope-intercept form, y = mx + b. To do this, find the rate of change or slope (m), and the y-intercept (b).

Using two pairs, (-7, -3) and (-8, -4),

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 -(-3)}{-8 -(-7)} = \frac{-1}{-1} = 1$

m = 1

To find b, substitute m = 1, x = -7 and y = -3 into y = mx + b.

Thus:

-3 = (1)(-7) + b

-3 = -7 + b

-3 + 7 = b

4 = b

b = 4.

Replace y with f(x), m with 1 and b with 4 in y = mx + b.

The function would be:

$f(x) = x + 4$

6 0

3 years ago