A triangular pyramid is sliced by a plane perpendicular to its base. Draw the cross section

Answer:

(a) w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

(b) -2u + 3v - 5w = ([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])

Step-by-step explanation:

Given:

u = (−2, 3, 1)

=> u = -2i + 3j + k                           --------------------------(i)

v = (−1, −1, 2)

=> v = -i - j + 2k                                --------------------(ii)

3u − 2v − 4w = (3, 2, −3)

=> 3u − 2v − 4w = 3i + 2j - 3k             ------------------(iii)

(A) TO FIND THE VECTOR w

Let:

w = (a, b, c) = ai + bj + ck

(a) Substitute u, v and w into equation (iii)

3u − 2v − 4w = 3i + 2j - 3k

3(-2i + 3j + k) - 2(-i - j + 2k) - 4(ai + bj + ck) = 3i + 2j - 3k

(b) Solve the equation in step (a) by opening the brackets and collecting like terms

(-6i + 9j + 3k) - (-2i - 2j + 4k) - (4ai + 4bj + 4ck) = 3i + 2j - 3k

open brackets

-6i + 9j + 3k + 2i + 2j - 4k - 4ai - 4bj - 4ck = 3i + 2j - 3k

collect like terms

-6i + 2i - 4ai + 9j + 2j - 4bj + 3k - 4k - 4ck = 3i + 2j - 3k

i(-4 - 4a) + j(11 - 4b) + k(-1 - 4c) = 3i + 2j - 3k

(c) Solve for a, b and c in step (b)

Comparing both sides of the equation, we have;

-4 - 4a = 3              ----------(*)

11 - 4b = 2              -----------(**)

-1 - 4c = -3             ------------(***)

From (*)

4a = -4 - 3

4a = -7

a = [tex]\frac{-7}{4}[/tex]

From (**)

4b = 11 - 2

4b = 9

b = [tex]\frac{9}{4}[/tex]

From (***)

-1 - 4c = -3

4c = -1 + 3

4c = 2

c = [tex]\frac{2}{4}[/tex]

c = [tex]\frac{1}{2}[/tex]

Remember that

w = (a, b, c)

w = ai + bj + ck

Therefore,

w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

(B) TO FIND -2u + 3v - 5w

Remember that;

u = (−2, 3, 1)

v = (−1, −1, 2),

w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

Substitute u, v, w into the expression as follows;

-2(−2, 3, 1) + 3(−1, −1, 2) - 5[tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

Expand

(4, -6, -2) + (−3, −3, 6) - [tex](\frac{-35}{4} , \frac{45}{4}, \frac{5}{2})[/tex]

Collect like terms

(4-3+[tex]\frac{35}{4}[/tex], -6-3-[tex]\frac{45}{4}[/tex], -2+6-[tex]\frac{5}{2}[/tex])

Solve

([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])

Therefore, -2u + 3v - 5w = ([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])

Answer:

-5 -9 -13....

Step-by-step explanation:

17-4=13 so you basically minus 3 each time.

Answer:

B) -6 (w - 4) + 8w = 2 (w + 9) has no solution

Step-by-step explanation:

Answer:

y = -5x + 32

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Write in known variables

slope m = -5

y = -5x + b

Step 2: Find b

7 = -5(5) + b

7 = -25 + b

b = 32

Step 3: Write linear equation

y = -5x + 32

Answer:

y - 7 = -5(x - 5)

Step-by-step explanation:

We are given that a line has a slope of -5 and contains the point (5,7).

We want to write the equation of this line.

The equation of this line can be written in three ways:

Either one of these ways works, but let's use point-slope form, as that form is the easiest.

We can immediately substitute the values into the formula to get the equation.

We can start with the slope; replace m with -5 in the formula.

[tex]y-y_1=m(x-x_1)[/tex] => [tex]y-y_1=-5(x-x_1)[/tex]

Now, we can replace [tex]x_1[/tex] and [tex]y_1[/tex] with 5 and 7 respectively to get:

y - 7 = -5(x - 5)

Answer:

$323.40

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

For the smaller figure to be a scaled copy, the figure would have to be half as wide as well,

Answer:

44 cm^2

Step-by-step explanation:

You can separate this figure into three rectangles. The area of the first rectangle is 20. The area of the second rectangle is 6. And the area of the third is 18. If you add those all together you get 44 cm^2

Steps to solve:

-2x - 4 > 8

~Add 4 to both sides

-2x > 12

~Divide -2 to both sides

x < -6

Best of Luck!

Answer:

The temperature drops 4° every hour

Step-by-step explanation:

Step 1:

24° ÷ 6

Step 2:

24 : 6 = 4 : 1

Answer:

4

Hope This Helps :)

Answer:

[tex]\boxed {\tt -4 \textdegree \ per \ hour }[/tex]

Step-by-step explanation:

This question asks us to find the average rate of change in temperature per hour.

Therefore, we must divide the temperature change by the hours.

[tex]rate \ of \ change =\frac{temperature \ change}{hours}[/tex]

The temperature dropped 24 degrees in 6 hours. Since it dropped, the change was negative.

[tex]temperature \ change = -24 \textdegree \\hours = 6 \ hours[/tex]

Substitute the values into the formula.

[tex]rate \ of \ change =\frac{-24 \textdegree}{6 \ hours}[/tex]

Divide.

[tex]rate \ of \ change = - 4 \textdegree / hour[/tex]

The average change in temperature was -4° per hour. The temperature dropped 4 degrees each hour.

Answer:

Answer is A

explanation:

there is no point (0.-3) on the graph.

Answer:

it's D edg 2020

Step-by-step explanation:

Answer:

Why is college important? It’s a question you may have heard among friends, or perhaps you’ve even wondered yourself about the benefits of earning a degree. And it’s a good question to be asking as you consider your future—and everything that will include, from earnings potential to starting or switching your career. Here are five facts you should know as you consider the value of a college education.

1. People with college degrees earn more on average.

According to averages calculated by the US Bureau of Labor Statistics (BLS), people with a bachelor’s degree earn around 64% more per week than individuals with a high school diploma, and around 40% more than those with an associate’s degree. Those with an associate’s degree earn around 17% more than those with a high school diploma.

Over the course of a year (52 weeks), those percentage differences add up. For example, if you compare the average median annual earnings for those with a bachelor’s degree to those with a high school diploma, you’ll discover a difference of almost $24,000 per year in income.

2. College can help you expand your network.

Salary is far from the only answer for why is college important. You may have heard this before, but who you know and who your friends know is important. No matter how talented you are, a strong network can help you start and advance in your career.

At an Art Institutes school, you’ll not only have the chance to connect with instructors* who have worked in their fields, but you can also meet students in a variety of creative fields. These diverse connections may well benefit you in the future. Plus, you can also participate in professional groups, community activities, and industry conferences where you can grow your circle even more. Your Career Services department may also connect you with alumni in your field and can continue to provide networking support after graduation!

3. Gaining new skills can help enhance your current career.

Building your skill set and industry knowledge can help you move forward in your current career, and the skills you learn go beyond the obvious. At The Art Institutes, not only can you build your technical and artistic skills, but you can also develop your critical thinking, communication, and teamwork.

Earning your degree can demonstrate to a current employer that you’re serious about your career, and that you’re prepared to take on bigger projects and more responsibility. In the long term, when you apply to new jobs in your field, having a degree can provide you with a competitive edge. Even if the job doesn’t require a degree, your education—along with the quality of your work—may help you stand out among applica

Step-by-step explanation:

Answer:

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.Jan 8, 2019

Step-by-step explanation:

Answer:

Smallest=849mi

Middle=927mi

Largest=1304mi

Step-by-step explanation:

My work is in the attachment but here are some notes:

Answer:

B the set of all natural numbers and the ser of all

Answer:

B D B C

Step-by-step explanation:

rational numbers, real numbers

3

irrational

rational

a. Z, Q, R b. Q, R c. N, Z, Q, R d. R

3

8

= 0.375, nonrepeating, terminating; 5

6

=

0.83, repeating, nonterminating; 12

15 = 0.8,

nonrepeating, terminating; 7

11 = 0.63,

repeating, nonterminating

real, irrational; real, rational, whole

Answers may vary. Sample: − 50

Answer:

Option C - Choosing 25 students at random from each of four different grade levels at a high school

Step-by-step explanation:

For us to achieve the conditions for a stratified random sample, the target population must be split into different groups which in this case, it's grade levels.

Looking at the 5 options given in the question, Options A, B, D and E are random but they are not truly stratified in their sampling approach. This is because the sample population must be selected at random from each of these groups and it's only option C which is choosing 25 students from each of four different grade levels or groups that reflects that.

Answer:

768

Step-by-step explanation:

Answer:

D) 7 1/5

Step-by-step explanation:

2 2/5 is equivalent to 12/5 then if you divide it by 1/3 you will get 7 1/5 or 7.2

Answer

:we are told that every year the temperature rises by 0.08degrees Centigrade,

So the difference between margin of error and the increase is much higher

That is

0.15-0.08=0.07

But remember Margin of error=Critical value *Standard deviation of population

And it is a quantity that measures accuracy

So the counter argument is that this is still an increase and it should be considered.

.

Answer:

The difference with any previous decade is much greater than the margin of error

Step-by-step explanation:

Answer:

(-4,0), (-3,0)

Step-by-step explanation:

The solution of a quadratic equation is simply when the graph crosses the x-axis. This is because at that point, the function will equal 0.

From the graph, we can see that the graph touches the x-axis at x=-4 and x=-3.

Therefore, our solutions for the graphed quadratic is x=-4 and x=-3.

And we're done!

Answer:

162.8 above her camp site she starts at the middle and drops 82.5 and then climbs 30.4 which puts her at 52.1 then by her repelling down another 45.5 drop she then proceeds to climb 25.2 which puts her at 72.4 and if you multiplie 45.4 by 2 it counts for the extra 90.4 drop which then concludes her climb to be bellow her site by 162.8 and the 1st word is supposed to be bellow my bad.

Step-by-step explanation:

step by step is above

Answer:

could you include the table?

Step-by-step explanation:

Answer:

Step-by-step

Rank Topic Problem Formatted Problem

77201 Solve for g 4g=24

4

g

=

24

4

g

=

24

77202 Solve for g 4g-2=22-8g

4

g

−

2

=

22

−

8

g

4

g

-

2

=

22

-

8

g

77203 Solve for g -4gh-8gi-2g+1=6h-6

−

4

g

h

−

8

g

i

−

2

g

+

1

=

6

h

−

6

-

4

g

h

-

8

g

i

-

2

g

+

1

=

6

h

-

6

77204 Solve for g 5g+2=3g+12

5

g

+

2

=

3

g

+

12

5

g

+

2

=

3

g

+

12

77205 Solve for g 5g=W

5

g

=

W

5

g

=

W

77206 Solve for g 5g-3g+g+8=2g+1+g+g

5

g

−

3

g

+

g

+

8

=

2

g

+

1

+

g

+

g

5

g

-

3

g

+

g

+

8

=

2

g

+

1

+

g

+

g

77207 Solve for g 6=-3/7g

6

=

−

3

7

g

6

=

-

3

7

g

77208 Solve for g -6g+36=12

−

6

g

+

36

=

12

-

6

g

+

36

=

12

77209 Solve for g 6g=100

6

g

=

100

6

g

=

100

77210 Solve for g 6g-3.5=8.5

6

g

−

3.5

=

8.5

6

g

-

3.5

=

8.5

77211 Solve for g 7(g-2)=5(g+4)

7

(

g

−

2

)

=

5

(

g

+

4

)

7

(

g

-

2

)

=

5

(

g

+

4

)

77212 Solve for g 7+(5g)/2=-13

7

+

5

g

2

=

−

13

7

+

5

g

2

=

-

13

77213 Solve for g 7200mg=g

7200

mg

=

g

7200

mg

=

g

77214 Solve for g 7800g=kg

7800

g

=

kg

7800

g

=

kg

77215 Solve for g 18-2g=4g

18

−

2

g

=

4

g

18

-

2

g

=

4

g

77216 Solve for g 18g+11=22g+27

18

g

+

11

=

22

g

+

27

18

g

+

11

=

22

g

+

27

77217 Solve for g 19*23=17g

19

⋅

23

=

17

g

19

⋅

23

=

17

g

77218 Solve for g 2.5g=17.5

2.5

g

=

17.5

2.5

g

=

17.5

77219 Solve for g 2|g+1|=14

2

|

g

+

1

|

=

14

2

|

g

+

1

|

=

14

77220 Solve for g 20+5g=10

20

+

5

g

=

10

20

+

5

g

=

10

77221 Solve for g g(x)=(x+6)/(x^2+2x-35)

g

(

x

)

=

x

+

6

x

2

+

2

x

−

35

g

(

x

)

=

x

+

6

x

2

+

2

x

-

35

77222 Solve for g 21.26=4g+3.54

21.26

=

4

g

+

3.54

21.26

=

4

g

+

3.54

77223 Solve for g 219÷104=2*(pv(1.34g))

219

÷

104

=

2

⋅

(

p

v

(

1.34

g

)

)

Answer:

For each one it is shown below

Step-by-step explanation:

The computation of the prime time viewing percentage for the following data is shown below:l;

but before that we need do the total which is

= 6.2% + 8.1% + 7.4% + 6.4% + 3.1% + 2.8%

= 34%

Now for each one the viewing percentage is

For ABC

[tex]= \frac{6.2}{34}[/tex]

= 18.24%

For CBS

[tex]= \frac{8.1}{34}[/tex]

= 23.82%

For NBC

[tex]= \frac{6.4}{34}[/tex]

= 18.82%

For Warner brothers

[tex]= \frac{3.1}{34}[/tex]

= 9.12%

For fox

[tex]= \frac{7.4}{34}[/tex]

= 21.76%

For UPN

[tex]= \frac{2.8}{34}[/tex]

= 8.24%

Answer:

a major arc

Step-by-step explanation:

A circle is the locus of  point in which has a given distance from a fixed point (center of the circle).

B is the center of the circle C B, D B, and E B are radii forming 3 congruent angle. Since the sum of angles in a circle is 360°, the 3 line segments form 3 congruent angles of 120° each (360/3).

Therefore the angle measure of Arc C D E =  Arc CD + Arc DE = 120° + 120° = 240°

A major arc is an arc greater than a semicircle (> 180°). This means that Arc C D E is a major arc

Answer:

a major arc

Step-by-step explanation:

a major arc

a major arc

a major arc

a major arc

a major arc

a major arc

a major arc

Answer:

Yes

Step-by-step explanation:

Pi is a rational number, because it goes on forever.

Answer:   175

Step-by-step explanation:

[tex]g(35)= \int\limits^{35}_0 {f(x)} \, dx =\int\limits^{30}_0 {f(x)} \, dx +\int\limits^{35}_{30} {f(x)} \, dx[/tex]

                            =     137.5   +      37.5

                            =  175

Answer:

g(35) = 137.5

Step-by-step explanation:

g(35) = g(30) + [g(35) - g(30)]

g(35) = 100 + 5(15)/2

g(35) = 137.5

Answer:

The side length is irrational

Step-by-step explanation:

Because the square root of 23 or 20+3 is a non-perfect square root and it's a never ending decimal.

Answer:

4 months and 7 months

Step-by-step explanation:

C = 30x + 50

C is cost so when we spend $170 we can solve for x.

$170 = 30x + 50

170 - 50 = 30x + 50 - 50

170 - 50 = 30x

120 = 30x

120/30 = 30x/30

120/30 = x

4 = x

So he has played 4 months when he spends $170

C is cost so when we spend $260 we can solve for x.

$260 = 30x + 50

260 - 50 = 30x + 50 - 50

260 - 50 = 30x

210 = 30x

210/30 = 30x/30

210/30 = x

7 = x

So he has played 7 months when he spends $260