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2 years ago

Which piecewise defined function is shown on the

Mathematics

1 answer:

ELEN [110]2 years ago

6 0

Answer: (4)

Step-by-step explanation:

The first part has a closed hole at x=0 and an open hole at x=4, so it should be $0 \leq x < 4$ .

This eliminates all the options except for (4).

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I can't figure out how to do (i + j) x (i x j)for vector calc

Vinil7 [7]

In three dimensions, the cross product of two vectors is defined as shown below

$\begin{gathered} \vec{A}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} \\ \vec{B}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k} \\ \Rightarrow\vec{A}\times\vec{B}=\det (\begin{bmatrix}{\hat{i}} & {\hat{j}} & {\hat{k}} \\ {a_1} & {a_2} & {a_3} \\ {b_1} & {b_2} & {b_3}\end{bmatrix}) \end{gathered}$

Then, solving the determinant

$\Rightarrow\vec{A}\times\vec{B}=(a_2b_3-b_2a_3)\hat{i}+(b_1a_3+a_1b_3)\hat{j}+(a_1b_2-b_1a_2)\hat{k}$

In our case,

$\begin{gathered} (\hat{i}+\hat{j})=1\hat{i}+1\hat{j}+0\hat{k} \\ \text{and} \\ (\hat{i}\times\hat{j})=(1,0,0)\times(0,1,0)=(0)\hat{i}+(0)\hat{j}+(1-0)\hat{k}=\hat{k} \\ \Rightarrow(\hat{i}\times\hat{j})=\hat{k} \end{gathered}$

Where we used the formula for AxB to calculate ixj.

Finally,

$\begin{gathered} (\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=(1,1,0)\times(0,0,1) \\ =(1\cdot1-0\cdot0)\hat{i}+(0\cdot0-1\cdot1)\hat{j}+(1\cdot0-0\cdot1)\hat{k} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=1\hat{i}-1\hat{j} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=\hat{i}-\hat{j} \end{gathered}$

Thus, (i+j)x(ixj)=i-j

8 0

1 year ago

Help! Select all of the potential solution(s) of the equation 2log5x = log54.

Nastasia [14]

Answer:

x = 2

Step-by-step explanation:

2 log₅ x = log₅ 4
2 log₅ x = log₅ 2²
2 log₅ x = 2 log₅ 2
log₅ x = log₅ 2
x = 2

7 0

3 years ago

Which equation is an identity?

kirza4 [7]

Answer:

Option (3).

Step-by-step explanation:

Option (1).

3(x - 1) = x + 2(x + 1) + 1

3x - 3 = x + 2x + 2 + 1

3x - 3 = 3x + 3 [Not True]

Therefore, this equation is not an identity.

Option (2).

x - 4(x + 1) = -3(x + 1) + 1

x - 4x - 4 = -3x - 3 + 1

-3x - 4 = -3x - 2 [Not true]

Therefore, this equation is not an identity.

Option (3).

2x + 3 = $\frac{1}{2}(4x + 2) + 2$

2x + 3 = 2x + 1 + 2

2x + 3 = 2x + 3 [True]

Therefore, this equation is an identity.

Option (4).

$\frac{1}{2}(6x-3)=3(x+1)-x-2$

3x - 1.5 = 3x + 3 - x - 2

3x - 1.5 = 2x + 1 [Not true]

Therefore, this equation is not an identity.

6 0

4 years ago

Read 2 more answers

Please Help!!! Will give brainliest

qaws [65]

36 cm^2

Step-by-step explanation:

Small window

Length: 2cm

Width: 2cm

Area: 4 cm^2

Big window

Length: 4cm

Width: 3cm

Area: 12 cm^2

Total area of the windows:

(Area of 4 small windows + area of 1 big window)

(4 cm^2 x 4 + 12cm^2)

= 28 cm^2

Above window (approx.)

Rectangle

Length: 3cm

Width: 2cm

Area: 6 cm^2

Triangle

Base: 1cm

Height: 1cm

Area: 2 x 0.5 cm^2 = 1 cm^2

Square (between the triangles)

Length: 1cm

Width: 1cm

Area: 1 cm^2

= 8 cm^2

TOTAL AREA OF ALL WINDOWS

= AREA OF 4 WINDOWS + AREA OF BIG WINDOW + AREA OF ABOVE WINDOW

= 16 cm^2 + 12 cm^2 + 8 cm^2

I hope I made the explanations clear enough to make it easier for you to understand!

8 0

1 year ago

1) A basket of apples are given to a group of students. If 3 apples are given to each student, there will be 8 apples left. If 5

sattari [20]

Answer:

1) either 5 or 6 students in the group

2) 6 rooms are booked

Step-by-step explanation:

1) x students

3x + 8 = apples

5 (x-1) + y (the one get less than 5 apples)

3x + 8 = 5 (x - 1) + y

3x + 8 = 5x - 5 + y

2x + y = 13

X 1 2 3 4 5 6

Y 11 9 7 5 3 1

because y < 5 so x = 5 or x = 6

2) x rooms are booked

4x + 20 total students

8 (x-1) + y (the students in room not full))

4x + 20 = 8 (x-1) + y

4x + 20 = 8x - 8 + y

4x + y = 28

X 1 2 3 4 5 6

Y 24 20 16 12 8 4

y < 8 answer is 6 rooms

4 0

4 years ago