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Fudgin [204]
3 years ago
10

What is the solution to the systems of equations? y= 2/3x + 3 x=-2

Mathematics
1 answer:
Romashka [77]3 years ago
8 0

Answer:

y = 8/3

Step-by-step explanation:

x = -2

y = 2/(3*-2) + 3

y = 2/-6 + 3

y = -1/3 + 3

y = -1/3 + 9/3

y = 8/3

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HELP!!!
ella [17]

Answer:

120

Step-by-step explanation:

We are given that the function for the number of students enrolled in a new course is f(x) = 4^{x}-1.

It is asked to find the average increase in the number of students enrolled per hour between 2 to 4 hours.

We know that the average rate of change is given by,

A = \frac{f(x)-f(a)}{x-a},

where f(x)-f(a) is the change in the function as the input value (x-a) changes.

Now, the number of students enrolled at 4 = f(4) = f(x) = 4^{4}-1 = 255 and the number of students enrolled at 2 = f(2) = f(x) = 4^{2}-1 = 15

So, the average increase A=\frac{f(4)-f(2)}{4-2} = A=\frac{255-15}{4-2} = A=\frac{240}{2} = 120.

Hence, the average increase in the number of students enrolled is 120.

3 0
3 years ago
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
What does tan^2(x) mean
Sever21 [200]

Answer:

Step-by-step explanation:

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6 0
3 years ago
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avanturin [10]

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7 0
1 year ago
Help on # three it’s due in 10 minuets!!
LuckyWell [14K]
16 = 48/3
48 divided by 2 = 24
There is 24 students in the club.
6 0
3 years ago
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