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AVprozaik [17]
3 years ago
5

A first play of football game resulted in a loss of 12.5 yards. Then a penalty resulted in another loss of 5 yards. What is the

total loss or gain?
Mathematics
1 answer:
lions [1.4K]3 years ago
8 0
The total loss is 17.5 yards.
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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
He total variance is $35000 f. the total materials variance is $14000 f. the total labor variance is twice the total overhead va
TiliK225 [7]
Assume that the total overhead variance is x
We are given that the total labor variance is twice the total overhead variance. This means that, the total labor variance is 2x

Total variance can be calculated as follows:
Total variance = Total materials variance + Total overhead variance
                          + Total labor variance

We have:
Total variance = $35000
Total materials variance = $14000
Total overhead variance = x
Total labor variance = 2x

Substitute in the equation and solve for x as follows:
35000 = 14000 + x + 2x
35000 - 14000 = 3x
21000 = 3x
x = 21000/3
x = 7000

Based on the above calculations:
Total overhead variance = x = $7000
Total labor variance = 2x = 2*7000 = $14000
4 0
3 years ago
Vugar has a maximum of 30 batteries for toys. Each toy helicopter uses the same number of batteries, and each toy car uses the s
Leno4ka [110]

Answer: 3H+4C<_ 30

The coefficients of the variables H and C represent the number of batteries each toy helicopter and each toy car uses.

Step-by-step explanation:

Each toy helicopter uses 3 batteries, and each toy car uses 4 batteries.

Now let's check whether Vugar has enough batteries for 5 toy helicopters and 4 toy cars. To do this, we substitute  H=5 and C= 4 in the given inequality:

Does Vugar have enough batteries to play with 5 toy helicopters and 4 toy cars?

No, because if you plug in the value for H and C:

3H + 4C<_ 30

3(5) + 4(4) <_30

15 + 16 <_ 30

31 <_ 30; false

Since the inequality is false, Vugar does not have enough batteries to play with 555 toy helicopters and 444 toy cars.

Each toy helicopter uses 333 batteries, and each toy car uses 444 batteries.

No, Vugar does not have enough batteries to play with 555 toy helicopters and 444 toy cars.

6 0
3 years ago
Read 2 more answers
Please solve 1 through 6
Degger [83]
1. 3x³-2x²+1x
2. 6y⁴+2y³-8y
3.-3m³-12m²+3m
4. 4d⁴-3d³+d²
5. -w⁵-3w³
6. -a⁴-3a³
7 0
3 years ago
A mathematical term that does not include an equal or inequality sign is called an
Evgen [1.6K]
The answer would be a mathematical phrase. Hope that helped.
3 0
3 years ago
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