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zepelin [54]
3 years ago
15

A mailbox that is 4 feet tall cast a shadow that is 12 feet long. A street lamp across the street is 10 feet tall. Use indirect

measurements to find the length of the street lamp's shadow.
Mathematics
2 answers:
Rus_ich [418]3 years ago
6 0
Draw it out first, so start out by drawing the mailbox (or just a line, it's math, not art) and then draw the 12 foot shadow. Okay, so now you know the other lamp is 10 feet tall.

The goal here is to find out the shadow of the 10 foot tall pole. So this would be x.

Making a proportion would help the most on this problem so you would say the following:

4 / 12 = 10/x, solve for x
Free_Kalibri [48]3 years ago
3 0
Proportion: 4/12=x/10
Answer: x=3 1/3
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Step-by-step explanation:

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8 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
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arlik [135]
<span>ΔABC is not a right triangle.</span>
3 0
3 years ago
Read 2 more answers
Solve system by Substitution<br> method, provide steps.<br> y = 5x - 18<br> -5x+6y = 17
Sedaia [141]

Answer:

x=5

Step-by-step explanation:

-5x+6(5x-18)=17

-5x+30x-108=17

25x-108=17

25x=17+108

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5 0
3 years ago
Dalvin answered 51 questions correctly on his multiple choice science final and earned a grade of 85%. How many total questions
Leona [35]

Answer:

60

Step-by-step explanation:

Divide the number of questions answered correctly by his percentage

51 / 85 = 0.6

Now multiply that answer by 100 to see how many questions are on the quiz

0.6 x 100 = 60

Check your work by dividing that number by the number he answered correctly

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4 0
3 years ago
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