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liberstina [14]
2 years ago
4

Find two equivalent ways to express the slope of the vector [cos θ sin θ]

Mathematics
1 answer:
MariettaO [177]2 years ago
7 0

Answer:

\frac{\sin\theta}{\cos \theta} = \frac{\Delta y}{\Delta x}

Step-by-step explanation:

For two-dimensional vectors, there are two equivalent ways to express the slope of vectors:

\frac{\sin\theta}{\cos \theta} = \frac{\Delta y}{\Delta x}

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A frog catches insects for his lunch. The frog likes to eat flies and mosquitoes in a certain ratio, which is shown in the diagr
avanturin [10]

Answer:

ON MONDAY:  35 mosquitos.

ON TUESDAY: 6 flies.

Step-by-step explanation:

As you can see in the diagram, the frog eats 3 flies for every 7 mosquitoes (for lunch). Then you can expresed this ratio as following:

3:7 or \frac{3}{7}

Based on the table:

-If the frog eats 15 flies on monday, then the number of mosquitos that it eats can be calculated as following:

\frac{3}{7}=\frac{15}{mosquitoes}\\\\mosquitoes=\frac{15*7}{3}\\\\mosquitoes=35

-If the frog eats 14 mosquitoes on tuesday, then the number of flies that it eats can be calculated as following:

\frac{3}{7}=\frac{flies}{14}\\\\flies=\frac{14*3}{7}\\\\flies=6

8 0
2 years ago
Kathi and Robert Hawn had a pottery stand at the annual Skippack Craft Fair. They sold some of their pottery at the original pri
grigory [225]

Answer:27 pieces were sold at the original price.

63 pieces were sold at the new price

Step-by-step explanation:

Let x represent the number of pieces of pottery that was sold at the original price.

Let y represent the number of pieces of pottery that was sold at the new price.

They sold some of their pottery at the original price of​ $9.50 for each​ piece. This means that the amount that they got from selling x pieces of pottery at the original price would be 9.5x

They later decreased the price of each piece by​ $2. This means that the new price was 9.5 - 2 = $7.5

This means that the amount that they got from selling x pieces of pottery at the new price would be 7.5y

If they sold all 90 pieces and took in ​$729​, then the equations are

x + y = 90

9.5x + 7.5y = 729 - - - - - - - - - -1

Substituting x = 90 - y into equation 1, it becomes

9.5(90 - y) + 7.5y = 729

855 - 9.5y + 7.5y = 729

- 9.5y + 7.5y = 729 - 855

- 2y = - 126

y = - 126/- 2 = 63

Substituting y = 63 into x = 90 - y, it becomes

x = 90 - 63 = 27

6 0
2 years ago
10. APPLICATION Inspector 47 at the Zap battery plant
alexdok [17]
2010 47 +ten thousand split decide and
3 0
2 years ago
Which angles are linear pairs? Check all that apply.
KengaRu [80]

Answer:

srtand trv

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
A four-person committee is chosen from a group of eight boys and six girls.
Stolb23 [73]

Answer:

The probability is approximately 0.0699. That's \displaystyle \frac{10}{143} to be exact.

Step-by-step explanation:

How many ways to choose four out of a total of 8 + 6 = 14 boys and girls?

\displaystyle {14\choose 4} = 1001.

How many ways to choose four boys out of a total eight boys?

\displaystyle {8\choose 4} = 70.

What's the probability that all four persons chosen out of the pack of fourteen are boys? All 1001 ways of choosing four out of fourteen are equally likely. However, only 70 satisfy the conditions. In other words, the probability of choosing four boys out of this group of eight boys and six girls is equal to:

\begin{aligned}&\frac{\text{Number of ways to choose four out of eight}}{\text{Number of ways to choose four out of fourteen}} \\= &\frac{70}{1001}\\=&  \frac{10}{143}\approx 0.0699\end{aligned}.

6 0
2 years ago
Read 2 more answers
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