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2 years ago

find the angle between vectors a =(1,2) and b = (1,-1/2). Brainliest for correct answer. Look at photo.

Mathematics

1 answer:

rosijanka [135]2 years ago

8 0

Answer:

90°

Step-by-step explanation:

The angle between the vectors can be found any of several ways. Here, we observe that the segments from the origin to the two points are at right angles to each other. (Their slopes are opposite reciprocals.) Hence the angle between the vectors is 90°.

The slope to point 'a' is y/x = 2/1 = 2.

The slope to point 'b' is y/x = (-1/2)/1 = -1/2.

The product of these slopes is (2)(-1/2) = -1, indicating the vectors are perpendicular. The angle between them is 90°.

We can also use the trig formula for the tangent of the difference of angles.

tan(α-β) = (tan(α) -tan(β))/(1 +tan(α)tan(β))

The tangents are the slopes, calculated above, so we have ...

tan(α -β) = (2 -(-1/2))/(1 +(2)(-1/2)) = (5/2)/0 = <em>undefined</em>

The tangent is <em>undefined</em> for angles that are odd multiples of 90°. The angle between the vectors is 90°.

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A right triangle (triangle 1) has a hypotenuse length of 115 mm and α = 31.2°. What are the measurements for a, b, and β? 2. A r

kirza4 [7]

Alright, lets get started.

A right triangle (triangle 1) has a hypotenuse length of 115 mm and α = 31.2°. What are the measurements for a, b, and β?

Please refer the diagram I have attached.

Using SOH CAH TOA,

$sin 31.2 = \frac{b}{115}$

$b = 115 sin31.2$

Plugging the value of sin 31.2

$b = 115*0.518 = 59.57$ mm

Similarly,

$cos31.2 = \frac{a}{115}$

$a = 115cos31.2$

Plugging the value of cos 31.2

$a = 115*.8553 = 98.36$ mm

Now, for angle β

tan β = $\frac{98.36}{59.57}$

tan β = 1.65

Using tan inverse

β = 58.78°

So, the answer is a = 98.36 mm, b = 59.57 mm and β = 58.78° : Answer

Hope it will help :)

A right triangle (triangle 1) has measurements of a = 505 mm and b = 286 mm. What are the measurements for c, α, and β?

Please refer the diagram I have attahced.

a and b are given, we could side c by using Pythagorean theorem.

$c^2 = a^2 +b^2$

$c^2 = 505^2 + 286^2$

$c^2 = 255025+81796$

$c^2 = 336821$

Taking square root on both sides

c = 580.36 mm

Using SOH CAH TOA,

tan α = $\frac{505}{286}$

taking tan inverse

α = 60.48°

Similarly,

tan β = $\frac{286}{505}$

taking tan inverse

β = 29.52°

So, the answer is c = 580.36 mm, α = 60.48° and β = 29.52° : Answer

Hope it will help :)

7 0

4 years ago

The population of the country was 314 million. What is the empirical probability of death by stroke during a single year

Marat540 [252]

Answer:

Empirical probability of deaths cause by stroke=0.004086

Empirical probability of deaths cause by kidney disease =0.001436

Death rate due to stroke is 4 times the death rate due to kidney disease.

Step-by-step explanation:

Consider the table attached in figure

No. of deaths cause by stroke = 128300

No. of deaths caused due t kidney disease = 45100

Total population = 314 x 10⁵

Formula to calculate empirical probability:

$P(A)=\frac{No.\, of\,\, times\,\, event\,\, occurs}{Total\,\, population}\\$

Empirical probability of deaths cause by stroke:

$P(A)=\frac{128300}{314\times 10^5}\\\\P(A)=0.004086$

Percentage of deaths cause by stroke =0.4%

Empirical probability of deaths cause by kidney disease:

$P(B)=\frac{45100}{314\times 10^5}\\\\P(B)=0.001436$

Percentage of deaths cause by kidney disease =0.1%

Ratio between deaths caused to stoke to deaths caused by kidney disease is 4:1 which means death rate due to stroke is 4 times the death rate due to kidney disease.

3 0

4 years ago

Trees planted by a landscaping firm have a 90% one-year survival rate, If they plant 16 trees in a park, what is the following p

irina1246 [14]

Answer:

Pr(all will survive in one year) = 0.35 to 2 decimal places

Pr(at least 8 will survive) = 0.39 to 2 decimal places.

Step-by-step explanation:

Probability of a tree surviving one year is 0.9. While not surviving probability is 1 - 0.9 = 0.1

This is obtained from the 90℅ surviving rate for one year planted by the landscaping firm.

Probability that if 10 trees are planted, all will survive for one year is:

0.9x0.9x0.9x0.9x0.9x0.9x0.9x0.9x0.9x0.9 = 0.9^10 = 0.349

Probability that at least 8 will survive in one year can be expressed as

8 survived x 2 not survived +(or) 9 survived x 1 not survived +(or) 10 survived

= [(0.9^8)x(0.1^2) + (0.9^9)x(0.1^1) + (0.9^10)] = 0.391

Step-by-step explanation:

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3 years ago

Given right triangle EFG with altitude FH drawn to the hypotenuse, find the lengths of EH, FH, GH. https://api.agilixbuzz.com/Re

pantera1 [17]

I need help with this question

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3 years ago

If I had 24 apples and X blue berries there are 9 times as many blueberries than apples.

Ganezh [65]

Answer: X=216

so, you have 216 blueberries

7 0

3 years ago

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