All categories

4 years ago

Find the angle θ between u = <7, –2> and v = <–1, 2>.

Mathematics

2 answers:

AlekseyPX4 years ago

8 0

Answer:

132.5°

Step-by-step explanation:

u•v = |u| |v| cos(theta)

(7×-1) + (-2×2) = sqrt(53) × sqrt(5) cos(theta)

-7-4 = sqrt(265) cos(theta)

cos(theta) = -11/sqrt(265)

theta = 132.510447078

Dmitry_Shevchenko [17]4 years ago

7 0

The angle between two vectors is:

CosФ = u - v / Magnitude(u) x magnitude(v)

Magnitude of u = SQRT(7^2 + -2^2) = SQRT(49 +4) = SQRT(53)

Magnitude of v = SQRT(-1^2 +2^2) = SQRT(1 +4) = SQRT(5)

u x v = (7 x -1) + (-2 x 2) = -7 + -4 = -11

cosФ = -11 / sqrt(53) x sqrt(5)

cosФ = -11sqrt265) / 265

Ф =cos^-1(-11sqrt265) / 265)

Ф=132.51 degrees.

You might be interested in

To the nearest hundredth, what is the sine of the acute angle formed by the line whose equation is y = 3x - 3 and the positive x

Serhud [2]

Answer:

The sine of the acute angle is $0.95$

Step-by-step explanation:

using a graphing tool

see the attached figure

Let

A-----> the acute angle formed by the given line and the positive x-axis

In the right triangle XYZ

we know that

$sin(A)=\frac{xy}{xz}$

we have

$xy=3\ units$

$yz=1\ units$

Applying the Pythagoras Theorem find the value of xz

$xz^{2}=3^{2}+1^{2}\\ \\xz^{2}=10\\ \\xz=\sqrt{10}\ units$

substitute

$sin(A)=\frac{3}{\sqrt{10}}=0.95$

5 0

4 years ago

In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,91

Maurinko [17]

Answer:

a) The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

b) Wider

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,911 of them had no strategic business plan.

This means that $n = 3900, \pi = \frac{1911}{3900} = 0.49$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 - 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.4768$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 + 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.5032$

The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

Question b:

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

The higher the confidence level, the higher the value of z, thus the higher the margin of error and the interval is wider. Thus, a 99% confidence interval is wider than a 90% confidence interval.

3 0

3 years ago

ਬਿੰਦੂ ‌‌‍A ਦੇ ਨਿਰਦੇਸ਼ ਅੰਕ ਪਤਾ ਕਰੋ ਜਿੱਥੇ AB ਇਕ ਚੱਕਰ ਦਾ ਵਿਆਸ ਹੈ ਜਿਸ ਦਾ ਕੇਂਦਰ (2,-3) ਹੈ ਅਤੇ B ਦੇ ਨਿਰਦੇਸ਼ ਅੰਕ (1,4) ਹਨ

Studentka2010 [4]

Answer:

https://youtu.be/iik25wqIuFo

इसका उत्तर इस लिंक में है

6 0

3 years ago

Plzz help, Find the volume of the figure

mezya [45]

Answer:

The answer is 896,000

Step-by-step explanation:

Just multiply all the numbers

6 0

3 years ago

Read 2 more answers

If f(x) = - 3x - 3. g(x) = 2x2 + 6x - 5. and h(x) = - 8x2 + 6. find f(-3). I REALLY NEED THIS

shepuryov [24]

Answer:

f(-3) = 6

Step-by-step explanation:

input -3 in f(x)

so f(-3) = -3(-3) - 3

multiple and add

f(-3) = 6

5 0

4 years ago