What is the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1) ?

The amount of oil it takes to cover the bottom of a frying pan.

murzikaleks [220]

Answer:

about 1 cup maybe less

Step-by-step explanation:

8 0

3 years ago

How do you simplify a fraction?

attashe74 [19]

You simplify a fraction by finding it's greatest common factor. A greatest common factor is what both numbers are divisible by. If they can both be divided by two, then you've simplified them a little bit. Keep going until you can't find a common number that can be divided by the two, and you've got your simplified fraction. For example, 10/5 = 1/2 since both 10 and 5 is divisible by 5.

5 0

4 years ago

In this question, i is a unit vector due east and j is a unit vector due north. A cyclist rides at a speed of 4 m/s on a bearing

d1i1m1o1n [39]

Answer:

a) 1.04i + 3.86j

b) magnitude = 8; bearing = 302.7°

Step-by-step explanation:

a)

The first diagram represents the velocity vector of the cyclist.

To express this vector in the form xi + yj, we have to find the components of the vector in the horizontal (i) and vertical (j) directions.

If we consider the horizontal component of the vector to be $x$ , and the vertical component to be $y$ , then:

• horizontal component ⇒ $sin (15^{\circ}) = \frac{x}{4}$

⇒ $x = 4\space\ sin(15^{\circ})$

⇒ $x \approx \bf 1.04$

• vertical component ⇒ $cos(15^{\circ}) = \frac{y}{4}$

⇒ $y = 4 \space\ cos(15^{\circ})$

⇒ $y \approx \bf 3.86$

Now that we have the values of both the horizontal and vertical component, we can write the vector in the form of xi + yj:

vector ⇒ 1.04i + 3.86j

b)

The second diagram shows the first vector (red), the second vector (blue), and the resultant vector v (black). The dashed lines represent the components of the respective vectors.

To add two vectors given their magnitudes and direction, we have to add their components.

In order to find the horizontal and vertical components of the given vectors, we can use a method similar to that used above, so that:

○ For the first vector (magnitude 6):

• horizontal component ⇒ $x = 6 \space\ sin (60^{\circ})$

⇒ $\bf 5.2$

• vertical component ⇒ $y = 6 \space\ cos(60^{\circ})$

⇒ $y = \bf 3$

○ For the second vector (magnitude 2):

• horizontal component ⇒ $x = 2 \space\ cos (40^{\circ})$

⇒ $\bf 1.5$

• vertical component ⇒ $y = 2 \space\ sin(40^{\circ})$

⇒ $\bf 1.3$

Now we can add the respective components together:

v = 5.2i + 3j + 1.5i + 1.3j

⇒ (5.2 + 1.5)i + (3 + 1.3)j

⇒ 6.7i + 4.3j

∴ Magnitude of v ⇒ $|v| = \sqrt{(6.7)^2 + (4.3)^2}$

⇒ $|v| \approx \bf 8$

To find the bearing of v, we have to first calculate the angle marked $\alpha$ :

$tan \alpha = \frac{4.3}{6.7}$

⇒ $\alpha = tan^{-1}(\frac{4.3}{6.7})$

⇒ $\alpha = \bf 32.7^{\circ}$

∴ Bearing = 270° + 32.7°

= 302.7°

8 0

2 years ago

Which expression can be expanded using the binomial theorem?

kirill [66]

Answer:

The third choice: (x² - 1)³

Step-by-step explanation:

That is the only expression that is a binomial. Binomial means "two numbers". For this expression, x² is one number, and -1 is the other. Choice 1 is a monomial (one number) and choices 2 and 4 are trinomials (three numbers)

7 0

3 years ago

$213 ski jacket 30% discount

andrezito [222]

213. 30/100 = 213. 3/10 =63.9
213-63.9=143.1

4 0

3 years ago

Read 2 more answers

What is the perimeter of a polygon with vertices at (−2, 1) , ​ (−2, 4) ​, (2, 7) , ​ (6, 4) ​, and (6, 1) ​?

What is the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1) ?