A trail designer is planning two trails that connect campsites A and B to a point on the river, line L. She

Over the weekend MRs. Kinston sold slices of cake at a bake sale fundraiser

stich3 [128]

What’s the question?

4 0

3 years ago

What value of n makes the equation 4(0.5n − 3) = n − 0.25(12 − 8n) true?

svlad2 [7]

Answer:

n = -9

Step-by-step explanation:

4(0.5n − 3) = n − 0.25(12 − 8n)

2n - 12 = n - 3 + 2n

2n - 12 = 3n - 3

2n - 3n = - 3 +12

-1n = 9

n = -9

8 0

2 years ago

Triangle ABC was reflected over line m, then dilated by a scale factor between 0 and 1. Which diagram illustrates these transfor

vova2212 [387]

Answer:

I think its A.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

In 2 hours the 3 boys picked a total of 1347 cherries. If they share the cherries evenly, then

Natasha_Volkova [10]

Each boy will get 449 cherries

7 0

1 year ago

Read 2 more answers

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