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3 years ago

Which is the equation of a line that is perpendicular to 6x – 4y = 9?

Mathematics

1 answer:

natulia [17]3 years ago

8 0

6x – 4y = 9

4y = 6x - 9

y = 6/4 x - 9/4

y = 3/2 x - 9/4 this line has slope = 3/2

perpendicular line, slope is opposite and reciprocal so slope of this line = -2/3

answer:

A. y= - 2/3 x - 4 (only this line has slope = -2/3)

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A boat sails on a bearing of 038°anf then 5km on a bearing of 067°.

I am Lyosha [343]

This question is not complete

Complete Question

A boat sails 4km on a bearing of 038 degree and then 5km on a bearing of 067 degree.(a)how far is the boat from its starting point.(b) calculate the bearing of the boat from its starting point

Answer:

a)8.717km

b) 54.146°

Step-by-step explanation:

(a)how far is the boat from its starting point.

We solve this question using resultant vectors

= (Rcos θ, Rsinθ + Rcos θ, Rsinθ)

Where

Rcos θ = x

Rsinθ = y

= (4cos38,4sin38) + (5cos67,5sin67)

= (3.152, 2.4626) + (1.9536, 4.6025)

= (5.1056, 7.065)

x = 5.1056

y = 7.065

Distance = √x² + y²

= √(5.1056²+ 7.065²)

= √75.98137636

= √8.7167296826

Approximately = 8.717 km

Therefore, the boat is 8.717km its starting point.

(b)calculate the bearing of the boat from its starting point.

The bearing of the boat is calculated using

tan θ = y/x

tan θ = 7.065/5.1056

θ = arc tan (7.065/5.1056)

= 54.145828196°

θ ≈ 54.146°

7 0

2 years ago

10 × 100+ 2749 × 1828827

Annette [7]

1000 + 5027445423 = 5027446423

6 0

3 years ago

Read 2 more answers

At a car dealership yesterday, the ratio of trucks sold to cars sold was 5.6. If the dealership sold 30 cars, how many trucks we

aleksley [76]

Answer:

Step-by-step explanation:

ratio 5:6

$\frac{5}{6} = \frac{x}{30}$

6x = 5(30)

6x = 150

x = 25

3 0

2 years ago

An aquarium has a base area of 6 square feet and a height of 2 feet. Will the aquarium fit in 15 cubic feet of space? Explain wh

Brums [2.3K]

Answer:

Yes, the aquarium will fit in 15 cubic feet of space.

Step-by-step explanation:

Given:

An aquarium has a base area of 6 square feet and a height of 2 feet.

Now, to find will the aquarium fit in 15 cubic feet of space or not.

So, as given the dimensions:

Base area = 6 square feet.

Height = 2 feet.

Now, to get the volume of aquarium by using formula:

$Volume=base\ area\times height\\\\Volume=6\times 2\\\\Volume=12\ cubic\ feet.$

As, the volume of aquarium is 12 cubic feet.

And, the aquarium to be fit in 15 cubic feet space. So, 15 is more than 12.

Thus, the aquarium will be fit in 15 cubic feet space.

Therefore, the aquarium will fit in 15 cubic feet of space.

7 0

2 years ago

Use lagrange multiplier techniques to find the local extreme values of f(x, y) = x2 − y2 − 2 subject to the constraint x2 + y2 =

dexar [7]

Given $f(x,\ y)=x^2-y^2-2$ subject to the constraint $x^2+y^2=16$

Let $g(x,\ y)=x^2+y^2$ .

The gradient vectors of $f$ and $g$ are:

$\nabla f(x,\ y)=\langle2x,-2y\rangle$ and $\nabla g(x,\ y)=\langle2x,2y\rangle$

By Lagrange's theorem, there is a number $\lambda$ , such that

$\langle2x,-2y\rangle=\lambda\langle2x,2y\rangle=\langle2\lambda x,2\lambda y\rangle$

$\lambda=\pm1$

It can be seen that $f(x,\ y)=x^2-y^2-2$ has local extreme values at the given region.

6 0

3 years ago