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4 years ago

Find the acute angle between the two given lines y=-2x and y=x

Mathematics

1 answer:

Marina CMI [18]4 years ago

3 0

Answer:

θ ≈ 71.6°

Step-by-step explanation:

The angle between two lines with slopes m₁ and m₂ is:

tan θ = | (m₂ − m₁) / (1 + m₁m₂) |

Here, m₁ = -2 and m₂ = 1.

tan θ = | (1 − (-2)) / (1 + (-2)(1)) |

tan θ = | 3 / -1 |

tan θ = 3

θ ≈ 71.6°

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Y = -9x - 2; (4, -37)

Karo-lina-s [1.5K]

Answer:

B. No the ordered pair does not satisfy the equation

Step-by-step explanation:

y = -9x - 2

Substitute the point in and see if it is true

-37 = -9(4) -2

-37 = -36 -2

-37 = -38

This is not true so the point is not a solution

6 0

4 years ago

Batman slings a 320 ft. climbing cable from a helicopter to his batmobile below. If the cable tightens up

Leokris [45]

Answer:

188 ft

Step-by-step explanation:

helicopter

___________________________________________

|\ 54°

| \

| \ 320 ft

| \

| 54° \

-------------+--------------+-------------------------------

cos 54° = x/(320 ft)

x = 320 ft × cos 54°

x = 188 ft

Answer: 188 ft

5 0

2 years ago

Help with these questions

balandron [24]

9514 1404 393

Answer:

16) No

17) (c)

Step-by-step explanation:

For a lot of multiple-choice matrix problems, a simple test is all that is needed to determine the correct answer.

16) The determinant of A is (-2)(-2) -(2)(-3) = 10. So, we expect to see values in the inverse matrix that are 0.2 and 0.3. Alas, they're not there. The matrices are not inverses.

A^-1 = [[-.2, .3][-.2, -.2]]

17) The matrices are both 3×3, so their product is possible (eliminates choice D). The upper left term is different among the answer choices, so we can determine the correct one by computing that term only.

BA=C

c11 = (5)(1) +(7)(5) +(3)(-1) = 5 +35 -3 = 37

This matches the third choice (C).

If you use a calculator to compute the full matrix product, it matches choice C in all details.

6 0

3 years ago

If a cylindrical tank holds 100,00 gallons of water which can be drained from thebottom of the tank in an hour, then Torricelli’

tatyana61 [14]

Answer:

First, I think the right formula is:

$V(t) = 100,000(1-\frac{t}{60} ),20\leq t\leq 60$

A) We first derive the formula given above:

$V'(t)=-\frac{100000}{60}$

V'(t) represent the drain rate of the tank volume.

B) the units is: gallons/time

C) at V'(10) = 100000/60 = 1666.66 gallons/time.

because the formula V'(t) is constant so it doesn't depend of time.

5 0

4 years ago

Find three consecutive integers whose sum is equal to −354. Three consecutive integers in ascending form are __,__,__

mixer [17]

Answer: -119, -120, and -121

Step-by-step explanation: This problem states that the sum of three consecutive integers is -354 and it asks us to find the integers. Three consecutive integers can be represented as followed.

X ⇒ first integer

X + 1 ⇒ second integer

X + 2 ⇒ third integer

Since the sum of our three consecutive integers is -354, we can set up an equation to represent this.

X + X + 1 + X + 2 = -354

Now, we can simplify on the left side of the equation.

3x + 3 = -354

-3 -3 ← subtract 3 on both sides of the equation

3x = -357

÷3 ÷3 ← divide both sides by 3

X = -119

X ⇒ first integer = -119

X + 1 ⇒ second integer = -120

X + 2 ⇒ third integer = -121

Therefore, our three consecutive integers are -119, -120, and -121.

6 0

3 years ago

Read 2 more answers