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lions [1.4K]
3 years ago
8

Given that tan theta = -4/7, and 270° < theta < 360°, what is the exact value of sec theta​

Mathematics
1 answer:
aleksley [76]3 years ago
6 0

Answer:

sec Θ = \frac{\sqrt{65} }{7}

Step-by-step explanation:

Using the trigonometric identity

sec²Θ = tan²Θ + 1

Since 270° < Θ < 360° ← that is fourth quadrant, then

sec Θ > 0, thus

sec²Θ = (- \frac{4}{7})² + 1 = \frac{16}{49} + 1 = \frac{65}{49}, then

sec Θ = \sqrt{\frac{65}{49} } = \frac{\sqrt{65} }{7}

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A company buys computers and printers. Each computer costs $550 and each printer costs $390. If the company spends $8160 and buy
maxonik [38]

Answer:the company bought 12 computers and 4 printers.

Step-by-step explanation:

Let x represent the number of computers that the company bought.

Let y represent the number of printers that the company bought.

The company buys a total of 16 machines. It means that

x + y = 16

Each computer costs $550 and each printer costs $390. If the company spends $8160 for all the computers and printers that was bought, it means that

550x + 390y = 8160 - - - - - - - - - - 1

Substituting x = 16 - y into equation 1, it becomes

550(16 - y) + 390y = 8160

8800 - 550y + 390y = 8160

- 550y + 390y = 8160 - 8800

- 160y = - 640

y = - 640/ - 160

y = 4

Substituting y = 4 into x = 16 - y, it becomes

x = 16 - 4

x = 12

6 0
3 years ago
- Write an equation of a line in standard
____ [38]

Answer:

3x+7

Step-by-step explanation:

Simply changing the y intercept will make both lines parallel without changing its slope

5 0
3 years ago
HELPPPP!!!
Anuta_ua [19.1K]

Answer:

  A = √29

Step-by-step explanation:

The short of it is that ...

  A² = 2² + 5² = 29

  A = √29

_____

<u>Amplitude</u>

If you expand the second form using the sum-of-angles formula, you get ...

  Asin(ωt +φ) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)

Comparing this to the first form, you find ...

  c₂ = 2 = Acos(φ)

  c₁ = 5 = Asin(φ)

The Pythagorean identity can be invoked to simplify the sum of squares:

  (Asin(φ))² + (Acos(φ))² = A²(sin(φ)² +cos(φ)²) = A²·1 = A²

In terms of c₁ and c₂, this is ...

  (c₁)² +(c₂)² = A²

  A = √((c₁)² +(c₂)²) . . . . . . . formula for amplitude

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<u>Phase Shift</u>

We know that tan(φ) = sin(φ)/cos(φ) = (Asin(φ))/(Acos(φ)) = 5/2, so ...

  φ = arctan(c₁/c₂) . . . . . . . formula for phase shift*

  φ = arctan(5/2) ≈ 1.19029 radians

___

* remember that c₁ is the coefficient of the cosine term, and c₂ is the coefficient of the sine term.

3 0
3 years ago
Which of the following are ordered pairs for the equation y = 1/3x + 1?
Brrunno [24]

answer : (0,1) (3,2) (6,3)

8 0
3 years ago
A young sumo wrestler goes on a special diet to gain weight.
Mama L [17]

Answer:

90.8

Step-by-step explanation:

w = 80 + 5.4t              (fill in your variable t, the number of months)

w = 80 + 5.4(2)           (Combine parentheses first)

w = 80 + 10.8              (Add the two together)

w = 90.8                      (Your answer)

I hope this helped :)

6 0
2 years ago
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