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anygoal [31]
2 years ago
10

If sin θ = 1 over 3 and tan θ < 0, what is the value of cos θ?

Mathematics
1 answer:
alexira [117]2 years ago
3 0

Answer:

2√2 / 3 (first answer choice)

Step-by-step explanation:

If tan Ф < 0, then Ф must be in either Quadrant II or Quadrant IV.

If sin Ф = +1/3, then Ф (for this problem) is in Quadrant II.

Remembering that sin Ф = opp / hyp = 1 / 3, we use the Pythagorean Theorem to find the adj side:

adj² + 1² = 3²,  or

adj² + 1 = 9, or    adj² = 8.  Since Ф is in Quadrant II, adj is negative.

The value of cos Ф = adj / hyp = √8 / 3 = 2√2 / 3

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10x - 4(2x + 1) simpifly PLEASE
Natasha_Volkova [10]

Answer:

2x - 4

Step-by-step explanation:

10x - 4 ( 2x + 1 )

= 10x - 8x - 4

= 2x - 4

3 0
2 years ago
6. What are the zeroes for the<br>function<br>f(x) = 2x3 + 12x – 10x2?<br>​
agasfer [191]

Answer:

<h2>x = 0, x = 5 + √13 and x = 5 - √13.</h2>

Step-by-step explanation:

f(x) = 2x^3 + 12x – 10x^2 can and should be rewritten in descending powers of x:  

f(x) = 2x^3 – 10x^2 + 12x

This, in turn, can be factored into f(x) = x·(x² - 10x + 12).

Setting this last result = to 0 results in f(x) = x·(x² - 10x + 12).

Thus, x = 0 is one root.  Two more roots come from x² - 10x + 12 = 0.

Let's "complete the square" to solve this equation.

Rewrite x² - 10x + 12 = 0  as  x² - 10x +              12 = 0.

a) Identify the coefficient of the x term.  It is -10.

b) take half of this result:  -5

c) square this last result:  (-5)² = 25.

d) Add this 25 to both sides of x² - 10x +              12 = 0:

     x² - 10x +  25      +      12 = 0 + 25

e) rewrite x² - 10x +  25 as the square of a binomial:

       (x - 5)² = 13

f)  taking the sqrt of both sides:  x - 5 = ±√13

g) write out the zeros:  x = 5 + √13 and x = 5 - √13.

The three roots are x = 0, x = 5 + √13 and x = 5 - √13.

8 0
3 years ago
Find the volume of a square pyramid with base edges of 30 cm and a slant height of 39 cm
belka [17]

Answer:

390cm

Step-by-step explanation:

5 0
3 years ago
Can I get some help on these two
tia_tia [17]

9514 1404 393

Answer:

  cone: 138.16 in²

  pyramid: 352 m²

Step-by-step explanation:

Use the appropriate formula from your list of area and volume formulas.

<u>Area of a Cone</u>

  A = πr(r +h) . . . . . where r is the radius and h is the slant height

The radius is half the diameter, so is 4 inches.

  A = π(4 in)(4 in + 7 in) = 44π in² ≈ 138.16 in²

__

<u>Lateral Area of a Square Pyramid</u>

  A = 2sh . . . . . where s is the side length of the base and h is the slant height

  A = 2(8 m)(22 m) = 352 m²

3 0
2 years ago
Help with question number one please
coldgirl [10]

Answer:

165 hits

Step-by-step explanation:

27.5% of 600 is 600 x 27.5 / 100 = 165

4 0
2 years ago
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