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Ira Lisetskai [31]
3 years ago
11

Tennis star Rafael Nadal lost at the Australian Open. How many Grand Slams has he won?

Mathematics
1 answer:
cluponka [151]3 years ago
4 0

Answer:

Nadal won but it is the only major he hasn't won at least twice with 13 at Roland Harris four at the U.S

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Find all solutions ​
Anton [14]

Answer:

The solutions of the equation are 0 , π

Step-by-step explanation:

* Lets revise some trigonometric identities

- sin² Ф + cos² Ф = 1

- tan² Ф + 1 = sec² Ф

* Lets solve the equation

∵ tan² x sec² x + 2 sec² x - tan² x = 2

- Replace sec² x by tan² x + 1 in the equation

∴ tan² x (tan² x + 1) + 2(tan² x + 1) - tan² x = 2

∴ tan^4 x + tan² x + 2 tan² x + 2 - tan² x = 2 ⇒ add the like terms

∴ tan^4 x + 2 tan² x + 2 = 2 ⇒ subtract 2 from both sides

∴ tan^4 x + 2 tan² x = 0

- Factorize the binomial by taking tan² x as a common factor

∴ tan² x (tan² x + 2) = 0

∴ tan² x = 0

<em>OR</em>

∴ tan² x + 2 = 0

∵ 0 ≤ x < 2π

∵ tan² x = 0 ⇒ take √ for both sides

∴ tan x = 0

∵ tan 0 = 0 , tan π = 0

∴ x = 0

∴ x = π

<em>OR</em>

∵ tan² x + 2 = 0 ⇒ subtract 2 from both sides

∴ tan² x = -2 ⇒ no square root for negative value

∴ tan² x = -2 is refused

∴ The solutions of the equation are 0 , π

4 0
3 years ago
Read 2 more answers
Which expression is equal to f(x)/g(x)
Pani-rosa [81]

Answer: i'd say c

Step-by-step explanation:

8 0
3 years ago
Question 26 pleaseee
LuckyWell [14K]

Answer:

The inequality is 55+10x\leq 105

The greatest length of time Jeremy can rent the jet ski is 5 and Jeremy can rent maximum of 135 minutes.

Step-by-step explanation:

Given: Cost of first hour rent of jet ski is $55

          Cost of each additional 15 minutes of jet ski is $10

          Jeremy can spend no more than $105

Assuming the number of additional 15-minutes increment be "x"

Jeremy´s total spending would be first hour rental fees and additional charges for each 15-minutes of jet ski.

Lets put up an expression for total spending of Jeremy.

\$55+ \$ 10\times x

We also know that Jeremy can not spend more than $105

∴ Putting up the total spending of Jeremy in an inequality.

\$ 55+\$10x\leq \$ 105

Now solving the inequality to find the greatest number of time Jeremy can rent the jet ski,

⇒ \$ 55+\$10x\leq \$105

Subtracting both side by 55

⇒ \$ 10x\leq \$50

Dividing both side by 10

⇒x\leq \frac{50}{10}

∴ x\leq 5

Therefore, Jeremy can rent for 60\ minutes + 5\times 15\\= 60\ minutes + 75= 135\ minutes

Jeremy can rent maximum of 135 minutes.

5 0
3 years ago
What is the domain of f?
zmey [24]

Answer:

I hope C

Step-by-step explanation:

if I'm wrong please let me know

8 0
3 years ago
Read 2 more answers
Help is appreciated! Thanks!
sukhopar [10]

Answer:

  1. 16√3
  2. -45+15i
  3. √255
  4. 6√2 +3√10

Step-by-step explanation:

1)

-4i\sqrt{-48}=-4i\sqrt{(-1)(4^2)(3)}=(-4i)(4i)\sqrt{3}=16\sqrt{3}

__

2)

(-5-5i)(3-6i)=-5(3-6i)-5i(3-6i)=-15+30i-15i+30i^2=-15-30+15i\\\\=-45+15i

__

3)

\sqrt{3}\sqrt{5}\sqrt{17}=\sqrt{3\cdot 5\cdot 17}=\sqrt{255}

__

4)

\sqrt{3}(\sqrt{24}+\sqrt{30})=\sqrt{3\cdot 24}+\sqrt{3\cdot 30}=\sqrt{6^2\cdot 2}+\sqrt{3^2\cdot 10}\\\\=6\sqrt{2}+3\sqrt{10}

_____

The applicable identities are ...

\sqrt{a^2b}=a\sqrt{b}\\\\i^2=-1

7 0
3 years ago
Read 2 more answers
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