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2 years ago

Given Sin x= 0.5, what is cos x?

Mathematics

1 answer:

Svetllana [295]2 years ago

3 0

Sin x = 0.5
sin x = 1/2
sin x = opp/hyp
therefore the ratio of opp/hyp = 1/2, (opp = 1, hyp = 2)

Find the opp side

1² + x² = 2²
1 + x² = 4
x² = 4 -1
x² = 3
x =√3

The opp side is √3

cos x = opp/hyp = √3/2 = 0.87 (round to the nearest hundredths)

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Your favorite craft store had a weekend sale. On the first day, all $10 items were 70% off. You bought some number of these of t

Svet_ta [14]

For the first day we have the following function:
f (n) = (0.3 * 10) n + 8
For the second day we have the following function:
f (n) = (0.4 * 10) n + 5
You spent the same amount of money as the day before:
(0.3 * 10) n + 8 = (0.4 * 10) n + 5
3n + 8 = 4n + 5
n = 8-5
n = 3 items
We evaluate each function for n = 3
f (3) = (0.3 * 10) * 3 + 8 = 17 $
f (3) = (0.4 * 10) * 3 + 5 = 17 $
The total amount of money is:
17 + 17 = 34 $
Answer:
you purchase 6 items
you spend at the craft store during the sale $ 34

8 0

3 years ago

A college writing seminar increased its size by 50\PP, percent from the first to the second day. If the total number of students

Jobisdone [24]

Answer: There were 10 students in the class on the first day.

Step-by-step explanation:

Let x be the number of students of the first day.

Given: A college writing seminar increased its size by 50 percent from the first to the second day.

i.e. Number of students on second day = (Number of students on first day)+(50% of Number of students on first day)

= x +50% of x

= x+0.50x

= (1.50)x

=1.50x

Since, it is given that the total number of students in the seminar on the second day was 15.

i.e. $1.50x=15$

$\Rightarrow\ x=\dfrac{15}{1.5}\Rightarrow\ x=\dfrac{150}{15}\\\\\Rightarrow\ x=10$

Hence, there were 10 students in the class on the first day.

7 0

3 years ago

a bookstore has 780,000 and sales revenue in 2005 $190,000 2011 assuming a constant annual rate of decrease what is the predicte

AysviL [449]

Answer5,90,000

Step-by-step explanation:

780,000 subtract 190,000 = 590,000

after every 6 years

i'm not sure if its correct. please let me know

7 0

2 years ago

Find the X and Y<br> Help ASAP please!!!

Aleksandr-060686 [28]

The answer is X=23 and y=9

4 0

3 years ago

Hi, the answer is K but can anyone show why

dlinn [17]

Let's do 51 and 52.

51. The contrapositive has the same truth value as the original statement. That's opposed to the converse, which may or may not be true independent of the original statement.

The contrapositive of IF P THEN Q is IF not Q THEN not P. They're equivalent. Here that's If the cat is not female then it is not tricolor.

Answer: C

52.

$(x^3)^{(4-b^2)}=1$

$x^{3(4-b^2)} = 1$

For the statement to be true, the exponent must be zero:

$3(4-b^2) = 0$

$b^2 = 4$

$b = \pm 2$

Both positive 2 and negative 2 have a square of 4.

Answer: K

By the way, usually we assume $0^0=1$ so the restriction that $x \ne 0$ isn't really necessary. Think of the definition of a polynomial or the binomial expansion:

$\displaystyle f(x)=\sum_{k=0}^n a_k x^k$

$\displaystyle(x+y)^n=\sum_{k=0}^n {n \choose k} x^{k}y^{n-k}$

For these common equalities to work when $x=0$ we need to define $0^0=1$

3 0

3 years ago