If sin θ = 0.57 then sin (π-θ)=?

Answers

Answer 1

Answer: In trigonometry laws, there's a equation to solve this problem :
sin (a-b) = sin(a) . cos(b) - sin (b) . cos(a),

so by assuming that a = π, b = θ, so the equation will be like this..
sin (π-θ) = sin(π) . cos(θ) - sin (θ) . cos(π),
= 0 . cos(θ) - sin(θ) . (-1)
= sin(θ) = 0.57

Hope this will help you :)

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Round to the nearest hundredth. 7.546
A. 7.546
B. 7.55
C. 7
D. 7.5

Answers

7.55 would be correct because if there is a 5 or greater it goes up a number if it is a 4 or lower it stays the same

B. 7.55

7.546⇒the underlined is the hundredths place
When rounding it to nearest hundredth, you will look at the digit next to it at the right.
7.546⇒six is greater than 5 so the hundredths place would round up to the next digit which is 5.
$7.546-7.55$

the sum of two numbers is 60. the larger number is 12 more than the smaller number. what is the number?

Answers

The larger number is: 36
The smaller number is: 24

Firstly, if a number is 12 more than the other, that means that the difference between the two numbers is 12

If you divide 60 by 2, you get two 30's. Then, if you add 6 to one of the 30's and then subtract 6 to the other 30, resulting in 36 and 24, you get set of numbers which equal 60 and also have a difference of 12.

Find the second derivative for y=(x+2)/(x-3)

Answers

Let's find the first derivative.

Using quotient rule

$f(x)=(g(x))/(h(x))$

$f'(x)=(g'(x)*h(x)-g(x)*h'(x))/(h^2(x))$

then:

$y=(x+2)/(x-3)$
$f(x)=y$

$g(x)=x+2$

$g'(x)=1$

$h(x)=x-3$

$h'(x)=1$

Let's replace

$f'(x)=(g'(x)*h(x)-g(x)*h'(x))/(h^2(x))$

$y'=(1*(x-3)-(x+2)*1)/((x-3)^2)$

$y'=(x-3-x-2)/((x-3)^2)$

$\boxed{y'=(-5)/((x-3)^2)}$

the second derivative is the derivative of our first derivative.

$y'=(-5)/((x-3)^2)$

We can write this function as

$y'=-5*(x-3)^(-2)$

now we have to use the Chain rule's

$f(u)=-5u^(-2)$

and

$g(x)=x-3$

$f[g(x)]=-5*(x-3)^(-2)$

then

$f'[g(x)]=f'(u)*g'(x)$

$f'(u)=-5*(-2)*u^(-3)=10*u^(-3)$

$g'(x)=1$

$f'[g(x)]=f'(u)*g'(x)$

Let's replace

$f'[g(x)]=10*u^(-3)*1$

Let's change u by $(x-3)$

$f'[g(x)]=10*u^(-3)$

$f'[g(x)]=10*(x-3)^(-3)$

$\boxed{\boxed{y''=(10)/((x-3)^(3))}}$

Examine the two-way frequency table below.Score: 90-100 Score: 70-89 Score: 0-69
Math Test 20 40 7
Science Test 15 35 5
Which percentage of students took the math test and received a grade of 90 or above?

16.39%

29.85%

57.14%

28.69%
Let event A = "math test" and event B = "Score: 90-100." Then find , where

Answers

To find the percentage of students who took the math test and received a grade of 90 or above, we need to calculate the conditional probability P(A ∩ B), which is the probability of event A ("math test") and event B ("Score: 90-100") happening simultaneously.

From the two-way frequency table:

The number of students who took the math test and received a grade of 90 or above is 20.

The total number of students who took the math test is 20 + 40 + 7 = 67.

Now, we can calculate the conditional probability:

P(A ∩ B) = (Number of students who took the math test and received a grade of 90 or above) / (Total number of students who took the math test) × 100%

P(A ∩ B) = 20 / 67 × 100% ≈ 29.85%

So, the percentage of students who took the math test and received a grade of 90 or above is approximately 29.85%.

Jennifer is going on a hike to the top of a mountain. It will take 3 hours and 55 minutes to hike up the mountain and 1 hour and 10 minutes to hike back down. If Jennifer wants to finish the hike by 3:45 P.M., what is the latest time she can start the hike up the mountain? Include A.M. or P.M. in your answer (for example, 11:58 A.M.).

Answers

Answer: 10:40 AM

====================================================

Explanation:

Add the minutes for now

55 minutes + 10 minutes = 65 minutes = 60 minutes + 5 minutes = 1 hour, 5 minutes

The minute portions add to 1 hour, 5 minutes. The hour portions add to 3+1 = 4.

Add on the "1 hour, 5 minute" portion and we get 5 hours, 5 minutes

This is the total duration of the round trip hike. Keep in mind that this does not include any time spent with Jennifer resting at the top of the mountain. This time duration assumes that once she gets to the top, she pretty much starts the hike back down the mountain.

----------------------------

Now convert 3:45 PM to military time. We add 12 hours to get 15:45

Subtract off 5 minutes to get 15:40

Then subtract off 5 hours to get 10:40, which converts back to 12-hour time notation to be 10:40 AM

Choose an object that is about the same length as a baseball bat

Answers

The length of the baseball bat differs in length depending on the type of tournament. The length varies from 29 to 34 inches. An example of an object with the length almost similar to these measurements is a 24 - 36 inches T-square.

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