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Mathematics

1 answer:

DaniilM [7]3 years ago

8 0

Answer:

what in the world is the first part

Step-by-step explanation:

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it cost $35 for one adult and two children to attend a show. It cost $60 for two adults and three children to attend the same sh

N76 [4]

Assume that,
adult = x
child = y

x+2y = 35 (1st equation)
2x+3y = 60 (2nd equation)
x = 35-2y (3rd equation)

Substitute 3 into 2 :

2(35-2y) + 3y =60
70-4y +3y = 60
y = 10

x+2y = 35
x+2(10) =35
x +20 =35
x = 15

One adult = $15

7 0

3 years ago

The sum of two numbers is 10. twice the first number is 4 more than twice the second. what are the two numbers?

Ludmilka [50]

X+ y = 10
2x = 2y+4

2x/2 = 2/2y+4/2
x = y + 2

x+y = 10
y+2+y=10
2y + 2 = 10
2y +2-2 =10-2
2y = 8
2y/2 =8/2
y = 4

x + y =10
x + 4 =10
x +4-4 =10-4
x = 6

Check
2x = 2y +4
2(6) = 2(4) +4
12 = 8+4
12= 12

6 0

3 years ago

Would appreciate the help !

aleksandr82 [10.1K]

This is one pathway to prove the identity.

Part 1

$\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{1}{\tan(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\cot(\theta) = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{\cos(\theta)}{\sin(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)*\sin(\theta)}{\sin(\theta)(1-\cos(\theta))}-\frac{\cos(\theta)(1-\cos(\theta))}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\$

Part 2

$\frac{\sin^2(\theta)}{\sin(\theta)(1-\cos(\theta))}-\frac{\cos(\theta)-\cos^2(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{\sin^2(\theta)-(\cos(\theta)-\cos^2(\theta))}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{\sin^2(\theta)-\cos(\theta)+\cos^2(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\$

Part 3

$\frac{\sin^2(\theta)+\cos^2(\theta)-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1}{\sin(\theta)} = \frac{1}{\sin(\theta)} \ \ {\checkmark}\\\\$

As the steps above show, the goal is to get both sides be the same identical expression. You should only work with one side to transform it into the other. In this case, the left side transforms while the right side stays fixed the entire time. The general rule is that you should convert the more complicated expression into a simpler form.

We use other previously established or proven trig identities to work through the steps. For example, I used the pythagorean identity $\sin^2(\theta)+\cos^2(\theta) = 1$ in the second to last step. I broke the steps into three parts to hopefully make it more manageable.