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If 0 < x < π/2, then both sin(x) and cos(x) are positive.

From the Pythagorean identity, we then have

cos²(x) + sin²(x) = 1

⇒   cos(x) = + √(1 - sin²(x))   and   sin(x) = + √(1 - cos²(x))

Then

√(1 - cos²(x))/sin(x) = sin(x)/sin(x) = 1

and

√(1 - sin²(x))/cos(x) = cos(x)/cos(x) = 1

so that the overall expression reduces to

1 - 1 = 0

Answer:

During the first half of the race, he walked 3 miles and ran at a rate of 5 miles per hour for x hours.y = 5x + 3

During the second half of the race, he walked for 2 miles and ran at a rate of 5.5 miles per hour for x hours. y = 5.5x + 2

Then using both equations will be:

y = 5x + 3

y = 5.5x + 2

Subtract the equations

0.5x = 1

x = 1/0.5 = 2

Therefore, the value of y will be:

y = 5x + 3 = 5(2) + 3 = 13

Answer: 15 DVDs

Step-by-step explanation:

C = 2D + 11

41 = 2D + 11

2D = 30

D = 15 DVDs

Answer:

pentagon

Step-by-step explanation:

5 degree angle

Answer:

4.  9  

5.    5x

Step-by-step explanation:

its an isocoles

Answer:

17,576,000 different combinations possible.

Step-by-step explanation:

Answer:

y-intercept: (0,5)

x-intercept: (5/2,0)

Step-by-step explanation:

[tex]-4x+7=2y-3[/tex]

[tex]-4(0)+7=2y-3[/tex]

[tex]0+7=2y-3[/tex]

[tex]7=2y-3[/tex]

[tex]10=2y[/tex]

[tex]5=y[/tex] <-- y-intercept: (0,5)

[tex]-4x+7=2y-3[/tex]

[tex]-4x+7=2(0)-3[/tex]

[tex]-4x+7=-3[/tex]

[tex]-4x=-10[/tex]

[tex]x=\frac{5}{2}[/tex] <-- x-intercept: (5/2,0)

Answer:4/9 pizzas

Step-by-step explanation:

The weight of substance remaining after 13 years is 2.25 g.

Given:

Present weight of substance = 12 g

After 8 years weight remains = 6 gm

Now, weight loss in 8 year will be,

12-6=6 gm

So, weight loss in 1 year will be,

[tex]\dfrac{6}{8} =\dfrac{3}{4}[/tex]

Total weight loss in 13 year will be,

[tex]\dfrac{3}{4}\times13=9.75[/tex]

The weight of substance remaining after 13 years will be,

[tex]12- 9.75 = 2.25 \;\rm g[/tex]

Therefore, the weight of substance remaining after 13 years is 2.25 g.

To know more about radioactive decay, refer to the link:

https://brainly.com/question/12116123

Answer:

19%

Step-by-step explanation:

Percentage increase = ( (final value - original value) / original value ) x 100

= ( ($71.40 - $60.00) / $60.00 ) x 100

= 19%

[tex]71.40 - 60 = 11.40[/tex]

to find the increase of percentage, divide the amount of increasing price with intial price and multiply with 100%

[tex] \frac{11.40}{60} \times 100\% = 19\%[/tex]

so the cost of jacket has increased 19%

Answer:

if it is (2x-y)8

then it is 16x - 8y

[tex]x^0[/tex]y = 1.y = y

so the co efficient of y is -8

Step-by-step explanation:

3x(1-4x)+2(1-4x)

3x-12x²+2-8x

-5x-12x²+2

Answer: If the dress orginially priced at 8080 dollars and put for 25 percent, that means that you have to move the decimal point to the left twice which will result as 0.25 and 10 percent tax ends up as 0.10. Multiply the two and the product, you have to add to the 8080!

Step-by-step explanation:

29 Nickels

15 Dimes

Hope this is helpful!

Answer:

C

Step-by-step explanation:

Answer:

y = 1/4x

Step-by-step explanation:

[tex]5x + 6x + 7x = 54 \\ = > 18x = 54 \\ = > x = 3[/tex]

Answer:

The numbers are 15, 18 and 21.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

3,120

Step-by-step explanation:

hope it will help you

Answer:

37

Step-by-step explanation:

38 + u actually thought lol

Answer:

The awnser should be 4. (3x4 = 12, 12 x 4 = 48, 48 x 12 = 192, 192 x 4 = 768. )

Step-by-step explanation:

(Hope this helps, Happy holidays!!)

Answer:

162/20 Would be your answer, however, it wouldn't make sense as you can not switch students into decimals. Therefore, you could make 7 classes of 20, and one of 22, and 6 classes of 20, and two of 21. Therefore, there are two combinations that are possible.

Step-by-step explanation:

Refer to the answer.

Answer:

56

Step-by-step explanation:

Answer:

0.2 seconds

Step-by-step explanation:

The graph of b(t) = -16t^2 + 5t + 15 is a parabola opening downward.  The maximum value of b(t) occurs at the vertex.  The t-coordinate of the vertex is t = -5 / (2(-16)) = 5/32 = 0.15625 sec ≈ 0.2 sec.  

Answer:

A) 0.2 seconds

Step-by-step explanation:

[tex]b(t)=-16t^2+5t+15[/tex]

[tex]v(t)=-32t+5[/tex] <-- Take the derivative

[tex]0=-32t+5[/tex] <-- Set equal to 0

[tex]-5=-32t[/tex]

[tex]\frac{5}{32}=t[/tex]

[tex]t=\frac{5}{32}[/tex]

[tex]t\approx0.2[/tex]

Therefore, it will take the ball about 0.2 seconds to reach its maximum height (which happens to be about 15.4 feet BTW).

Alternatively, another non-calculus approach is the fact that the parabola opens downward, and as such, the maximum of [tex]b(t)[/tex] occurs at the vertex where [tex]t=-\frac{b}{2a}[/tex], therefore [tex]t=-\frac{5}{2(-16)}=\frac{-5}{-32}=\frac{5}{32}\approx0.2[/tex]

Answer:

  $24,000

Step-by-step explanation:

The difference for principal amount P is ...

  (8% × P) - (7 3/4% × P) = $60

  0.0025P = $60

  P = $24,000 . . . . . multiply by 400

His principal was $24,000.

Answer:

x = 4

Step-by-step explanation:

Square both sides

x+5 = 25-10sqrt(x)+x

20 = 10sqrt(x)

sqrt(x) = 2

Square both sides again

x=4

Verify sol

x = 4

Answer:

y = 4x + 5

Step-by-step explanation:

4 times the number of shirts, which is unknown, +$5 no matter how many.

Answer:

4x + 5

Step-by-step explanation:

Four multiplied by the number of shirts purchased (x) plus five dollars for shipping.

I hope this helps!!

Answer:

20 gallons of water.

Step-by-step explanation:

4 water bottles = 8 gallons

1 water bottle = 2 gallons

X = Number of Water bottles

N = Gallons Per Water Bottle

X * N

10 * 2

20

I can't see anything dude, you on something?

The distance across the river, given the angle of the line of sight and the

distance along the shoreline is found using trigonometric ratios.

Reasons:

The distance along the the shore Shawna walked before sighting across the river = 90 feet

The angle made by the line of sight and the shoreline, θ = 65°

Required:

The distance across the river.

Solution:

Taking the initial location of Shawna to be the closest place to point she wanted to go across the river, we have;

The shortest distance across the river = A perpendicular line

Therefore, the following sides, form a right triangle;

Where:

The line of sight = The hypotenuse side

The distance she walked = The adjacent side to angle 65° angle

The closest distance across the river = The opposite side to the 65° angle

By trigonometric ratio, we have;

Which gives;

Opposite side to angle = tan(θ) × Adjacent side to angle

Therefore;

Distance across the river = tan(65°) × 90 feet ≈ 193.0 feet

Learn more about trigonometric ratios here:

https://brainly.com/question/10270672

https://brainly.com/question/2560921

this answers is 8 am I right