O que é temperatura?

5. A leaky faucet drips at the rate of 300 mL per hour. How long will it take to fill a 10 liter container?

In-s [12.5K]

it will take to fill a 10 liter container= 33.3 hours

6 0

3 years ago

9. A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

SSSSS [86.1K]

Answer:

Part 4) $r=84\ units$

Part 9) $sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) $sin(\theta)=-\frac{9\sqrt{202}}{202}$

Step-by-step explanation:

Part 4) A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

we know that

The circumference of a circle subtends a central angle of 360 degrees

The circumference is equal to

$C=2\pi r$

using proportion

$\frac{2\pi r}{360^o}=\frac{56\pi}{120^o}$

simplify

$\frac{r}{180^o}=\frac{56}{120^o}$

solve for r

$r=\frac{56}{120^o}(180^o)$

$r=84\ units$

Part 9) Given cos(∅)=-2/3 and ∅ lies in Quadrant III. Find the exact value of sin(∅) in simplified form

Remember the trigonometric identity

$cos^2(\theta)+sin^2(\theta)=1$

we have

$cos(\theta)=-\frac{2}{3}$

substitute the given value

$(-\frac{2}{3})^2+sin^2(\theta)=1$

$\frac{4}{9}+sin^2(\theta)=1$

$sin^2(\theta)=1-\frac{4}{9}$

$sin^2(\theta)=\frac{5}{9}$

square root both sides

$sin(\theta)=\pm\frac{\sqrt{5}}{3}$

we know that

If ∅ lies in Quadrant III

then

The value of sin(∅) is negative

$sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) The terminal side of ∅ passes through the point (11,-9). What is the exact value of sin(∅) in simplified form?

see the attached figure to better understand the problem

In the right triangle ABC of the figure

$sin(\theta)=\frac{BC}{AC}$

Find the length side AC applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=11^2+9^2$

$AC^2=202$

$AC=\sqrt{202}\ units$

so

$sin(\theta)=\frac{9}{\sqrt{202}}$

simplify

$sin(\theta)=\frac{9\sqrt{202}}{202}$

Remember that

The point (11,-9) lies in Quadrant IV

then

The value of sin(∅) is negative

therefore

$sin(\theta)=-\frac{9\sqrt{202}}{202}$

5 0

3 years ago

Express 20 cm to 400 mm in simplest form

solong [7]

Answer:

Step-by-step explanation:

36/24 or 3/2

4 0

3 years ago

Classify the triangle based on its sides

Klio2033 [76]

<h2>It is an equilateral triangle </h2>

If you are helped with my answer pls tag me brianliest

I really want it

THANK YOU........

8 0

2 years ago

A square in a rectangle have the same perimeter. The length of a side of the square is 4x-1. The length of the rectangle is 2x+2

Thepotemich [5.8K]

The value x is 1, if the perimeter of square and rectangle are same. The perimeter of square and rectangle is 12 units.

Step-by-step explanation:

The given is,

A square in a rectangle have the same perimeter

The length of a side of the square is 4x-1

The length of the rectangle is 2x+2 and width is 2x

Step:1

Let, a - Side of square

l - Length of the rectangle

w - Width of the rectangle

Step:2

Formula for perimeter of square is,

$p=4a$ .............................(1)

Formula for perimeter of rectangle is,

$p=2(l+w)$ ....................(2)

Step:3

From given,

Equation (1) = Equation (2)

$4a = 2 (l+w)$

where,

a = 4x-1

l = 2x+2

w = 2x

Substitute the values,

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

16x - 4 = 2 (4x + 2)

16x - 4 = 8x + 4

16x - 8x = 8

8x = 8

x = 1

Step:4

Substitute the values of x,

a = 4(1)-1 = 3

l = 2(1)+2) = 4

w = 2(1) = 2

Perimeter of square and rectangle is 12 units

Result:

The value x is 1, if the perimeter of square and rectangle are same. The perimeter of square and rectangle is 12 units.

5 0

2 years ago

O que é temperatura?​

O que é temperatura?