Simplify the trigonometric function

Answer:

the answer is c

Step-by-step explanation:

Answer: C. 25π/3 cm²

Step-by-step explanation:

The sector is an area of a circle bounded by two radii. The formula for determining the area of a sector is expressed as

Area of sector = θ/360 × πr²

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = 10 cm

θ = 30 degrees

Therefore,

Area of sector = 30/360 × π × 10²

= 3000π/360 = 25π/3 cm²

Answer:

[tex]625 m^2[/tex]

Step-by-step explanation:

In this problem, we are told that the area of the garden is given by the expression

[tex]A(w)=-(w-25)^2+625[/tex]

where

w is the width of the garden (in meters)

Here we want to find the maximum possible area.

The maximum of a function f(x) can be found by requiring that its first derivative is zero:

[tex]f'(x)=0[/tex]

Therefore, here we have to calculate the derivative of [tex]A(w)=0[/tex] and find the value of w for which it is equal to zero.

Let's start by rewriting the area function as

[tex]A(w)=-(w^2-50w+625)+625=-w^2+50w[/tex]

Now we calculate the derivative with respect to w:

[tex]A'(w)=-2w+50[/tex]

Now we require this derivative to be zero, so

[tex]-2w+50=0\\w=-\frac{50}{-2}=25 m[/tex]

So now we can substitute this value of w into the expression of A(w) to find the maximum possible area:

[tex]A(25)=-(25-25)^2+625 = 625 m^2[/tex]

This value is allowed because we know that the maximum length of the perimeter of the fence is 100 meters; If the garden has a square shape, the length of each side is [tex]L=\frac{100}{4}=25 m[/tex], and the area of the squared garden is

[tex]A=L^2=(25)^2=625 m^2[/tex]

Which is equal to what we found earlier: this means that the maximum area is achieved if the garden has a squared shape.

Answer:

Step-by-step explanation:

Answer:

Sol set = {12, 13, 14, 15, 16, 17,....... ".}

Step-by-step explanation:

[tex](z + 4) > 15 \\ z + 4 > 15 \\ z > 15 - 4 \\ z > 11 \\ z = \{12, \: 13, \: 14, \: 15, \: 16, \: 17, ........... \}[/tex]

Replacing the ordered pairs into the equation, we find that the correct option is:

The equation is:

[tex]y + 1 = 3(x - 4)[/tex]

An ordered pair (x,y) is a solution to the equation if we replace (x,y) in the equation and get an identity.

Test if (4,-1) is a solution:

[tex]-1 + 1 = 3(4 - 4)[/tex]

[tex]0 = 0[/tex]

Identity, so it is.

Test if (5,2) is a solution:

[tex]2 + 1 = 3(5 - 4)[/tex]

[tex]3 = 3[/tex]

Identity, so it is.

Hence, both is the correct option.

You can learn more about ordered pairs at https://brainly.com/question/10585472

Final answer:

To find the length of the child's shadow, set up a proportion comparing the woman's height and shadow length to the child's height and unknown shadow length. Solving the proportion 64/40 = 58/Child's shadow, we find that the child's shadow is approximately 36.25 inches long.

Explanation:

The question involves using proportions to calculate the length of the child’s shadow. Since the child is shorter than the woman, we can expect that the child’s shadow will also be shorter in proportion to her height. The woman is 5 feet and 4 inches tall, which converts to 64 inches. The shadow to height ratio is the same for both individuals because they are standing under the same lighting conditions.

We can set up a proportion using the woman’s height and shadow length to find the child’s shadow length:

Woman’s height / Woman’s shadow = Child’s height / Child’s shadow

64 inches / 40 inches = 58 inches / Child’s shadow

To solve for the child’s shadow, we cross-multiply:

64 * Child’s shadow = 58 * 40

Child’s shadow = (58 * 40) / 64

Child’s shadow = 2320 / 64

Child’s shadow = 36.25 inches

Therefore, the child’s shadow is roughly 36.25 inches long.

Answer:

1.24 kilograms per cubic meter.

Step-by-step explanation:

The air density is "[tex]1.24\ \frac{kg}{m^3}[/tex]"

The initial weight of 7 ball [tex]= 0.615 \ kg\\\\[/tex]

weight of 7 inflated balls[tex]= 0.624 \ kg\\\\[/tex]

Calculating the mass (weight) of 7 air:

[tex]\to 0.624-0.615\ kg\\\\ \to 0.009\ kg\\\\[/tex]

Calculating the diameter of 7 balls:

[tex]\to 0.24 \ m\\\\[/tex]

Calculating the Radius of the ball:

[tex]\to \frac{\text{diameter}}{2}\\\\ \to \frac{0.24}{2}\\\\ \to 0.12\ m\\\\[/tex]

Calculating the volume of air in the ball:

[tex]\to \frac{4}{3} \pi r^3\\\\\to \frac{4}{3} \pi (0.12)^3 \\\\ \to 1.333333 \times 3.14 \times 0.001728 \\\\ \to 0.00723456\\\\[/tex]

Calculating the density of air:

[tex]\to \text{Air density}=\frac{\text{Mass}}{\text{volume}}\\\\[/tex]

                      [tex]=\frac{ 0.009}{0.00723456}\ \frac{kg}{m^3}\\\\ =1.244\ \frac{kg}{m^3} \\\\=1.24\ \frac{kg}{m^3}[/tex]

Therefore, the air density is "[tex]1.24\ \frac{kg}{m^3}[/tex]".

Find out more information about the air density here:

brainly.com/question/6070675

Answer:  7 yards will be your answer.

Step-by-step explanation:  I tried.  Sorry if the answer is wrong!

Answer:

8 yards

Step-by-step explanation:

The small triangle is inside the big triangle and shares two of it's legs which means it is similar to the big triangle.

12:15

x:10

4:5

x must be 8

Answer:

C) 109.5

Step-by-step explanation:

Use cosine of 64°

cos 64° = 48/x

Put x on one side

x = 48/ cos 64°

x = 109.4962576

Answer:

The answer is C or 109.5 units

Step-by-step explanation:

We have to use the trig function cosine to find the answer.

cosine = [tex]\frac{adjacent}{hypotenuse}[/tex]

cosine of 64 = 0.438371147

the equation is:      cos 64 = [tex]\frac{48}{hypotenuse}[/tex]

So using this equation,

we must divide 48 by the cosine of 64 to get the hypotenuse

this equals 109.5

The hypotenuse is our length that we need to find so the question is solved.

Hope This helps

Branliest is appreciated!

Answer:

20π or 62.8 roughly

Step-by-step explanation:

Hello!

The formula for finding the circumference of a circle is 2rπ:

In that case, all we have to do is substitute 10m for our r.

2 × 10 = 20.

So circumference will be 20π.

Using 3.14 for π:

We get that 62.8 is a rough estimate for the circumference.

Really, it's 62.831..... going on forever since π is irrational.

Thus, the answer exactly is [tex]\boxed{20\:\pi}}[/tex].

Hope this helps!

Final answer:

The circumference of a clock with a radius of 10m is calculated using the formula C = 2πr, resulting in a circumference of 20π m or approximately 62.83185 m when using the approximate value of π (3.14159).

Explanation:

The circumference of a clock can be calculated using the formula for the circumference of a circle which is C = 2πr, where C is the circumference and r is the radius of the clock. Given that the radius of the clock is 10m, we substitute the value into the formula to get the circumference.

So, the circumference of the clock is C = 2π(10m) = 20π m.

The exact value of π (π is approximately 3.14159) would allow us to find the numerical value for the circumference, which would be approximately C ≈ 62.83185 m.

Answer:

The answer is b

Step-by-step explanation:

Because i just did it and got it right

Answer:

B

Step-by-step explanation:

just got it right

Answer: 36 pi over 7.5

Step-by-step explanation:

Answer:

The area is 0.002m² to 3 dp

Step-by-step explanation:

This problem bothers on the mensuration of flat shapes(I.e cross sectional area of pipe ) , this time the a circle.

It requires us to look for the area of the shape

Given data

Diameter d = 5cm

Converting to mm = 5/100= 0.05m

Radius of circle r=d/2=0.05/2 =0.025mm

Given the area of the circle

A=πr²

A=3.14*0.025²

A=0.0019m²

To 3 dp we have area as 0.002m²

Answer:

45

Step-by-step explanation:

Taking into account the definition of equation and percentage, 30 percent of 120 is the same as 80 percent of 45.

An equation is defined as an established equality between two expressions, in which there may be one or more unknowns or variables.

So solving an equation consists of finding the value or values ​​of the variables so that they fulfill the equality represented in the equation. That is, when changing the variable for the solution found, the equality must be true.

On the other side, the percentage is a value that represents the proportionality between two established quantities. That is, the percentage tells what part of a total represents a quantity.

Mathematically, the percentage is the division between an initial quantity and the total quantity, all multiplied by one hundred.

And to calculate the percentage of a quantity, the quantity is multiplied by the percentage and divided by 100. Then, 30 percent of 120 can be expressed as: (30×120)÷100

On the other hand, 80 percent of a number can be expressed as: (80×number)÷100

Since 30 percent of 120 must be the same as 80 percent of an unknown number, the following equation can be expressed:

(30×120)÷100= (80×number)÷100

Solving:

3600 ÷100= (80×number)÷100

36= (80×number)÷100

36×100= 80×number

3600= 80× number

3600÷ 80= number

45= number

The, 30 percent of 120 is the same as 80 percent of 45.

Learn more about percentage with this examples:

Answer:

d

Step-by-step explanation:

{MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF}

Use a tree diagram to list the possibilities.

Answer:

The answer is D

Step-by-step explanation:

Answer:

The expression that represents the total amount of money raised from selling [tex]\(x\)[/tex]  flowerpots is [tex]\(15x\)[/tex].

Explanation:

The total amount of money raised from selling [tex]\(x\)[/tex] flowerpots can be represented by the expression:

[tex]\[ \text{Total amount of money} = \text{Price per flowerpot} \times \text{Number of flowerpots sold} \][/tex]

Given that each flowerpot sells for $15, and [tex]\(x\)[/tex] represents the number of flowerpots sold, the expression would be

[tex]\[ \text{Total amount of money} = 15x \][/tex]

So, the expression that represents the total amount of money raised from selling [tex]\(x\)[/tex] flowerpots is [tex]\(15x\)[/tex].

Answer:

14

Step-by-step explanation:

Answer: The answer is: 14

Step-by-step explanation: I just took that test!

Have a great day!

-Sunny

Answer:

The ratio of the surface areas and volume is 8((5y+5x) /25xy)

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes.

Let us assume that the radius =x

Radius r=5x/4

And the height =y

Height h= 5y/4

We know that the total surface area of a cylinder is

A total = 2πrh+2πr²

We can factor out 2πr

A total = 2πr(h+r)

The volume of a cylinder is given as

v= πr²h

The surface area and volume ratios

Can be expressed as

2πr(h+r)/πr²h= 2(h+r)/rh

= (2h+2r)/rh= 2h/rh + 2r/rh

= 2/r + 2/h

= 2(1/r + 1/h)

Substituting our value of x and y

For radius and height we have

= 2(1/5x/4 + 1/5y/4)

=2(4/5x + 4/5y)

=2*4(1/5x + 1/5y)

= 8 (5y+5x/25xy)

Answer:

Ratio of surface area = 25/16

Ratio of volume = 125/64

Step-by-step explanation:

The surface area and volume of a cylinder are given by the formulas:

Surface area = 2*(pi*r^2 + pi*r*h)

Volume = pi*r^2*h

If we increase the radius and height by 5/4, we have that:

New surface area = 2*(pi*(5/4*r)^2 + pi*(5/4)*r*(5/4)*h) = (5/4)^2 * 2*(pi*r^2 + pi*r*h) = (5/4)^2 * Surface area

New volume = pi*(5/4*r)^2*(5/4)*h = (5/4)^3 * pi*r^2*h = (5/4)^3 * Volume

So the ratios are:

ratio of surface area = New surface area / Surface area = (5/4)^2 = 25/16

ratio of volume = New volume / Volume = (5/4)^3 = 125/64

Answer:

99000 meters.

Step-by-step explanation:

We have the swimmer going at 50 m / s, and we want to know where he is going in 33.3 minutes.

The first thing is to pass the time from minutes to seconds, we know that 1 minutes is 60 seconds, therefore:

33.3 min * 60 s / 1 min = 1998 seconds

Now to know the distance is to multiply this time by the speed they give us, like this:

1998s * 50m / s = 99900 m

Which means that in that time and at the speed of the swimmer, he has traveled 99000 meters.

Answer:

1. D & F

2. A, C, D

Step-by-step explanation:

DID ON EDGE

None of the given graphs are identical. Their differences arise from the distinct characteristics of their specific square root or cube root functions, as well as the range of x-values they apply to.

None of the aforementioned graphs are identical. The syntax y=√x corresponds to the graph of the square root function, which is always positive and only defined for x≥0. On the other hand, the syntax y=-√x describes the graph that's a reflection of y=√x in the x-axis. However, y=∛x and y=-∛x both entail the cube root function, which is distinguishable from the square root function by its shape and the fact it includes values for negative x. Lastly, y=√-x and y=∛-x are not properly defined real functions, since taking square or cube roots of negative x values leads to complex numbers.

https://brainly.com/question/35883921

#SPJ2

Answer:

$81,269.53

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 3.4% into a decimal:

3.4% -> [tex]\frac{3.4}{100}[/tex] -> 0.034

Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:

[tex]A=56,000(1+\frac{0.034}{4})^{4(11)}[/tex]

[tex]A=81,269.53[/tex]

After 11 years, you will have $81,269.53

In this scenario, a bungee jumper's total distance traveled can be calculated using a geometric series. The initial drop is the bridge's total height, and each following jump is 75% of the previous one. Summing this series gives the total downward and upward travel.

This problem is a classic example of a geometric series used in mathematics. The first downward travel is the entire height of the bridge, 876 feet. Each consecutive downward travel will be 75% of the previous downward travel, as the question specifies that the jumper rebounds 75% of the distance fallen.

For the downward distance after 10 jumps, you sum the geometric series with first term (a) of 876 feet, common ratio (r) of 0.75, and n terms (n) being 10. The sum S of such a series can be calculated as: S = a * (1 - r^n) / (1 - r). The upward travel distance will be 75% of the total downward distance.

To find out the total distance before the jumper comes to rest, we look at the situation when the sum of the geometric series tends to infinity (i.e., as the number of terms n approaches infinity) which can be calculated as S = a / (1 - r).

https://brainly.com/question/30264021

#SPJ12

Answer:

i.)12 feet

Step-by-step explanation:

ut+1/2gt^2

7×1+1/2×10×1^2 =12

Answer:

B. 1/2

Step-by-step explanation:

This problem involves the use of the Pythagorean theorem. In the unit circle, the hypotenuse of any right triangle formed is 1 while the coordinates of the point are then the two legs that make up the triangle.

a = 1 (given)

b = √3/2 (given)

a² = b² + c² (Pythagorean Theorem)

1² = (√3/2)² + c² (Substitute information)

Now, we need to solve for c

1 = (3/4) + c² (square the hypotenuse and one of the legs)

1 - (3/4) = (3/4) + c² - (3/4) (subtract 3/4 on both sides)

1/4 = c² (combine like terms)

√(1/4) = √(c²) (square root both sides)

√1 / √4 = c (square root both sides)

1/2 = c (final answer)

Therefore the other leg of the right triangle is 1/2, this also means that the other coordinate, or x, is 1/2, so the answer is B. 1/2.

Final answer:

The x-coordinate for the point (x, √3/2) on the unit circle is determined using the Pythagorean theorem for a unit circle. After substituting √3/2 for y and solving for x, the x-coordinate can be ±1/2. The correct option from the given choices is B. 1/2.

Explanation:

If the point (x, √3/2) is on the unit circle, we must use the Pythagorean theorem that applies to the unit circle, which states that x² + y² = 1, where x and y are the coordinates of a point on the circle. For a unit circle, the radius is 1. Since the y-coordinate is given as √3/2, we can substitute this value into the equation and solve for x:

x² + (√3/2)² = 1

x² + (3/4) = 1

x² = 1 - 3/4

x² = 1/4

x = ±√(1/4)

x = ±(1/2)

Therefore, x could be either 1/2 or -1/2. Since the question doesn't specify which quadrant the point is in, both answers are correct. However, within the given options, the correct answer is B. 1/2.

U means "Union" or all the numbers from one set and all the numbers from the other set combined.  So your answer is any of the numbers included in one set or the other or both.

Answer:

y = 5x - 13

Step-by-step explanation:

Use the formula  y = mx + b to solve for b. Then plug in known values.

Answer:

y=5x-13

Step-by-step explanation:

Answer:

Evaluate The Integral To Find The Volume. This problem has been solved! See the answer. Sketch the solid and set up the triple integral in Cartesian coordinates that gives the volume of the solid bounded below by the cone z = \sqrt{x^2+y^2} and bounded above by the sphere x2 + y2 + z2 = 8. Evaluate the integral to find .

Step-by-step explanation:

took it

Answer:

32pi cm or 100.530964915 mm

Step-by-step explanation:

To find this answer you will need to use the equation 2*pi*r or pi*d.

Your value 32 can be plugged in as your value of d which can then be substituted to make 32 pi or if you use a calculator you get 100.530964915.

hope this helps!

Answer: 100.5 mm

Step-by-step explanation: The formula to find the circumference of a circle is 2(pi)r

Since we know the diameter is 32, divide 32 by 2 to get the radius: 16

2(pi)(16) = 100.5309

To the nearest tenth, that would be 100.5

Answer:

$16

Step-by-step explanation:

-Given that her balance after buying one pizza is half her weekly allowance.

#We multiply her balance times 2 to determine her total weekly allowance:

[tex]Total \ Allowance=Balance \times 2\\\\=8\times 2\\\\=\$16[/tex]

Hence, her total weekly allowance is $16

Answer:

The lines will have one positive y-intercept and one negative y-intercept is NOT true.

Step-by-step explanation:

If a graphed system has infinitely many solutions, that means that the two equations are the exact same. This means that they'll have the same slope, y-intercept, and will share all of the same points. Answer b is the only choice left.

The lines will have one positive y-intercept and one negative y-intercept that is not true.

The graph is a diagram showing the relation between variable quantities, typically of two variables, each measured along with one of a pair of axes at right angles.

The lines will have one positive y-intercept and one negative y-intercept is NOT true.

If a graphed system has infinitely many solutions, that means that the two equations are the exact same. This means that they'll have the same slope, and y-intercept, and will share all of the same points. Answer b is the only choice left.

Learn more about the Graph:

https://brainly.com/question/4291574

#SPJ2

Answer:

-16

Step-by-step explanation:

-20 + 4 Equals -16. Try it on a number line.

Answer:-16

Step-by-step explanation:

-20+4=-16