Please I need this answer

x = ±π/6 + πn, ±11π/12 + πn, where n is an integers are solutions of the equation  cos²x = sin²x + 1/2

To solve the equation cos²x = sin²x + 1/2, we can use the trigonometric identity sin²x + cos²x = 1.

Rearranging the equation, we have:

cos²x - sin²x = 1/2

Using the identity cos²x - sin²x = cos(2x), we can rewrite the equation as:

cos(2x) = 1/2

The solutions to this equation can be found by taking the inverse cosine (or arccosine) of both sides:

2x = ±π/3 + 2πn, ±11π/6 + 2πn, where n is an integer

Dividing both sides by 2, we get:

x = ±π/6 + πn, ±11π/12 + πn, where n is an integers

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ1

The interest rate that satisfies the assumption is approximately 5.33%.

We have,

To find the interest rate that satisfies the assumption, we can use the formula for compound interest:

[tex]A = P \times (1 + r)^t[/tex]

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (in decimal form)

t = Time (in years)

In this case, we have:

P = $400

A = $684

t = 11 years

Let's substitute these values into the formula and solve for r:

$684 = $400 x [tex](1 + r)^{11}[/tex]

Dividing both sides by $400, we get:

[tex]1.71 = (1 + r)^{11}[/tex]

Now, we need to isolate (1 + r) by taking the 11th root of both sides:

[tex](1 + r) = 1.71^{1/11}[/tex]

Using a calculator, we find:

(1 + r) ≈ 1.0533

Subtracting 1 from both sides, we get:

r ≈ 0.0533

To express the interest rate as a percentage, we multiply by 100:

r ≈ 5.33%

Therefore,

The interest rate that satisfies the assumption is approximately 5.33%.

Learn more about compound interest here:

https://brainly.com/question/13155407

#SPJ1

Answer:

(a) The function has a minimum value

(b) The minimum value is 2

Step-by-step explanation:

(a)Currently y = x^2 + 4x + 6 is in standard form, whose general equation is

y = ax^2 + bx + c.  

We know that for our function a = 1.

Thus, y = x^2 + 4x + 6 must have a minimum value.

(b) Whenever a problem asks for the minimum value, it's asking for the y-coordinate of the minimum.

Step 1:  First we can find the x-coordinate of the minimum using the equation -b/2a from the quadratic formula.  

Plugging in 4 for b and 1 for a, we get:

x-coordinate of minimum = -4 / 2(1)

x-coordinate of minimum = -4 / 2

x-coordinate of minimum = -2

Step 2:  Now we can plug in -2 for x in the quadratic function.  The result will be our minimum value:

f(-2) = (-2)^2 + 4(-2) + 6

f(-2) = 4 - 8 + 6

f(-2) = -4 + 6

f(-2) = 2

Thus, the minimum value of the quadratic function is 2.

The triangles ABC and CDE are similar

The width AB of the river is 172.73 ft

From the question, we have the following parameters that can be used in our computation:

The triangles ABC and CDE

The above triangles have corresponding angles and they also have similar side lengths

This means that the triangles are similar

Here, we have the following ratio

AB : 100 = 38 : 22

So, we have

AB/100 = 38/22

This gives

AB = 100 * 38/22

Evaluate

AB = 172.73

Hence, the width AB of the river is 172.73 ft

Read more about similar triangles at

https://brainly.com/question/14285697

#SPJ1

Answer:

Step-by-step explanation:24 ft

By the Centroid Theorem, the lengths are given as follows:

4. GZ = 12 units.

5. OT = 14.4 units.

The Centroid Theorem states that the centroid of a triangle is located two-thirds of the total distance from each vertex to the midpoint of the opposite side.

Hence for length GZ we have that:

GZ = 2GU/3

GZ = 2 x 18/3

GZ = 12 units.

For length OT, we have that:

ZT = 1/3OT

OT = 3ZT

OT = 3 x 4.8

OT = 14.4 units.

More can be learned about the centroid theorem at https://brainly.com/question/30866257

#SPJ1

Step-by-step explanation:

Wherever the fxn = 0  is where it touches the x -axis

0=(x-5)^3 (x+2)^2   means that one or both of the factors is 0

     (x-5)^3    is zero at   x = 5

      (x+2)^2  is zero at    x = -2

sooo    5 and  -2  

The price for which the designer will sell the maximum number of shirts is given as follows:

$11.

As the amount sold is modeled by a concave down quadratic function, the price for which the designer will sell the maximum number of shirts is given by the x-coordinate of the vertex of the quadratic function.

The function in the context of this problem is given as follows:

S(x) = -4x² + 88x - 160.

The coefficients are given as follows:

a = -4, b = 88, c = -160.

Hence the x-coordinate of the vertex is obtained applying it's formula as follows:

x = -b/2a

x = -88/-8

x = 11. -> price of $11.

More can be learned about quadratic functions at https://brainly.com/question/1214333

#SPJ1

To solve this problem, we need to use Charles's law, which states that, at constant pressure, the volume of a sample of gas is directly proportional to its temperature.

The law can be expressed mathematically as:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{ \frac{V_1}{T_1}=\frac{V_2}{T_2} } \end{gathered}$} }[/tex]

Where:

Now we obtain the data to continue solving:

Now, we will convert the temperatures to Kelvin:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_1=220 \ ^{\circ}C+273=493 \ Kelvin} \end{gathered}$} }[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_2=40 \ ^{\circ}C+273= 313 \ Kelvin} \end{gathered}$} }[/tex]

Now we solve for V₂:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{V_1T_2}{T_1 } } \end{gathered}$} }[/tex]

Where:

Now, we substitute the values in the formula:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{(0.5 \ L\times313\not{k} )}{493\not{k} } } \end{gathered}$} }[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2\approx0.32 \ Liters } \end{gathered}$} }}[/tex]

The proof that there is no set X such that P(X) ⊂ X is below

From the question, we have the following parameters that can be used in our computation:

There is no set X such that P(X) ⊂ X

The above means that

There is no set X such that the power set of X is a subset of set X

By definition, the power set is the set of all subsets of the a Set which includes the set itself and the null or empty set

Using the above as a guide, we have the following:

Because Y is in X, then by definition of the power set P(X), Y is a subset of X.

However, this is a contradiction because it is not possible for a set to be a proper subset of itself.

Read more about sets at

https://brainly.com/question/24713052

#SPJ1

The correct option is b, the solutions of the quadratic equation are x = ±2

Here we want to solve the following quadratic equation:

3x² = 12

To solve this, we need to isolate the variable, so let's start by dividing both sides by 3, then we will get:

x² = 12/3

x² = 4

Now we can apply the square root in both sides:

√x² = ±√4

x = ±2

These are the two solutions, then the correct option is b.

Learn more about quadratic equations at:

https://brainly.com/question/1214333

#SPJ1

The length of the radius of the given circle whose central angle has been given would be = 7cm.

To calculate the radius of the given circle, the formula that should be used will be given below as follows:

Length of arc = 2πr×∅/360

Length of arc = 14cm

∅ = 115°

14 = 2×3.14×r ×115/360

make R the subject of formula;

r = 14/2.006

= 6.9

= 7cm

Learn more about area here:

https://brainly.com/question/28470545

#SPJ1

The volume of the moon can be shown to be 3.07% of the volume of the planet.

First, calculate the radius of the planet and the moon.

The radius (r) of the planet is half of its diameter:

r = 27, 998 mi / 2

= 13, 999 mi

The volume of the planet is V:

= 4 / 3 π ( 13, 999 mi)³

=  11, 493, 372, 846 cubic miles

The volume of the moon is:

V = 4 / 3 π (4,059.71 mi) ³

=  352, 432, 952 cubic miles

The Percent volume :

= ( Volume of moon / Volume of planet) x 100

= ( 352, 432 ,952 cubic miles / 11, 493,372,846 cubic miles) x 100

= 3.07 %

Find out more on percentage at https://brainly.com/question/14263075

#SPJ1

The measure of each missing indicated side of the triangle would be given as follows;

1.) X = 2.7

2.) X = 15.2

For question 1.)

Using the sine formula such as given below;

a/sinA = b/sin B

where ;

a = X

A = 27°

b = 6

B = 90°

That is;

X/sin27° = 6/sin90°

X = 6×0.453990499/1

= 2.7

For question 2.)

a/sinA = b/sin B

where ;

a = X

A = 47.4°

b = 14

B = 180-(47.4+90)

= 180-137.4

= 42.6

That is;

X/sin47.4° = 14/sin42.6°

X = 14×0.736097087/0.676875969

= 10.305359218/0.676875969

= 15.2

Learn more about triangle here:

https://brainly.com/question/28470545

#SPJ1

Size of the house should be 2900 ft².

Correct option is B.

We have,

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

Equation for the line that expresses price of house

y = 0.06x + 60.5

where y is the price in thousand dollars, x is area in square feet.

Price of the house = $235000

⇒ y = 235

Then,

235 = 0.06x + 60.5

0.06x = $235 - 60.5

0.06x = 174.5

x = 174.5/0.06

x = 2908.33 ≈ 2900

Hence, 2900 ft² should be the size of the house.

Learn more about linear equation here:

brainly.com/question/29739212

#SPJ1

complete question:

A house is listed for sale at $235,000, but the listing does not include square

footage of the house. Based on the comps, the line of best fit is

y=0.06x + 60.5. If the price is fair, what size (in square feet) should the house

be?

OA. 2850 ft2

OB. 2900 ft2

OC. 20,000 ft²

OD. 2350 ft²

The number of terminates are 2,384.78.

An exponential function can be used to illustrate the daily growth of termites.

If "t" represents the number of days, then "N" represents the number of termites.

⇒ N = [tex]1600(1 + 0.042)^{t}[/tex]

Where 0.042 is the decimal form of 4.2%.

Using this formula,

It can be  calculate the number of termites after any number of days t.

For example,

After 10 days, the number of termites would be:

⇒ N = [tex]1600(1 + 0.042)^{10}[/tex]

⇒ N = [tex]1600(1.042)^{10}[/tex]

⇒ N ≈ 2,384.78 termites

Hence,

⇒ N =  2,384.78 termites

To learn more about exponential function visit:

https://brainly.com/question/14355665

#SPJ1

Hello!

[tex]-5x - 7 > 3x + 1\\\\-5x - 3x > 1+7\\\\-8x > 8\\\\\boxed{x < -1}[/tex]

The graph of the equation y = -1 is a horizontal line passing through (0, -1), and the graph of the equation 3x - y = 4 is a line passing through the points (-2, -10), (0, -4), and (2, 2).

To graph the given equations, we'll plot the points that satisfy each equation and then connect them to form a line.

Equation 1: y = -1

This equation represents a horizontal line passing through the y-coordinate -1. Regardless of the x-coordinate, the y-value remains constant at -1. Therefore, we plot a point at (0, -1) and draw a horizontal line through that point.

Equation 2: 3x - y = 4

To graph this equation, we can rewrite it in terms of y:

y = 3x - 4

Now we can choose a few x-values, substitute them into the equation, and solve for y to obtain the corresponding y-values. Let's select three x-values: -2, 0, and 2.

For x = -2:

y = 3(-2) - 4

y = -6 - 4

y = -10

For x = 0:

y = 3(0) - 4

y = -4

For x = 2:

y = 3(2) - 4

y = 6 - 4

y = 2

Now we have three points: (-2, -10), (0, -4), and (2, 2). Plotting these points on the graph, we can draw a line connecting them.

In summary, the graph of the equation y = -1 is a horizontal line passing through (0, -1), and the graph of the equation 3x - y = 4 is a line passing through the points (-2, -10), (0, -4), and (2, 2).

for such more question on graph

https://brainly.com/question/13473114

#SPJ8

The price per shirt when 100 shirts are sold is of $5.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

From the graph of the function, two points are given as follows:

(0, 20) and (20, 100).

Hence the slope is given as follows:

m = (100 - 20)/(20 - 0)

m = 4.

Hence the cost function is of:

y = 4x + 20.

For 20 shirts, the cost is of $100, hence the cost per shirt is given as follows:

100/20 = $5 per shirt.

The problem is given by the image presented at the end of the answer.

More can be learned about linear functions at https://brainly.com/question/15602982

#SPJ1

Answer:

a)

Step-by-step explanation:

the function is 11x6=66+13=79x¹=79

hope it helps

The missing root is -24 - 5i.

To find the missing root of the polynomial function f(x) = x^3 - x^2 + 24x + 26, we can use the fact that the sum of all the roots of a polynomial equation is equal to the negation of the coefficient of the second-to-last term divided by the coefficient of the leading term.

In this case, the coefficient of the second-to-last term is 24, and the coefficient of the leading term is 1. Therefore, the sum of all the roots is -24/1 = -24.

We already know that -1 and 1 + 5i are roots, so we can subtract them from the sum to find the missing root:

Missing root = -24 - (-1) - (1 + 5i) = -24 + 1 - 1 - 5i = -24 - 5i.

Note that the missing root is a complex number, indicating that the polynomial has at least one complex root.

For more such questions on complex root

https://brainly.com/question/13663525

#SPJ8

The range of the reciprocal function f(x) = -7/(3x + 11) is all real numbers except for the value x = -11/3.

The range of the reciprocal function f(x) = -7/(3x + 11), we need to determine the set of all possible values that f(x) can take.

The reciprocal of a number is obtained by taking the multiplicative inverse, which means that the reciprocal of a non-zero number a is 1/a.

We are looking for the range of the reciprocal function, so we need to consider the range of the expression (3x + 11).

The range of (3x + 11) is the set of all real numbers, except when the denominator becomes zero.

The range of the reciprocal function f(x) = -7/(3x + 11) is all real numbers except when (3x + 11) equals zero.

To find the x-value when (3x + 11) equals zero, we solve the equation:

3x + 11 = 0

Subtracting 11 from both sides, we get:

3x = -11

Dividing by 3, we find:

x = -11/3

The reciprocal function is undefined at x = -11/3, as it would result in a division by zero.

For similar questions on reciprocal function

https://brainly.com/question/16152266

#SPJ8

Step-by-step explanation:

I believe it is asking for the probability that x is greater than the mean + two standard deviations .....

  look at the mean ....count up two SD ( labelled at the bottom)  ....then see what is to the right of this point  : 2.35 % + .15 % =  2.5%  is greater

By the Central Limit Theorem, the mean of the sampling distribution of sample means would be 5.7 years.

Since, The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean μ and standard deviation σ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean μ and standard deviation s = σ / √n.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

The mean for the entire population is 5.7 years.

So, by the Central Limit Theorem, the mean of the sampling distribution of sample means would be 5.7 years.

Learn more about the standard deviation visit:

https://brainly.com/question/475676

#SPJ1

The value of 13.3km/L corresponds to 30.595 miles/gal

The conversion required is 13.3km/L to mile/gal

converting km to miles

1km = 0.621371 miles

13.3 km = ?

cross multiplying results to

? = 13 * 0.621371 = 8.077 miles

converting L to gallons

1 liters = 0.264172

hence we have that

= 8.077 / 0.264

= 30.595

thus, 13.3km/L is equal to 30.595 miles/gal

Learn more about unit conversion at

https://brainly.com/question/13016491

#SPJ1

Answer:

c) y=-x^2/4 - 2x - 7

Step-by-step explanation:

Answer:

The answer is the third option

Step-by-step explanation:

When an exponent is raised to the power of another exponent, both exponents are multiplied.
Recall that a number without an exponent is thought to be raised to the power of 1.

So after multiplying the exponents of all of the variables by 4, we are left with a solution identical to the third option.

The calculated coordinates of point B on line AB is (-1, 0)

From the question, we have the following parameters that can be used in our computation:

P =  (1,2)  

A = (2,4)

Also, we have

m : n = 1 : 2

The coordinates of point P are calculated using

P = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

Substitute the known values in the above equation, so, we have the following representation

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

Evaluate

(3, 6) = (x + 4, y + 6)

So, we have

x = -1 and y = 0

Hence, the coordinates of point B on line AB is (-1, 0)

Read more about line segment ratio at

brainly.com/question/17374569

#SPJ1

Answer: [tex]\sf\$6.48[/tex]

Step-by-step explanation:

If a six-pack of cola is sold for $1.50, then the price per can is:

[tex]\sf\implies\$1.50 \div 6 = \$0.25[/tex]

A 24 pack of cola contains 24 cans, so the total cost of the 24 pack is:

[tex]\sf\implies 24 \times \$0.25 = \$6.00[/tex]

The sales tax is 8%, so the tax on the purchase is:

[tex]\sf\implies \dfrac{8}{100} \times \$6.00 = \$0.48[/tex]

Therefore, the total charge including sales tax is:

[tex]\sf\implies\$6.00 + \$0.48 = \$6.48[/tex]

Chi-Chiribi! EmergerOrpheus at your service. Hope it helps!