what is the difference between the maximum and minimum values of f ?
f(x) = cos (2x) + cos x
how do i find the max and min of such?

Answer:

  a) tangent

  b) radius

  c) diameter

  d) chord

Step-by-step explanation:

You want the vocabulary words associated with various segments in and around a circle.

A tangent is a line or segment that is external to the circle and intersects it at one point. A tangent is always perpendicular to a radius. (Segment a is a tangent.)

A radius of a circle is a line segment between the center and a point on the circle. (Segment b is a radius.)

A chord is a line segment internal to the circle that joins two points on the circle. (Segment d is a chord.)

A diameter of a circle is a chord that contains the center of the circle. (Segment c is a diameter, and also a chord. The more specific descriptor is "diameter.")

Answer: 5x-2

Step-by-step explanation:

2x+5 + 3x-7

2x-2 + 3x

5x-2

An angle bisector is a line that is drawn between the angle, which divides the angle into two equal parts. For example, if we bisect an angle that is 70°, then it will be two angles of 35°

We can draw an angle bisector either by measuring the angle using a protractor or marking the half. But the commonly used method is by using a compass.

Step 1

Draw the angle with vertex a, b, and c

Step 2

Draw a circle with b as the Centre, that intersects with each side of the angle.

Step 3

Draw congruent circles or arcs, centered at each intersection point on the sides of the angle.

Step 4

Use a straight line to connect point b with the intersection of two overlapping circles or arcs.

The properties of angle bisectors are

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An extraneous solution is A root of a converted equation that is not a root of the original equation because it was left out of the original equation's domain. It comes from correct solution steps and is not a valid solution of the equation.

We are aware that when we solve an equation, the values that result from the answer are always accurate. When we address the problem, there are various solutions that we may be able to get. The non-extraneous solutions are those that, if plugged back in, would produce the original equation, whereas the extraneous solutions are those that do not.

Therefore, the only way we can tell if something is unnecessary or not is if we re-enter the data we have and check to see if the equation still produces the same answer.

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Answer:

[tex]1.9x+3.7[/tex]

Step-by-step explanation:

[tex]3.6x-1.7x+5.9-2.2=1.9x+3.7[/tex]

7^(3/5) * 7^(1/5) is equivalent to (7^3)^(1/5) * (7^1)^(1/5), which is equivalent to 343^(1/5) * 7^(1/5) = 343^(1/5) * (7^(1/5))^1 = 343^(1/5) * 7.

When you see an expression like 7^(3/5) * 7^(1/5), it is helpful to think about the properties of exponents. One property is that when you have the same base raised to different exponents, you can multiply the exponents. So, for example, 7^3 * 7^1 = 7^(3+1) = 7^4.

Another property is that when you have a base raised to a power, and then that result is raised to another power, you can multiply the exponents. So, for example, (7^3)^2 = 7^(3*2) = 7^6.

Using these properties, we can simplify the original expression as follows:
7^(3/5) * 7^(1/5) = (7^3)^(1/5) * (7^1)^(1/5) = 343^(1/5) * 7^(1/5) = 343^(1/5) * (7^(1/5))^1 = 343^(1/5) * 7

So, 7^(3/5) * 7^(1/5) is equivalent to 343^(1/5) * 7

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Answer:

3.) B

How to solve:

Just get the cubed root of all the numbers inside the fraction

In the given algebraic expression if [tex]x^2+y^2[/tex] = 225 and dy/dt = 4, then dx/dt when y = 9 is ±3.

An algebraic expression is a mathematical expression that can contain numbers, variables, and operators. Examples of algebraic expressions are: [tex]2x + 3, (x^2 - y^2) / (x-y)[/tex], and [tex]4y + 2x^2[/tex]. These expressions can be evaluated by replacing variables with specific values ​​and simplifying the expressions in order of operations.

Given, [tex]x^2+y^2[/tex]  = 225

dy/dt = 4

We have to find dx/dt.

When y = 9,

⇒ [tex]x^2+9(2)[/tex]  = 225

⇒ [tex]x^2+81[/tex] = 225

⇒ [tex]x^2[/tex] = 225 - 81

⇒ [tex]x^2[/tex] = 144

Taking square root,

⇒ x = ±12

Differentiating with respect to t,

2x ([tex]\frac{dx}{dt}[/tex]) + 2y ([tex]\frac{dy}{dt}[/tex]) = 0

x ([tex]\frac{dx}{dt}[/tex]) + y ([tex]\frac{dy}{dt}[/tex])=0

Put dy/dt = 4 in the above expression,

(±12) ([tex]\frac{dx}{dt}[/tex]) + (9)(4)=0

(±12)([tex]\frac{dx}{dt}[/tex]) + 36 = 0

(±12) ([tex]\frac{dx}{dt}[/tex]) = −36

[tex]\frac{dx}{dt}[/tex] = ( -36/ ± 12)

dx/dt = ±3

Therefore, dx/dt = ±3

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The measures of the angles of the triangles are

m∠1 = 55°

m∠2 = 125°

m∠3 = 35°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the first triangle be represented as ΔABC

Let the second triangle be represented as ΔCDE

And ∠BAC = m∠1

And , ∠CDE = m∠3

Now , from the triangle ΔABC

∠ABC = 180° - 110° ( Angle of a straight line is 180° )

So , the measure of angle ∠ABC = 70°

The sides of the triangle AC and BC are similar

So , The angles of the triangle are = 70° + x + x = 180°

On simplifying the equation , we get

70° + m∠1 + m∠1 = 180°

Subtracting 70° on both sides of the equation , we get

2m∠1 = 110°

Divide by 2 on both sides of the equation , we get

m∠1 = 55° = ∠ACB

And , ∠ACB and m∠2 are on a straight line

So , m∠2 = 180° - 55°

On simplifying the equation , we get

m∠2 = 125°

The triangle ΔCDE is a right triangle with ∠DCE = m∠1 ( vertically opposite angles )

So , the angles of the triangle are = 90° + 55° + m∠3 = 180°

On simplifying the equation , we get

145° + m∠3 = 180°

Subtracting 145° on both sides of the equation , we get

m∠3 = 35°

Hence , the measures of the angles of the triangles are are m∠1 = 55° , m∠2 = 125° , m∠3 = 35°

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Answer:

n = 20

Step-by-step explanation:

there is a common difference between consecutive terms , tat is

0 - (- 3) = 3 - 0 = 3

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 3 and d = 3 with [tex]a_{n}[/tex] = 54 , then solving for n

- 3 + 3(n - 1) = 54 ( add 3 to both sides )

3(n - 1) = 57 ( divide both sides by 3 )

n - 1 = 19 ( add 1 to both sides )

n = 20

there are 20 terms in the sequence.

The solution does not exist, as the equation does not satisfy any value of x and y

What is the equation?

An equation is a mathematical statement that asserts the equality of two expressions. It is a statement that asserts the equality of two expressions, and it is represented by an "equals" sign (=) between them. The expressions on either side of the equals sign are called the left-hand side and the right-hand side of the equation. Equations can be written in different forms, such as the standard form, factored form or in the form of roots.

The equation x - 2y = -4 represents a straight line in the x-y plane. To find the solution to this equation, we can find the x and y coordinates that satisfy the equation.

We can solve for one of the variables by adding or subtracting the constant from both sides of the equation.

x = 2y + 4

We can then substitute this expression for x into the other equation to find the value of the other variable.

x-2y=-4

2y+4-2y=-4

4 = -4

Hence, The solution does not exist, as the equation does not satisfy any value of x and y

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Answer:

1 is the answer.After you minus and plus it,you will definitely get 1 as the answer.Trust me guys.

The principal investment required to get a total amount of $3,700.00 from compound interest at a rate of 3.5% per year compounded 365 times per year over 15 years is $2,287.26.

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Given Data

Rate = 3.5%

Final Amount = $3,700

Time = 15 Years

First, convert R as a percent to r as a decimal

r = R/100

r = 3.5/100

r = 0.035 per year,

Then, solve the equation for P

P = A / (1 + r/n)^nt

P = 3,700.00 / (1 + 0.035/365)(365)^(15)

P = 3,700.00 / (1 + 0.00010137)^(4745)

P = $2,287.26

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Answer:

Step-by-step explanation:

include the inequality.

The interval notation for all real numbers greater than or equal to 5, is [ ∞, 5 ].

Continuous sets of real numbers can be represented using interval notation by the numbers that bound them. When written, intervals resemble ordered pairs in several ways.

When writing in interval notation, using " [ " means that the number next to this is to be included in the interval.

All real numbers greater than 5 would therefore mean real numbers till infinity so the symbol is ∞. The interval notation would therefore be :

[ ∞, 5 ]

This includes both all the real numbers and 5.

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Full question is:

Write in interval notation, all real numbers greater than or equal to  5

Answer:

18 men

Step-by-step explanation:

3:7  ==> there are 3 men for every 7 women.

42 / 7 = 6  ==> divide the total number of women by the supposed ratio.

6 * 3 = 18 men

Answer:

It lasted for 3 hours 15 minutes.

Answer:

$16.90

If this help please set brainliest.

Step-by-step explanation:

To calculate the tip, you first need to multiply the cost of the meal by the tip percentage: $13 * 30% = $3.90.

Then, you can add the cost of the tip to the cost of the meal to find the total cost before tax: $13 + $3.90 = $16.90.

That means the total cost of Mayerlin's meal plus the tip, before tax, was $16.90.

Answer:

$16.90

Step-by-step explanation:

First, we would need to figure out what 30% of $13 is.

0.30 (or 0.3) × 13 = 3.9

This means her tip was $3.90

Now we need to add that to the total price of her bill.

3.9 + 13 = 16.90

Therefore, Mayerlin spent sixteen dollars and ninety cents on her meal.

Answer:

72%

Step-by-step explanation:

18/25 are pink.

18*4 = 72.

72 percent.

Answer: x-4 i think

Step-by-step explanation:

Answer: f^(-1)(x) = 4x (inverse function desired)

Explanation: For if one let f(f^(-1)(x)) = x, (f^(-1)(x))/4 = x, and hence f^(-1)(x) = 4x.

Hypotenuse² = Perpendicular² + Base²

10² = 1²+x²

x²= 100 -1

x=√99

x≈9.94

It will take 3 weeks for both of us to have collected  the same amount. Each of us will have collected 23 items at that  time.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Let x = weeks

Me: y = 14+3x

Friend: y = 8+5x

Equating the two equations

14+3x=8+5x

14=8+2x

6=2x

dividing both sides by 2

3=x

y=14+3(3)=23

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The slope of line pq is 0 and the slope of line mn is undefined. Both lines mn and pq are parallel to each other.

In the given question, we have to find the slope of line pq and the slope of line mn.

We also have to find how the two lines are related.

The graph of the line pg and mn is given below:

As we know that the slope of the line is

m = {y(2)-y(1)}/{x(2)-x(1)}

From the graph we can see that the line pq passes through the points p(-8,2) and q(4,2).

So x(1) = -8, y(1) = 2, x(2) = 4 and y(2) = 2

So, the slope of the line pq is:

m(pq) = (2-2)/(4-(-8))

m(pq) = 0/(4+8)

m(pq) = 0

From the graph we can see that the line mn passes through the points m(8,6) and n(8,-8).

So x(1) = 8, y(1) = 6, x(2) = 8 and y(2) = -8

So, the slope of the line mn is:

m(mn) = (-8-6)/(8-8)

m(mn) = (-8-6)/0

m(mn) = ∞

Lines PQ and MN are horizontal and vertical, respectively. The lines are therefore parallel to one another.

As a result, PQ's slope is 0 while MN's slope is unknown. The lines are parallel.

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The two lines are related in that the slope of both lines can be determined by the same formula. Depending on the coordinates of the two points, the two lines may have the same or different slopes.

The slope of line pq is given by the formula m = (y2-y1)/(x2-x1). Let's say that line pq has points (p1,q1) and (p2,q2). The slope of this line is then given by m = (q2-q1)/(p2-p1).

Now, the slope of line mn is given by the formula m = (y2-y1)/(x2-x1). Let's say that line mn has points (m1,n1) and (m2,n2). The slope of this line is then given by m = (n2-n1)/(m2-m1).

The two lines are related in that the slope of both lines can be determined by the same formula. The two lines may or may not have different slopes, depending on the coordinates of the two points. For example, if the two lines have points (1,2) and (3,4) for line pq, and points (3,4) and (5,6) for line mn, then the slope of line pq is m = (4-2)/(3-1) = 2/2 = 1. The slope of line mn is m = (6-4)/(5-3) = 2/2 = 1. Therefore, the two lines have the same slope of 1.

On the other hand, if the two lines have points (1,2) and (3,4) for line pq and points (1,3) and (3,5) for line mn, then the slope of line pq is m = (4-2)/(3-1) = 2/2 = 1. The slope of line mn is m = (5-3)/(3-1) = 2/2 = 1. Therefore, the two lines have different slopes of 1 and 2 respectively.

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A mathematical state of the presumed relationship between two or more variables is called a model.

A model is a simplified representation of a real-world system that allows us to better understand and predict the behavior of the system. A model is a simplified representation of a real-world system that allows us to better understand and predict the behavior of the system.

In order to create a model, we need to understand the relationships between the variables in the system. These relationships can be represented mathematically.

Once we have a mathematical representation of the relationships between the variables, we can use this model to make predictions about the behavior of the system.

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The scalar product of two parallel unit vectors,  is equals to one i.e., i.e.,  [tex]\hat{i}[/tex]⋅[tex]\hat{i}[/tex] = 1 ,[tex]\hat{j}[/tex] ⋅[tex]\hat{j}[/tex] = 1  and [tex]\hat{k}[/tex]⋅[tex]\hat{k}[/tex]= 1 .                                                                                                                                                                                                                                                                                                                          Scalar Product: The scalar product is also known as dot product.             The scalar product of two vectors can be constructed by taking the component of one vector in the direction of the other vector and multiplying it by magnitude of other vector. That gives scalar as a result. Scalar don't have a direction associated with them. Mathematically,                                                                                         [tex]$\vec{A}$[/tex][tex]\vec{A}$.[/tex][tex]\vec{B}$[/tex] = |A| |B| cosθ

We have to determine the scalar product of [tex]\hat{i} . \hat{i}[/tex], [tex]\hat{j} .\hat{j}[/tex], and [tex]\hat{k} .\hat{k}[/tex] . Here [tex]\hat{i}[/tex] and [tex]\hat{i}[/tex] are the unit vectors in the direction along the x-axis. So, they are parallel to each other, that's why θ = 0° and |[tex]\hat{i}[/tex]| = 1 . Therefore, [tex]\hat{i} .\hat{i}[/tex] = ( 1) (1) cos 0° = 1. Similarly    [tex]\hat{j} .\hat{j}[/tex]  = 1 ( unit vectors in direction along the y-axis) and  [tex]\hat{k} .\hat{k}[/tex]= 1         ( along z-axis). Hence, the dot product of the two unit vectors  [tex]\hat{i} .\hat{i}[/tex], [tex]\hat{j}.\hat{j}[/tex], and [tex]\hat{k} .\hat{k}[/tex] is equal to one for each.

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The number of times that the actual flag is wider than Reagan's model would be = 3 times.

Rectangle: What is it?

A rectangle is a particular kind of quadrilateral with opposite sides that are parallel and equal to one another and four right angles, according to the definition.

The rectangular flag measures 39 inches in length in actuality.

Reagan's model measured 13 inches in length.

The formula: = Length of actual flag / Length of model = 39/13 = 3 will tell you how many times broader the model is than the real flag.

The real flag is three times wider than Ronald Reagan's model, for a total of four times.

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The numeric value of the function C(68) at f = 68 is given as follows:

C(68) = 20.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

C(f) = 5/9 x (f - 32).

The input at which we want to find the numeric value for the function is then given as follows:

f = 68.

Which means that the lone instance of f in the definition of the function is replaced by 68, and then the numeric value is calculated as follows:

C(68) = 5/9 x (68 - 32) = 5/9 x 36 = 5 x 4 = 20.

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The function for x = -2 is 56, x = 0 is 0 and x=2 is 24 for function g(x)= 10x² - 8x

A relation is a function if it has only One y-value for each x-value.

The given function is g(x)= 10x² - 8x

we need to find the value when x is -2

Replace x with -2

g(-2)=10(-2)²-8(-2)

=10×4+16

=40+16=56

Now when x =0

g(0)= 10(0)² - 8(0)=0

Now when x =2

Replace x with 2

g(2)=10(2)²-8(2)

=40-16

=24

Hence, the function for x = -2 is 56, x = 0 is 0 and x=2 is 24 for function g(x)= 10x² - 8x

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The slope of the line that passes through the points (-4, 7) and (-6, -4) is 5.5

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

(-4, 7), (-6, -4

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (-4, 7) and (-6, -4)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (-4, 7) and (-6, -4)

Substitute the known values in the above equation

So, we have the following equation

Slope = (-4 - 7)/(-6 + 4)

Evaluate

Slope = 5.5

Hence, the slope of the line is 5.5

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What’s the answer for the slope of (-4, 7), (-6, -4)?