Linearise cos^5(x). Help asap please

detailed answer (so much details are needed)

and what is the formula for cos^3 (x)

Answer:

Step-by-step explanation:

Given the expression \(log_81000 = log_210\), to prove this expression is true using the properties of logarithm, we will follow the following steps.

Starting from the Left Hand Side:

Answer:

Step-by-step explanation:

I. the point is is moved 4 to the right of the center point and 2 down. So it is (4, -2)

P. This point is moved negative 4 (to the left) and down 3 . So it is: (-4, -3)

G. This point is moved 5 to the right and then up 2 which makes it (5, 2)

Q.  This point is moved 6 to the right and 4 down which makes it (6, -4)

R. This point is moved 2 to the left and 2 up which makes it (-2, 2)

S. (6, 4)

J. (-2, -4)

U. (-5, 0)

H. (3, -1)

K. (-6, -5)

Answer:

66-18b or maybe 11/3

Step-by-step explanation:

-6+9(8-2b)

-6+72-18b

72-6=66

66-18b

Answer:

54

Step-by-step explanation:

9(0.5)(12)

54

Answer:

54

Step-by-step explanation:

Area of a triangle is (base*height)/2

9*12=108

108/2=54

The R= {y | y is an integer and -5 ≤ y ≤ -4} is null set because there is no integers between -5 and -4.

The set is

R= {y | y is an integer and -5 ≤ y ≤ -4}

An integer is a combination of number zero, all the positive numbers and negative numbers without any fraction.

Any set that does not contains any numbers or elements is called null set, which is also called empty set or void set. Null set can be denoted as {} or ∅.

The set is R= {y | y is an integer and -5 ≤ y ≤ -4}

There is no integers between -5 and -4, therefore it is a null set

Hence, The R= {y | y is an integer and -5 ≤ y ≤ -4} is null set because there is no integers between -5 and -4.

The complete question is :

Write the set in roaster form R= {y | y is an integer and -5 ≤ y ≤ -4}

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The image vertices of N'M'O, when the preimage triangle NMO is reflected over x = -5, are N'(5, 2), M'(2, 1), and O'(3, 3).

To determine the image vertices of N'M'O when the preimage triangle NMO is reflected over the line x = -5, we can apply the reflection transformation by changing the sign of the x-coordinate while keeping the y-coordinate the same.

The line x = -5 is a vertical line passing through the x-coordinate -5. When reflecting a point over this line, the x-coordinate of the image will be the reflection of the original x-coordinate with respect to the line.

Vertex N(-5, 2):

When reflected over x = -5, the x-coordinate changes sign, and the y-coordinate remains the same. Therefore, the image vertex N' is (-(-5), 2) = (5, 2).

Vertex M(-2, 1):

Applying the reflection transformation, the x-coordinate changes sign while the y-coordinate remains the same. Thus, the image vertex M' is (-(-2), 1) = (2, 1).

Vertex O(-3, 3):

By reflecting over x = -5, the x-coordinate changes sign, and the y-coordinate remains the same. Hence, the image vertex O' is (-(-3), 3) = (3, 3).

Therefore, the image vertices of N'M'O, when the preimage triangle NMO is reflected over x = -5, are N'(5, 2), M'(2, 1), and O'(3, 3)

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Answer: Alexander's monthly income is $1,750.

Step-by-step explanation:

Working backwards is the easiest solve method for problems like this:

$1,680/12=$140 per month

$140=2/25 monthly income

Monthly income = ($140)25/2 = $1750

Answer:

174 cm²

Step-by-step explanation:

The figure given is a prism with isosceles trapezoid as base.

Its surface area can be calculating the area of each face that makes up the prism, and summing all together.

There are 6 faces. Their dimensions and areas can be calculated as follows:

2 isosceles trapezium:

It has 2 parallel bases, (a and b), of 4cm and 6cm,

Height (h) = 2.8cm

Area = ½(a+b)*h

Area = ½(4+6)*2.8

Area = ½(10)*2.8 = 5*2.8 = 14 cm²

4 rectangles of different dimensions:

Rectangle 1 (down face): l = 10cm, b = 4cm

Area = 10*4 = 40 cm²

Rectangle 2 and 3 (side faces): l = 10cm, b = 3cm

Area = 2(l*b) = 2(10*3) = 60cm²

Rectangle 4 (top face) = l = 10cm, b = 6cm

Area = 10*6 = 60cm²

Surface area of the figure = 14 + 40 + 60 + 60 = 174 cm²

Answer:

66

Step-by-step explanation:

the difference of 54 and 32 is 54 - 32 = 22

the difference of 8 and 5 is 8 - 5 = 3

then

22 × 3 = 66

The total surface area is 28 square units.

Each of the 6 faces in the original cube has an area of 2* 2 = 4 square units. Thus, the original figure's surface area as a whole was 24 square units.

The new figure has the same surface area as the old one, plus six new faces that each have an area of one dollar per square unit, for a total surface area increase of six dollars. However, the 1 square unit of the bigger cube's top and the 1 square unit of the smaller cube's bottom are not surfaces and do not contribute to the surface area.

This results in a total surface area of 24 + 6 - 1 - 1 = 28 square units.

Therefore, The total surface area is 28 square units.

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Answer: Height = 20 inches, Width = 36 inches

Step-by-step explanation:

Let the height be \(h\) and the width be \(h+16\).

Using the formula for the perimeter of a triangle,

\(2(h+h+16)=112\\\\2(2h+16)=112\\\\2h+16=56\\\\2h=40\\\\h=20 \implies h+16=36\)

To find the polar equation of a conic with focus at the pole, directrix y=3, and eccentricity of 2, we can use the definition of a conic in polar coordinates.

The general form of the polar equation for a conic with focus at the pole is given by:

r = \(\frac{ed}{1+e\cos(\theta-\theta_0)}\)

Where:

- r is the distance from the origin (pole) to a point on the conic.

- e is the eccentricity.

- d is the distance from the pole to the directrix.

- θ is the angle between the polar axis and the line connecting the pole to a point on the conic.

- θ_0 is the angle between the polar axis and the line connecting the pole to the focus.

In this case, the focus is at the pole, so θ_0 = 0. The directrix is y = 3, which means its distance from the pole is d = 3. The eccentricity is given as 2, so e = 2.

Substituting these values into the general equation, we get:

r =\(\frac{2\cdot3}{1+2\cos(\theta-0)}\)

Simplifying further:

r =\(\frac{6}{1+2\cos(\theta)}\)

Therefore, the polar equation of the conic with focus at the pole, directrix y=3, and eccentricity of 2 is:

r =\(\frac{6}{1+2\cos(\theta)}.\)

This equation describes the shape of the conic in polar coordinates, where r represents the distance from the origin to a point on the conic, and θ represents the angle between the polar axis and the line connecting the origin to the point.

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The value of the fraction, negative 5 and 1 over 7 ÷ negative 7 and 3 over 4 is 144/217

A fraction can be described as the part of a whole element or value.

The different types of fractions are;

Examples of proper fractions; 2/4, 5/6, 7/9

Examples of improper fractions; 4/2, 3/2, 6/5

Examples of mixed fractions; 2 1/4, 4 6/7, 8 1/2

Examples of simple fractions; 1/ 3, 3/4, 1/2

Now, from the information given, we have;

Convert into improper fractions

-36/7 ÷ -31/4

take inverse of the divisor and multiply

-36/ 7 × 4/-31

-144/-217

144/217

Hence, the value is 144/217

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Answer:

2 pairs if running shoes

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

We should add the number of each type to get the total number of types. So the answer is

12+12+7=31

Answer: 28 cm

Step-by-step explanation:

x - the length of the shorter piece

2x - the length of the longer piece

Together they are 42 cm long.

Compose te equation:

2x + x = 42

3x = 42

x = 14 cm

The shorter piece is 14 cm, the longer piece is twice longer, 2x, or 2( 14 ).

Two times longer than 14 is 28. The longer piece is 28 cm.

The required amount of the space available is 0.045 cubic meter.

We need to determine Space inside the steps.

The Volume is defined as the mass of object per unit density.

The required space = 0.3*0.4*0.5 - 0.15*0.5*0.2

                                 =  0.06 - 0.015

                                 =    0.045 cubic meter

Hence, the required amount of the space available will be 0.045 cubic meter.

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Answer:

D?

Step-by-step explanation:

I'm not completely sure, but there are 2 different 180 degree lines that y falls on. On one line (y+70=180) it is for sure 110 degrees

When measured on the other line it is (y+70+x=180) I'm not too familiar with this??

The linear rule for the sequence is f(n) = 7/20 + 3/20(n - 1)

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

35/100,5/10,65/100

In the above sequence, we can see that 15/100 is added to the previous term to get the new term

This means that

First term, a = 35/100

Common difference, d = 15/100

The nth term is then represented as

f(n) = a + (n - 1) * d

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

f(n) = 35/100 + 15/100(n - 1)

So, we have

f(n) = 7/20 + 3/20(n - 1)

Hence, the explicit rule is f(n) = 7/20 + 3/20(n - 1)

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Answer:

Step-by-step explanation:

The length of the line segment between two points in a plane can be calculated using the distance formula. Given two points (x1, y1) and (x2, y2), the distance between them is given by the following formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the two points are (3, 5) and (7, 3). Plugging these values into the formula, we get:

d = √((7 - 3)^2 + (3 - 5)^2)

d = √((4^2) + (2^2))

d = √(16 + 4)

d = √20

So, the length of the line segment between the two points (3, 5) and (7, 3) is √20.

The value of,

Given function f(x) = cx for 1 ≤ x ≤ 2

a) To find the value of constant x, we have to use the following p.d.f condition as shown below,

\(\int\limits^a_b {x} \, dx =1\)

here, a is -∞ and b is ∞.

From the above condition to find the value of c,

\(\int\limits^2_1{cx^2} \, dx\) = 1

c * [\(\frac{x^3}{3}\)]²₁ = 1

c * [8/3 - 1/3] = 1

c * 7/3 = 1

c = 3/7.

b) To find the value of P(x>3/2) we have to substitute the value of 3/2 in the given expression of f(x) = 3/7 * x²

f(3/2) = 3/7 * (3/2)²

         = 3/7 * 9/4

         = 27/28.

From the above solution, we solved both problems.

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Answer:

1/12

Step-by-step explanation:

First we have to calculate the sample space i.e. The total number of outcomes,

(H represents heads, T represents Tails and Numericals represent the number on the die)

H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6

= 12 sample spaces

Ok now so what is the probability that the die lands on 4 and it pops up as heads. So when we see the total outcomes we see that such event has only one such outcome

The number of outcomes/Total number of outcome

So therfore we can represent it in fraction as

1 / 12

The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

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The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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The value of the function operation f - g(x) is 3x² + x

Function operations refer to mathematical operations that can be performed on functions, such as addition, subtraction, multiplication, and composition.

Addition and subtraction of functions:

A function can be added or subtracted with another function if both of them have the same domain. The result is a new function with the same domain as the original functions.

Multiplication of functions:

Two functions can be multiplied together to create a new function. The result is a new function whose value at each point in the domain is the product of the original functions' values at that point.

Composition of functions:

Function composition is the application of one function to the result of another function. The result is a new function that is the composition of the original functions. It is represented by (f ∘ g) (x) = f(g(x)) where f and g are the functions being composed.

In this problem, we have two functions which are;

The value of (f - g)(x) = 3x² + x

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Answer:

Step-by-step explanation:

a

The mathematical function that models Autumn's situation of saving $500 that she keeps at home and does not add to the savings is G(x) = 500 + 0x.

A mathematical function is an equation, expression, rule, or law defining the relationship between the independent variable and the dependent variable.

There are many types of mathematical function, including:

The amount that Autumn saved = $500

The amount that Autumn adds to the savings = $0

Let the number of periods that Autumn saves the above amount = x

G(x) = 500 + 0x

Thus, based on the linear function above, the amount that Autumn saved would remain $500 after many periods.

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