Evaluate the definite integral from pi/2 to put of cos theta/sqrt 1+ sin theta.​

An expression is defined as a set of numbers, variables, and mathematical operations. The simplified version of the given expression is (3√2-2)√x³.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression [tex]\sqrt{32x^3} - \sqrt{16x^3} + \sqrt{4x^3} -\sqrt{2x^3}[/tex] can be simplified as shown below.

[tex]\sqrt{32x^3} - \sqrt{16x^3} + \sqrt{4x^3} -\sqrt{2x^3}\\\\=\sqrt{x^3}(\sqrt{32}-\sqrt{16}+\sqrt{4}-\sqrt{2}})\\\\= \sqrt{x^3} (4\sqrt{2}-4+2-\sqrt2)\\\\= \sqrt{x^3} (3\sqrt{2}-2)[/tex]

Hence, The simplified version of the given expression is (3√2-2)√x³.

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Answer:

The slope of the line is -1.

Step-by-step explanation:

SLOPE OF A LINE FORMULA

SLOPE = Y2 - Y1/ x2 - x1

m = Y2 - Y1/ x2 - x1

m = 3 - 7 / 2- (-2)

m = -4/4

m = -1

The slope of the line is -1.

Answer:

answer is option C

Step-by-step explanation:

just take 6n as common and divine each value by it

The factored form of expression 6n⁴ - 24n³ + 18n is

6n (n² - 2n + 1) (n² - 2n + 3).

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example: so

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

First, we can factor out the greatest common factor of the expression, which is 6n:

6n(n³ - 4n² + 3n)

Next, we can factor the expression inside the parentheses by grouping:

n³ - 4n² + 3n = n²(n-4) + 3(n-4) = (n²+3)(n-4)

Substituting this back into the original expression.

6n (n² + 3) (n - 4)

However, we can further simplify by noticing that the expressions

(n² - 2n + 1) and (n² - 2n + 3) are both equivalent to (n - 1)² + 1 and (n - 1)² + 2, respectively.

Thus,

The factored form can also be written as 6n [ (n - 1)² + 1 ] [ (n - 1)² + 2 ]

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Answer:

The next 3 numbers will be 1 3/4, 2, and 2 1/4

Step-by-step explanation:

The numbers in the sequence are increase by 1/4. So to find the next number in the sequence and 1/4 to the previous number. Don't foget to simplify your answers. Ex.) Rather than saying 2 2/4 you would say 2 1/2.

Step-by-step explanation:

Did you mean.

[tex] \text{what \: is \: the \:sin \: of } \: - \frac{4\pi}{3} \: ?[/tex]

[tex] \: [/tex]

[tex] = \sin( - \frac{4\pi}{3} ) [/tex]

[tex] = \sin( - \frac{4 \times 180 \degree}{3} ) [/tex]

[tex] = \sin( - \frac{4 \times \cancel{180} \degree}{ \cancel3} ) [/tex]

[tex] = \sin( - 4 \times 60 \degree) [/tex]

[tex] = \sin( - 240 \degree) [/tex]

[tex] = \sin(0 - 240 \degree) [/tex]

[tex] = \sin(360 \degree - 240 \degree) [/tex]

[tex] = \sin(120 \degree) [/tex]

[tex] = \frac{1}{2} \sqrt{3} \: \: \text{is \: the \: answer}[/tex]

Answer:

15°

Step-by-step explanation:

angle FGH = angle HGI ( since GH bisects angle FGI)

that means

(2x + 1) = (3x - 9)

= -x = -8

x = 8

angle HGI = (3x - 9)

= 3(8) - 9

24 - 9

= 15°

Answer:

21

Step-by-step explanation:

To find the measure of <HGI we first need to find the value of x

GH bisects angle <FI which means it divided the angle into two equal parts:

<FGH = <HGI

2x + 1 = 3x - 9 transfer like terms to the same side of the equation

1 + 9 = 3x - 2x

10 = x now replace x with 10

3*10 - 9 = 21

Step-by-step explanation:

2y+9= 4

2y=-5

y=-5/2

y= -2and 1/2

Answer:

the distance between DE is 2

The distance of EF is 5

The distance of FD is [tex]\sqrt{29}[/tex]

Perimeter is 7+[tex]\sqrt{29}[/tex]

Step-by-step explanation:

Distance of DE

[tex]\sqrt{(-3-(-3))^2+(3-1)^2}[/tex]

sqrt([tex](-3+3)^2+(2)^2[/tex])

sqrt([tex](0)^2+4[/tex])

[tex]\sqrt{4}[/tex]

=2

Distance of EF

[tex]\sqrt{(2-(-3))^2+(3-3)^2}[/tex]

Solve that like DE and it equals 5

Distance of FD

[tex]\sqrt{(2-(-3))^2+(3-1)^2}[/tex]

equals to [tex]\sqrt{29}[/tex]

P=DE+EF+FD

P=2+5+[tex]\sqrt{29}[/tex] = 7+[tex]\sqrt{29}[/tex]

Answer:

The table on the far left is a linear function.

Step-by-step explanation:

The table on the far left is the function

[tex]y = \frac{1}{2} x[/tex]

Answer:

15

Step-by-step explanation:

divide the perimeter by two and minus 1

Answer: 15ft

Step-by-step explanation:

Start off by drawing a rectangle with the given information. Since it is a rectangle we know that the opposite side is also 1. So subtract 2 from 32 to get 30. Divide this by 2 and you will get your width of your rectangle. Hope this helps!

Answer:

Using the method of ratio and proportion, we find that the length of the side of Polygon D is 0.8in.

Step-by-step explanation:

Given that Polygon C and Polygon D are similar. This means that the ratio of the length of one side of Polygon C to the length of corresponding side of Polygon D will stay same even if we change the lengths.

Perimeter of polygon C = 60in

Perimeter of polygon D = 12in

Length of side of polygon C = 4in

Let us take the number of sides of both the polygons same. Let the length of the side of polygon D x inches. Let the number of sides be n.

First equation, 4n = 60

Second equation, xn = 12

Dividing second by first

(xn) / (4n) = 12 / 60

x / 4 = 1 / 5

x = 4 / 5 = 0.8in

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Answer:

it should be 319

Step-by-step explanation:

Answer:

639 is the answers for the question

Step-by-step explanation:

please mark me as brainlest

Answer:

The function [tex]2(3^x)[/tex] has an initial value of [tex]2[/tex].

Step-by-step explanation:

An exponential function is a mathematical function of the following form: [tex]f(x)=a^x[/tex]where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e, which is equal to approximately 2.71828. The exponential value can be found by solving the expression to proceed with a solution.

At the initial value,  the exponential function is in the [tex]y[/tex] direction and [tex]x[/tex] is [tex]0[/tex] .

[tex]f(x)=2(3^x)\\f(x)=2(3^0)\\f(x)=2[/tex]

Therefore, the function that has an initial value of [tex]2[/tex] is [tex]2(3^x)[/tex].

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1) Given

2) Segment addition postulate

3) Substitution property

4) Segment addition postulate

5) Transitive property of equality

Answer:

Step-by-step explanation:

Answer:

(-1,4)

Step-by-step explanation:

Step 1) Change both equations to slope intercept form

3x+y=1 ---> y=-3x+1

5x+y=-1 ---> y=-5x-1

Step 2) Plot lines accordingly on graph

Lines intersect at (-1,4)

"Law of conservation of Mass and Energy", is the reason for which it is important to keep the two sides of an equation balanced when solving.

The other properties that we should consider while rewriting the expressions of an equation is that we should not multiply or divide the expressions by zero on both the sides.

According to the law of conservation of mass, mass is neither generated nor destroyed during a chemical process. For instance, when coal is burnt, the carbon atom in it transforms into carbon dioxide. The carbon atom transforms from a solid to a gas, yet its mass remains constant. Similar to this, according to the law of conservation of energy, energy cannot be generated or destroyed. For instance, kinetic energy is converted to potential energy when a toy vehicle is rolled down a ramp and collides with a wall.

While rewriting expressions of an equation, we should not multiply or divide them by zero, as multiplying or dividing by zero makes two non-equal expressions equal (0 and ∞ respectively.

This is the reason why is it important to keep the two sides of an equation balanced, and that the expressions should not be multiplied or divided by zero.

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Answer:$440, 9

Step-by-step explanation:

The relationship between the number of the times eating out in the total budget represent a linear function.

"A linear functions are those whose graph is a straight line."

Given, I already spent $160 on groceries for the week.

Each time I eat out you will spend another $40.

Let, I eat 'x' times during vacation.

Therefore, the required function will be:

f(x) = 160 + 40x

Hence, the function is a linear function.

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The true statement about the triangle is (a) b^2 + c^2 > a^2

The sides are given as:

a, b and c

The angle opposite of side length a is an acute angle

The above means that:

The side a is the longest side of the triangle.

The Pythagoras theorem states that:

a^2 = b^2 + c^2

Since the triangle is not a right triangle, and the angle opposite a is acute.

Then it means that the square of a is less than the sum of squares of other sides.

This gives

a^2 < b^2 + c^2

Rewrite as:

b^2 + c^2 > a^2

Hence, the true statement about the triangle is (a) b^2 + c^2 > a^2

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Answer:

congruent/alternate interior angles

Step-by-step explanation:

just took the quiz

The expected length of the arc containing the point (1,0) is; π

First of all, it is pertinent to note that the lengths of the four arcs in which the circle is divided by the three points and (1, 0) have identical distributions.

The problem is same as dividing a circle of length 2π at four points chosen at random, and labelling one of them (1, 0). Now, let us make L₁, L₂, L₃, L₄ to be the lengths of the four arcs determined by those four points.

Thus, we have;

L₁ + L₂ + L₃ + L₄ = 2π

Whereas, the expected value of several random variables is additive as;

E[ L₁ + L₂ + L₃ + L₄] =  [EL₁] + [EL₂] + [EL₃] + [EL₄]

By symmetry the lengths have the same probability distribution and as such; [EL₁] = [EL₂] = [EL₃] = [EL₄] and the sum must be 2π. Thus, we can say that each expected value is 2π/4 = π/4.

Finally, the expected value of the arc containing the point (1, 0) is the sum of the expected values of the two arcs that are adjacent to (1, 0), i.e.,

π/2 + π/2 = π

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Gene earns 2% interest after depositing $150 into his account , Option D.

A function is a law that relates an independent variable and a dependent variable with each other.

The function given is

f(x) = 0.02 x +150

Option D , Gene earns 2% interest after depositing $150 into his account

So this verbal description matches the function given as it represents , the total account balance of Gene .

Therefore Option D is the correct answer.

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Answer:

$864.94

Step-by-step explanation:

So the amount of money over time can be given with an exponential function y=a(b)^x or more specifically y=a(1+r)^x    where r is the growth rate (interest rate)

So the equation can be written as

[tex]m= P(1.04)^t[/tex]    where m represents the amount of money over time, P represents the principle amount, and t represents time in years. Since we're given the amount of interest paid and not the total amount which includes the initial amount borrowed you have to subtract P from the equation. This will give us the equation that we'll use to find the initial amount

[tex]I = P(1.04)^t-P[/tex]  where I represents the interest paid.

plug the values into the equation

[tex]108 = P(1.04)^3-P\\108 = P(1.124864) - P\\108 = 0.124864P\\\\864.941 = P[/tex]

Answer:

3x²y²(1 - 4xy²z)

Step-by-step explanation:

________________________________________
Factor 3 out of 12
Factor x² out of x³
Factor y² out of y⁴

you will get the GCF of 3x²y² and left with (1 - 4xy²z)

3x²y²(1 - 4xy²z)
________________________________________

Hoped this helped

Answer:

C

Step-by-step explanation:

(1/4)^x-2 is the answer

Answer:

Is the second expression written correctly?  It reduces to y>-2, since no x is in the equation.

Step-by-step explanation:

We can graph the two equations.  See attached image.  If y>2 is the correct expression, all points to the right.

If the equation was meant to read y=-3x+1, then graph the revised expression.

The range:
[tex]{x|70\leq x\leq 82[/tex]

The value of angle x is 67 degree.

A right angled Triangle is a triangle with one angle as 90 degree.

It is given that the for the angle x , the base of the triangle is 28 ft.

The hypotenuse = 72ft.

The trigonometric ratios can be used to find the value of x

cos x = 28 /72

x = cos⁻¹ (28/72)

x = 67 degree (Rounded off to nearest tenth)

Therefore the value of angle x is 67 degree.

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Answer:

Step-by-step explanation:

Calculate 50% of 684 m.

Give your answer in metres (m).

50% = 1/2

so

684 : 2 = 342 m

Step-by-step explanation:

50% of 684

50/100 × 684

342m ans