please solve this please​

Adding and subtracting integrals is a fundamental technique in calculus that allows you to combine multiple integrals into a single expression. The process involves using the properties of integrals and the rules of algebra to simplify the expression.

How to add integrals?

To add two integrals, you simply add the integrands and integrate over the same limits of integration. For example, if you have two integrals, ∫f(x) dx and ∫g(x) dx

The sum of the two integrals would be

∫[f(x) + g(x)] dx

How to subtract integrals?

To subtract two integrals, you subtract the integrands and integrate over the same limits of integration. For example, if you have two integrals ∫f(x) dx and ∫g(x) dx

The difference of the two integrals would be ∫[f(x) - g(x)] dx

It's important to note that when adding or subtracting integrals, you must ensure that the limits of integration are the same. If they are not the same, you must first adjust one or both integrals to have the same limits of integration.

Another important point to keep in mind is that the properties of integrals allow you to simplify expressions before integrating. For example, if you have an integral of the form:

∫f(x) dx + ∫g(x) dx

You can simplify it as ∫[f(x) + g(x)] dx

before integrating.

In conclusion, adding and subtracting integrals is a straightforward process that involves using the rules of algebra and the properties of integrals. By following these techniques, you can simplify complex expressions and solve integration problems more efficiently.

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Correct question is "How to add and subtract integrals?"

Answer: $128

Step-by-step explanation: So first Bob earned 8 dollars. Then he started earning 10 dollars a day every week for 2 weeks. that would have been 148 dollars (plus the 8 dollars he earned in the beginning), but he took a break once a week, subtracting 20 dollars from his pay, giving him 128 dollars in total.

Let me know if this was helpful! :D

Answer:

6

Step-by-step explanation:

Using the equation y = 3x + 4, find the value of y if the function g is such that g(x) = x3 − 3x 2 – 2x + 1 ...6.

Step 1: Isolate the Sin Operator

\(8 sin(\frac{\pi }{6} x)=2\\sin(\frac{\pi }{6} x)=0.25\\\\\)

Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable

Note that since trig functions have 2 general solutions, this will give us one of our general solutions.

\(x=\frac{6 arcsin(0.25)}{\pi } =0.48\)

x₁= 0.48

Solving for x₂

Use the period identity for Sin Functions

\(sin(x)=sin(\pi -x)\)

X in this case is arcsin(0.25)

\(\frac{\pi }{6} x=\pi -arcsin(0.25) = 5.52\)

So our two general solutions are 0.48 and 5.52

Step 3: Period

Trig Functions have periodic behavior and this function period is

\(\frac{2\pi }{1} (\frac{6}{\pi } )= 12\)

So our general solutions are

0.48±12k, where k is an integer

5.52±12k, where k is an integer

Let k=1, and we get our next set of solutions:

12.48 and 17.52

So our answer is 0.48,5.52,12.48,17.52

Answer:

0.753

Step-by-step explanation:

do 753/1000 and do the long division

The Number of Soccer Balls is 16 and the Number of T-Shirts is 68

What is Linear Equation in Two Variables?

A linear equation in two variables is one that is stated in the form         ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let,

Number of Soccer Balls = x

Number of T-Shirts = y

Equation 1:

x + y = 84 -----------(i)

Equation 2:

25x + 9.5y = 1046 ----------(ii)

Multiplying Equation 1 by 25

25x + 25y = 2100 ---------(iii)

Substracting Equation2 from Equation 1

15.5y = 1054

y = 68

So, x = 16

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1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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Answer:

A, 1:2 ratio

Explanation:

Since 1 is half of 2, and the problem states that RSTUV is half of JKLMN, A is the correct ratio.

Answer:

c

Step-by-step explanation:

The pair of functions are f(g(x)) = √(x² + 1) +4  and g(f(x)) = x² + 4√x + 17

The function is defined as a mathematics expression that defines a relationship between one variable and another variable.

Given the system of functions as

f(x) = √x +4,

And g(x) = x² + 1

To determine the values of f(g(x)) and g(f(x)).

f(g(x)) = g(x) of f(x)

⇒ f(x) = √x +4,

Substiute the values of g(x) in the f(x)

⇒ f(g(x)) = √(x² + 1) +4

g(f(x)) =  f(x) of g(x)

⇒ g(x) = x² + 1

Substiute the values of f(x) in the g(x)

⇒ g(f(x)) = (√x +4)² + 1

⇒ g(f(x)) = (√x)² +4² + 4√x + 1

⇒ g(f(x)) = x² + 4√x + 17

Hence, the pair of functions are f(g(x)) = √(x² + 1) +4  and g(f(x)) = x² + 4√x + 17

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The correct answer is, by choosing a = -2 and b = 1, we satisfy both inequalities .a < b:

To make both inequalities true, we need to select values for a and b that satisfy the given conditions:

a < b: This inequality means that the value of a should be less than the value of b.

|b| < |a|: This inequality means that the absolute value of b should be less than the absolute value of a.

One possible solution that satisfies both conditions is:

a = -2

b = 1

With these values, we have:

-2 < 1 (a < b)

|-1| < |2| (|b| < |a|)

Therefore, by choosing a = -2 and b = 1, we satisfy both inequalities.a < b:

This inequality states that the value of a should be less than the value of b. In other words, a needs to be positioned to the left of b on the number line. To satisfy this condition, we can choose a to be any number that is less than b. In the example I provided, a = -2 and b = 1, we can see that -2 is indeed less than 1, fulfilling the requirement.

|b| < |a|:

This inequality involves the absolute values of a and b. The absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value. The inequality states that the absolute value of b should be less than the absolute value of a. To satisfy this condition, we can choose b to be any number with a smaller absolute value than a. In the example I provided, |1| is less than |(-2)|, as 1 is closer to zero than -2, fulfilling the requirement.

By selecting a = -2 and b = 1, we satisfy both inequalities: a < b and |b| < |a|. The specific values of -2 and 1 were chosen as an example, but there are multiple other values that would also satisfy the given conditions. The important aspect is that a is indeed less than b, and the absolute value of b is smaller than the absolute value of a.

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Answer:

36

Step-by-step explanation:

largest share = 9parts = 108

1 part = 108÷9 = 12

smallest share = 3parts = 12×3 = 36

Answer:

y-int = 2 lbs  and slope = 1/2

Step-by-step explanation:

Find where the line meets the y-axis to find your y-intercept.

Find 2 points on the line and use the slope formula (change in y/change in x or rise/run). I used (0,2) and (4,4).

(4-2)/(4-0) = 2/4 which simplifies to 1/2

Answer:

8.9

Step-by-step explanation:

If you think of 8.9 as 8.90, then it's obvious that 8.90 (or 8.9) is greater than 8.83.

Answer:

8.9

Step-by-step explanation:

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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Answer:

48

Step-by-step explanation:

3x2^2x4=48

Answer:

48

Step-by-step explanation:

To calculate the distance between two points:

We apply the following formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

The points are:

We substitute data and solve:

\(\bf{d=\sqrt{(6-(-3))^2+(-8-8(-8))^2 } }\\ \\ \bf{ d=\sqrt{9^2+0^2}=\sqrt{81+0} }\\ \\ \bf{d=\sqrt{81}=9 }\)

The distance between the points (−3,− 8), (6, – 8) is 9.

Answer:

2.964

Step-by-step explanation:

Answer:

x=0, y=1

Step-by-step explanation:

Answer: D do all of the above and you will get good grades

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

C is congruent to A

Answer:

A) x = 113°

Explanation:

Given three sides: 6.4 cm, 5.8 cm, 10.2 cm

Use the cosine rule:

c² = a² + b² - 2ab cos(C)

Insert/put variables:

\(\rightarrow \sf 10.2^2 = 5.8^2 + 6.4^2 - 2(5.8)(6.4) cos(x)\)

\(\rightarrow \sf -74.24 cos(x) = 10.2^2 - 5.8^2 - 6.4^2\)

\(\sf \rightarrow -74.24 cos(x) = 29.44\)

\(\rightarrow \sf cos(x) = \dfrac{29.44}{-74.24}\)

\(\rightarrow \sf x = cos^{-1}(-\dfrac{23}{58})\)   = 113.36°  ≈ 113°  (rounded to nearest degree)

Answer:

  D.  f(0) = 11, f(n) = f(n-1) +13

Step-by-step explanation:

You want the recursive definition for the sequence ...

  11, 24, 37, 50, 63, ...

The first term is 11. This means the initial value for the recursive definition will be 11:

  f(0) = 11 . . . . .   eliminates choices A and B

Each term of a recursive sequence is defined in terms of previous terms. That is, f(n) will be defined in terms of f(n-1). Here, the previous term has 13 added to it. (11 +13 = 24, for example).

The remaining part of the recursive definition is ...

  f(n) = f(n -1) +13 . . . . .  eliminates choice C

The recursive definition is ...

<95141404393>

The length of side X in simple radical form with a rational denominator is 25/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 5 × 5/√3

Hypotenuse, x = 25/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

75

Step-by-step explanation:

f(4) means to use 4 in place of x.

f(x) = 3(5)^(x-2)

fill in 4 for

f(4) = 3(5)^(4-2)

do the 4-2 subtraction first

f(4) = 3(5)^2

do the 5 to the 2nd power next.

f(4) = 3(25)

last, multiply.

f(4) = 75

This is just following the typical order of operations.

The value of cos(2α + β) using trigonometric identities is; -1.0155

We are given;

α = sin⁻¹(4/5)

β = tan⁻¹(12/5)

Thus;

sin α = 4/5

tan β = 12/5

From trigonometric ratios, we can say that;

cos α = 3/5

sin β = 12/13

cos β = 5/13

We know from trigonometric identities that  cos (a + b) = cos a cos b - sin a sin b.

Thus;

cos(2α + β) = cos 2α cos β - sin 2α sin β

Thus;

cos(2α + β) = 2(3/5) * (5/13)) - ((2 * 4/5 * 12/13))

= 0.4615 - 1.477

= -1.0155

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Answer:

Step-by-step explanation:

If we assume that the first two flips are to the right, for some flip distance f, Croakie will land at ...

  B = A + 2 +2f

He will land back at A (the origin) after 1 flip and a slide of 8 ft to the left:

  B -f -8 = A

Subtracting A from both equations and substituting for B-A, we have ...

  B -A = 2 +2f

  B -A -f -8 = 0

  (2 +2f) -f -8 = 0 . . . . substitute for (B-A)

  f -6 = 0 . . . . simplify

  f = 6 . . . . . add 6

The length of a flip is 6 feet.

__

  B -A = 2 +2f = 2 +2(6) = 14

The distance between A and B is 14 feet.

Answer:

3^5

Step-by-step explanation:

exponents:

1 - ( - 4 ) = 5

Therefore,

3^5