Evaluate the following integrals

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Answer:

We can see that for this case the vertex is [tex] V= (0,0)[/tex]

The values for a and b are:

[tex] a = \sqrt{169}=13, b= \sqrt{25}=1[/tex]

Then the ellipse have the major axis on x.

In order to find the two foci we need to use the following formula:

[tex] c =\sqrt{a^2 -b^2}[/tex]

And replacing we got:

[tex] c =\sqrt{169-25}= \pm 12[/tex]

And then the two foci are (12,0) and (-12,0)

And the covertex are on this case (-13,0) (13,0) and (0,5) (0,-5) on the y axis

Step-by-step explanation:

For this problem we have the following equation given:

[tex]\frac{x^2}{169} + \frac{y^2}{25}= 1[/tex]

If we compare this with the general expression of an ellipse given by:

[tex] \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}= 1[/tex]

We can see that for this case the vertex is [tex] V= (0,0)[/tex]

The values for a and b are:

[tex] a = \sqrt{169}=13, b= \sqrt{25}=1[/tex]

Then the ellipse have the major axis on x.

In order to find the two foci we need to use the following formula:

[tex] c =\sqrt{a^2 -b^2}[/tex]

And replacing we got:

[tex] c =\sqrt{169-25}= \pm 12[/tex]

And then the two foci are (12,0) and (-12,0)

And the covertex are on this case (-13,0) (13,0) and (0,5) (0,-5) on the y axis

Answer:

You need to add 150 mL of 65% alcohol solution.

Step-by-step explanation:

You have 300 mL of 20% solution.

300 mL of 20% alcohol solution has 20% * 300 mL of alcohol.

You have 65% solution.

Let the volume of 65% solution you add be x.

In 65% solution, 65% of the volume is alcohol, so the amount of alcohol in x amount of 65% solution is 65% * x.

You want 35% solution.

The total amount of 35% solution you will make is 300 mL + x. The amount of alcohol in that amount of solution is 35% * (x + 300).

Equation of alcohol content:

20% * 300 + 65% * x = 35% * (x + 300)

60 + 0.65x = 0.35x + 105

0.3x = 45

x = 150

Answer: You need to add 150 mL of 65% alcohol solution.

Answer:

x = 8 ± 2i[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Given

x² - 16x + 60 = - 12 ( subtract 60 from both sides )

x² - 16x = - 72

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 8)x + 64 = - 72 + 64, thus

(x - 8)² = - 8 ( take the square root of both sides )

x - 8 = ± [tex]\sqrt{-8}[/tex] = ± 2i[tex]\sqrt{2}[/tex] ( add 8 to both sides )

x = 8 ± 2i[tex]\sqrt{2}[/tex]

The solution of the given expression is ±2√2i+8

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that

x² - 16x + 60 = - 12

Then subtract 60 from both sides;

x² - 16x = - 72

To complete the square then add ( half the coefficient of the x- term )² to both sides

x² + 2(- 8)x + 64 = - 72 + 64,

(x - 8)² = - 8 ( take the square root of both sides )

x =  ±2√2i+8

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None of these options seem to be correct. You can check each result by differentiation:

[tex](e^x\sec^2x)'=e^x(\sec^2x+2\sec^2\tan x)=e^x\sec^2x(1+\tan x)[/tex]

[tex](e^x\sec x)'=e^x(\sec x+\sec x\tan x)=e^x\sec x(1+\tan x)[/tex]

[tex](e^x\tan^2x)'=e^x(\tan^2x+2\tan x\sec^2x)=e^x\tan x(\tan x+2\sec^2x)[/tex]

[tex](e^x\tan x)'=e^x(\tan x+\sec^2x)[/tex]

But none of these are equivalent to [tex]e^x(\sec x+\tan^2x)[/tex]...

Answer:

∠CAB ≅ ∠SAB is not true

Step-by-step explanation:

CPCTC means id ABC = XYZ, than A=X, AB=XY, C=Z and so on. Basically the number numbers that come in the same order as the other one is equal.

So ∠CAS ≅ ∠BAS is true but ∠CAB ≅ ∠SAB is not.

Hope this helps. If you have any follow-up questions, feel free to ask.

Have a great day! :)

Answer:

sap

Step-by-step explanation:

Answer: 24 because you add 5 for every number ex: 9+5=14

Answer:

24

Step-by-step explanation:

The difference can be calculated by subtracting the second term with the first term.

d = 14 - 9

d = 5

The difference is 5.

Add 5 to 19.

19 + 5 = 24

Answer:

4.2 in

Step-by-step explanation:

let us first visualize the sail as a triangular shape

the angle of the triangle from top is 40°

the height of the triangle is give as 5 in

we can apply SOH CAH TOA to solve for the base of the sail

the opposite = the base of the sail

the adjacent = the height of the sail= 5 in

therefore

Tan∅= Opp/Adj

Tan(40)= Opp/5

Opp= Tan(40)*5

Opp= 0.8390*5

Opp= 4.195 in

Hence the width of the sail is 4.2 in to the nearest tenths

Answer:

4.2

Step-by-step explanation:

Please find attached

thank you

The area of Integral is 19 sq units.

An integral in calculus is a mathematical concept that can be used to represent an area or an expanded version of an area. The basic components of calculus are integrals and derivatives. The terms antiderivative and primal are additional terms for integral.

In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).

Given:

∫ 3 0 | 8 x − 10 | d x

Now, the graph touches the x axis  

when 8x- 10 = 0

x= 10/8

x= 5/4

and, When x = 0, y = 10.

So, the limit range will be x = 0 to x = 5/4.

Now, Area of First triangle

= 10 x 5/4 x 1/2

= 25/4

and, Area of second triangle

= 14 x (3- 10/8) x 1/2

= 7 x 7/4

= 49/4

Hence, the total Area = 25/4 + 49/4 = 19 sq. units

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Answer:

Net present value is $61,058.

Step-by-step explanation:

Net present value is the difference between present value of cash inflows and the present value cash outflows over the period of time. NPV method is used in capital budgeting to analyze profitability of the project.

Less: initial cost is $29,000

Add: Year 1: Cost saving due to new furnace is $5,600 (2,800 oil gallons * $ 2 per gallon)

Year 2: Cost saving due to new furnace is $7,000 (2,800 oil gallons * $ 2.50 per gallon)

Year 3- 20: Cost saving due to new furnace is $8,400 (2,800 oil gallons * $ 3 per gallon)

Less : Maintenance expenditure is $1,200

The furnace will benefit for 20 years and the price per gallon will increase by $0.50 year.

The annuity factor is applied at discount factor of 6% and then present value of each cash inflow and outflow is calculated. The net present value is $61,058.

Answer:

C

Step-by-step explanation:

I suppose you have learned that for the sides of a triangle to work, it has to be a + b > c, the 4 is the a, the 8 is the b, the 12 is the c.

So: 4 + 8 > 12; however this is not true, they are equal so the triangle wont be a triangle, it would be lines that never connect.

Answer:

probability that all of the sprinklers will operate correctly in a fire: 0.0282

Step-by-step explanation:

In order to solve this question we will use Binomial  probability distribution because:

A binomial distribution is a probability of a success or failures outcomes in an  repeated multiple or n times.

Number of outcomes of this distributions are two.

The formula is:

b(x; n, P) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]

b = binomial probability  also represented as P(X=x)

x =no of successes

P = probability of a success on a single trial

n = no of trials

[tex]C_{n,x}[/tex] is calculated as:

[tex]C_{n,x}[/tex] = n! / x!(n – x)!

        = 10!  / 10!(10-10)!

        = 1

According to given question:

probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.

number of trials i.e. n = 10 as number of sprinklers are 10

To find: probability that all of the sprinklers will operate correctly in a fire

X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them

So putting these into the formula:

P(X=x) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]

           = C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰

           =  1 * 0.0282 * (0.3) ⁰

           = 1 * 0.0282 * 1

  P(X=x)        = 0.0282

Answer:

∛-2

Step-by-step explanation:

The aritmetic expressión is:

∛-2

Answer:

D. is used to reveal an underlying pattern in the data.

Step-by-step explanation:

Smoothing a time series is achieved when a computer uses some pre-programmed calculation methods to remove noise from large volumes of data. Smoothing helps a user detect patterns in a set of data, thus making it possible to make future predictions. For example, smoothing can be used in the prediction of the rise and fall of stock prices. This helps the traders to have an idea of what to expect in the cost of trading.

Although smoothing reveals the patterns in a set of data, it provides no explanation as to why it is so. It is left to the researcher to draw conclusions as to the reasons for the patterns.

Answer:

[tex] x = 16 [/tex]

Step-by-step explanation:

x = length of diagonal, can be calculated using the Law of Cosines as explained below:

a² = b² + c² - 2bc(cosA),

Where,

a = x

b = 17

c = 13

A = 64°

Plug in the values into the formula:

[tex] x^2 = 17^2 + 13^2 - 2(17)(13)*cos(64) [/tex]

[tex] x^2 = 289 + 169 - 442*0.4384 [/tex]

[tex] x^2 = 458 - 193.77 [/tex]

[tex] x^2 = 264.23 [/tex]

[tex] x = \sqrt{264.23} [/tex]

[tex] x = 16.255 [/tex]

Length of diagonal, [tex] x = 16 [/tex] (to nearest whole number)

Answer:

7t+5

Step-by-step explanation:

Answer:

7t +5

Step-by-step explanation:

6t+7−2+t

Combine like terms

6t+t  + 7-2

7t +5

Answer:

[tex](x + {y}^{2}) = {x}^{2} + 2x {y}^{2} + {y}^{4} [/tex]

Thanks!!!!

Incomplete question. I've made some assumptions to provide clarity.

Answer:

a. $45,743.07

b. $44,843.07

Step-by-step explanation:

Let's assume Victor is a single filer with an income of $100,000.

Using the 2017 tax bracket rates for single filers, Victor would be expected to pay:

- 10 percent on the first $9,325 = 10% x 9525 =$932.5

- plus 15 percent of the amount between $9,326 and $37,950 (37950-9326) x 15% = $4293.6

- plus 25 percent of the amount between $37,951 and $91,900 (91900-37,951 ) x25% = $13487.25

- plus 28 percent of the amount over $91,901-$191,650 (191650-91901) x 28% = 27929.72

Total=  $46,643.07

Minus $900 tax credit= $46,643.07-$900= $45,743.07

Minus $900 charitable contribution = $45,743.07-$900= $44,843.07

Answer:

18167474898

Step-by-step explanation:

I used a calculator.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

work is shown and pictured

Answer:

Image is attached.

Answer: The second option;  y =  (x - a)^2*(x-b)^4

Step-by-step explanation:

Ok, we have that a and b are real numbers different than zero.

In the graph, we can see that the line touches the x-axis in two values. Now, if we would have an equation like:

y = x*(x - a)^3*(x - b)^3

then when x = 0 we would have:

y = 0*(0-a)^3*(0-b)^3 = 0

But in the graph, we can see that when x = 0, the value of y is different than zero, so we can discard options 1 and 3.

So the remaining options are:

y = (x - a)^2*(x-b)^4

y = (x - a)^5*(x - b)

Now, another thing you can see in the graph is that it is always positive.

Particularly the second option allows negative values for y because it has odd powers, then we can also discard this option.

(For example, if x > a and x < b we would have a negative value for y)

Then the only remaining option is y =  (x - a)^2*(x-b)^4

Answer:

B.y =  (x - a)^2*(x-b)^4

Step-by-step explanation:

EDGE 2020 Brainliest please

Answer:

Option (D)

Step-by-step explanation:

Zero of any function is defined by the x-value of the function when y = 0.

Let the equation of the line given in the graph is,

y = mx + b

where m = slope of the line

b = y-intercept of the line

Slope of a line passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined by the formula,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

If the passes through (0, -3) and (-2, 0)

m = [tex]\frac{-3-0}{0+2}[/tex]

m = [tex]-\frac{3}{2}[/tex]

Fro the graph,

y-intercept 'b' = -3

Therefore, equation of the line is,

[tex]y=-\frac{3}{2}x-3[/tex]

For y = 0,

[tex]0=-\frac{3}{2}x-3[/tex]

[tex]\frac{3}{2}x=-3[/tex]

x = -2

Therefore, option (D) will be the answer.

Answer:

d- -2

Step-by-step explanation:

Answer:

The slope of the given line is 2

Answer -1/2 is the line perpendicular

Step-by-step explanation:

This can be rewritten in fraction form as 2/1 since x/1 = x.

Answer:

D

Step-by-step explanation:

Any number multiplied by an even number will always be even. 10 is an even number.

Answer:

d. 10 times a number is always even

Step-by-step explanation:

multiples of 9 contain 81 and 36 which one is even and the other is odd

multiples of 10 ONLY contain even numbers because   the unit digit for a multiple of 10 is 0.

So whenever you multiply a number by 10 it will be even

Answer:

C. x+4y=-8

Step-by-step explanation:

The standard form of an equation is Ax+Bx=C

y= -[tex]\frac{1}{4}[/tex]x-2

Multiply 4 by both sides

4y= -x-8

1+4y= -8

Answer:

54.5 years.

Step-by-step explanation:

From the above question, we are asked to find the time

The formula for Time(t) =

t = log(A/P) / n[log(1 + r/n)]

A = Amount accumulated after a particular interest and period of time = $80,000

P = Principal (Money invested) = $4,000

r = rate = 5.5% = 0.055

n = compounding frequency = compounding continuously

n = number of days in a year × number of hours in a day

= 365 days × 24 hours = 8760

t = log(A/P) / n[log(1 + r/n)]

t = log(80,000/4,000) /8760[log(1 + 0.055/8760)]

t = log(80000 ÷ 4000) ÷ (8760 × [log(1 + 0.0000062785)]

t = 54.468367222 years

Approximately to the nearest tenth of a year, therefore, the length of time it will it take for his money to reach $80,000 is 54.5 years

Answer:

54.5

Step-by-step explanation:

The correct answer is D. 23

Explanation:

Histograms similar to other graphs represent numerical information, usually by using bars, as well as ranges. For example, in the case presented the information presented belongs to the scores obtained in a test, which are shown using ranges. Moreover, it is possible to know the total of people that took the test by adding each of the frequencies, as the frequency in the y-axis shows the number of times the range repeated and it is expected each grade registered belongs to 1 person. This means the total of people is equal to 2 (score from 60-69) + 9 (score from 70-79) + 7 (score from 80-89) + 5 (score from 90-99) = 23 people.

Answer:

the answer is 23

Step-by-step explanation:

hopes this helps:)

Answer:

the solution to the problem is D

Answer:

Movies: x gig

pictures: x/2 gig

music:  10 - x - x/2 = 10 - (3/2)x

The amount of gigabytes of music stored on the computer is:

[tex]y = 5 - x[/tex]

In which x is the amount stored in movies.

We solve this question representing the amount of music as a variable, that I will call y.

The total amount of data is 10 gigabytes.

Division of the 10 gigabytes:

Half in pictures, that is, 10/2 = 5 gigabytes.

x are movies.

The rest, y, are music.

Thus, since the sum of this all is 10, we have that:

[tex]5 + x + y = 10[/tex]

[tex]y = 10 - 5 - x[/tex]

[tex]y = 5 - x[/tex]

Thus, the amount of gigabytes of music stored on the computer is [tex]y = 5 - x[/tex], considering x as the amount of gigabytes of movies stored.

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Answer:

There is a solution. The ordered pair is (4, 2).

Step-by-step explanation:

Solve the system of equations by using the substitution method.

[tex]x+y=6\\x=2y[/tex]

Substitute x as 2y in the first equation and solve for y.

[tex]2y+y=6\\ 3y=6\\(3y)/3=6/3\\y=2[/tex]

Substitute y as 2 in the second equation and solve for x.

[tex]x=2(2)\\x=4[/tex]

Assuming angle A is opposite to side a, B is the opposite to side b, and angle C is the opposite to side c.

Answer:

The right triangle has the following angles:

A = 48.31º, B = 41.69º and C = 90º.

The sides are:

[tex] \\ a = 37.26[/tex], [tex] \\ b = 33.12[/tex] and c = 49.9.

Step-by-step explanation:

The inner sum of a triangle = 180º.

A=48.31º,

C=90º

A + B + C = 180º

48.31º+ B + 90º = 180º

B = 180º - 90º - 48.31º

B = 41.69º

We can apply the Law of Sines to solve for unknown sides:

[tex] \\ \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]

We know that sin(90º) = 1.

[tex] \\ \frac{a}{sin(48.31)} = \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]

Then, a is:

[tex] \\ \frac{a}{sin(48.31)} = \frac{49.9}{1}[/tex]

[tex] \\ a = 49.9*sin(48.31)[/tex]

[tex] \\ a = 49.9*0.7467[/tex]

[tex] \\ a = 37.26[/tex]

Thus, b is:

[tex] \\ \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]

[tex] \\ b = 49.9*sin(41.69)[/tex]

[tex] \\ b = 33.12[/tex]