For the regions bounded by y = 6cosx and y = one fourth x squared minus 7.

Part A: Find the limits of integration. (10 points)

Part B: Write the expression representing the total area. (10 points)

Part C: Solve for the total area. (10 points)

Answers

Answer 1

For the regions bounded by y = 6cosx and y = one-fourth x squared minus 7, the limits of integration, the expression representing the total area, and the total area are mathematically given as

A=27.03squnit

What are the limits of integration, the expression representing the total area, and the total area.?

Generally, the equation for expression is mathematically given as

y = 6cosx

y=(1/4)x^2-7

therefore

[tex]A=\int^{b}_a (f(x)-g(x))dx[/tex]

The limits are

a=0 b=2\pi

Hence

[tex]A=\int ^{2\pi}_0 (6cosx -((1/4)x^2-7))dx\\\\solving\\\\A=\int^{2\pi}_0 (6cosx -((1/4)x^2-7))dx[/tex]

A=27.03squnit

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Related Questions

You invested $7,000 into a money market account for 10 years at an annual interest rate of 3%. How much is the accrued interest?

Answers

The total interest accrued is $2,407.41 if you invested $7,000 into a money market account for 10 years at an annual interest rate of 3%.

What is invested amount?

An investment is a payment made to acquire the securities of other firms with the intention of making a profit.

We are assuming the interest will be compounded annually

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

We have:

P = $7000

r = 3% = 0.03

t = 10 years

n = 1

[tex]\rm A = 7000(1+\dfrac{0.03}{1})^{1\times10}[/tex]

After calculating:

A = $9407.41

I = A - P = 9407.41 - 7000 = $2,407.41

Thus, the total interest accrued is $2,407.41 if you invested $7,000 into a money market account for 10 years at an annual interest rate of 3%.

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According to the graph, what is the factorization of x² - 5x+6?
OA. (x-3)(x+2)
OB. (x+3)(x-2)
OC. (x+3)(x+2)
OD. (x-3)(x-2)
y xẻ 5Xtộ

Answers

Answer:

OD.(x-3)(x-2)

Step-by-step explanation:

we need two numbers (negative ir positive) that multiply to get 6 abd add to get -5.

so its OD

as -3×-2=6

and -3+-2=-5


Complete the remainder of the
table for the given function rule:
y = ²x + 4
X-6 -3 03 3 6
y 0 [?] [] [] []

Answers

Answer: 2, 4, 6, 8

Step-by-step explanation:

Just plug x into the equation for each one.

x = -3

[tex]y=\frac{2(-3)}{3} +4\\y=\frac{-6}{3} +4\\y=2[/tex]

With this one, you can see it is a linear equation and for every increase of 3 on x, y in increased by 2.

x   -6   -3   0   3   6

y   0   2    4   6   8

John is buying a new car. The value of one car he is considering is $20,000. The value of the car as it ages can be modeled by the function V = 20 , 000 ( 0 . 84 ) t , where t is the number of years from the time of purchase. One of the factors John is using to make his decision is the value of the car over time until it reaches half its original value. What values of domain are reasonable for the given function in this context?
A. all real numbers greater than or equal to 0 and less than 2.8
B. all real numbers greater than or equal to 10,000 and less than or equal to 20,000
C. all real numbers greater than or equal to 0
D. all real numbers greater than or equal to 0 and less than 4

Answers

Option D is the correct answer.

All real numbers greater than or equal to 0 and less than 4.

What is Domain?

The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined.

Here, The function of the car value is given as:

V(x) = 20000 X (0.84)ˣ

When the car reaches half its value, we have:

V(x) = 10000

Substitute V(x) = 10000 in V(x) = 20000 * (0.84)ˣ

10000 = 20000 X (0.84)ˣ

Divide both sides by 20000

0.84ˣ = 0.5

Take the logarithm of both sides

x log(0.84) = log(0.5)

Divide both sides by log(0.84)

           x = 4

This means that the maximum value of x is 4.

Thus, all real numbers greater than or equal to 0 and less than 4.

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Josh made $35,000 in taxable income last year.
Suppose the income tax rate is 15% for the first $8500 plus 17% for the amount over $8500.
How much must Josh pay in income tax for last year?

Answers

First you take 8500 and mutiply it by .15 to get 1275 take 8500-1275 to get 7225
Then take 26500 which you get from taking 8500 from 35000. Then you 26500 times .17 to get 4505 then 26500-4505 to get 21995 then for the total do 21995+7225=29220

The table below shows the results of a screening program organized by Level 300 students of the department physiotherapy of the College Health Sciences of the University of Ghana. Complete the table and answer the questions below it using your understanding of probability and its applications to biomedical data.
True Diagnosis for presence of E. Coli

Test results Disease No Disease Total
Positive 35 15
Negative 10 60
Total

a. What is the efficiency of the test? 3 marks
b. What is the sensitivity of the screening kit? 3 marks
c. What is the specificity of the screening kit? 3 marks
d. What is the predictive value (PPV) of the test? 3 marks
e. What is the negative predictive value (NPV) of the test? 3 marks
(15 marks)
2. In double blinded randomized control trial for hypertensive patients attending Cocoa Clinic, thirty (30) 50-59-year-old were admitted into an intervention program for 6 weeks. During the trial, the average improvement in their systolic blood pressure was 15. The average improvement in systolic blood pressure in the general population of hypertensive patients is 20 with a standard deviation of 2.

i. What are the null and alternative hypotheses in this RCT? (2 marks)
ii. What tail is required in this test? (2 marks)
iii. What is the most appropriate statistical test for this study? (2 marks)
iv. State the assumptions of the test. (2 marks)
v. Test the above hypothesis using the appropriate statistical tool (7 marks)
Critical value =3.6

Answers

The correct answer is C because they are asking for the specific screening kit marks

please help me.
Which quantity is multiplied by pi () in the formula for the area of a circle?
A. d
OB. 2
O c. d
D. r

Answers

Answer: B) r^2

Detailed Explanation:

The formula for calculating the Area of a Circle is πr^2 where π is being multiplied with r^2. Hence, the correct option is B.

The temperature of a chemical reaction ranges between -10 degrees Celcius and 50 degrees Celcius. The temperature is at its lowest point when t=0, and the reaction completes 1 cycle during a 6 hour period. What is a cosine function that models this reaction?

Answers

Answer:

The cosine function is f(t) = -30sin(π÷3)t + 20

Step-by-step explanation:

Given : The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period.

To find : What is a cosine function that models this reaction?

General form of cosine function is f(x) = A cos(Bx)+C

Where A is the amplitude

B=2π÷Period

C is the midline    

Now, We have given

The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius.

A is the average of temperature,

i.e,

A=(-10-50)÷2 = -30

Period of 1 cycle is 6 hour

So,

B = 2π÷6 = π÷3

The temperature is at its lowest point when t = 0 and we know lowest point is -10

So,

f(t) = A cos t + C

-10 = -30 cos 0 + C

Therefore, C = 20

Substituting the values, we get

The cosine function is f(t) = -30sin(π÷3)t + 20

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Please hurry!!!! What is the domain of the function on the graph?
all real numbers
all real numbers greater than or equal to –2
all real numbers greater than or equal to –5
all real numbers greater than or equal to 0

Answers

A. all real numbers

the doman are the x values and in this equation they are infinite making the domain all real numbers

The price of 11 pizzas and 5 hamburgers is 40$. The price of 1
hamburger is 2.50$. What is the price of a hamburger?

Answers

Step-by-step explanation:

you mean, what is the price of a pizza, right ? and I guess it is pizza slices ...

1 hamburger = $2.50

5 hamburgers = 5×1 hamburger = 5×2.5 = $12.50

that leaves for the 11 pizzas (slices)

40 - 12.5 = $27.50

so, 1 pizza (slice) is

27.5 / 11 = $2.50

Answer:

One hamburger costs $2.50

One pizza also costs $2.50

Step-by-step explanation:

Let's say Nigel is the one purchasing lots of food for no reason.

Nigel bought 11 pizzas and 5 hamburgers for $40 (DAMMMM WHAT COUPON IS THAT??)

We can write this algebraically:

11p + 5b = 40

We know that the price of 1 Hamburger is $2.50.

Now we can plug that into out equation and find the price of one pizza:

11p + 5(2.50) = 40

11p + 12.5 = 40

11p = 27.5

p = 2.5

Now, we have the price of one pizza, $2.50

what is the slope of the line represented by the equation y = 4/5x -3?

Answers

Answer:

4/5

Step-by-step explanation:

Slope

    Slope y-intercept of a line: y = mx + b

Where m is the slope and b is the y-intercept.

 [tex]\sf y =\dfrac{4}{5}x-3\\\\\boxed{Slope = \dfrac{4}{5}}[/tex]

hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა

⊱┈────────────────────────┈⊰

[tex]\large \bold {ANSWER}[/tex]

[tex]\large \boxed { \large \sf \green{m = \frac{4}{5} }}[/tex]

[tex]\large \bold {EXPLANATION}[/tex]

This line is in slope-intercept form, y=mx+b, where m represents the slope and b represents the y-intercept.

So that we can conclude that the slope is 4/5.

find the distance between the pair of points (7,6) and (4,10)​

Answers

Answer:

5 units

Step-by-step explanation:

to find out the answer for this you must first find the distance between 7 and 4 and then 6 and 10

then you would square them and then add them

lastly you would take the square root of that and youd have your answer

so

7 - 4 = 3

6 - 10 = -4 (just use 4)

3^2 + 4^2 = 9  + 16 = 25

then you take the square root of this

sqrt(25) = 5

that is your answer

To solve this problem, you will use the Distance Formula to find the distance between two coordinate points.

Set Up the Distance Formula

The Distance Formula is defined as follows:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

We must title our points by the standard coordinate naming system:

[tex](x_1, y_1) \ \text{and} \ (x_2, y_2)[/tex]

Therefore, our points can be labeled:

[tex]x_1 = 7[/tex][tex]y_1 = 6[/tex][tex]x_2 = 4[/tex][tex]y_2 = 10[/tex]

Substitute Known Values for Variables

Now, substitute the known values as the variables in the Distance Formula:

[tex]d=\sqrt{(4 - 7)^2 + (10 - 6)^2}[/tex]

You must know the BPEMDAS acronym, which stands for:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Simplify the expression using BPEMDAS:

[tex]d=\sqrt{(-3)^2 + (4)^2}[/tex]

Remember that when a number is raised to the 2nd power, it is the same thing as multiplying the number by itself:

[tex]-3\times-3 = 9[/tex]

[tex]4\times4=16[/tex]

Simplify further by removing the parentheses:

[tex]d=\sqrt{9+16}[/tex]

Compute the additive operation:

[tex]d=\sqrt{25}[/tex]

Simplify the Radicand

The number that is placed inside of a square root symbol (or a radical symbol) is referred to as the radicand.

In this situation, the radicand is 25.

To simplify the radicand, you may either use a calculator to compute the result, or you can determine which number raised to the 2nd power will result in a final answer of 25.

In this case, we can determine that 5² will result in a final answer of 25.

[tex]5^{2} = 25[/tex]

The final answer is 5 units.

Find the value of x which satisfies the following equation.
log2(x−1)+log2(x+5)=4

Answers

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: x = 3[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: log_{2}(x - 1) log_{2}(x + 5) = 4[/tex]

[tex]\qquad \tt \rightarrow \: log_{2} \{(x - 1)(x + 5) \} = 4[/tex]

[ log (x) + log (y) = log (xy) ]

[tex]\qquad \tt \rightarrow \: ( x - 1)(x + 5) = {2}^{4} [/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + 5x - x - 5 = 16[/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + 4x - 5 - 16 = 0[/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + 4x -21 = 0[/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x - 3x - 21 = 0[/tex]

[tex]\qquad \tt \rightarrow \: x(x + 7) - 3(x + 7) = 0[/tex]

[tex]\qquad \tt \rightarrow \: (x + 7)(x - 3) = 0[/tex]

[tex]\qquad \tt \rightarrow \: x = - 7 \: \: or \: \: x = 3[/tex]

The only possible value of x is 3, since we can't operate logarithm with a negative integer in it.

[tex]\qquad \tt \rightarrow \: x = 3[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Help with a composition of two functions! 20 pts for a solution!

Answers

The function (fog)(x) would be (x^4 + 10x² + 27). Also, the domain of (fog)(x) is all the real numbers.

What is a function?

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

f(x) = x² + 2

g(x) =  x² + 5

so, to take the composition of f and g (fog) replace the x in f(x)  with g(x);

(fog)(x) = (x² + 5)² + 2

(fog)(x) = (x^4 + 25 + 10x² )+ 2

(fog)(x) = (x^4 + 10x² + 27)

Also, the domain of (fog)(x) is all the real numbers.

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vertical angles must : check all that apply
A. be complementary
B. have the same vertex
C. be congruent
D. be acute

Answers

Answer: B and C

Step-by-step explanation: For A, vertical angles can be complimentary or supplementary. For D, vertical angles can sometimes be acute but not always.

Need help with this geometric question

Answers

Answer: A

Step-by-step explanation:

[tex]V=\frac{1}{2}(6)(4)(2)=\boxed{24}[/tex]


[15 PTS] PLS HELP!!!

What is the end behavior of the function?

Answers

The correct answer is the fourth option.

Somebody help me solve;

(1)A fair die is being rolled.
a) Find the probability that at least 5 rolls are needed to obtain the first
one.
b) Find the probability that it will take fewer than seven rolls to obtain the
second one if the first one occurs on the third roll.

Answers

P(at least 5 rolls until 1) = P(4 rolls are not 1) = 5/6 x 5/6 x 5/6 x 5/6 = 0.4823 (4sf)

Fewer than 7 rolls to get second 1 after first takes 3 rolls means second occurs on 4th, 5th or 6th roll
The probability of each of these is 1/6, 5/6 x 1/6 and 5/6 x 5/6 x 1/6 respectively.
P(second 1 on 4th, 5th or 6th roll) = 1/6 + 5/36 + 25/216 = 91/216 = 0.4213 (4sf)

Can you do this because it is confusing to me

Answers

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The volume of the cylinder is 1330.4644 cm³.

What is a cylinder?

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.

Given the height of the cylinder is 14 cm, while the diameter of the cylinder is 11 cm. Therefore, the volume of the cylinder can be written as,

The volume of the cylinder = (π/4)×(D²) × H

                                               = (π/4)×(11)² × 14

                                               = 1330.5 cm³

Hence, the volume of the cylinder is 1330.5cm³.

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Select the correct answer. Consider functions h and k. Every x value has a relationship in k of x. What is the value of (h o k)(1)? A. 28 B. 4 C. 1 D. 0

Answers

Answer: 0

Step-by-step explanation:

[tex](h \circ k)(1)=h(k(1))=h(4)=\boxed{0}[/tex]

y=x^2 -2x -3 im not sure how to solve this

Answers

Answer:

It is solved on a graph

Step-by-step explanation:

A quadratic graphical solution.

4. During a camping trip, a group went one-third of the total distance by boat, 10km by foot and One-sixth of it by riding horses. Find the total distance of the trip. Plss answer thiissss ​

Answers

Answer:

20 km

Step-by-step explanation:

So 1/3 = 2/6
2/6 = distance traveled by boat + 1/6 traveled by riding horses = 3/6 = 1/2

Meaning the 10 km by foot left is the other half

Graph the feasible region for the follow system of inequalities by drawing a polygon around the feasible region. Click to set the corner points. 2 x + 4 y ≤ 36 7 x + 5 y ≤ 63 x ≥ 0 y ≥ 0 { 2x+4y ≤ 36 7x+5y ≤ 63 x ≥ 0 y ≥ 0

Answers

Feasible region for the given inequalities is shaded via black color in graph.

What is Inequalities?

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Here, given Inequalities are;

      2 x + 4 y ≤ 36

      7 x + 5 y ≤ 63

      x ≥ 0 y ≥ 0

The graph of given inequalities are given below and the feasible region is shaded with the black color.

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A building has a height of 40 feet and a length of 20 feet. On a scale drawing of the building, the height is 20 centimeters. What is the length of the building on the scale drawing in centimeters?

Answers

Answer:

10 centimeters

Step-by-step explanation:

For the height:

40 ft / 20 cm = 2 ft / cm

With this ratio, we find the length as follows:

2 ft / cm = 20 ft / x cm

[tex]2 = \frac{20}{x} [/tex]

[tex]2x = 20[/tex]

[tex]x = 10[/tex]

Answer:

10 cm

Step-by-step explanation:

Look at the answer

Y=-1/3x+2

A.
B.
C.
D.

Answers

Answer:

C

Step-by-step explanation:

The slope is -1/3, so it will go down and to the right. Down 1, to the right 3 (rise over run!)

The y intercept is 2.

The circle below is centered at the point (-1, 2) and has a radius of length 3.
What is its equation?
O A. (*+ 1)2 + (y- 2)2 = 9
O B. (x- 2)2 + (y + 1)? =
32
O c. (x- 1)2 + (y + 2)2 = 9
l
O D. (x+ 2)2 + (y- 1)2 =
32

Answers

Answer:

it should be option A

and in option there should be "x" instead of "*"

Equation of circle is,

⇒ (x + 1)² + (y - 2)² = 9

What is mean by Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The circle below is centered at the point (-1, 2) and has a radius of length 3.

Now, We get;

The equation of circle is,

⇒ (x - (- 1))² + (y- 2)² = 3²

⇒ (x + 1)² + (y - 2)² = 9

Thus, Equation of circle is,

⇒ (x + 1)² + (y - 2)² = 9

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If BC is 1

CD is 2

DA is 3

AB is 4,

what is EF?

Answers

The length of the side EF will be 1 unit, approximately.

The complete figure is attached below.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The figure is given below.

The length of EF will be

EF = CF – CE

Then the value of CF will be

CF = BC × cos 30

CF = 2 × 0.866

CF = 1.732

Then the value of CE will be

CE = BC × cos 42

CE = 1 × 0.743

CE = 0.743

Then we have

EF = 1.732 – 0.743

EF = 0.989 ≈ 1

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How to do this please?️​

Answers

Step-by-step explanation:

Using dimensional analysis, let convert km to cm.

[tex] \frac{4cm}{1km} \times \frac{km}{100000 \: cm} [/tex]

Cancel out the km

[tex] \frac{4cm}{100000 \: cm} [/tex]

[tex] \frac{1}{25000 } [/tex]

So n= 25000

iii.

Dimensional Analysis

[tex] \frac{3 \: cm}{1 } \times \frac{km}{100000 \: cm} [/tex]

[tex] \frac{3 \: km}{100000} [/tex]

Or

[tex]0.00003 \: km[/tex]

2. Ahmed has ¢15.25 and spent $7.50 at the
Total Shop. How much money does he have
left?

Answers

Answer:

D)¢ 8.75

Step-by-step explanation:

that is my answer please


dollars per pint
pints per dollar.

Find the unit rates. If necessary, round your answers to the nearest hundredth.
$6.79 for 16 pints

Answers

Answer:

0.42 dollar per pint

2.36 pints per dollar

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Supposing the minimum height of the Ferris Wheel occurs when t=0, write the sinusoidal function for the height as a function of time. Last graph on a coordinate plane, label the key points. A recipe calls for 4 cups of peanuts for 5 cups of flour. Using the same recipe, how many cups of flour will you need for 3 cups of peanutsI really need help Profitability, consumer relations, and competition are involved in what kinds of concerns in the design process? Read the Greek myth "Midas" retold by Thomas Bulfinch and answer the question.[1] Bacchus, on a certain occasion, found his old schoolmaster and foster-father, Silenus, missing. The old man had been drinking, and in that state wandered away, and was found by some peasants, who carried him to their king, Midas. Midas recognized him, and treated him hospitably, entertaining him for ten days and nights with an unceasing round of jollity.[2] On the eleventh day he brought Silenus back, and restored him in safety to his pupil. Whereupon Bacchus offered Midas his choice of a reward, whatever he might wish. He asked that whatever he might touch should be changed into gold. Bacchus consented, though sorry that he had not made a better choice.[3] Midas went his way, rejoicing in his new-acquired power, which he hastened to put to the test. He could scarce believe his eyes when he found a twig of an oak, which he plucked from the branch, become gold in his hand. He took up a stone; it changed to gold. He touched a sod; it did the same. He took up an apple from the tree; you would have thought he had robbed the garden of the Hesperides. His joy knew no bounds, and as soon as he got home, he ordered the servants to set a splendid repast on the table. Then he found to his dismay that whether he touched bread, it hardened in his hand; or put a morsel to his lip, it defied his teeth. He took a glass of wine, but it flowed down his throat like melted gold.[4] In consternation at the unprecedented affliction, he strove to divest himself of his power; he hated the gift he had lately coveted. But all in vain; starvation seemed to await him. He raised his arms, all shining with gold, in prayer to Bacchus, begging to be delivered from his glittering destruction. Bacchus, merciful deity, heard and consented. "Go," said he, "to River Pactolus, trace its fountain-head, there plunge yourself and body in, and wash away your fault and its punishment." He did so, and scarce had he touched the waters before the gold-creating power passed into them, and the river sands became changed into gold, as they remain to this day.Select a possible theme of the myth. A. Gold is a symbol of wealth and authority. B. Greed can result in negative consequences. C. People who expect a reward for good deeds are selfish. D. Money does not bring as much happiness as friendship. Ammonia gas occupies a volume of 450. mL at a pressure of 720. mm Hg. What volume will it occupy at standard pressure?Show your work Please!!!! Which best describes the difference between internal and thermal energy? A. Internal energy is the total potential energy in a substance, and thermal energy is the total kinetic energy in a substance. B. Thermal energy is the total potential energy in a substance, and internal energy is the total kinetic energy in a substance. C.Internal energy is the total potential and kinetic energies in a substance, and thermal energy is the part of internal energy that can be transferred to another substance.D. Thermal energy is the total potential and kinetic energies in a substance, and internal energy is the part of internal energy that can be transferred to another substance.ITS C!!!!!!!!!!!!!!! Which kind of diet helps prevent cancerMax is gearing up for her lacrosse match. What safety measures can help Max stay safe for the big event? determine domain and range from graph Jessie bought a vacuum cleaner priced at $79 with a 6% sales tax rate. What is the total cost of the vacuum cleaner after-tax?