Which is the area between the x-axis and y=x from x=1 to x=5

Answers

Answer 1

Answer:

[tex]\displaystyle A = 12[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

FunctionsFunction NotationGraphing

Calculus

Integrals

Definite IntegralsArea under the curve

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

y = x

Interval: x = 1 to x = 5

Step 2: Sort

Graph the function. See Attachment.

Bounds of Integration: [1, 5]

Step 3: Find Area

Substitute in variables [Area of a Region Formula]:                                   [tex]\displaystyle A = \int\limits^5_1 {x} \, dx[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]:                     [tex]\displaystyle A = \frac{x^2}{2} \bigg| \limits^5_1[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:           [tex]\displaystyle A = 12[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Which Is The Area Between The X-axis And Y=x From X=1 To X=5

Related Questions

What goes in the blanks? The measure of angle θ is 7π/4. The measure of its reference angle is _____°, and tan θ is ______?

Answers

Answer:

The measure of angle θ is 7π/4. The measure of its reference angle is 45°, and tan θ is -1.

Answered by GAUTHMATH

What is the value of x?

Answers

Hello,

The sum of the angles of a triangle is equal to 180°.

So :

x = 180 - 40 - 55 = 85°

Have a nice day :)

can someone help me to solve this question. the questions is about to calculate the value of x . please help me thankyou​

Answers

Answer:

180-(63+63)

=180-126

=54

180-(37+90)

180-127

53

180-(54+53)

=180-107

=73°

Answer:

Step-by-step explanation:

AC = AD So,  Δ ACD is as isosceles triangle.

∠ADC ≅∠ACD = 63°

In ΔACD ,

    63 + 63 + ∠DAC = 180   {Angle sum property of triangle}

            126 + ∠DAC = 180

                     ∠DAC = 180- 126

                     ∠DAC = 54°

In ΔABC,

90+ 37 + ∠CAB = 180

        127 + ∠CAB = 180

                 ∠CAB = 180 - 127

                 ∠CAB = 53

∠EAD + ∠DAC + ∠CAB = 180   {Straight line angles}

x + 54  + 53 = 180

        x + 107  = 180

                  x = 180 -107

x = 73°

     

please help i have class soon :(

John used digits from 0 to 6 only to create a three-digit PIN code. He forgot his PIN code. He remembers that his code contains different ascending digits. What is the maximum number of combinations John has to check to find his PIN code?

Answers

this was incorrect.

im sorry :(

Answer:

35

Step-by-step explanation:

We know that the numbers have to be in ascending order. If, for example, the first digit is 0, and second digit is 1, then we would have 5 other numbers in the ones place that would be larger. If the second digit is 2, then would would have 4 other numbers that would be larger, and so on. So if 0 is the first digit, then we would have 5+4+3+2+1=15 combinations. If 1 is the first digit, then we would have 4+3+2+1 combinations. Eventually, we would get 35.

If f(-x) = 0, what is x?
O only
-6 only
-2,1, or 3 only
-6,-2, 1, or 3 only​

Answers

Answer:

3rd option

Step-by-step explanation:

f(x) = 0 are the points on the x- axis where the graph crosses, the zeros

The graph crosses the x- axis at - 2 , 1 and 3

please help and dont get it wrong! thank you =)))

Answers

Answer:

tanong mo sa may mga nakaka alam niyan para walang mali, thanks

Find the angle between u = (8,-3) and v = (-3,8). Round to the nearest tenth of a degree.

Answers

Mark Brainliest please

Answer is 90 degrees

What
Is the volume of this object

Answers

Answer:

100

Step-by-step explanation:

5x4=20

20x5=100

If you times the length by with: 5x4 you get 20. Then you multiply 20x5 then you get your volume: 100

What is One-third divided by one-fourth?

Answers

Answer:

The answer is 1 and 1/3

Step-by-step explanation:

hope its correct

Answer:

1/3 ÷ 1/4

= 1/3 × 4×1

=4/3

=1⅓

What is the answer of the question?​

Answers

Answer:

A. 2

Step-by-step explanation:

[tex] \int_0^1 \: 5x \sqrt x \: dx \\ \\ = \int_0^1 \: 5x . \: {x}^{ \frac{1}{2} } \: dx \\ \\ = 5\int_0^1 \: {x}^{ \frac{3}{2} } \: dx \\ \\ = 5 \bigg( \frac{ {x}^{ \frac{3}{2} + 1 } }{ \frac{3}{2} + 1 } \bigg)_0^1\\ \\ = 5 \bigg( \frac{ {x}^{ \frac{5}{2} } }{ \frac{5}{2}} \bigg)_0^1 \\ \\ = 5 \times \frac{2}{5} \bigg({x}^{ \frac{5}{2} } \bigg)_0^1 \\ \\ = 2 \bigg( {1}^{ \frac{5}{2} } - {0}^{ \frac{5}{2} } \bigg) \\ \\ = 2(1 - 0) \\ \\ = 2[/tex]

Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]

Here 5 is a constant so it can come out . So that,

[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]

Now we can write √x as ,

[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]

Simplify ,

[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]

On simplifying we will get ,

[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]

Carlos is 46 years old, 5’10” and weighs 225 pounds. He has diabetes and dislikes taking his diabetes medications. What wellness strategy would his doctor most likely recommend to help him reduce his diabetes medications?
A.
lose weight
B.
use stress management techniques
C.
get immunized
D.
brush his teeth regularly
E.
increase his daily fruit intake

Answers

A. lose weight i guess

What is the domain of the following function ?

Answers

Answer:

{-6, 1, 5, 8}

Step-by-step explanation:

The domain is the set of x-coordinates or inputs.

{-6, 1, 5, 8}

Answer is A
-6, 1, 5, 8

Domain is always gonna be in the left side of the relation, while range is the right (7, -2.)

Write the equation of the line (in y = ax+b form) in the
graph below. do not use any spaces when typing your
answer

Answers

Answer:

y=3x-8

Step-by-step explanation:

Can someone help me with this math homework please!

Answers

Answer:

same after 3 years

because .............................

Answer:

The populations of orangutans will be same after 3 years

Step-by-step explanation:

Let the populations or orangutans is the same after n years

Decrease in population of oragnutans in the first study

=784-25n=784−25n

Decrease in population of oragnutans in the second study

=817-36n=817−36n

According to the question

784-25n=817-36n784−25n=817−36n

\implies 36n-25n=817-784⟹36n−25n=817−784

\implies 11n=33⟹11n=33

\implies 11n=33⟹11n=33

\implies n=\frac{33}{11}⟹n=

11

33

\implies n=3\text{ years}⟹n=3 years

Therefore, the populations of orangutans will be equal after 3 years

Hope this is helpful.

Solve the inequality 6 is greater or equal than m- 1

Answers

Answer:

7 ≥ m OR m ≤ 7

Step-by-step explanation:

You can actually solve this in two ways , either :

6 ≥ m - 1

6 + 1 ≥ m

7 ≥ m

OR

m -1 ≤ 6

m ≤ 6 + 1

m ≤ 7

Both are correct.

Find the length of CZ

A. 32
B. 45
C. 9
D. 1

Answers

Answer:

c

Step-by-step explanation:

just took it

Answer:

D. 1

Step-by-step explanation:

CA = 17

ZA = 16

CZ + ZA = CA

CZ + 16 = 17

CZ = 1

D. 1

Which of the following are remote interior angles of _1? Check all that apply.
u A. 25
I B. 26
III C. 21
D. 24
E. 23
F. 22

Answers

Answer:

angle 3

angle 2

Step-by-step explanation:

Mathematically, from the angle sum theorem of triangles, the sum of two opposite interior angles of a triangle equals the exterior angle on the third side

Now, for angle 1, it is an exterior angle for angle 4

The two other opposite interior angles that would make angle 1 is simply angles 3 and 2

Can someone help me with this math homework please!

Answers

Answer:

1. Both Egyptian and Chinese number systems use base 10.

3. All three cultures had unique symbolism to represent their numbers . (Earlier symbols were used to depict things)

4. There are two primary sources for ancient Egyptian mathematics

Step-by-step explanation:

I didn't know this question so I just searched on Brainly and someone already asked this question before, so I'm using their answers (just letting you know lol)

Credit: chisnau & metchelle

algebra help pls answer

Answers

Answer:

[tex]\frac{-1+1}{0-(-2)}=0[/tex]

[tex]ANSWER: A)~0[/tex]

------------------------------

HOPE IT HELPS

HAVE A GREAT DAY!!

I need help with this, Im never good with these

Answers

Answer:

(a) basketball

(b) hat

(c) stuffed animal

explanation:

I'm not sure if got right but from what i see;

Chances from 1-23 you get a stuffed boi

Chances from 24-54 you get a hat (why)

Chances from 55-100 you get a basketball

Winner 5 got 90, which is between 55-100

Winner 6 got 35, which is between 24-54

winner 8 got a 7, which is between 1-23

Hope I didn't read it wrong

Does every integer have a successor?

Answers

Answer:

Yes every integer has a successor and a predecessor

Step-by-step explanation:

please help i have to resit math final so bare with me


help me with this equation : x^2 - 7 = 0 IN QUADRATIC EQUATION

PS. 1st one to answer gets a brainly crown :)

Answers

I hope this is the correct answer

find the missing side of each triangle. i need help!!!

Answers

Answer:

√161 yd

Step-by-step explanation:

Hi there!

We're given a right triangle (notice the right angle), the measure of one of the legs (one of the sides that make up the right angle) as 8 yd, and the hypotenuse (the side opposite to the right angle) as 15 yd.

We need to find x, which is the other leg in the triangle

If we are given 2 sides and need to find a third, we can use Pythagorean Theorem, which states that a²+b²=c² if a and b are legs and c is the hypotenuse

In this case, a=8, b=x, and c=15

So let's substitute those values into the formula

(8)²+x²=(15)²

raise everything to the second power

64+x²=225

subtract 64 from both sides

x²=161

take the square root of both x and 161

x=√161, x=-√161

-√161 cannot work in this case, as distance cannot be negative.

The question asks for the answer to be in simplified radical form, but √161 cannot be simplified down further

so the answer is √161 yd

Hope this helps! :)

Taking a discount of 50% off followed by a discount of 50% off results in a total discount of_______. A. 25% B. 50% C. 75% D. 100%​

Answers

Answer:

A. 25%

Step-by-step explanation:

50% = 1/2

1/2 of 1/2 = 1/2 * 1/2=

1/4 = 25%

Answer:

100%-50%=50% so the answer is B

The third National Health and Nutrition Examination Survey collected body fat percentage (BF%) and gender data from 13,601 subjects ages 20 to 80. The average BF% for the 6,580 men in the sample was 23.9, and this value was 35.0 for the 7,021 women. The standard error for the difference between the average men and women BF%s was 0.114. Do these data provide convincing evidence that men and women have different average BF%s. You may assume that the distribution of the point estimate is nearly norma

Answers

Answer:

Yes, the data provides convincing evidence that men and women have different average BF%s

Step-by-step explanation:

The given parameters are;

The number of the subjects ages 20 to 80 = 13,601

The body fat percentage, BF%, for the 6,580 men, [tex]\overline x_1[/tex] = 23.9

The body fat percentage, BF%, for the 7,021 women, [tex]\overline x_2[/tex] = 35.0

The standard error for the difference between the average men and women = 0.144

The null hypothesis, H₀; [tex]\overline x_1[/tex] = [tex]\overline x_2[/tex]

The alternative hypothesis, Hₐ; [tex]\overline x_1[/tex] ≠ [tex]\overline x_2[/tex]

The test statistic = (35.0 - 23.9)/(0.114) = 97.368

Therefore, given that the z-test is larger than the critical-z, we reject the null hypothesis, H₀, therefore, there is convincing statistical evidence to suggest that men and women have different body average BF%

the first 4 questions​

Answers

Answer:

(3)(4)(4)(2)

Step-by-step explanation:

1.

7 > 0.7 > 0.07 > 0.007

2.

5h - 15hg

taking 5h common

5h (1 - 3g)

3.

5(2x- 1) = 35

dividing both sides by 5

2x - 1 = 7

2x = 7 + 1

2x = 8

x = 4

4.

if x is an odd number x + 2 will also be odd.

for example

11 is an odd number

on adding 2 we get 13 which is also an odd number.

x² -23n +132 pls help​

Answers

Answer:

(x-11)(x-12)

Step-by-step explanation:

To clarify, there was a likely typo written in your question since it is impossible to solve two unknown values with only one equation. I'm supposing that the equation was supposed to be

[tex] {x}^{2} - 23x + 132[/tex]

The first step is to split the term into factorable terms.

Since the highest power is power of 2, the equation would look like this if factorized:

[tex](ax + b)(cx + d)[/tex]

If the terms were added properly, the expanded equation would be:

[tex](ac \times {x}^{2} ) +( (ad + bc) \times x) + (bd)[/tex]

Generally, we do not see decimal values or fractions in factorization with some exceptions. Otherwise, the equation could get very complicated.

In this case, we can determine the following:

[tex]a \times c = 1[/tex]

[tex](a \times d) + (b \times c) = - 23[/tex]

[tex]b \times d = 132[/tex]

First, we can determine a and c to be one since one only has one factor, which is itself.

This leaves us with two equations left

[tex]b + d = - 23[/tex]

[tex]b \times d = 132[/tex]

There are two ways to solve the remaining two terms. We can either find the factors or do quadratic equation. Finding the factors is the easier way out here.

b and d will add up to negative values but multiplying these values give positive values. The most likely reason is that b and d are negative values.

Now, we can find the factors of 132.

The factors are 1, 2, 3, 4 , 6, 11, 12, 22, 33, 44, 66 and 132. However, the values flip around.

In fact, the "factors" we are looking for are the negative values of the actual factors. To solve this, we should find two factors that add up to 23.

In this case, 11+12=23.

To verify, 11*12 is also 132.

Since we are looking for the negative values, the values we are looking for are -11 and -12.

The values can be plugged in anywhere in b or d.

After cleaning up, we can plug in the values into our factorization and we will get:

[tex](1x - 11)(1x - 12)[/tex]

or

[tex](x - 11)(x - 12)[/tex]

answer : (x-11) (x-12)

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 8 to 5. If there were 4605 no votes, what was the total number of votes?

I need it by tonight for a pop quiz tomorrow

Answers

Answer:

Try to do it yourself, since you have a test tomorrow

Good luck

Step-by-step explanation:

5: 4605

13 (8+5):

[tex] \frac{4605}{5} \times 13 = [/tex]

=Your answer

find the next four terms of the sequence 5, 4, 9, 13, 22

Answers

Answer:

38

Step-by-step explanation:

The first term of the given sequence is 9.

The second term is 13

= 9 + 4 . = 9 + 2 × 2.

The next number is 22.

= 13 + 9 . = 13 + 3 × 3 .

In the same way the next number of the given sequence will be

22 + 4 × 4 .

= 22 + 16 = 38.

Which product is negative?
(-3/8)(-5/7)(1/4)

(3/8)(-5/7)(-1/4)

(3/8)(5/7)(1/4)

(-3/8)(-5/7)(-1/4)

Answers

Answer:

[tex]( - \frac{ 3}{8} )( - \frac{5}{7} )( - \frac{1}{4} )[/tex]

Step-by-step explanation:

[tex]( - \frac{ 3}{8} )( - \frac{5}{7} )( - \frac{1}{4} )[/tex][tex] \frac{3}{8} \times \frac{5}{7} \times (- \frac{1}{4} )[/tex][tex] \frac{3 \times 5}{8 \times 7} ( - \frac{1}{4} )[/tex][tex] - \frac{15}{56 \times 4} [/tex][tex] - \frac{15}{224} [/tex]Hope it is helpful.....
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