The sum of 2 positive numbers is 151. The lesser number is 19 more than the square root of the greater number. What is the greater number?

The question is a college-level mathematics problem involving taking the third derivative of the function f(x) = 2x/(x^2 - 1). The process requires the application of quotient rule and chain rule of differentiation.

The student question involves calculating the third derivative of the function f(x) = 2x/(x2 - 1). This function is a rational function and can be differentiated using the quotient rule and chain rule of differentiation. Let's proceed with the derivative calculations.

First, we should recall that the function can be rewritten as:

f(x) = 2x/(x2 - 1) = 2x/[(x - 1)(x + 1)]

Now we can calculate the derivatives. For the first derivative f'(x), we use the quotient rule:

f'(x) = [(x2 - 1)(2) - (2x)(2x)]/(x2 - 1)2

For the second derivative f''(x), we differentiate f'(x) again:

f''(x) = Derivative of f'(x) with respect to x

The third derivative f'''(x) is then the derivative of f''(x). Calculations for the second and third derivatives can be a bit complex and lengthy, and it is necessary to apply the quotient rule and product rule carefully.

Through this process, we will arrive at the third derivative, f'''(x), which is what the question asks for.

Answer:

The answer is 40

Step-by-step explanation:

First, since roger has 3 times as many grapes as Marissa. do 10 times 3. The answer is 30. Roger has 30 grapes. The question is asking how much they have all together. Add 30 plus 10 and the answer that you will get is 40. The answer is 40

Answer:

73

Step-by-step explanation:

Givens

d = 3

Equation 7d^2 + 10 = ?

Solution

7*3*3 + 10                

7*9 + 10

63 + 10 = 73

Answer:

Step-by-step explanation:

Do the multiplication and you'll find the right answer.

Answer:

$7.50

Step-by-step explanation:

10 divided by 4 = $2.50

so, $2.50 x 3 = $7.50

Answer:

$7.5 Dollars

Step-by-step explanation:

The cost of 4 bottles is $10. So, 1 bottle is going to be $2.50 (division)

Now, to find the cost of 3 water-bottles, we have to multiply.

$2.50 * 3 = $7.50.

So, the answer to this question is  3 bottles = $7.50

(Hope this helps!)

Answer:

The % of the increase in population from 1980 to 2000 will be 72.8%

Step-by-step explanation:

Let the population in the year of 1980 was x.

If the population from 1980 to 1990 has increased by 20%, then the population in the year 1990 will be [tex]x(1 + \frac{20}{100}) = 1.2x[/tex].

Now, from 1990 to 2000, the population has again increased by 20%.

So, the population in the year 2000 will be [tex]1.2x(1 + \frac{20}{100}) = 1.44x[/tex].

Again, from 2000 to 2010, the population has increased by 20%.

Therefore, the population in the year 2010 will be [tex]1.44x(1 + \frac{20}{100}) = 1.728x[/tex].

Now, the population increased from x to 1.728x between the years 1980 to 2010.

Hence, the % of the increase in population from 1980 to 2000 will be [tex](\frac{1.728x - x}{x}) \times 100\% = 72.8\%[/tex] (Answer)

Answer:

[tex]A=65.97\ cm^2[/tex]

Step-by-step explanation:

The complete question is

The shaded region is the area outside the smaller circle and inside the larger circle

we know that

The area of the shaded region is equal to subtract the area of the smaller circle from the area of the larger circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

The area of the shaded region is

[tex]A=\pi [r_1^2-r_2^2][/tex]

where

[tex]r_1=12.5/2=6.25\ cm[/tex] ---> radius of the larger circle (is half the diameter)

[tex]r_2=8.5/2=4.25\ cm[/tex] ---> radius of the smaller circle (is half the diameter)

assume

[tex]\pi =3.1416[/tex]

substitute

[tex]A=3.1416[(6.25)^2-(4.25)^2][/tex]

[tex]A=65.97\ cm^2[/tex]

Answer:

3x-2y^2-2

Step-by-step explanation:

3x-(2y^2+2)=3x-2y^2-2

Answer:

3.75

Step-by-step explanation:

the number you want to turn into apercentage over the total value so you end up with a fraction. Then, turn the fraction into a decimal by dividing the top number by the bottom number. Finally, multiply the decimal by 100 to find the percentage.

Answer:

Grover has $24, Percy has $31 and Annabeth has $19.

Step-by-step explanation:

Create equations to represent the situation.

let a be Annabeth

let g be Grover

let p be Percy

a + g = 43      Together, Annabeth and Grover have $43

g + p = 55    If Grover and Percy combine their money, they have $55

p = g + 7        Percy has $7 more than Grover

See if any of the equations can be combined. For example, we know p is g+7.

Substitute p for g+7 in an equation that has the variable p.

g + p = 55

g + g + 7 = 55    Combine like terms (g)

2g + 7 = 55   Start isolating g. Subtract 7 from both sides

2g = 55 - 7

2g = 48     Divide both sides by 2

g = 48/2    

g = 24         Money Grover has

Use the equation p = g + 7. Find "p" by substituting g for 24.

p = g + 7

p = 24 + 7   Add

p = 31    Money Percy has

Substitute g for 24 in the last equation, a + g = 43, to find a.

a + g = 43

a + 24 = 43    Subtract 24 from both sides

a = 43 - 24

a = 19     Money Annabeth has

Therefore Grover has $24, Percy has $31 and Annabeth has $19.

Answer:

Grover has $24, Percy has $31 and Annabeth has $19.

Create equations to represent the situation.

let a be Annabeth

let g be Grover

let p be Percy

a + g = 43      Together, Annabeth and Grover have $43

g + p = 55    If Grover and Percy combine their money, they have $55

p = g + 7        Percy has $7 more than Grover

See if any of the equations can be combined. For example, we know p is g+7.

Substitute p for g+7 in an equation that has the variable p.

g + p = 55

g + g + 7 = 55    Combine like terms (g)

2g + 7 = 55   Start isolating g. Subtract 7 from both sides

2g = 55 - 7

2g = 48     Divide both sides by 2

g = 48/2    

g = 24         Money Grover has

Use the equation p = g + 7. Find "p" by substituting g for 24.

p = g + 7

p = 24 + 7   Add

p = 31    Money Percy has

Substitute g for 24 in the last equation, a + g = 43, to find a.

a + g = 43

a + 24 = 43    Subtract 24 from both sides

a = 43 - 24

a = 19     Money Annabeth has

Therefore Grover has $24, Percy has $31 and Annabeth has $19.

Answer:

The perimeter of crater lake is 17.27 miles.

Step-by-step explanation:

Given as :

The shape of the lake is like a circle

The diameter of lake = d = 5.5 miles

∵ shape pf lake is circle, so the diameter of circle = d = 5.5 miles

Let The perimeter of crater lake = p miles

Now, As we know

The perimeter of circle = [tex]\pi[/tex] × diameter

the value of  [tex]\pi[/tex] = 3.14

Or, p =  [tex]\pi[/tex] × d

Or, p =  [tex]\pi[/tex] × 5.5 miles

Or, p =  3.14 × 5.5 miles

∴ p = 17.27 miles

So, The perimeter of circle = perimeter of lake = p = 17.27 miles

Hence, The perimeter of crater lake is 17.27 miles. Answer

Answer:

[tex]3 \leqslant y < 10[/tex]

The inequality that represents the given situation is (3 ≤ y < 10).

So, the inequality will be:

Which means:

So, the inequality will be:

Therefore, the inequality that represents the given situation is (3 ≤ y < 10).

Know more about inequalities here:

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Answer:

commutative property of addition

Step-by-step explanation:

Answer:

The answer to your question is commutative property of addition

Step-by-step explanation:

commutative property of addition means switching up the numbers of the equation but the sum is still the same.

Like in your qustion 1+7=8 but 7+1=8 also. The numbers 7 and 1 are switched around but the answer is still 8.

Answer:

No Solution.

Step-by-step explanation:

5x-y=2

5x-y=-2

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

-(5x-y)=-2

5x-y=-2

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

-5x+y=-2

5x-y=-2

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

0=-4

no solution

Answer:

(1, 1 )

Step-by-step explanation:

Given the 2 equations

3x +2y = 5 → (1)

x - 2y = - 1 → (2)

Adding the 2 equations term by term will eliminate the term in y, that is

(3x + x) + (2y - 2y) = (5 - 1)

4x = 4 ( divide both sides by 4 )

x = 1

Substitute x = 1 in either of the 2 equations and solve for y

Substituting in (1)

3(1) + 2y = 5

3 + 2y = 5 ( subtract 3 from both sides )

2y = 2 ( divide both sides by 2 )

y = 1

Solution is (1, 1 )

Answer: x=3 y=-2

Step-by-step explanation:

The other dude is wrong, I just did it and got

Marked wrong. It’s (3,-2)

Answer:

there are 1,440 minutes in 24 hrs a day

Step-by-step explanation:

Now thank me and rate me

Hope your year has been going great !!

The answer is 1440 if im correct

Answer:

n=(9v-4f)/k

Step-by-step explanation:

kn+4f=9v

kn=9v-4f

n=(9v-4f)/k

Answer:

n = (-4f + 9v) ÷ k

Step-by-step explanation:

All you have to do is... flip the equation

Answer:

The correct answer is C. 15 ¹⁵√x⁵y³

Correct question and statement:

Express 15x^1/3 y^1/5 using a radical, as it is written in the graph attached.

Step-by-step explanation:

15x^1/3 y^1/5

15 * (x^1/3 y^1/5)

For multiplying two fractional exponents with different bases, we need to equal the denominator of the fractional exponents.

Therefore, we have:

1/3 * 5/5 = 5/15 ⇒ 1/5 * 3/3 = 3/15

15 * (x^5/15 y^3/15)

Now we can express the fractional exponents as an only radical, this way:

x^a/b = ᵇ√xᵃ

15 * ¹⁵√x⁵y³

The correct answer is C. 15 ¹⁵√x⁵y³

Answer:

Therefore, Point M( 1 , -2 ) is the Mid point of segment ST.  

Step-by-step explanation:

Given:

Let,

point S( x₁ , y₁) ≡ ( -1 , 1)  

point T( x₂ , y₂) ≡ (3 , -5)

Point M( x , y ) is the Mid point of segment ST.  

To Find:

Point M( x , y )= ?

Solution:

As Point M( x , y ) is the Mid point of segment ST.

So we have Mid Point Formula as

[tex]Mid\ pointM(x,y)=(\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2})[/tex]

On substituting the given values in above equation we get

[tex]M(x,y)=(\frac {-1+3}{2},\frac{-5+1}{2})\\\\M(x,y)=(\frac{2}{2},\frac{-4}{2}) \\\\M(x,y)=(1,-2)\ \textrm{which the required midpoint}[/tex]

Therefore, Point M( 1 , -2 ) is the Mid point of segment ST.  

Answer:

x=0

Step-by-step explanation:

8x=12x

12x-8x=0

4x=0

x=0/4

x=0

Answer: x1=-2

x2=2

Step-by-step explanation:

5x²+4x-19=4x+1

5x²+4x-19-4x-1=0

5x²-20=0

5x²=20

x²=20/5

x²=4

x1=-√4=-2

x2=+√4=2

To solve the simultaneous equations, set the two equations equal to each other, simplify, solve for x, and substitute the values of x back into one of the original equations to solve for y. The solutions are (2, 9) and (-2, -7).

To solve the simultaneous equations:

y = 5x^2 + 4x - 19

y = 4x + 1

Let's set the two equations equal to each other:

5x^2 + 4x - 19 = 4x + 1

Now, simplify and solve for x:

5x^2 + 4x - 4x - 19 - 1 = 0

5x^2 - 20 = 0

Divide both sides by 5:

x^2 - 4 = 0

Factor the equation:

(x - 2)(x + 2) = 0

Set each equation equal to zero:

x - 2 = 0 or x + 2 = 0

Solve for x:

x = 2 or x = -2

Now, substitute the values of x back into one of the original equations to solve for y:

When x = 2:

y = 5(2)^2 + 4(2) - 19

y = 20 + 8 - 19

y = 9

When x = -2:

y = 5(-2)^2 + 4(-2) - 19

y = 20 - 8 - 19

y = -7

Therefore, the solutions to the simultaneous equations are (2, 9) and (-2, -7).

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Answer:

The graph with B(2,-3) i.e) y=[tex]\frac{-3}{2}[/tex] x goes through the point M(-10,15).

Step-by-step explanation:

Consider M(-10,15) and given that equation is y = kx.

Now, substitute M(-10,15) in the equation

⇒ 15 = k × -10

⇒ k = [tex]\frac{15}{-10}[/tex] = [tex]\frac{-3}{2}[/tex]

⇒ y = [tex]\frac{-3}{2}[/tex] x

Now, check with the given points B(2,-3) and B([tex]3\frac{1}{3}[/tex] , -2)

1) B(2,-3)

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

⇒(-3) = [tex]\frac{-3}{2}[/tex] × 2

⇒ -3 = -3 ⇒ LHS = RHS

⇒ B(2,-3) is the required point.

2) for b([tex]3\frac{1}{3}[/tex] , -2)

LHS ≠ RHS.

So,The graph with B(2,-3) i.e) y=[tex]\frac{-3}{2}[/tex] x goes through the point M(-10,15).

Answer:

Quartile 1 (Q1) = 24

Quartile 2 (Q2) = 47

IQR = 23

Step-by-step explanation:

Given:

The set of data are:

13, 23, 24, 25, 26, 26, 37, 47, 47, 48, 50

The data are in increasing order. The number terms are, [tex]n = 11[/tex].

Therefore, the middle term = [tex]\frac{n+1}{2}=\frac{11+1}{2}=6^{th}\ term[/tex]

So, the median = 26

Now, the median divides the set of data into two parts. The median of first part is the quartile 1 and the median of second part is quartile 2.

So, the first part has the following terms:

13, 23, 24, 25, 26

Here also, [tex]n=5[/tex]. So, the third term is the median.

∴ Q1 = 24

The second part has the following terms:

37, 47, 47, 48, 50

Here also, [tex]n=5[/tex]. So, the third term is the median.

∴ Q2 = 47.

Now, IQR = Q2 - Q1 = 47 - 24 = 23.

Answer:

1/8x___________=7/8 the answer is 6

Answer:

1. 2:3 = 6:9

2. 4:7 = 24:42

3. 2(6):48=3:12

Step-by-step explanation:

Answer:

its B

Step-by-step explanation:

Answer:

Roberta earns $164.4 on an 8 hr shift.

Step-by-step explanation:

In one hour  Roberta makes $9

So if she works for 8 hours she will be making

=> ( 9 X 8)$

=>72$

Also she earns a commission of 10.5% on selling a jewellery  worth $880

So 10.5% of 880 is

=> [tex]\frac{10.5}{100}\times 880[/tex]

=>  [tex] 0.105\times 880[/tex]

=> 92.4

Hence  Roberta will be earning a total amount of

(72+ 92.4)

=>$164.4

Answer:

[tex]V=200\ yd^3[/tex]

Step-by-step explanation:

we know that

The volume of the prism is equal to

[tex]V=LWH[/tex]

where

L is the length

W is the width

H is the height

we have

[tex]L=10\ yd\\W=5\ yd\\H=4\ yd[/tex]

substitute

[tex]V=(10)(5)(4)=200\ yd^3[/tex]

Answer:

C.) 200 yd3

Step-by-step evaluation:

Step 1.) 4 x 5 = 20

Step 2.) 20 x 10 = 200

Step 3. (Final answer).) C.) 200 yd3

Explanation:

4 times 5 will equal 20 because, 4 + 4 + 4 + 4 + 4, or 5 + 5 + 5 + 5, equals 20.

20 times 10 will equal, the answer, 200 hundred because 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 = 200, and that's our answer.

Final answer:

C.) 200 yd3

Answer:

Step-by-step explanation:

(2,-4)....x1= 2 and y1 = -4

(p,8).....x2 = p and y2 = 8

slope(m) = 1/2

now use the slope formula (y2 - y1) / (x2 - x1) and sub in what we know...

slope(m) = (y2 - y1) / (x2- x1)

1 / 2 = (8 - (-4) / (p - 2)

1 / 2 = (8 + 4) / (p - 2)

1/2 = 12 / (p - 2) .....now multiply both sides by (p - 2)

1/2(p - 2) = 12

1/2p - 1 = 12

1/2p = 12 + 1

1/2p = 13

p = 13 / (1/2)

p = 13 * 2/1

p = 26

so the value of p is 26