d = 10.2 ft, r = 0.5 ft/h​

The second derivative of the composition between two functions is described by the following expression:

[tex]\frac{d^{2}}{dx^{2}} (f\,\circ\,g\,(x)) = \frac{d^{2}f}{dg^{2}}\cdot \frac{dg}{dx} + \frac{df}{dg} \cdot \frac{d^{2}g}{dx^{2}}[/tex]

Mathematically speaking, a composition between two functions is defined by the following operation:

[tex]f\,\circ\,g\,(x) =f(g(x))[/tex] (1)

By Chain Rule we get the first and second derivatives of the composition:

First derivative

[tex]\frac{d}{dx} (f\,\circ\,g\,(x)) = \frac{df}{dg}\cdot \frac{dg}{dx}[/tex] (2)

Second derivative

[tex]\frac{d^{2}}{dx^{2}} (f\,\circ\,g\,(x)) = \frac{d^{2}f}{dg^{2}}\cdot \frac{dg}{dx} + \frac{df}{dg} \cdot \frac{d^{2}g}{dx^{2}}[/tex] (3)

The second derivative of the composition between two functions is described by the following expression:

[tex]\frac{d^{2}}{dx^{2}} (f\,\circ\,g\,(x)) = \frac{d^{2}f}{dg^{2}}\cdot \frac{dg}{dx} + \frac{df}{dg} \cdot \frac{d^{2}g}{dx^{2}}[/tex]

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Answer:

Step-by-step explanation:

Let,

The req. number be = x

So,

Two - thirds of the number

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

Then, it is reduced by 13

[tex] = \frac{2}{3} x - 13[/tex]

After that,

The req. result we get is = 7

Therefore,

By the problem,

[tex] = > \frac{2}{3} x - 13 = 7[/tex]

[tex] = > \frac{2}{3} x = 7 + 13[/tex]

[tex] = > \frac{2}{3}x = 20[/tex]

[tex] = > \frac{2}{3} x \times \frac{3}{2} = 20 \times \frac{3}{2} [/tex]

=> x = 30

Hence,

The req. number is 30.

Given that :

To Find :

Solution :

Let's assume the number as x

According to the question :

[tex]\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x - 13 = 7 }[/tex]

Adding 13 to both sides we get :

[tex]\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x - 13 + 13 = 7 + 13 }[/tex]

[tex]\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x = 20 }[/tex]

Now, Multiplying both sides by [tex] \dfrac{3}{2} [/tex] we get :

[tex]\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x \times \dfrac{3}{2} = 20 \times \dfrac{3}{2} }[/tex]

[tex]\qquad \sf \: { \dashrightarrow \dfrac{ \cancel2}{ \cancel3}x \times \dfrac{{ \cancel3}}{ \cancel{2}} = \cancel{20} \times \dfrac{3}{ \cancel{2}} }[/tex]

[tex]\qquad \sf \: { \dashrightarrow x = 10 \times {3} }[/tex]

[tex]\qquad \bf \: { \dashrightarrow x = 30 }[/tex]

Therefore, The number is 30.

Answer:

116

Step-by-step explanation:

this is the correct answer

Answer:

x=7°

Step-by-step explanation:

From the picture it tells us that all side are equal

so that means every side is 60°

Let's make an equation

9x-3°=60°

add 3 on both sides

9x=63°

divide both sides by 9

x=7°

Answer:

x = 11

Step-by-step explanation:

5(x+8) = 2x - 7 + 8 (x - 1)

5x + 40 = 2x - 7 + 8x - 8

5x + 40 = 2x + 8x - 7 - 8

5x + 40 = 10x - 15

40 + 15 = 10x - 5x

55 = 5x

5x = 55

x = 55/5

x = 11

x=11

Step-by-step explanation:

5x+40=2x-7+8x-8

5x+40=10x-15

10x-5x=40+15

5x=55

x=55/5

x=11

Answer:

Step-by-step explanation:

h = 44sin13 = 9.89784... = 9.90 ft

Answer:

x = 10

Step-by-step explanation:

RO and OQ are congruent

Since RO = 50, and RQ = 12x - 20,

OQ = 12x - 20 - 50 = RO

50 = 12x - 70

120 = 12x

x = 10

-Chetan K

Answer:

3e-3/2f-3/8

Step-by-step explanation:

You multiply everything in the parenthesis with 1/2. 1/2*6e=3e, 3f*1/2=3/2f, 3/4*1/2=3/8. This would be the answer.

Answer:

Is ka answers D ha.........

Answer:

The answer is D.

Step-by-step explanation:

(8 ,33) = ([tex]x_{1} , y_{1} )[/tex]

m = 3

To find the equation, use the formula:

y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])

Put the values in the equation

y - 33 = 3(x - 8)

y - 33 = 3x - 24

Now to get only the y, put the [tex]y_{1}[/tex]

y - 33 = 3x - 24

    33           33

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

   y    =  3x + 9

Step-by-step explanation:

The domain is set of x-values:

The range is set of y-values:

Answer:

The inverse tangent of √33 is θ=30° θ = 30 ° . This is the result of the conversion to polar coordinates in (r,θ) form.

The inverse tangent of √33 is θ=30° θ = 30 ° . This is the result of the conversion to polar coordinates in (r,θ) form.

The polar form of a complex number is a different way to represent a complex number apart from the rectangular form. Usually, we represent the complex numbers, in the form of z = x+iy where 'i' is the imaginary number.

But in polar form, the complex numbers are represented as the combination of modulus and argument.

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Answer:

no

Step-by-step explanation:

Generally oblique is used to describe the relationship between 2 lines, but only 1 is given. Oblique means slanted to a degree other than a multiple of 90°, usually in reference to the other line.

x = 7 is a vertical line, and that is exactly 90°, -90°, or even 270° or -270° depending on how you look at it, so it is not oblique on its own.

Answer:

x = 7 is not an oblique line.

Step-by-step explanation:

x = 7 is the standard equation for a vertical line, x = a, with an undefined slope.  Vertical lines do not have horizontal change. Hence, its line will not be oblique (or slanted).  

The equations in slope-intercept form (y = mx + b), standard form (Ax + By = C), and point-slope form [y - y₁ = m(x - x₁)] will most likely represent an oblique line, as long as its slope (m) ≠ 0.  A line with a zero slope is a horizontal line (which is also not an oblique line).

Therefore, x = 7 is not an oblique line, but rather a vertical line.  

Answer:

x=-21

Step-by-step explanation:

make the equation

2x+9x-1+40=6(x-11)

simplify

11x+39=6x-66

solve

5x=-105

x=-21

Answer:

Perimeter = (Length + Width)×2

=(17.8cm + 4.6cm)×2

=(22.4 × 2)cm

= 44.8cm

Answer:

Step-by-step explanation:

-3 (xy+2y)+5y-x

-3xy-6y+5y-x

-3xy-y-x

a.

Lauren was 10 miles away from her house when he started.

Since the expression for Lauren's distance from her house, d = -2t + 10, to determine the number of miles away from his house that Lauren starts, we input t = 0, since this is the time Lauren starts walking.

So, with t = 0, d = -2t + 10

= -2(0) + 10

= 0 + 10

= 10 miles.

So, Lauren was 10 miles away from her house when he started.

b.

Lauren was moving at a rate of -2 mph towards her house.

To find how fast Lauren was moving towards her house, we differentiate d with respect to t.

So, dd/dt = d(-2t + 10)/dt

= d(-2t)/dt + d(10)/dt

= -2 + 0

= -2 mph

So, Lauren was moving at a rate of -2 mph towards her house.

c.

The rate is negative because her distance towards her house is decreasing

The rate is negative because her distance towards her house is decreasing since she is moving towards her house.

d.

Lauren is 2 miles away from her house after 4 hours

To find this, we input t = 4 into the equation for d.

So, d = -2t + 10

= -2(4) + 10

= -8 + 10

= 2 miles.

So, Lauren is 2 miles away from her house after 4 hours

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Answer:

Step-by-step explanation:

d = 277/tan12 = 1,303.1825... m = 1.3 km

The nearest tenth of a foot, the distance from the town to the base of the cliff is approximately 1337.3 feet.

The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

The angle of depression is 12 degrees, and the side opposite the angle is the height of the cliff (277 feet), while the side adjacent to the angle is the distance from the town to the base of the cliff (which we want to find).

Let's denote the distance from the town to the base of the cliff as "d."

The tangent of the angle of depression is given by:

tan(12°) = opposite / adjacent

tan(12°) = 277 / d

Now, solve for "d":

d = 277 / tan(12°)

Using a calculator:

d ≈ 1337.25 feet

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Answer:

0.002

Step-by-step explanation:

the digit "2" in this equation represents 0.02 or also 2/100

1/10 of 2/100 would be like multiplying 1/10 and 2/100 and that would get us 2/1000

2/1000 is also 0.002

0.002 is the value of the digit 2 in the number 1,947.5286​.

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.

here we have,

the number 1,947.5286​.

the digit "2" in this equation represents 0.02 or also 2/100

1/10 of 2/100 would be like multiplying 1/10 and 2/100

and that would get us 2/1000

i.e.

2/1000 is also 0.002

Hence, 0.002 is the value of the digit 2 in the number 1,947.5286​.

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Answer:

16. 1 4/5

17. 2 2/3

18. 4/11

19. 4 1/2

20. 4/7

21. 1/2

22. 1 2/5

23. 2 1/2

24. 4 2/3

Step-by-step explanation:

1. subtract whole numbers first

2. subtract fractions next (simplify if you can)

3. subtract fractions and whole numbers

Answer:

0.3ml

Step-by-step explanation:

0.1 g = 0.1 ml

Answer: The answer is to this math question is 18.75% of the students play the soccer after school.

Step-by-step explanation: Here are the following steps in order to convert the given fraction to percentage of the students play the soccer after school:

Step 1. First I add the total of the students in school and then added the total of the students play the soccer after school that looks like this: [tex]163+157=320[/tex] and [tex]27+33=60.[/tex]

Step 2. Using the online fraction to percentage calculator, first I find The Greatest Common Factor of 60 and 320 that looks like this: GCF(60,320) = 20.

Step 3. I can reduce this fraction by dividing both the numerator and denominator by 20 that looks like this: 60÷20/320÷20=[tex]\frac{3}{16}.[/tex]

Step 4. I know that [tex]\frac{3}{16}[/tex] is the same as 3÷16, then using The Long Division for 3 divided by 16 that gives us: 0.1875.

Step 5. I multiply the given decimal number by 100% in order to convert the fraction to percentage of the total students play the soccer after school that looks like this: 0.1875×100=18.75%.

I hope that my given answer with my given step-by-step explanation is very helpful to your own math question about how to find the percentage of the total students play the soccer after school, please mark me as brainliest and have a great P.A. Day and weekend! :D

Sincerely,

Jason Ta,

The ambitious of Brainly and the role of The TDSB and WHCI Student of the high school.

Answer: 15.6

Step-by-step explanation:

In 15.56, the digit in the tenths place is the second 5. 15.56. So look at the hundredths place (6). If the digit in the hundredths place is smaller than 5, round down. If it's 5 or more, round up. 6 > 5, so we round the tenths place up by one number to get 15.6.

The two positive numbers whose product is 300 and such that the sum of the first and four times the second is a minimum are 7.66 and 39.16

Let the two variables be x and y

If the product of the numbers is 300, hence

xy = 300

x = 300/y ........ 1

If the sum of the first and four times the second is a minimum, then;

P(x, y) = x + 4y .................. 2

Substitute equation 1 into equation 2:

P(x, y) = x + 4y

P(y) = 300/y + 4y

If this function is at mimimum, hence dP/dy = 0

dP/dy = -300/y² + 4 = 0

-300/y² + 4 = 0

-300 + 4y² = 0

4y² = 300

y² = 300/4

y²=   75

y = 7.66

Since xy = 300

x = 300/7.66

x = 39.16

Hence the two positive numbers whose product is 300 and such that the sum of the first and four times the second is a minimum are 7.66 and 39.16

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Answer:

(2,0)

Step-by-step explanation:

The minimum is 4 units from the x intercept on the x axis.

Since this is a quadratic, values on the same y should be equidistant from the min or max on the x axis.

6+4=10

6-4=2

The other x intercept is at (2,0)

If 2 sides of a triangle is 12 cm and perimeter is it 28cm prove it is a isosceles triangle

Answer:

if it has two equal sides the triangle is isosceles by definition

Definition of

Isosceles Triangle

A triangle with two equal sides.

The angles opposite the equal sides are also equal.

Answer:

The answer would be B. You solve it by substituting the x and y values in the expression, and seeing if it makes a true statement.

Step-by-step explanation:

Answer:

I believe that it is $901.20

Step-by-step explanation:

I make this assumption Because when we withdraw, we take away. If Kayla wrote these for checks, you just simply add them up and you get a total of $901.20.

We aren’t sure how much she had before withdrawing this money

Answer:

75

Step-by-step explanation:

60 divided by 4/5 is 75