a father is 4 times as old as his son. in 20 years the father will be twice as old as his son. find the present age of each.

The general expression for the slope of the tangent line is m = y'(x) = 4x + 2. the value of m is - 10 for x = - 3 and is 4 for x = 0.5.

A line that only touches a curve once is said to be tangent to it. The point (x₀ , y₀) where a line with the equation of a tangent to a curve

y = f ( x ) is given by:

T' (x) = f'(x) (x ₋ x₀)  ₊ y₀

The slope of the tangent line to a curve at a point is computed by getting the first derivative of the curve.

y(x)=2x²y

y'(x) = (2)2x²⁻¹ ₊ (1)2x¹⁻¹

y'(x) = 4x¹ ₊ 2x°

y'(x) = 4x ₊ 2(1)

y'(x) = 4x ₊ 2

The slope at a point

P (x, y) is computed by substituting the x-coordinate of the point to the first derivative. This is the general expression for the slope:

m = y'(x) = 4x + 2

For x = - 3

m = 4 (- 3) + 2

m = - 12 + 2

m = - 10

For x = 0.5

m = 4 (0.5) + 2

m = 2 + 2

m = 4

Therefore, the general expression for the slope of the tangent line is m = y'(x) = 4x + 2. the value of m is - 10 for x = - 3 and is 4 for x = 0.5.

Learn more about tangent here:

https://brainly.com/question/17040970

#SPJ9

Answer:

×=2 , y= -2

Step-by-step explanation:

3x+y=4______(1)

x-3y=8_______(2)

by substitution method...

multiplying eq (1) by 3..

9x+3y=12_____(3)

x-3y=8_______(4)

10x=20

x=2

putting the value of x in eq (1)

3x+y=4

3(2)+y=4

6+y=4

y=4-6

y=-2

×=2 , y= -2

The area of the circle inscribed inside the square is 64π cm²

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

The circle inside the square as shown in the diagram have a diameter of 16 cm. Hence:

Radius = diameter / 2 = 16/2 = 8 cm

Area of circle = π * radius² = π * 8² = 64π cm²

The area of the circle inscribed inside the square is 64π cm²

Find out more on equation at: https://brainly.com/question/13763238

#SPJ1

The equation in terms of x that represents the given relationship is (7 + x)x = 555

The given parameters are

Length = L

Width = x

Area = 555 yd^2

From the question, we have

L = 7 + x

The area of a rectangle is

A = Lx

Substitute 7 + x for L

So, we have

A = (7 + x)x

Substitute 555 for A

So, we have

(7 + x)x = 555

Hence, the equation in terms of x that represents the given relationship is (7 + x)x = 555

Read more about areas at

https://brainly.com/question/24487155

#SPJ1

Answer:

a, b, a/2, b/2

Step-by-step explanation:

The coordinates of C are (a,b).

You find the midpoint by taking the averages of the coordinates.

There isn't a ton of info provided in your question, however, I believe the solution is 1 = 1.

Answer:

7 gramos = 0,247 onzas

Explanation

Fórmula

para obtener un resultado aproximado, divida el valor de la masa por 28,35

7 ÷ 28,35

= 0.247 onzas

Answer: $11,379 i believe

Step-by-step explanation: Multiplying 9 times the percentage value at which the cars value depreciates it gives you, 13.5%. Dividing 13155 by that 13.5% will give you the absolute value of $11379.075 in which would be $11,379.

Hope this helps!

Answer:

answer.3.4,6.8,9.12

Step-by-step explanation:

get 12+16=28.

12/28=6/14=3/7

16/28=8/14=4/7.

now get 3/7and 4/7.

subtruct 3 from 12 and also subtract 4 from 16 to get 9.12

Answer:

.324

Step-by-step explanation:

.3244   if underlined digit >= 5     round the thousandth digit up o/w leave it as is  

After 15 seconds Juan moves (6, 5).

In the given question,

given that,

A marching band uses a grid to determine the members’ positions.

Juan starts at (2, 2).

Every 15 seconds, he moves 4 yards east and 3 yards north.

2 + 4 = 6.

2 + 3 = 5.

so after 15 seconds Juan moves (6, 5).

Hence we get the (6,5) as the main answer.

Learn more about Coordinate geometry here:

brainly.com/question/7243416

#SPJ9

Answer:

9 6/7

This is the answer

Answer:      2200

Hope it helps!

Recalling that SAT scores are always expressed as multiples of 10, then the points we get on the test will be 628.

In statistics, Standard deviation is a measure of the variation of a set of values.

σ = standard deviation of population

N = number of observation of population

X = mean

μ = population mean

WE have been given that SAT scores are normally distributed, with a mean of 500 points and a standard deviation of 100 points.

The solution as follows;

Let be X: scores of SAT

P(X ≥ x) = 0.9

P((X - 500)/100 ≥ (x - 500)/100) = 0.9

P(Z ≥ z) = 0.9

z = 1.28

1.28 = (x - 500)/100

128 + 500 = x

x = 628

Recalling that SAT scores are always expressed as multiples of 10, then the points we get on the test will be 628.

Learn more about standard deviation and variance:

https://brainly.com/question/11448982

#SPJ1

Answer: Is the absolute difference if a is a positive number, when a = any rational number.

Step-by-step explanation:

Define Positive numbers:

Positive numbers are the numbers which are greater than zero that lies on the right side of the number line.

Example: 0, 1, 2, 3, 4…

Define Negative numbers:

Negative numbers are the numbers which are less than zero that lies on the left side of the number line.

Example: … -5, -4, -3, -2, -1, 0.

Given data,

Let a = any rational number. Is the absolute difference if a is a positive number.

Because,

Let us take,     a  =  any rational number

We have to know → Is the absolute value of a different if a is a positive number or negative number.

Define Modulus (|x|) of a number :

The modulus or absolute value of a number means the distance that goes from the number to its origin, this is, to the point 0 (zero) that makes part of the real straight line. For instance, the distance from point 6 to its origins is 6, but the distance from point -6 to its origins is also 6.

The modulus operator formula is :

             |x|  = { x if x ≥ 0     and     -x if x ≤ 0

Given question,

Assume any rational number   x/y

Using the Modulus property :

                |x|   = { x/y if x/y ≥ 0    and      -x/y if x/y ≤ 0

Therefore, if the rational number is less then zero (say -2).

Then the absolute value will be = - (- 2) = 2

and for any rational number greater than 0 (say 2)

Then its absolute value will be = 2 only.

Hence,

Is the absolute difference if a is a positive number, when a = any rational number.

Learn more about information here: brainly.com/question/11411542

#SPJ9

The surface area of the sphere is approximately equal to 615.752 square miles.

The surface area of a solid is the area comprised by all faces of a solid, in the case of a sphere, there is only one face whose extension is determined by the following formula:

A = 4π · r²

Where:

If we know that r = 7 miles, then the surface area of the sphere is:

A = 4π · (7 mi)²

A ≈ 615.752 mi²

To learn more on surface areas: https://brainly.com/question/2835293

#SPJ1

Answer:

The easiest way to find percentage is to multiply the number by 100. Like if you were required to find the percentage of 0.87 you multiply it by 100 and get 87 there for 0.87 is equal to 87%.

Step-by-step explanation:

Hope it helps! =D

Answer:

The answer A,B,C

The distinction between present value and future value is that the former is required now and the latter is needed at a future period

What is the difference between present value and future value?

The present value indicates today's worth or dollars of a future value  of a  flow whereas the future value determines the future worth of an investment or deposit made today or deposits over a number of years at a time in the future

The amount that Claudia would have in a year's time is future value because the present value is the initial deposit made today

The amount that Steven would  have to deposit today in order to accumulate $400,000 in 15 years is the present value

The amount that a deposit of $4,500 made today would worth in 6 years is the future value because the initial deposit is the present value.

Joe would have to deposit payments in expectation of future value after 3 years and the deposit required today to earn a rate of return of 5% in order to have $1000 in 5 years is a present value

Find out more about present value on:brainly.com/question/14860893

#SPJ1

From the given discrete probability distribution, we have that:

a) Because the sum of all probabilities is of 1, we can verify that this is a probability model.

b) P(3 or 4) = 0.229.

c) P(at least one) = 0.908.

d) P(4) = 0.035.

e) Since both P(X ≤ 4) and P(X ≥ 4) > 0.05, 4 is not an unusual event.

The probability distribution in this problem gives the probability of a household having a number of TV sets, given as follows:

For item a, we have to add all the probabilities, hence:

0.092 + 0.275 + 0.101 + 0.194 + 0.035 + 0.303 = 1.

Because the sum of all probabilities is of 1, we can verify that this is a probability model.

For item b, we take the probabilities from the table as follows:

P(3 or 4) = P(X = 3) + P(X = 4) = 0.194 + 0.035 = 0.229.

For item c, we follow a similar procedure to item b, taking the probabilities from the table as follows:

P(at least one) = 1 - P(X = 0) = 1 - 0.092 = 0.908.

For item d, from the table, we have that:

P(4) = 0.035.

For item e, we have that:

Since both P(X ≤ 4) and P(X ≥ 4) > 0.05, 4 is not an unusual event.

More can be learned about discrete probability distributions at https://brainly.com/question/24802582

#SPJ1

Answer:

[tex](x + 1)^2 + (y-8)^2 = 173[/tex]

Step-by-step explanation:

[tex]\textsf{The standard form of the equation of a circle is }\\\\ \sf (x -h)^2 + (y-k)^2 = r^2 \;where\; (h, k) \textsf{ are the coordinates of the center of the circle and \;r\; is the radius}[/tex]

Here h = -1, k = 8

So we get
[tex](x - (-1)) ^2 + (y - 8)^2 = r^2[/tex]

[tex](x + 1)^2 + (y - 8)^2= r^2\\\\[/tex]

Since the circle passes through the point (-3, -5) we can plug in these values of x = -3 and y = -5 to get r squared

[tex](-3 + 1)^2 + (-5 -8)^2 = r^2\\\\(-2)^2 + (-13)^2 = r^2\\\\4 + 169 = r^2\\\\r^2 = 173\\\\\\[/tex]

So the equation of the circle is
[tex](x + 1)^2 + (y-8)^2 = 173[/tex]

Answer:

60/7 ft

Step-by-step explanation:

Using similar triangles, if we let the height of the tree in ft be x,

[tex]\frac{x}{24}=\frac{5}{14} \\ \\ x=\frac{60}{7}[/tex]

It should be noted that the value of -4 + 8 36/87 will be 4 12/29.

It should be noted that based on the information illustrated, the fraction given is illustrated as:

= -4 + 8 36/87

= -4 + 8 12/29

= 4 12/29

Therefore, it should be noted that the value of -4 + 8 36/87 will be 4 12/29.

Learn more about fractions on:

brainly.com/question/17220365

#SPJ1

Answer:

Step-by-step explanation:

4/50 * 20 = 8/5 miles

Answer:

49 mile per hour

Step-by-step explanation:

Divide 634 miles by 13 hours to get 48.7, which we can round to the nearest mile (49) to match the significant digits in the problem.