Isaac's father is 49 years old. He is four years older than three times Isaac's age. How old is Isaac

Answer:

[tex] \displaystyle \frac{17}{5} [/tex]

Step-by-step explanation:

we are given

[tex] \displaystyle3 \frac{2}{5} \times 3 \times \frac{1}{3} [/tex]

since ⅓ is a reciprocal of 3 therefore if we multiply it we'd get 1

[tex] \displaystyle3 \frac{2}{5} \times \cancel{ \: 3} \times \frac{1}{ \cancel{ \: 3}} [/tex]

[tex] \displaystyle 3\frac{2}{5} [/tex]

remember that

[tex] \displaystyle \rm c\frac{a}{b} \xrightarrow{ \text{improper fraction}} \frac{b \times c + a}{b} [/tex]

so,

[tex] \displaystyle \frac{17}{5} [/tex]

Answer:

C. Is the answer

A positive second derivative means that the solution curve is concave up. Therefore, all solution curves for the given differential equation in Quadrant II are concave up.

(b) To find the second derivative of y with respect to x, we can use the chain rule. Since y is a function of x, we have [tex]dy/dx = f(x) and d^2y/dx^2 = d/dx(dy/dx) = d/dx(f(x)) = f'(x).[/tex]

To find f'(x), we can use the product rule and the given differential equation:

[tex]f'(x) = d/dx(xy^4) = y^4 + xy^4dy/dx = y^4 + xy^4f(x)[/tex]

Now, to determine the concavity of the solution curves, we need to find the sign of f'(x).

In Quadrant II, x and y are both positive, so [tex]x*y^4[/tex] is positive. Therefore, f'(x) is positive as well.

A positive second derivative means that the solution curve is concave up. Therefore, all solution curves for the given differential equation in Quadrant II are concave up.

(c) To find a particular solution to the differential equation with the given initial condition, we can use separation of variables.

The equation can be rewritten as [tex]dy/y^4 = x dx[/tex]

Integrating both sides gives:

[tex]\int\limits^ {} \,dy/y^4 = \int\limits^ {} \, dx* dx\\-1/y^3 = (x^2)/2 + C\\y^3 = -1/(x^2/2 + C)\\y = (-1/(x^2/2 + C))^(1/3)[/tex]

Using the initial condition f(4) = -1, we can find the value of C:

[tex](-1) = (-1/(4^2/2 + C))^(1/3)\\(-1)^3 = -1/(4^2/2 + C)\\-1 = -1/(16/2 + C)\\C = 15/2[/tex]

So the particular solution is:

[tex]y = (-1/(x^2/2 + 15/2))^(1/3)[/tex]

To know more about differential equations visit:

brainly.com/question/28099315

#SPJ4

Complete question is: Consider the differential equation dy/dx=xy^4.

(b) Find ⅆ2yⅆx2 in terms of x and y. Determine the concavity of all solution curves for the given differential equation in Quadrant II. Give a reason for your answer.

(c) Find the particular solution y=f(x) to the given differential equation with initial condition f(4)=−1.

Answer:

Formula-W=A/L

Legnth-17

Step-by-step explanation:

Using the formula to find width of a rectangle, (width= area divided by legnth), you get 17. You can check by multiplying 26 by 17 to get 442. Hope this helps (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧

Answer:

Formula : L x W

Length : 17.

Step-by-step explanation:

26 times 17 is 442

Answer:

A) first quadrant

hope it helps.

Answer:

$3228

Step-by-step explanation:

39236 - 500 = 38736

38736 / 12 = 3228

If the leg of the triangle is equal to a, then:

The second leg is also equal to a.

the given hypotenuse is a√2.

The given area is equal to a²/2; and

The perimeter equals a (2 + √2).

Now, looks easy, but from where does it come? There are various of methods to prove that equation, the most popular of them are:

By using the Pythagorean theorem, we can do that.

As you know one leg length a, then you know the length of the other as well, as both of them are equal.

The given 45 45 90 triangle shows the remaining parameters. Now you know that:

hypotenuse length is - 9 in * √2 = 12.73 in.

area is - 9 in * 9 in / 2 = 40.5 in²; and

perimeter - 9 in + 9 in + 9 in * √2 = 30.73 in.

Find the hypotenuse from the Pythagorean theorem:

a² + b² = c² => a² + a² = c² so c = √(2a²) = a√2

To know more about Triangle:

https://brainly.com/question/2773823

#SPJ4

Answer:

d

Step-by-step explanation:

sorry if im wrong

Answer:

3.1 is the answer.

Answer: 2=who

3=who

4=whom

5=I

Step-by-step explanation:

Answer:

half of 20 is 10

10 is your new radius so

10^2 = 100

100 x 3.14 = 314

Now we multiply by the height:

314 x 11 = 3,454 cm^3

The volume of the solid is option (a) 3454 cm³.

Volume of a three dimensional shape is the space occupied by the shape.

Given is a cylinder.

Volume of a cylinder = π r² h

Here r is the radius of the circular base and h is the height of the cylinder.

Given,

Diameter of circular base = 20 cm

Radius = Diameter / 2 = 20/2 = 10 cm

Height = 11 cm

Substituting,

Volume = π r² h

             = (3.14) (10²) (11)

             = 3454 cm³

Hence the volume of the cylinder shown is 3454 cm³.

Learn more about Volume here :

https://brainly.com/question/16134180

#SPJ2

Since, Kim works on commission and her trend of monthly earnings are not constant, Calculate the average from the data and estimate for the whole year , The answer is C) $15,720

Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It helps to make sense of large amount of data and use it to draw conclusions and make informed decisions. It provides methods to summarize, describe and analyze data, as well as techniques to infer characteristics of a population from a sample.

The mean is a measure of central tendency and a way to describe the average value of a dataset. It is calculated by adding up all the values in a dataset and then dividing by the number of values. The resulting value is the mean of the dataset, also known as the arithmetic average. Mean is commonly used to describe a large data set, while median is used to describe data with values have outliers.

salary for four months = $1625, $960, $1235, and $1420.

Average = ($1625 + $960+ $1235+$1420) /4 = $1310

for whole year = $1310 * 12 = $15,720

To learn more about mean visit:

https://brainly.com/question/11822836

#SPJ1

Answer:

199

Step-by-step explanation:

Ok, lets do the math, 41,790 is going to be the number we divide by, and than we use 210 to divide it with, meaning the final answer is 199.

Answer:

7.84  ×  10 ^7

Step-by-step explanation:

Answer:

Circumference of the circle = 15.70 units.

Step-by-step explanation:

In this question three sides of a triangle has been given as 3, 4 and 5 units.

These are the sides of a right angle triangle.

3² + 4² = 5² [By Pythagoras theorem]

9 + 16 = 25

If this triangle is inscribed in a circle then Hypotenuse of the triangle will be the diameter of the circle.

Theorem for the angle formed in the semicircle says, "angle formed by drawing the the lines from the ends of the diameter of a circle to it's circumference form a right angle."

Therefore, radius of the circle will be  units

Now we know the formula of circumference of the circle = 2πr

= 2π(2.5)

= 2(3.14)(2.5)

= 15.70 units

P(even) is  50%

It is simple to calculate the likelihood of one die roll.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

First, keep in mind that a prime number is an integer that has exactly two factors: 1 and the number itself (which is why 1 does not qualify: it has only one factor). The appropriate numbers from 6 onward are 2,3,5. Your response, given that there are six sides, is: P(prime) = 3/6 = 1/2 = 50%

Know more about probability at:

https://brainly.com/question/25870256

#SPJ4

Answer:

m=10

Step-by-step explanation:

hypotenuse is 15+5=20

to find shorter leg m divide the hypotenuse by 2

20÷2=10

Answer:

42.92 square

Step-by-step explanation:

The radius of the circles is 5m

So, area of 1 circle is π(5×5)=78.54 square

Two areas will  (78.54+78.54)=157.08 square

Rectangles height is ( 5+5)=10m

Rectangles area is (10×20)=200 square

Shaded region=(200-157.08) square =42.92 square

Answer:

x = 2, y = 0

Step-by-step explanation:

find y in terms of x:

8x - 4y = 16

4y = 8x - 16

y = 2x - 4

substitute y:

8x + 4y = 16

8x + 4(2x - 4) = 16

8x + 8x - 16 = 16

16x = 32

x = 2

find y:

8x + 4y = 16

16 + 4y = 16

y = 0

Answer:

35 cubic meters along with 35 cubes.

Answer:

The Answer is length 7m Width 5 m Height 1 m number of cubes 35 and volume 35

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

Angles x and 157 are linear pairs,

x + 157 = 180

x = 180 - 157

x = 23

Answer:

23°

Step-by-step explanation:

180-157= 23

Answer:

B

Step-by-step explanation:

Note that i² = - 1

Given

(4 - 2i)(1 + 7i) ← expand factors using FOIL

= 4 + 28i - 2i - 14i²

= 4 + 26i + 14

= 18 + 26i → B

Answer:   The mystery number is 5.5

5.5 converts to the fraction 11/2.

=================================================

Explanation:

The phrasing "subtract 10 from the number, then square the result" leads to the expression [tex](\text{x}-10)^2[/tex]

The phrasing "Square the number, then subtract 10 from the result" means we have [tex]\text{x}^2-10[/tex]

Set those expressions equal to one another so we can solve for x like shown in the steps below.

[tex](\text{x}-10)^2 = \text{x}^2-10\\\\\text{x}^2-20\text{x}+100 = \text{x}^2-10\\\\-20\text{x}+100 = -10\\\\-20\text{x} = -10-100\\\\\text{x} = -110/(-20)\\\\\text{x}=11/2\\\\\text{x} = 5.5[/tex]

The x^2 terms cancel out in the third step (since we subtract x^2 from both sides).

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

Check:

[tex](\text{x}-10)^2 = \text{x}^2-10\\\\(5.5-10)^2 = (5.5)^2-10\\\\(-4.5)^2 = (5.5)^2-10\\\\20.25 = 30.25-10\\\\20.25 = 20.25[/tex]

The answer is confirmed.

The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in determining if the lines are parallel, perpendicular, or none at all.      

The slope intercept form of a line is y = mx + c              

Where, c - y-intercept and m - the slope of the line

Given that

The cost of using the internet at an internet cafe is equal to a fee plus a certain rate per minute.

4 minutes of internet costs $ 3

8 minutes of internet costs $ 4  

[ We can represent the given situation as given below ]      

And the coordinates formed are (4, 3) and (8, 4)

The slope of the line formed = (4 - 3)/(8 - 4) = 1/4

Let y = mx + c be the equation to the model situation

=> y = (1/2)x + c

=> 2y = x + c ---- (1)

As we know (1) will pass through (4, 3)

=> 2(3) = 4 + c

=> 6 = 4 + c

=> c = 6 - 4

=> c = 2

=> 2y = x + 2

=> x - 2y + 2 = 0

Therefore,

The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.

Learn more about Slope of an equation at

https://brainly.com/question/15874858

#SPJ1

As you can see, 5y is an external angle of triangle ABC

we know that 5y=180-x

since angle B is 40, and angle A=x and C=x, we have

x%2Bx%2B40=180

2x=180-40

x=140%2F2

x=70

so, angle A=70 and C=70

then

5y=180-70

5y=110

y=110%2F5

y=22

To learn more about AC of ABC lies refer to:

https://brainly.com/question/22612939

#SPJ1

Answer:

0

Step-by-step explanation:

Well, since the line has the same y coordinates, you know it's a horizontal line.

All slopes of horizontal lines are 0.

Answer:

50

Step-by-step explanation:

angleQPR=50

becauseQR=RP

so angleRQP=RPQ

x=50

Answer:

50

Step-by-step explanation:

angle QPR = 50 because QR= rp