Dave and Kyle are 40 miles apart on a path when they start moving toward each other. Dave runs at a constant speed of 8 miles per hour, while Kyle walks at a constant speed of 5 miles per hour. How long does it take until they meet?

Answer:

Start off by expanding the square:

x^6 -2x³ + 1.

Now, we can integrate it in dx:

∫x^6 - 2x^3 + 1 dx = ∫x^6 dx - 2∫x^3 dx + ∫1 dx = (x^7)/7 - 2((x^4)/4) + x = (x^7)/7 - (x^4)/2 + x.

That's the result!

[tex]\\ \sf\longmapsto {\displaystyle{\int}}(1-x^3)^2dx[/tex]

[tex]\\ \sf\longmapsto {\displaystyle{\int}}(1-x^6+2x^3)dx[/tex]

[tex]\\ \sf\longmapsto x-\dfrac{x^{6+1}}{6+1}+2\dfrac{x^{3+1}}{3+1}[/tex]

[tex]\\ \sf\longmapsto x-\dfrac{x^7}{7}+2\dfrac{x^4}{4}[/tex]

[tex]\\ \sf\longmapsto x-\dfrac{x^7}{7}+\dfrac{x^4}{2}[/tex]

Answer:

75.36

Step-by-step explanation:

 Using the formula C = 2πr, we can calculate circumference.

Since we are using 3.14 for π, we plug that and the radius in.

C = 2(3.14)(12).

When you multiply all that you get 75.36

Answer:

B. [tex]\frac{\pi }{4} Rad>30^{0}[/tex]

Step-by-step explanation:

[tex]\frac{\pi }{4} Rad=(180/4)^{0} =45^{0}[/tex]

Hope this helps

Answer:

2

Step-by-step explanation:

the coefficient is the number in front of the variable (the number being multiplied by the variable).

Notice that

a + ar³ + ar⁶ + ar⁹ + ... = a + r³ (a + ar³ + ar⁶ + ...)

but the grouped sum on the right side is the same as the sum on the left side. This means that, if the sum we want to compute

a + ar³ + ar⁶ + ar⁹ + ...

converges to S, then

S = a + r³ S

Solve for S :

S - r³ S = a

(1 - r³) S = a

S = a/(1 - r³)

Similarly, knowing the value of the first sum, we have

a + ar + ar² + ar³ + ... = a + r (a + ar + ar² + ...)

but we know

a + ar + ar² + ... = 15

so

15 = a + 15r

and knowing the value of the second sum, we have

a + ar² + ar⁴ + ... = a + r² (a + ar² + ar⁴ + ...)

so

9 = a + 9r²

Solve these two equations for a and r :

15 = a + 15r   ⇒   a = 15 - 15r

9 = a + 9r²   ⇒   9 = 15 - 15r + 9r²   ⇒   3r² - 5r + 2 = (3r - 2) (r - 1) = 0

⇒   r = 2/3 or r = 1

We cannot have r = 1, since that would mean

a + a + a + ... = 15

since the left side is adding infinitely many copies of some constant; such a sum can never converge to a finite number. So it must be that r = 2/3, and it follows that a = 15 - 15 (2/3) = 5.

Then the sum we want has a value of

S = 5/(1 - (2/3))³ = 135/19

Answer:

Step-by-step explanation:

  a + ar¹ + ar² + ar³ + ... = 15       #1

r(a + ar¹ + ar² + ar³ + ...) = 15r

       ar¹ + ar² + ar³ + ... = 15r      #2

subtract #2 from #1

a = 15 - 15r

     a + ar² + ar⁴ + ar⁶ + ... = 9         #3

r²(a + ar² + ar⁴ + ar⁶ + ... )= 9r²

         ar² + ar⁴ + ar⁶ + ... = 9r²       #4

subtract #4 from #3

a = 9 - 9r²

15 - 15r = 9 - 9r²

9r² - 15r + 6 = 0

3r² - 5r + 2 = 0

r = (5 ±√(5² - 4(3)(2))) / (2(3)

r = (5 ± 1) / 6

r = 1

or

r = 4/6 = 2/3

if r = 1 then a = 15 - 15(1) = 0 and a series of zeros added together can never equal 15 so r = 2/3 must be true.

a = 15 - 15(2/3) = 5

   a + ar³ + ar⁶ + ar⁹ + ... = C           #5

r³(a + ar³ + ar⁶ + ar⁹ + ...) = Cr³

         ar³ + ar⁶ + ar⁹ + ... = Cr³          #6

subtract #6 from #5

a = C - Cr³

a = C(1 - r³)

C = a/(1 - r³)

C = 5/(1 - (2/3)³)

C = 5/(1 - 8/27)

C = 5/(19/27)

C = 5(27/19)

C = 135/19 = 7.1052631578947368....

You want to find t such that

45 - 7t - 6t² = 25

or

6t² + 7t = 20

Solve for t. By completing the square, we have

6t² + 7t = 20

t² + 7/6 t = 10/3

t² + 7/6 t + (7/12)² = 10/3 + (7/12)²

(t + 7/12)² = 529/144

t + 7/12 = ± 23/12

t = -7/12 ± 23/12

t = -5/2   or   t = 4/3

We ignore the negative solution, so the ball reaches a height of 25 feet at t = 4/3 seconds, or about 1.33 seconds after being thrown.

Answer:

f(-3)= 1

f(1)= -1

If f(x)= -2 then x = 3

If f(x) = 2 then x = -5

Step-by-step explanation:

f(x) can be replaced with any number. It just means y. For example, let's replace the (x,y) with the (-5,2). For this point, this is f(-5) = 2. When they ask for f(x), they are just asking what y is with a given coordinate x. So when they ask what f(-3) is, they are asking what y is with -3 being the x coordinate.

So, f(-3) = 1

f(1) = -1

For these questions:

If f(x) = -2 then x = ?

If f(x) = 2 then x = ?

They are asking what x is when y is -2 or 2. So here:

If f(x) = -2 then x = 3

If f(x) = 2 then x = -5

Answer:

ASA

Step-by-step explanation:

Angle marked the same way are congruent, so the two triangles have a side in common and the two adjacent angles congruent, so it's ASA

Answer:

The answer is Option B.) ASA

Explanation:

With the ASA rule, all triangles are congruent.

Answer:

[tex]\frac{5}{1}[/tex] is the same as 5:1

Answer:

2.35

Step-by-step explanation:

2 x 2 eqaul 9 times 2

Answer:

The last one

Step-by-step explanation:

A ratio table means that each number in the first column is multiplied by the same number to get the answer in the 2nd column

Answer:

3+3+3+3

Step-by-step explanation:

Hopefully I didn't get confused

3^4 vs 3+3+3+3 vs (3^2)(3^2) vs 3x3x3x3

Well the best way to do it is to do each

3^4=81

3+3+3+3=12

3^(2+2)=81

3x3x3x3=81

Therefore 3+3+3+3 is not equilvilent

now, we're assuming that the prism has a volume of 10³ and is filled with cubes of sides 1/2 long, Check the picture below.

now notice the bottom-right part of the picture, if we put two small cubes next to each other, they add up to 1, so to get 10 units from that, we'll need 20 of those halves, or 20/2 = 10, meaning we'll need 20 cubes side by side to make a length of 10 horizontally.

The same will be true for getting cubes to make up 10 vertically, we'll need 20, the same is true to fill up from back to front, we'll need 20 cubes.

so we can say that the rectangular prism will need 20 cubes from front to back, 20 horizontally and 20 vertically, that'll be 20*20*20 cubes, or 20³ or 8000 cubes.

mind you that we used a Cube for the prism, but the same will be true if we were to rearrange the cubes and make the prism taller or wider, same 8000 cubes will fill it in.

Answer:

first option

Translate seven left followed by mirror over y = 2

Step-by-step explanation:

The solution is Option A.

The translation of triangle MNP to triangle STR is a translation of 7 units to the right and a reflection along R = 2

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:  y=f(x+c) (same output, but c units earlier)

Right shift by c units:  y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the triangle be represented as MNP

Now , the transformed triangle be STR

Now , the translation is given as

Step 1 :

The coordinates of triangle is MNP

M = M (-5 , 2 )

N = N ( - 8 , 5 )

P = P ( -2 , 4 )

Now , the translation of 7 units to the right will result in

M' = M' ( 2 , 2 )

N' = N' ( -1 , 5 )

P' = P' ( 5 , 4 )

Step 2 :

The coordinates of the translated triangle M'N'P' is

M' = M' ( 2 , 2 )

N' = N' ( -1 , 5 )

P' = P' ( 5 , 4 )

Now , on reflection of triangle M'N'P' by R = 2 , we get

S = S ( 2 , 2 )

T = T ( -1 , -1 )

R = R ( 5 , 0 )

Hence , the translation of triangle MNP to triangle STR is a translation of 7 units to the right and a reflection along the R = 2

To learn more about transformation of function click :

https://brainly.com/question/26896273

#SPJ2

Answer:

1/1

Step-by-step explanation:

Answer:

For a function, it is the change in the y-value divided by the change in the x-value for two distinct points on the graph

Step-by-step explanation:

Answer:

i think that you can find the average rate of change between 2 points on a curve by dividi  the change in the output value (Y)  by the change in the input value (X)

Step-by-step explanation:

Answer:

D. 35, 60, 85

Step-by-step explanation:

All angles of a triangle have to add up to 180 degrees.

35+60+85 = 180

Answer:

the quantity seven minus three divided by two

Step-by-step explanation:

its math

a.

The rate of the plane in still air is 700 km/h

Let V = rate of plane in still air and v = rate of wind.

When flying against the wind, an airplane travels 5220 kilometers in 9 hours, we have that since distance = speed × time

(V - v) × 9 = 5220

V - v = 5220/9

V - v = 580  (1)

Also, flying with the wind, the same plane travels 6560 kilometers in 8 hours, we have that since distance = speed × time

(V + v) × 8 = 6560

V + v = 6560/8

V + v = 820 (2)

Adding equations (1) and (2), we have

V - v = 580  (1)

+

V + v = 820 (2)

2V = 1400

V = 1400/2

V = 700 km/h

So, the rate of the plane in still air is 700 km/h.

b.

The rate of the wind is 120 km/h

Substituting V into (1), we have

V - v = 580  (1)

700 - v = 580  

v = 700 - 580

v = 120 km/h

So, the rate of the wind is 120 km/h

Learn more about rate of plane here:

https://brainly.com/question/18848032

Answer:

  E  840 cm

Step-by-step explanation:

For a 20×20 grid, there will be 21 strands in the vertical direction, and 21 in the horizontal direction. Each strand wil be 20 cm long. The total length is ...

  (20 cm)(2 × 21) = 840 cm

_____

Additional comment

In this case, we take "similar" to mean that the grid squares are 1 cm, and the wire encloses a larger array of those squares.

In geometry, the term "similar" would mean the larger grid is simply a scaled-up version of the smaller one, with squares that are 20/3 cm, instead of 1 cm. The length of wire required in that case is (4+4)(20 cm) = 160 cm = (20/3)×(24 cm).

Step-by-step explanation:

49² + 98 + 1 compared to a² + 2ab + b² means that

a = 49

b = 1

as this would be 49² + 2×49×1 + 1² = 49² + 98 + 1

so, we have actuality

(49 + 1)² = 50² = 2500

Answer:

49² + 98 + 1 compared to a² + 2ab + b² means that

a = 49

b = 1

as this would be 49² + 2×49×1 + 1² = 49² + 98 + 1

so, we have actuality

(49 + 1)² = 50² = 2500

Step-by-step explanation:

Answer:

1) 9

2) 34

Step-by-step explanation:

For the first one, it would be

= (6×3)/2

= 18/2

= 9

The second one is,

= 36- (12/6)

= 36 - 2

= 34

Answer:

I need help with this too!!!

Step-by-step explanation:

Answer:

what does it mean?

Step-by-step explanation:

I do not understand.

Answer:

1.20 or 120 cents

Step-by-step explanation:

First, we need to calculate the total due for the book. 15 cents(3 days) = 0.45

Next, we need to calculate the total due for the video. 25 cents(3days) =0.75

0.75+0.45=1.2 dollars, or 120 cents

Answer:

yes this right cuz ye or nah?

Step-by-step explanation:

yes cuz 0 1 2 3 4 5 6 7 8 9 are the numbers

Answer: [?] is 6

Step-by-step explanation:

x=5

so, 2x=10

10-4 is 6

Answer:

∠GHD is 85°

Step-by-step explanation:

180°-95°

85°

Answer:

-7/2

Step-by-step explanation:

-4(-2u+3)-u=3(u-7)-5

8u-12-u=3u-21-5

8u-u-12=3u-26

7u-12=3u-26

7u-3u-12=-26

4u-12=-26

4u=-26+12

4u=-14

u=-14/4

simplify

u=-7/2

Answer:

u = - 3.5

Step-by-step explanation:

Before solving this you have to know that,

(-) × (-) = (+)

(-) × (+) = (-)

(+) × (+) = (+)

Let us solve now.

[tex]-4(-2u+3)-u=3(u-7)-5[/tex]

[tex]8u-12-u=3u-21-5[/tex]

[tex]7u-12=3u-26[/tex]

[tex]7u-3u=12-26[/tex]

[tex]4u=-14[/tex]

[tex]\frac{4u}{4} = \frac{-14}{4}[/tex]

[tex]u=-3.5[/tex]

Hope this helps you.

Let me know if you have any other questions :-)

Answer:

32. A.

Step-by-step explanation: because i did 4/5 of 40 and got 32.

Answer:

É 5x3=15

Step-by-step explanation: