Let $f(x) = x^3 + 3x ^2 + 4x - 7$ and $g(x) = -7x^4 + 5x^3 +x^2 - 7$. What is the coefficient of $x^3$ in the sum $f(x) + g(x)$?

Answer:

triangular prism

Answer:

it will be triangular prism

Answer:

The doomsday is 146 days

Step-by-step explanation:

Given

[tex]\frac{dy}{dt} = ky^{1 +c}[/tex]

First, we calculate the solution that satisfies the initial solution

Multiply both sides by

[tex]\frac{dt}{y^{1+c}}[/tex]

[tex]\frac{dt}{y^{1+c}} * \frac{dy}{dt} = ky^{1 +c} * \frac{dt}{y^{1+c}}[/tex]

[tex]\frac{dy}{y^{1+c}} = k\ dt[/tex]

Take integral of both sides

[tex]\int \frac{dy}{y^{1+c}} = \int k\ dt[/tex]

[tex]\int y^{-1-c}\ dy = \int k\ dt[/tex]

[tex]\int y^{-1-c}\ dy = k\int\ dt[/tex]

Integrate

[tex]\frac{y^{-1-c+1}}{-1-c+1} = kt+C[/tex]

[tex]-\frac{y^{-c}}{c} = kt+C[/tex]

To find c; let t= 0

[tex]-\frac{y_0^{-c}}{c} = k*0+C[/tex]

[tex]-\frac{y_0^{-c}}{c} = C[/tex]

[tex]C =-\frac{y_0^{-c}}{c}[/tex]

Substitute [tex]C =-\frac{y_0^{-c}}{c}[/tex] in [tex]-\frac{y^{-c}}{c} = kt+C[/tex]

[tex]-\frac{y^{-c}}{c} = kt-\frac{y_0^{-c}}{c}[/tex]

Multiply through by -c

[tex]y^{-c} = -ckt+y_0^{-c}[/tex]

Take exponents of [tex]-c^{-1[/tex]

[tex]y^{-c*-c^{-1}} = [-ckt+y_0^{-c}]^{-c^{-1}[/tex]

[tex]y = [-ckt+y_0^{-c}]^{-c^{-1}[/tex]

[tex]y = [-ckt+y_0^{-c}]^{-\frac{1}{c}}[/tex]

i.e.

[tex]y(t) = [-ckt+y_0^{-c}]^{-\frac{1}{c}}[/tex]

Next:

[tex]t= 3[/tex] i.e. 3 months

[tex]y_0 = 2[/tex] --- initial number of breeds

So, we have:

[tex]y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}[/tex]

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

We have the growth term to be: [tex]ky^{1.01}[/tex]

This implies that:

[tex]ky^{1.01} = ky^{1+c}[/tex]

By comparison:

[tex]1.01 = 1 + c[/tex]

[tex]c = 1.01 - 1 = 0.01[/tex]

[tex]y(3) = 16[/tex] --- 16 rabbits after 3 months:

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

[tex]y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}[/tex]

[tex]16 = [-0.01 * 3 * k + 2^{-0.01}]^{\frac{-1}{0.01}}[/tex]

[tex]16 = [-0.03 * k + 2^{-0.01}]^{-100}[/tex]

[tex]16 = [-0.03 k + 0.9931]^{-100}[/tex]

Take -1/100th root of both sides

[tex]16^{-1/100} = -0.03k + 0.9931[/tex]

[tex]0.9727 = -0.03k + 0.9931[/tex]

[tex]0.03k= - 0.9727 + 0.9931[/tex]

[tex]0.03k= 0.0204[/tex]

[tex]k= \frac{0.0204}{0.03}[/tex]

[tex]k= 0.68[/tex]

Recall that:

[tex]-\frac{y^{-c}}{c} = kt+C[/tex]

This implies that:

[tex]\frac{y_0^{-c}}{c} = kT[/tex]

Make T the subject

[tex]T = \frac{y_0^{-c}}{kc}[/tex]

Substitute: [tex]k= 0.68[/tex], [tex]c = 0.01[/tex] and [tex]y_0 = 2[/tex]

[tex]T = \frac{2^{-0.01}}{0.68 * 0.01}[/tex]

[tex]T = \frac{2^{-0.01}}{0.0068}[/tex]

[tex]T = \frac{0.9931}{0.0068}[/tex]

[tex]T = 146.04[/tex]

The doomsday is 146 days

Answer: 50.8

Step-by-step explanation:

The volume of the given cone is 50.8 m³.

A cone is a shape created by connecting all the points of a circular base (which does not contain the apex) to a common point known as the apex or vertex using a series of line segments or lines.

Given that,

Height = h  = 4.2 m

Radius  of base = r  = 3.4 mm

Since we know that,

volume of cone = πr²h/3

now put the values

we get,

volume of cone =  π(3.4)²(4.2)/3

                          = 50.8 square m

Hence,

The volume = 50.8 m³

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Answer:

1. 1/2

2. 99/100

3. 3/20

4. 2

Answer:

The slope is 1/2

Step-by-step explanation:

Use the slope-intercept form  y  =  m x + b  to find the slope  m

Hope this helps:)

Step-by-step explanation:

Area = l × b

= 9ft × 8ft

= 72ft²

Answer:

72 feet

Step-by-step explanation:

8 (length) • 9 (width) = 72 sq ft

Answer:

No solutions

Step-by-step explanation:

There are no solutions because the two lines have the same gradient (they are parallel)

Have a great day <3 and pls love me

Answer:

4990

Step-by-step explanation:

Multiply 638 by 5 then add 1800 and that's your answer

Answer:

4990

Step-by-step explanation:

638 x 5 = 3190

There is already a population of 1800, so then you add 3190 and 1800 to get 4900. The reason you add these numbers is because the population grows by 638 every year. They want to know how much it will grow in 5 years. You you multiply n (number) by y (year) to get t ( total).

Hope this helps!

Yours Truel, TheAnimeCatUwU

Answer:

41

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

Answer:

7/6 or 1*1/6

Step-by-step explanation:

Answer:

the answer is in the picture

Answer:

x=11

Step-by-step explanation:

4x+11=5x (angle adb and edf are the same)

11=5x-4x

11=x

x=11

if you want you can check by doing...

(14*11-29)+(5*11)=180

Step-by-step explanation:

It means "a divided by 3". You need to divide a by 3. You can also write it as "1/3a".

Answer:

the answer is above me or below me

8 is a perfect cube number. So, option A.) is correct.

A number is said to be a perfect cube if it can be multiplied by itself three times. X must equal [tex]y^3[/tex] if it is a perfect cube of Y. As a result, a natural integer, not a fraction, is obtained when we take the cube root of a perfect cube. Therefore, [tex]3\sqrt{x}[/tex] equals y.

Let, a be a integer number then for a number to be perfect cube

Number= [tex]a^3[/tex]..............................................where a is integer number

8= [tex]a^3[/tex]

So, a=2

9= [tex]a^3[/tex]

No, integer value exist, whose cube is 9.

16= [tex]a^3[/tex]

No, integer value exist, whose cube is 16.

25= [tex]a^3[/tex]

No, integer value exist, whose cube is 25.

Thus, 8 is a perfect cube number. So, option A.) is correct.

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Answer:

P is price per lawn, 20 is the money made per lawn, L is the number of lawns mowed, 100 is his initial cost.

Step-by-step explanation:

Where the above ratio are given, the length of the side of the smaller square is approximately 14.7 feet.

The area of a square is calculated by squaring the length of its side. Given that the area of the larger square is 324 square feet, we have:

(3/2)x² = 324

To solve for x, we can rearrange the equation and take the square root of both sides  -

x² = (324 * 2) / 3

x² = 216

x ≈ √216

x ≈ 14.7

Hence , the length of the side of the smaller square is approximately 14.7 feet.

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Answer:

C 62.4square centimetres

Answer:

8 * (2y⁶ - 5z²) ( 4y¹² +10 y⁶z² + 25z⁴)

Step-by-step explanation:

64y¹⁸ – 1000z⁶ = 8 * (8y¹⁸ - 125z⁶) = 8 * ((2y⁶)³ - (5z²)³)

= 8 * (2y⁶ - 5z²) ( 4y¹² +10 y⁶z² + 25z⁴)

9514 1404 393

Answer:

Step-by-step explanation:

Let w represent the width of the field. Then w+175 is its length. The perimeter is ...

  P = 2(L+W)

  818 = 2((w+175) +w) . . . . . fill in given values

  818 = 4w +350 . . . . . . . . . simplify

  468 = 4w . . . . . . . . . subtract 350

  117 = w . . . . . . . . divide by 4

  w+175 = 292 . . . . find the corresponding length

The width of the field is 117 feet; the length is 292 feet.

Answer:

A) WZ

Step-by-step explanation:

B,C, and D, come before RU

Answer:

40 mi

Step-by-step explanation:

area= width*length  

Answer:

40 mi

Step-by-step explanation:

probally a jok e

[tex]A=l*w[/tex]

[tex]A = 5*8[/tex]

[tex]A=40[/tex]

Answer:

19 / (19+19+13) = 0.37254901... = ~ 37%

Step-by-step explanation:

19 is self-explanatory

(19+19+13) = 52

19 / 52 = 0.37254901...

0.37254901... = ~37%

brainliest plz

Answer:

D. 105 students

Step-by-step explantation: 11+10+21+6+2=50. So, 21 times 250 is 5250 and divided by 50 is 105.

Answer:

The correct answer is the tor mar nada tor buda tor buni ami chai

Answer: Find the volume of cone, whose radius is 8 cm and height is 5 cm. Thus, the volume of the cone is 334.93 cm3.

Answer:

251.33cm^3

Step-by-step explanation: Use the formula V= π • (d/2)^2 • H

HOPEFULLY THIS HELPS

You mean Sigma notation not stigma ^^

Answer:

Look the attachment