Does anybody know the answer to this?

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

[tex]\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt[/tex]

Evaluate the integral to solve for y :

[tex]\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt[/tex]

[tex]\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x[/tex]

[tex]\displaystyle y = x^3+2x^2+kx - 2[/tex]

Use the other known value, f(2) = 18, to solve for k :

[tex]18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}[/tex]

Then the curve C has equation

[tex]\boxed{y = x^3 + 2x^2 + 2x - 2}[/tex]

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

[tex]\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2[/tex]

The slope of the given tangent line [tex]y=x-2[/tex] is 1. Solve for a :

[tex]3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1[/tex]

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

[tex]x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1[/tex]

So, the point of contact between the tangent line and C is (-1, -3).

Answer:

17

Step-by-step explanation:

This flight makes a right triangle

The sides are 8 and 15. The hypotenuse isnt know and that is the answer.

8^2 + 15^2 = c^2

c^2 = 289

c = 17

They are exempt from income tax and we would get the income tax withheld as $340.

The person does not have another source of income, and there are no exceptions that are claimed by the person.

The withheld tax which is held every week can be calculated as;

Amount of income tax = 30 % of 1,166

Amount of income tax = $339.6

Amount of income tax = $340

Hence, they are exempt from income tax and we would get the income tax withheld as $340.

Read more about taxable income here:

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Answer:

224 ÷ 4 = 56

Step-by-step explanation:

14 × 4 = 56

56 × 4 = 224

224 ÷ 4 = 56

[tex]y=-\dfrac 14 x~~....(i)\\\\x+2y = 4~~...(ii)\\\\\text{Substitute}~~ y= -\dfrac 14 x ~~ \text{in equation (ii):}\\ \\ \\x+2\left(-\dfrac 14 x \right) = 4\\\\\implies 4x -2x = 16~~~~;\left[\text{Multiply both sides by 4} \right]\\\\\implies 2x = 16\\\\\implies x =\dfrac{16}2 \\ \\\implies x =8\\\\\text{Substitute x = 8 in equation (i);}\\\\y= -\dfrac 14 \cdot 8 = -2\\\\\text{Hence,}~ (x,y) = (8,-2)[/tex]

Answer:

[tex]y = - \frac{1 }{4} x \\ [/tex]

[tex]x + 2y = 4 \\ [/tex]

[tex]x + 2( - \frac{1}{4} x) = 4 \\ [/tex]

[tex]x + ( - \frac{2}{4} x) = 4 \\ [/tex]

[tex]x - \frac{1}{2} x = 4 \\ [/tex]

[tex] \frac{2x - 1x}{2} = 4 \\ [/tex]

[tex]2x - x = 8[/tex]

[tex]x = 8[/tex]

[tex]x + 2y = 4 \\ [/tex]

[tex]8 + 2y = 4[/tex]

[tex]2y = 4 - 8[/tex]

[tex]2y = - 4[/tex]

[tex]y = - 2[/tex]

Answer:

m∠Z=146

m∠X=34

Step-by-step explanation:

Since this is an Isosceles Trapezoid, we can assume that m∠Z=m∠Y, because an isosceles trapezoid has two pairs of congruent angles, therefore m∠Z=146.

Since angle Y and Angle X are same side interior and line ZY║WX, we can assume that m∠X+m∠Y=180. Substitute values:

[tex]146+X=180\\Y=34[/tex]

Answer:

The answer is 20

Step-by-step explanation:

There's two ways in which you can do this. The first one, and the simpliest one is finding the derivative of the equation P(x). After finding the derivative, set the dy/dx to be zero (so set the derivative to be zero). Then solve for x. This should give you the point at which there's no increase or decrease in the value of P, thus meaning the point at which its the maximum.

The second method is simply ploting a graph and finding the highest point.

Answer:

see below

Step-by-step explanation:

Move R side to the L side to get

2y^2 -4y +3  = 0

Use quadratic formula to find y = 1 +- i sqrt (2) / 2

Answer:

A

Step-by-step explanation:

m( n+ p)

it's also known as m × n + p

Answer:

-25

Step-by-step explanation:

Answer:

$24

Step-by-step explanation:

PRICE=$80

DISCOUNT=70٪ OF $80=(70/100)×80=70×80/100=$56

HENCE DISCOUNT=$56

NOW THE PRICE=$80-$56=$24

I HOPE IT HELPED YOU

Answer: 24

Step-by-step explanation:

Multiply the original price by how much is being discounted.

80 x .70 = 56

Subtract the answer from the original price.

80 - 56 = 24

Check the picture below, so hmm we know that much, and we can also more or less see that PR is the longest side, let's check the length of the other two sides

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{6}~,~\stackrel{y_1}{1})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{[3 - 6]^2 + [5 - 1]^2}\implies PQ=\sqrt{(-3)^2+4^2}\implies \boxed{PQ=5} \\\\[-0.35em] ~\dotfill\\\\ Q(\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad R(\stackrel{x_2}{11}~,~\stackrel{y_2}{11})~\hfill QR=\sqrt{[11 - 3]^2 + [11 - 5]^2} \\\\\\ QR=\sqrt{8^2+6^2}\implies \boxed{QR=10}[/tex]

if that's true, the triangle is indeed a right-triangle, then hmmmm most likely using the pythagorean theorem PR² = PQ² + QR², let's check

[tex](\sqrt{125})^2~~ = ~~5^2~~ + ~~10^2\implies 125=25+100\implies 125=125~~\textit{\Large \checkmark}[/tex]

Answer:

2x^2+10-3x

Step-by-step explanation:

start by multiplying numberes into the parentheses.

2x^2+10-3x-3+3

now combine like terms

2x^2+10-3x

The inequality of the expression is a greater than inequality, and the required inequality is 2x + y > 34

From the question, we have the following representations:

A field goal has 2 points, while a foul shot has 1 point.

So, the number of points in a game is:

Score = 2x + y

The team is behind by 34 points.

So, the team must attain above 34 points

This means that the score must be greater than 34.

So, the inequality is:

2x + y > 34

See attachment for the graph of the inequality

Read more about inequality at:

https://brainly.com/question/11234618

#SPJ1

t=2 hrs-------so 2 hrs after the second plane leaves it will catch the first plane

CK

720+240*2=600*2

720+480=1200

1200=1200

The least amount of wrapping paper that Amy needs to wrap the present is 1936in².

Surface area is simply the amount of space covering the outside of a 3-dimensional object.

The surface area of a rectangular prism is expressed;

A = 2( wl + hl + hw )

Given the data in the question;

To determine the least amount of wrapping paper that Amy needs to wrap the present in the shape of a rectangular prism, we substitute our given values into the expression above.

A = 2( wl + hl + hw )

A = 2( (16in×20in) + (18in×20in) + (18in×16in) )

A = 2( 320in² + 360in² + 288in² )

A = 2( 968in² )

A = 1936in²

Therefore, the least amount of wrapping paper that Amy needs to wrap the present is 1936in².

Learn more about the surface area of a rectangular prism here: https://brainly.com/question/14987814

slope intercept form: y = mx + b    [ where m is slope and b is y-intercept ]

[tex]\dashrightarrow \ \sf9x + 3y = 27[/tex]

[tex]\dashrightarrow \ \sf 3y = 27 -9x[/tex]

[tex]\dashrightarrow \ \sf y = \dfrac{27 -9x}{3}[/tex]

[tex]\dashrightarrow \ \sf y = -3x + 9[/tex]

Here, the "slope is -3"  and  "y-intercept is 9"

Slope intercept form:-

Now convert

Cancel 3

Answer:

6

Step-by-step explanation:

[tex]h \sqrt{28 } \\ \sqrt{28} = \sqrt{4 \times 7} \\ \sqrt{28} = \sqrt{4} \times \sqrt{7} \\ 2 \sqrt{7} \\ 8 \sqrt{7} - 2 \sqrt{7} = 6 \sqrt{7} [/tex]

hope this helps :D have a good day

Answer:

Danil received 147 euros

Step-by-step explanation:

Let, Danil,Gabriel and Hardly share some money of 3x:5x:9x ratio then,

From the question,

9x - 5x= 196

or, 4x= 196

or, x = 196/4

or, x = 49 euros

Again,Danil received 3x share of money

=3*49

=147 euros

Answer:

Step-by-step explanation:

Ratio = 3 : 5 : 9

Money received by  Danil = 3x  

Money received by Gabriel = 5x

Money received by Hadley = 9x

Difference in the amount between Gabriel and Hadley = 196 euros

9x - 5x = 196

       4x = 196

         x = 196/4

        x = 49

Money received by Danil = 3*49

                                           = € 147

Answer:

x=5

Step-by-step explanation:

6:5

x:4, so x =5

The side also looks a little bigger than 4.

Hope it Helps

The correct solution of the given quadratic equation was found using the formula.

The given equation is:

[tex]9x+2=8x^{2} +6x[/tex]

[tex]8x^{2} +6x-9x-2=0[/tex]

[tex]8x^{2} -3x-2=0[/tex]....(1)

An equation of the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where [tex]a\neq 0[/tex].

We can solve equation (1) by the formula

[tex]x=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]

So, [tex]x=\frac{3+-\sqrt{(-3)^{2} -4(8)(-2)} }{2(8)}[/tex]

[tex]x=\frac{-3+-\sqrt{73} }{16}[/tex]

Hence, the correct solution of the given quadratic equation was found using the formula.

To get more about quadratic equations visit:

https://brainly.com/question/1214333

Answer:

pounds and ounces

Randomly pick 25 fish from the entire pond and weigh each of them

Step-by-step explanation:

Centimeters, feet and inches measure length, not weight.

To find the average weight of fish living in a large pond, the scientist will randomly pick 25 fish from all over the pond. Next, each fish will be weighed. The weight of all 25 fish will be added and the total will be divided by 25. This will give you the average weight of a fish living in the large pond.

Answer:

1 dime

Step-by-step explanation:

didvide 1 pound by the weight or the dime to get the answer

Answer:

21300

Step-by-step explanation:

120∑n=13n−4

Split the summation into smaller summations that fit the summation rules.

120∑n=1 3n−4=3120∑n=1 n+120∑n=1 −4

Evaluate

3120∑n=1 n.

21780

Evaluate  

120∑n=1 −4 −480

Add the results of the summations.

21780−480

Subtract 480 from 21780.

21300

Answer:

The triangle which is congruent to triangle QRS is YXZ

Answer:

14, 48 and 50

Step-by-step explanation:

The volume of the cone and pyramid are the same.

Formula for volume of cone = ⅓(144π × h)

Volume of cone = ⅓[πr² × height of cone)

Volume of triangular pyramid = ⅓[(½bh × height of pyramid)]

Also note the following:

Area of a circle = πr²

Area of a triangle = ½bh

Part A:

Area of circle 1 = πr² = π(12²) = 144π units²

Area of circle 2 = πr² = π(6²) = 36π units²

Area of circle 3 = πr² = π(3²) = 9π units²

Area of triangle 1 = ½(24)(12π) = 144π units²

Area of triangle 2 = ½(12)(6π) = 36π units²

Area of triangle 3 = ½(6)(3π) = 9π units²

Part B: Based on our results in part A, the volumes of the cone and pyramid, having the same height are the same.

Part C:

Volume of pyramid = ⅓(144π × h)

Using this measurement and our conclusion in part B:

Formula for the Volume of a cone = ⅓(144π × h)

Learn more about the volume of cone and pyramid on:

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Answer:

69 degrees

Step-by-step explanation:

See attached image.