look at the image below

Answer:

[tex]\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1[/tex]

Step-by-step explanation:

Since the vertex of the parabola is at (4,0), it has the vertex on the x axis (horizontal axis). The standard equation of an ellipse with horizontal major axis is given by:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

Where (h,k) is the center of the ellipse, a is the vertex and ±√(a²- b²) is the focus (c).

Since the ellipse center is at (0, 0), h = 0 and k = 0. Also the vertex is at (4, 0) therefore a = 0

To find b we use the equation of the focus which is:

[tex]c=\sqrt{a^2-b^2}\\ \\Substituing:\\\\3=\sqrt{4^2-b^2} \\4^2-b^2=3^2\\b^2=4^2-3^2\\b^2=16-9\\b^2=7\\b=\sqrt{7}[/tex]

Substituting the values of a, b, h and k:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\\\\\frac{(x-0)^2}{4^2}+\frac{(y-0)^2}{\sqrt{7} ^2}=1\\\\\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1[/tex]

Answer:

5/8

Step-by-step explanation:

Add the two fractions

3/8 + 1/4

Get a common denominator

3/8 + 1/4 *2/2

3/8 + 2/8

5/8

Points are

[tex]\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{3-13}{-2+2}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{-10}{0}[/tex]

[tex]\\ \sf\longmapsto m=0[/tex]

Answer:

L ≈ 1023.0562

Step-by-step explanation:

We are given;

x = t² - 2t

dx/dt = 2t - 2

Also, y = t^(5)

dy/dt = 5t⁴

The arc length formula is;

L = (α,β)∫√[(dx/dt)² + (dy/dt)²]dt

Where α and β are the boundary points. Thus, applying this to our question, we have;

L = (1,4)∫√[(2t - 2)² + (5t⁴)²]dt

L = (1,4)∫√[4t² - 8t + 4 + 25t^(8)]dt

L = (1,4)∫√[25t^(8) + 4t² - 8t + 4]dt

Using online integral calculator, we have;

L ≈ 1023.0562

The length of the curve is 1023.0562 and this can be determined by doing the integration using the calculator.

Given :

First, differentiate x and y with respect to 't'.

[tex]\rm \dfrac{dx}{dt}=2t-2[/tex]

[tex]\rm \dfrac{dy}{dt}=5t^4[/tex]

Now, determine the length of the curve using the below formula:

[tex]\rm L = \int^b_a\sqrt{\left(\dfrac{dx}{dt}\right)^2+\left(\dfrac{dy}{dt}\right)^2} dt[/tex]

Now, substitute the value of the known terms in the above formula and then integrate it.

[tex]\rm L = \int^4_1\sqrt{(2t-2)^2+(5t^4)^2} dt[/tex]

[tex]\rm L = \int^4_1\sqrt{25t^8+4t^2-8t+4} \;dt[/tex]

Now, simplify the above integration using the calculator.

L = 1023.0562

For more information, refer to the link given below:

https://brainly.com/question/18651211

━━━━━━━☆☆━━━━━━━

▹ Answer

18x⁴ + 36x³ - 9x²

▹ Step-by-Step Explanation

9x²(4x + 2x² - 1)

36x³ + 18x⁴ - 9x²

18x⁴ + 36x³ - 9x²

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

$50

Step-by-step explanation:

Let x represent the cost of the cell phone.

Since the TV cost 5 times as much as the cell phone, its cost can be represented by 5x.

Since the computer cost 2.5 times as much as the TV, its cost can be represented by 12.5x.

Create an equation to represent the situation, and solve for x:

x + 5x + 12.5x = 925

18.5x = 925

x = 50

So, the cell phone cost $50

Answer:

$50

Step-by-step explanation:

Let x represent the cost of the cell phone.

Since the TV cost 5 times as much as the cell phone, its cost can be represented by 5x.

Since the computer cost 2.5 times as much as the TV, its cost can be represented by 12.5x.

Create an equation to represent the situation, and solve for x:

x + 5x + 12.5x = 925

18.5x = 925

x = 50

So, the cell phone cost $50

Answer:

  -j, 0, j-k

Step-by-step explanation:

j is a positive number, so -j will be less than 0.

j is a number greater than k, so j - k will be greater than 0.

From least to greatest, the order is ...

  -j, 0, j-k

Answer:

Step-by-step explanation:

Answer:

A

[tex]f(x) = x^3 - 2x^2 -3x + 6[/tex]

Step-by-step explanation:

According to the Factor Theorem, if (x - k) is a factor of a polynomial P(x), then P(k) must equal zero.

We are given that a polynomial function has the zeros 2, √3, and -√3. So, we can let k = 2, √3, -√3.

So, according to the Factor Theorem, P(2), P(√3) and P(-√3) must equal 0.

Testing each choice, we can see that only A is true:

[tex]\displaystyle f(x) = x^3 - 2x^2 - 3x + 6[/tex]

Testing all three values yields that:

[tex]\displaystyle \begin{aligned} f(2) &= (2)^3 - 2(2)^2 -3(2) + 6 \\ &= (8) - (8) -(6) + (6) \\ &= 0\stackrel{\checkmark}{=}0 \\ \displaystyle f(\sqrt{3}) &= (\sqrt{3})^3 - 2(\sqrt{3})^2 - 3(\sqrt{3}) + 6 \\ &=(3\sqrt{3}) -(6)-(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0 \\ f(-\sqrt{3}) &= (-\sqrt{3})^3 - 2(-\sqrt{3})^2 - 3(-\sqrt{3}) + 6 \\ &=(-3\sqrt{3}) -(6)+(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0 \end{aligned}[/tex]

Hence, our answer is A.

Answer:

The Taylor series of f(x) around the point a, can be written as:

[tex]f(x) = f(a) + \frac{df}{dx}(a)*(x -a) + (1/2!)\frac{d^2f}{dx^2}(a)*(x - a)^2 + .....[/tex]

Here we have:

f(x) = 4*cos(x)

a = 7*pi

then, let's calculate each part:

f(a) = 4*cos(7*pi) = -4

df/dx = -4*sin(x)

(df/dx)(a) = -4*sin(7*pi) = 0

(d^2f)/(dx^2) = -4*cos(x)

(d^2f)/(dx^2)(a) = -4*cos(7*pi) = 4

Here we already can see two things:

the odd derivatives will have a sin(x) function that is zero when evaluated in x = 7*pi, and we also can see that the sign will alternate between consecutive terms.

so we only will work with the even powers of the series:

f(x) = -4 + (1/2!)*4*(x - 7*pi)^2 - (1/4!)*4*(x - 7*pi)^4 + ....

So we can write it as:

f(x) = ∑fₙ

Such that the n-th term can written as:

[tex]fn = (-1)^{2n + 1}*4*(x - 7*pi)^{2n}[/tex]

In this exercise we must calculate the Taylor series for the given function in this way;

[tex]f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}[/tex]

The Taylor series of f(x) around the point a, can be written as:

[tex]f(x) = f(a) + f'(a)(x-a)+\frac{1}{2!} f''(a)(x-a)^2+....[/tex]

Here we have:

[tex]f(x) = 4cos(x)\\a = 7\pi[/tex]

Then, let's calculate each part:

[tex]f(a) = 4cos(7\pi) = -4\\df/dx = -4sin(x)\\(df/dx)(a) = -4sin(7\pi) = 0\\(d^2f)/(dx^2) = -4cos(x)\\(d^2f)/(dx^2)(a) = -4cos(7\pi) = 4[/tex]

Here we already can see two things:

1) The odd derivatives will have a sin(x) function that is zero when evaluated in [tex]x=7\pi[/tex].

2) We also can see that the sign will alternate between consecutive terms.

So we only will work with the even powers of the series:

[tex]f(x) = -4 + (1/2!)*4*(x - 7\pi)^2 - (1/4!)*4*(x - 7\pi)^4 + ....[/tex]

So we can write it as:

[tex]f(x)=\sum f_n[/tex]

Such that the n-th term can written as:

[tex]f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}[/tex]

See more abour Taylor series at: brainly.com/question/6953942

Answer:

Use Guathmath app. you will get answer with explaination and full formula.

download Guathmath if you have interest to do this activity.

Answer:

The mean, variance, and standard deviation of the binomial distribution are 10, 8, and 2.83 respectively.

Step-by-step explanation:

We have to find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p, i.e; n = 50 p = 0.2.

Let X = binomial random variable

So, X ~ Binom(n = 50, p = 0.2)

Now, the mean of the binomial distribution is given by;

         Mean of X, E(X) = n [tex]\times[/tex] p

                                    = 50 [tex]\times[/tex] 0.2 = 10

Now, the variance of the binomial distribution is given by;

        Variance of X, V(X) = n [tex]\times[/tex] p [tex]\times[/tex] (1 - p)

                                         = 50 [tex]\times[/tex] 0.2 [tex]\times[/tex] (1 - 0.2)

                                         = 10 [tex]\times[/tex] 0.8 = 8

Also, the standard deviation of the binomial distribution is given by;

        Standard deviation of X, S.D.(X) = [tex]\sqrt{\text{n} \times \text{p} \times (1 - \text{p})}[/tex]

                                                              = [tex]\sqrt{\text{50} \times \text{0.2} \times (1 - \text{0.2})}[/tex]

                                                              = [tex]\sqrt{8}[/tex] = 2.83

Answer:

( n+1) /2 *( 3n+2)

Step-by-step explanation:

n/2 * ( 3n-1)

We want the n+1 term

Replace n with n+1

( n+1) /2 *( 3( n+1) -1)

Distribute

( n+1) /2 *( 3n+3 -1)

( n+1) /2 *( 3n+2)

Answer:

[tex]\large \boxed{\sf C. \ \frac{n+1}{2} (3n+2)}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{n}{2} (3n-1)[/tex]

To find the (n+1)st term, replace the n variable with n+1.

[tex]\displaystyle \frac{n+1}{2} (3(n+1)-1)[/tex]

Expand brackets.

[tex]\displaystyle \frac{n+1}{2} (3n+3-1)[/tex]

Subtract like terms in brackets.

[tex]\displaystyle \frac{n+1}{2} (3n+2)[/tex]

Answer:

15.7 in  

Step-by-step explanation:

A slice of a round pie is a sector of a circle.

The perimeter of a slice is the arc length s plus twice the radius r.

P = s + 2r

s = rθ = r(16/360) = r/22.5. So,

16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5

16 × 22.5 = 46r

360 = 46r

r = 7.826  

D = 2r = 2 × 7.826 = 15.7 in

The diameter of the cake should be 15.7 in.

Check:

[tex]\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}[/tex]

It checks.

Answer:

x=18

Step-by-step explanation:

x/6 - 7 = -4

x/6 = 3

(x/ 6) * 6 = 3*6

x = 18

https://youtu.be/ipEbWgC-6nA

Answer:

x = -3

Step-by-step explanation:

12 -4x-5x = 39

Combine like terms

12 - 9x = 39

Subtract 12 from each side

12-9x-12 = 39-12

-9x = 27

Divide by -9

-9x/-9 = 27/-9

x = -3

Answer:

x = -3

Step-by-step explanation:

12 - 4x - 5x = 39

Combine like terms

12 - 9x = 39

Subtract 12 from both sides

12 - 12 - 9x = 39 - 12

-9x = 27

Divide both sides by -9

-9x/-9 = 27/-9

x = -3

By the supplementary angles theorem, we know that both of the angles add up to equal 180°, so:

(4x + 22) + (8x - 10) = 180

12x + 12 = 180

12x = 168

x = 14

Now you just have to plug in x into the value for ∠ABC:

∠ABC = 4x + 22

∠ABC = 4(14) + 22

∠ABC = 46 + 22

∠ABC = 68°

Answer:

D = 78

Step-by-step explanation:

The two angles form a straight line so they add to 180

4x+22 + 8x-10 = 180

Combine like terms

12x +12 =180

Subtract 12 from each side

12x+12-12 = 180-12

12x = 168

Divide by 12

12x/12 =168/12

x=14

We want to find ABC

4x+22 = 4*14+22 = 56+22 = 78

Answer:

[tex] - 8 = 8( - 3 + a) \\ - 8 = - 24 + 8a \\ 8a = 16 \\ a = 2[/tex]

Answer:

2

Step-by-step explanation:

-8 = 8a - 24

16 = 8a

a =2

Answer:

see below

Step-by-step explanation:

x^2+8x+26

Take the coefficient of the x term

8

Divide by 2

8/2 = 4

square it

4^2 =16

we need to add 16 to 26 = 16+10

x^2 + 8x+16  +10

(x+4)^2 +10

The answer you are looking for is (x+4)²+10.

Solution/Explanation:

Selecting the "x" term's coefficient,

It would be 8.

Now, dividing it by 2,

8/2=4.

Squaring 4,

4²=16.

So, now, since (x+4)²=x²+8x+16, you must solve for 26-16, which equals 10, which you would supplement into the equation.

So, therefore, (x+4)²+10.

I hope this has helped you. Enjoy your day.

Answer:

f(2) = 2

Step-by-step explanation:

f(x)=x^2-2x+2

Let x=2

f(2)=2^2-2*2+2

    = 4 -4 +2

    = 2

Answer:

The total   profit is [tex]p = 17x + 2124[/tex]

Step-by-step explanation:

From the question we are told that

   The profit made on each mp3 is  k  =  $35

    The profit made on each mp3 is  y =  $18

     The total amount sold is   n  =  118

 Now given that the amount of mp3 sold is x then the amount of  DVD sold is mathematically evaluated as

                      [tex]n - x[/tex]

Now the profit made on the x number of mp3 sold is  

                      [tex]x * 35 = 3x[/tex]

And the the profit made from the n-x number of  DVD  sold is  18 (n-x ) =  18 - 18x

 So the total profit made last week from the sales of both mp3 and DVD  is  

                   [tex]p = 35x + 18n - 18x[/tex]

                    [tex]p = 17x + 18(118)[/tex]

                    [tex]p = 17x + 2124[/tex]

Answer:

[tex]a\cdot b[/tex] = 1

Step-by-step explanation:

Given that,

Vector [tex]a=5i+7j[/tex]

Vector [tex]b=-4i+3j[/tex]

We need to find [tex]a{\cdot} b[/tex] means the dot product of a and b. So,

[tex]a{\cdot} b=(5i+7j){\cdot} (-4i+3j)[/tex]

We know that,

[tex]i{\cdot}i, j{\cdot}j,k{\cdot}k=1\ \text{and}\ i{\cdot}j= j\cdot i=0[/tex]

So,

[tex]a{\cdot} b=(5i+7j){\cdot} (-4i+3j)\\\\=5i{\cdot}(-4i)+5i{\cdot} 3j+7j\cdot(-4i)+7j\cdot 3j\\\\=-20+21\\\\=1[/tex]

So, the value of [tex]a\cdot b[/tex] is 1.

Answer:

1

Step-by-step explanation:

[tex]\\ \sf\longmapsto 122^2[/tex]

[tex]\\ \sf\longmapsto (100+22)^2[/tex]

[tex]\\ \sf\longmapsto 100^2+2(100)(22)+22^2[/tex]

[tex]\\ \sf\longmapsto 10000+4400+484[/tex]

[tex]\\ \sf\longmapsto 14400+484[/tex]

[tex]\\ \sf\longmapsto 14884[/tex]

112²

(a + b)² = (a² + 2ab + b²)

⇛122²

⇛(100 + 22)²

⇛(100)² + 2 × 100 × 22 + (22)²

⇛10000 + 4400 + 484

⇛14400 + 484

⇛14884

Hey there! I'm happy to help!

When graphing a system of equations, the solution is the point where the two lines meet. We see that they intersect at (-2,4).

Therefore, the solution to the system of equations is (-2,4).

Have a wonderful day! :D

Answer:

A

Step-by-step explanation:

edge 2020 Dec 9

Answer:

C = 2pie(r)

r= d/2= 13/2= 6.5

C = 2*3.14*6.5

C= 41

Step-by-step explanation:

Amount of Interest=7152-6400=752=I

We know

[tex]\boxed{\sf I=\dfrac{PRT}{100}}[/tex]

[tex]\\ \sf\longmapsto T=\dfrac{PR}{100I}[/tex]

[tex]\\ \sf\longmapsto T=\dfrac{6400(6)}{100(752)}[/tex]

[tex]\\ \sf\longmapsto T=\dfrac{38400}{75200}[/tex]

[tex]\\ \sf\longmapsto T\approx 0.5year[/tex]

[tex]\\ \sf\longmapsto T\approx 6months[/tex]

Answer:

The answer is D  

Step-by-step explanation:

there are 8 1/6 five and one sixth in 2/3

[tex]_6C_3=\dfrac{6!}{3!3!}=\dfrac{4\cdot5\cdot6}{2\cdot3}=20[/tex]

Answer:

the answer should be B

Step-by-step explanation:

take the total of people who got the flu(63) and the amount of them who were vaccinated(35) and write it as a fraction. 35/63 in its simplest form is 5/9