Please help fast, thanks.

Answer:

See below for Part A.

Part B)

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

Step-by-step explanation:

Part A)

The parabola given by the equation:

[tex]y^2=4ax[/tex]

From 0 to h is revolved about the x-axis.

We can take the principal square root of both sides to acquire our function:

[tex]y=f(x)=\sqrt{4ax}[/tex]

Please refer to the attachment below for the sketch.

The area of a surface of revolution is given by:

[tex]\displaystyle S=2\pi\int_{a}^{b}r(x)\sqrt{1+\big[f^\prime(x)]^2} \,dx[/tex]

Where r(x) is the distance between f and the axis of revolution.

From the sketch, we can see that the distance between f and the AoR is simply our equation y. Hence:

[tex]r(x)=y(x)=\sqrt{4ax}[/tex]

Now, we will need to find f’(x). We know that:

[tex]f(x)=\sqrt{4ax}[/tex]

Then by the chain rule, f’(x) is:

[tex]\displaystyle f^\prime(x)=\frac{1}{2\sqrt{4ax}}\cdot4a=\frac{2a}{\sqrt{4ax}}[/tex]

For our limits of integration, we are going from 0 to h.

Hence, our integral becomes:

[tex]\displaystyle S=2\pi\int_{0}^{h}(\sqrt{4ax})\sqrt{1+\Big(\frac{2a}{\sqrt{4ax}}\Big)^2}\, dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax}\Big(\sqrt{1+\frac{4a^2}{4ax}}\Big)\,dx[/tex]

Combine roots;

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax\Big(1+\frac{4a^2}{4ax}\Big)}\,dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax+4a^2}\, dx[/tex]

Integrate. We can consider using u-substitution. We will let:

[tex]u=4ax+4a^2\text{ then } du=4a\, dx[/tex]

We also need to change our limits of integration. So:

[tex]u=4a(0)+4a^2=4a^2\text{ and } \\ u=4a(h)+4a^2=4ah+4a^2[/tex]

Hence, our new integral is:

[tex]\displaystyle S=2\pi\int_{4a^2}^{4ah+4a^2}\sqrt{u}\, \Big(\frac{1}{4a}\Big)du[/tex]

Simplify and integrate:

[tex]\displaystyle S=\frac{\pi}{2a}\Big[\,\frac{2}{3}u^{\frac{3}{2}}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[\, u^\frac{3}{2}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

FTC:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[(4ah+4a^2)^\frac{3}{2}-(4a^2)^\frac{3}{2}\Big][/tex]

Simplify each term. For the first term, we have:

[tex]\displaystyle (4ah+4a^2)^\frac{3}{2}[/tex]

We can factor out the 4a:

[tex]\displaystyle =(4a)^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =8a^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

For the second term, we have:

[tex]\displaystyle (4a^2)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =(2a)^3[/tex]

Hence:

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

Thus, our equation becomes:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[8a^\frac{3}{2}(h+a)^\frac{3}{2}-8a^3\Big][/tex]

We can factor out an 8a^(3/2). Hence:

[tex]\displaystyle S=\frac{\pi}{3a}(8a^\frac{3}{2})\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Hence, we have verified the surface area generated by the function.

Part B)

We have:

[tex]y^2=36x[/tex]

We can rewrite this as:

[tex]y^2=4(9)x[/tex]

Hence, a=9.

The surface area is 1000. So, S=1000.

Therefore, with our equation:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

We can write:

[tex]\displaystyle 1000=\frac{8\pi}{3}\sqrt{9}\Big[(h+9)^\frac{3}{2}-9^\frac{3}{2}\Big][/tex]

Solve for h. Simplify:

[tex]\displaystyle 1000=8\pi\Big[(h+9)^\frac{3}{2}-27\Big][/tex]

Divide both sides by 8π:

[tex]\displaystyle \frac{125}{\pi}=(h+9)^\frac{3}{2}-27[/tex]

Isolate term:

[tex]\displaystyle \frac{125}{\pi}+27=(h+9)^\frac{3}{2}[/tex]

Raise both sides to 2/3:

[tex]\displaystyle \Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}=h+9[/tex]

Hence, the value of h is:

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

You seem to have left out that 0 ≤ x ≤ h.

From y² = 4ax, we get that the top half of the parabola (the part that lies in the first quadrant above the x-axis) is given by y = √(4ax) = 2√(ax). Then the area of the surface obtained by revolving this curve between x = 0 and x = h about the x-axis is

[tex]2\pi\displaystyle\int_0^h y(x) \sqrt{1+\left(\frac{\mathrm dy(x)}{\mathrm dx}\right)^2}\,\mathrm dx[/tex]

We have

y(x) = 2√(ax)   →   y'(x) = 2 • a/(2√(ax)) = √(a/x)

so the integral is

[tex]4\sqrt a\pi\displaystyle\int_0^h \sqrt x \sqrt{1+\frac ax}\,\mathrm dx[/tex]

[tex]=\displaystyle4\sqrt a\pi\int_0^h (x+a)^{\frac12}\,\mathrm dx[/tex]

[tex]=4\sqrt a\pi\left[\dfrac23(x+a)^{\frac32}\right]_0^h[/tex]

[tex]=\dfrac{8\pi\sqrt a}3\left((h+a)^{\frac32}-a^{\frac32}\right)[/tex]

Now, if y² = 36x, then a = 9. So if the area is 1000, solve for h :

[tex]1000=8\pi\left((h+9)^{\frac32}-27\right)[/tex]

[tex]\dfrac{125}\pi=(h+9)^{\frac32}-27[/tex]

[tex]\dfrac{125+27\pi}\pi=(h+9)^{\frac32}[/tex]

[tex]\left(\dfrac{125+27\pi}\pi\right)^{\frac23}=h+9[/tex]

[tex]\boxed{h=\left(\dfrac{125+27\pi}\pi\right)^{\frac23}-9}[/tex]

Step-by-step explanation:

[tex]\bullet\hookrightarrow\sf 7 (x+4)=21 [/tex]

[tex]\bullet\Rrightarrow\sf 7x+28=21 [/tex]

[tex]\bullet\rightarrowtail\sf 7x=21-28 [/tex]

[tex]\bullet\twoheadrightarrow\sf 7x=-7 [/tex]

[tex]\bullet\looparrowright\sf x=\dfrac{-7}{7}[/tex]

[tex]\bullet\rightharpoonup\sf x=-1 [/tex]

Answer:

2.755778

Step-by-step explanation:

Just search how much pounds is 1.25 kg?

Answer:

Cant you just type that in the calculator 18 times lol

Step-by-step explanation:

use a calculator

Answer:

where is the pic............

Answer:

(-3*6.3x)+(-3*1.5y)

(-18.9x)+(-4.5y)

Answer:

200

Step-by-step explanation:

Answer:

this doesnt make sense is there any type of picture or more explanation on the question? i'll still help :)

Step-by-step explanation:

Answer:

polygon

Step-by-step explanation:

A polygon is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. A rhombus has 4 sides.

Hope this helps:) Have a great day!

Answer:

3

Step-by-step explanation:

Step-by-step explanation:

formula to fine slope

m=tan()=y2-y1/x2-x1

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

Explanation:

We basically mix red and blue to get purple. The ratio needed is 2 parts red, and 3 parts blue. We can shorten this by writing 2:3

Note how we can double both parts of the ratio to get 4:6, showing that 4 drops of red correspond to 6 drops of blue, which is the answer we want.

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

Another approach:

x = some positive real number

(2 parts red)/(3 parts blue) = (4 parts red)/(x parts blue)

2/3 = 4/x

2x = 3*4 .... cross multiply

2x = 12

x = 12/2 .... divide both sides by 2

x = 6

So 6 drops of blue go with 4 drops of red.

Answer:

kinetic energy

Step-by-step explanation:

When a person runs, their body must convert potential energy into kinetic energy.

Answer:

U GO TO DHS

Step-by-step explanation:

Step-by-step explanation:

√z is defined only when z >= 0

Therefore √x - 1 is defined only when (x - 1) >= 0, x >= 1.

The only graph that shows the domain x >= 1 is graph Y.

La fórmula de interés simple, nos permite calcular I, que es el interés ganado o pagado de un préstamo. Según esta fórmula, la cantidad de interés está dada por I = C·i·t, donde C es el capital, i es la tasa de interés anual en forma decimal, y t es el período de tiempo expresado en años Tenemos que:

C = 700 dólares

i  = ???

t = 90/360 = 0.25 (Expresado en años)

I = C*i * t

i = I / C*t

i = 63/ (0.25*700)

i = 0.36

R/ Debe elegir una tasa de interés de 36% anual.

The interest on the amount invested for 90days given $63 as interest is 36.5%

Simple interest is the amount of money added to money invested. It is calculated as:

[tex]SI = \frac{PRT}{100}[/tex]

P is the amount invested (principal) = $700

R is the rate

T is the time (in years) = 90/365

SI is the interest = $63

Substitute the given values into the formula

[tex]63=\frac{700 \times R \times 90}{365 \times 100}\\63=\frac{63000R}{36500}\\63= 1.72602R\\R=36.5\%[/tex]

This shows that the interest on the amount invested for 90days given $63 as interest is 36.5%

Learn more here: https://brainly.com/question/21640787

Answer:

the answer is D. 24

Step-by-step explanation:

the smaller triangle is half the size of the bigger triangle so just divide 48 by 2

Answer:

a

Step-by-step explanation:

Answer:

The value is [tex]UCL = 10.8[/tex]  

Step-by-step explanation:

From the question we are told that

    The sample mean is  [tex]\= x = 9 \ ounce[/tex]

    The sample size is  n =  25

    The standard deviation is  [tex]\sigma = 3 \ ounce[/tex]

Given that the sample size is not large enough i.e  n<  30  we will make use of the student t distribution table  

From the question we are told the confidence level is  99.7% , hence the level of significance is    

      [tex]\alpha = (100 -99.7 ) \%[/tex]

=>   [tex]\alpha = 0.003[/tex]

Generally the degree of freedom is  [tex]df = n- 1[/tex]

=>  [tex]df = 25 - 1[/tex]

=>  [tex]df = 24[/tex]  

Generally from the student t distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of [tex]df = 24[/tex]   is  

   [tex]t_{\frac{\alpha }{2} , 24 } = 3.0 [/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = t_{\frac{\alpha }{2} , 24} *  \frac{\sigma }{\sqrt{n} }[/tex]

=>     [tex]E = 3.0 *  \frac{3 }{\sqrt{25} }[/tex]

=>     [tex]E =1.8 [/tex]

Gnerally the  upper control chart limit  for 99.7% confidence is mathematically represented as

         [tex]UCL = \= x + E[/tex]

=>      [tex]UCL = 9 + 1.8[/tex]  

=>      [tex]UCL = 10.8[/tex]  

Answer:

5x + 23

Step-by-step explanation:

3 ( x+5) + 2 ( x+4 )

3x+15+2x+8

3x+2x+8+15

5x+23

Answer:

1

Step-by-step explanation:

|7-8| • 4 + 3 (-1) =

= |-1| • 4 + (-3)

= 1 • 4 - 3

= 4 - 3

= 1

Answer:

(105 x 30) + (105 x 5) + m

Step-by-step explanation:

Answer:

(105 x 30) + (105 x 5) + m

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:

B

Step-by-step explanation:

trust

Answer:c) 4/5

Step-by-step explanation:

y= mx+c, here, m is the slope.

In this case, m= 4/5, c= -3

Step-by-step explanation:

Since x² + kx + (k + 3) is tangent to the x-axis, the quadratic function has a repeated root.

The discriminant is zero, so b² - 4ac = 0.

=> k² - 4(1)(k + 3) = 0

=> k² - 4k - 12 = 0

=> (k - 6)(k + 2) = 0

Hence k = 6 or k = -2.

The value of k is -2 and 6.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x² + kx + (k + 3) is tangent to the x-axis.

This means,

The equation has roots.

Now,

The determinant of the equation is equal to zero.

D = b² - 4ac

x² + kx + (k + 3) is in the form of ax² + bx + c.

a = 1

b = k

c = k + 3

Now,

D = 0

k² - 4(k + 3) = 0

k² - 4k - 12 = 0

k² - (6 - 2)k - 12 = 0

k² - 6k + 2k - 12 = 0

k(k - 6) + 2(k - 6) = 0

(k + 2) (k - 6) = 0

k + 2 = 0

k = -2

k - 6 = 0

k = 6

Thus,

k = -2 and 6.

Learn more about equations here:

https://brainly.com/question/17194269

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Answer:

1000

Step-by-step explanation:

There is no question so currently, I am unable to help you.

Answer: n= -20?

Step-by-step:

Simplify both sides of the equation

1/5n+4=0

Then subtract 4 from both sides

1/5n + 4 - 4 = 0 - 4

1/5n= -4

Then multiply both sides by 5

5*(1/5n)=5*(-4)

Answer:

0=n

Step-by-step explanation:

1. 0=4+n/5

add 4 and n

2. 0=4n/5

×5. ×5

3. 0=4n

-- --

4 4

4. 0=n

Look at the picture for a more detailed steps

Answer:

4/4

Step-by-step explanation:

Hope this helped have an amazing day!