Simplify: (- sqrt x-4)^2
-X + 4
X-4
2x - 8

Answer:

1 day: 4480

2 days: 8960

3 days: 13440

[tex]f^{-1}(x) = \sqrt{\frac{x -4}{4}}[/tex] ---- function inverse

Step-by-step explanation:

Given

[tex]f(x) = 70 \cdot 64x[/tex]

Solving (a): The amount present after 1 day.

Here, [tex]x =1[/tex]

So:

[tex]f(1) = 70 \cdot 64*1= 4480[/tex]

Solving (b): The amount present after 2 days.

Here, [tex]x =2[/tex]

So:

[tex]f(2) = 70 \cdot 64*2= 8960[/tex]

Solving (c): The amount present after 3 days.

Here, [tex]x = 3[/tex]

So:

[tex]f(3) = 70 \cdot 64*2= 13440[/tex]

Solving (d): The inverse function of:

[tex]f(x)= 4x^2 + 4[/tex]

Replace f(x) with y

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

Swap x and y

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

Rewrite as:

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

Divide by 4

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

Take square roots

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

Replace y with function inverse

[tex]f^{-1}(x) = \sqrt{\frac{x -4}{4}}[/tex]

Answer:

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

2/6

4/12

6/18

Answer:

x = 18

Step-by-step explanation:

We can write ratios

2      2+4

---- = -----

6       x

Using cross products

2x = 6(2+4)

2x = 6(6)

2x = 36

Divide by 2

2x/2 = 36/2

x = 18

Answer:

I believe the question was written twice on accident

y=7x-38

Step-by-step explanation:

y-4=7(x-6)

y-4=7x-42

y=7x-38

Answer:

Step-by-step explanation:

[tex]\frac{9-3y}{1-9y} = \frac{8}{5}[/tex]

do cross multiplication

[tex]5(9 - 3y) = 8(1 - 9y)\\45 - 15y = 8 - 72y\\45 - 8 = -72y + 15y\\37 = -57y\\\frac{37}{-57} = y[/tex]

Answer:

Step-by-step explanation:

[tex]3(3−y) \times 5=(1−9y) \times 8[/tex]

[tex]45−15y=(1−9y) \times 8[/tex]

[tex]45−15y=8−72y[/tex]

[tex]45+57y=8[/tex]

[tex]57y=8−45[/tex]

[tex]57y=−37[/tex]

Answer:

option A

Step-by-step explanation:

X- axis

A . the x-axis

Step-by-step explanation:

The lines never meet

Answer:

A.

Step-by-step explanation:

The a^3 would cancel out, currently leaving just b^5 on the top and ab on the bottom. The b would also cancel out, finally leaving just b^4/a. Therefore A is the answer equivalent to the original expression.

Answer:

more

Step-by-step explanation:

The answer is (5x+3)(-5x+3)

Answer:

The correct answer is:

(a) 44.6 lb

(b) 0.371

Step-by-step explanation:

Given values are:

Mean,

[tex]\mu=36.6[/tex]

Standard deviation,

[tex]\sigma=11.9[/tex]

(a)

The z distance third quartile will be:

⇒ [tex]P(Z<0.674)=0.75[/tex]

                       [tex]z =0.674[/tex]

By using the z-score formula, we get

⇒ [tex]x=z\times \sigma+ \mu[/tex]

       [tex]=0.674\times 11.9+36.6[/tex]

       [tex]=44.62[/tex]

(b)

⇒ [tex]P(27.5<x<39.5) = P[{\frac{(27.5-36.6)}{11.9} <\frac{(x-\mu)}{\sigma} <\frac{(39.5-36.6)}{11.9} }][/tex]

                                  [tex]=P(-0.76<z<0.24)[/tex]

                                  [tex]=P(z<0.24)-P(z<-0.76)[/tex]

By using the z table, we get

                                  [tex]=0.5948-0.2236[/tex]

                                  [tex]=0.371[/tex]

Answer:

c) 11/2

Step-by-step explanation:

(-4, 7) and (-6, -4)

To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-4 - 7) / (-6 - (-4))

Simplify the parentheses.

= (-11) / (-6 + 4)

= (-11) / (-2)

Simplify the fraction.

-11/-2

= 11/2

This is your slope.

Hope this helps!

9514 1404 393

Answer:

  1.  4463

  2. no

Step-by-step explanation:

1. Put the value of x into the equation and do the arithmetic.

  f(4) = 5000(0.972^4) ≈ 5000·0.8926168 ≈ 4463.08

There will be about 4463 lemmings in 4 years.

__

2. An exponential function has the variable in the exponent. When the variable is the base of a term that has an integer constant exponent, we call it a polynomial function.

The function is NOT an exponential function.

Answer:

[tex] \displaystyle 1)48.2 \: \: \text{sec}[/tex]

[tex] \rm \displaystyle 2)3021.6 \: m[/tex]

Step-by-step explanation:

so when flash down occurs the rocket will be in the ground in other words the elevation(height) from ground level will be 0 therefore,

to figure out the time of flash down we can set h(t) to 0 by doing so we obtain:

[tex] \displaystyle - 4.9 {t}^{2} + 229t + 346 = 0[/tex]

to solve the equation can consider the quadratic formula given by

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

so let our a,b and c be -4.9,229 and 346 Thus substitute:

[tex] \rm\displaystyle t = \frac{ - (229) \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)} [/tex]

remove parentheses:

[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)} [/tex]

simplify square:

[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 4( - 4.9)(346)} }{2.( - 4.9)} [/tex]

simplify multiplication:

[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 6781.6} }{ - 9.8} [/tex]

simplify Substraction:

[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 45659.4} }{ - 9.8} [/tex]

by simplifying we acquire:

[tex] \displaystyle t = 48.2 \: \: \: \text{and} \quad - 1.5[/tex]

since time can't be negative

[tex] \displaystyle t = 48.2 [/tex]

hence,

at 48.2 seconds splashdown occurs

to figure out the maximum height we have to figure out the maximum Time first in that case the following formula can be considered

[tex] \displaystyle x _{ \text{max}} = \frac{ - b}{2a} [/tex]

let a and b be -4.9 and 229 respectively thus substitute:

[tex] \displaystyle t _{ \text{max}} = \frac{ - 229}{2( - 4.9)} [/tex]

simplify which yields:

[tex] \displaystyle t _{ \text{max}} = 23.4[/tex]

now plug in the maximum t to the function:

[tex] \rm \displaystyle h(23.4)- 4.9 {(23.4)}^{2} + 229(23.4)+ 346 [/tex]

simplify:

[tex] \rm \displaystyle h(23.4) = 3021.6[/tex]

hence,

about 3021.6 meters high above sea-level the rocket gets at its peak?

Answer:

Step-by-step explanation:

y/5                  That's your quotient

y/5 + 2            That's the quotient with 2 added on.

y/5 + 2 = 4      And that's your answer.

Always break the statements into the smallest possible steps that you can. Notice that I broke it down to 3 parts that are not quite equal in length.

Answer:

x = 10 + log(1/a^12)/(2 log(a)) + (i π n)/log(a) for n element Z

Step-by-step explanation:

Solve for x:

a^(20 - 2 x) = a^12

Take reciprocals of both sides:

a^(2 x - 20) = 1/a^12

Take the logarithm base a of both sides:

2 x - 20 = log(1/a^12)/log(a) + (2 i π n)/log(a) for n element Z

Add 20 to both sides:

2 x = 20 + log(1/a^12)/log(a) + (2 i π n)/log(a) for n element Z

Divide both sides by 2:

Answer: x = 10 + log(1/a^12)/(2 log(a)) + (i π n)/log(a) for n element Z

Step-by-step explanation:

quadratic formula

-b+-√b^2

2a

-2+-√2^2-4×1×-16

2×1

-2+-√68

2

either

x= 3.125

or

x= -5.125

Answer:

15 feet 1 inch

Step-by-step explanation:

Given :

Length of boards placed end to end :

Board 1 = 4 feet 5 inches

Board 2 = 6 feets 9 inches

Board 3 = 3 feets 11 inches

The length is the addition of the lengths of the 3 boards :

4 ft 5in + 6 ft 9 in + 3 ft 11 in

(4+6+3) ft + (5+9+11) in

13ft + (25in)

1 ft = 12 in

25 in = 2 ft 1 in

13 ft + 2ft 1 in

15 ft 1 in

Answer:

Sure i can help you

Step-by-step explanation:

Answer:

Sure! What’s the question?

Step-by-step explanation:

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

Explanation:

The diameter is 24 inches, so the radius is half that at r = d/2 = 24/2 = 12 inches.

We'll use this along with the approximation pi = 3.14 to get the area

A = pi*r^2

A = 3.14*12^2

A = 452.16 square inches

Your teacher should have used "square inches" instead of "inches" as the unit.

We can abbreviate the "square inches" into "sq in" or "in^2".

This value is approximate since pi = 3.14 is approximate. Use more decimal digits of pi to find a more accurate value.

The exact area is 144pi

Answer:

D. 452.16 sq inches

Step-by-step explanation:

d = 24 ==> r = 24/2= 12 inches

the area = π×r²

= 3.14 × 12²

= 3.14 × 144

= 452.16 sq inches

Answer:

v=πr^2h

3.14×2cm×2cm×5cm=62.8cm^3

There are infinitely many coterminal angles since we can continue adding or subtracting multiples of 360°.

To find an angle that is coterminal with 112°, we can add or subtract multiples of 360°, which represents one full revolution in the same direction.

To find a positive coterminal angle, we can add multiples of 360°:

112° + 360° = 472°

112° + 2(360°) = 832°

112° + 3(360°) = 1192°

and so on...

To find a negative coterminal angle, we can subtract multiples of 360°:

112° - 360° = -248°

112° - 2(360°) = -608°

112° - 3(360°) = -968°

and so on...

Therefore, some coterminal angles with 112° are 472°, 832°, 1192° for positive angles, and -248°, -608°, -968° for negative angles. There are infinitely many coterminal angles since we can continue adding or subtracting multiples of 360°.

To know more about Angles here

https://brainly.com/question/25716982

#SPJ2

Step-by-step explanation:

I'm sorry I can't answer that but I know something so you can answer that. search Chrome quickmath all your problems, equations and more can be solved

Answer:

c = 3/2x + −3/2

Step-by-step explanation:

Let's solve for c

-3x+2c=-3

Step 1: Add 3x to both sides.

2c −3x + 3x = −3 + 3x

2c = 3x −3

Step 2: Divide both sides by 2.

2c = 3x−3

2        2

c = 3/2x + −3/2

Answer:

c = 3/2x + −3/2

Answer:

the answer is h=0.5m+2 I think

Answer:

4270

Step-by-step explanation:

9514 1404 393

Answer:

  £300

Step-by-step explanation:

Simple interest is computed using the formula ...

  I = Prt

where P is invested at rate r for t years.

Using the given values, the interest is ...

  I = £1500·0.10·2 = £300

Connor will get back £300 in interest.

Answer:

Step-by-step explanation:

[tex]{hope it helps}}[/tex]

Answer:

Hello There!!

Step-by-step explanation:

The answer is 3,9,15,21.

hope this helps,have a great day!!

~Pinky~

Answer:

the common difference is 6. So, the missing two terms are 9 and 15 using

3 + (n-1)(6)

9514 1404 393

Answer:

  d.  $30

Step-by-step explanation:

When price and demand are linearly related like this, revenue is a quadratic function. Its maximum will be halfway between the prices that give a revenue of 0. Those prices are $60 (where demand is 0) and $0 (where demand is irrelevant). The halfway point is ($60 +0)/2 = $30.

As a check, you can figure revenue for some nearby points.

  at $30, revenue is ($30)(15) = $450

  at $24, revenue is ($24)(18) = $432

  at $36, revenue is ($36)(12) = $432

This confirms revenue is maximized at a price of $30.

Answer:

V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π

Step-by-step explanation:

Since we have the radius of the sphere R = 4, we have R² = r² + z² where r = radius of cylinder in z-plane and z = height² of cylinder.

So, r = √(R² - z²)

r = √(4² - z²)

r = √(16 - z²)

Since the region is above the plane z = 2, we integrate z from z = 2 to z = R = 4

Our volume integral in cylindrical coordinates is thus

V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π

Answer:

[tex]\displaystyle V = \int\limits^{2 \pi}_{0} \int\limits^{2\sqrt{3}}_{0} \int\limits^{\sqrt{16 - r^2}}_2 {r} \, dz \, dr \, d\theta[/tex]

General Formulas and Concepts:

Multivariable Calculus

Cylindrical Coordinate Conversions:

Volume Formula [Cylindrical Coordinates]:
[tex]\displaystyle V = \iiint_T \, dV \rightarrow V = \iiint_T {r} \, dz \, dr \, d\theta[/tex]

Step-by-step explanation:

Step 1: Define

Identify given.

Solid sphere w/ radius 4 centered at (0, 0, 0) → x² + y² + z² = 4²

Plane z = 2

Step 2: Find Volume Pt. 1

Find bounds of z.

∴ 0 ≤ r ≤ 2√3

Step 2: Find Volume Pt. 2

∴ 0 ≤ θ ≤ 2π

Step 3: Find Volume Pt. 3

∴ 2 ≤ z ≤ √(16 - r²)

Step 4: Find Volume Pt. 4

∴ the volume of the region is found with the integral above.

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Learn more about multivariable calculus: https://brainly.com/question/17203772

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Topic: Multivariable Calculus

Unit: Triple Integral Applications