an airplane travels 480 miles in 3 hours with the Wind. the return trip against the wind takes 4 hours. what is the wind speed and the speed of the airplane in still air?​

Answer:

25= (x-2)² + (y+4)²

Hope this helps!!!

Answer:

[tex](x-2)^2+(y+5)^2=36[/tex]

Step-by-step explanation:

The standard form of a circle is given by the equation:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where (h, k) is the center and r is the radius.

We know that the center is (2, -5). So, we can substitute 2 for h and -5 for k. This yields:

[tex](x-(2))^2+(y-(-5))^2=r^2[/tex]

Simplify:

[tex](x-2)^2+(y+5)^2=r^2[/tex]

Now, we need to determine r. We know that a point on the circle is (-4, -5). Thus, we can determine r by substituting -4 for x and -5 for y. This yields:

[tex](-4-2)^2+(-5+5)^2=r^2[/tex]

Evaluate:

[tex](-6)^2+(0)^2=r^2[/tex]

Evaluate:

[tex]36=r^2[/tex]

Hence, the radius squared is 36.

We do not actually need to solve for r, as we will square it anyways.

We will substitute 36 for r squared. Hence, our equation is:

[tex](x-2)^2+(y+5)^2=36[/tex]

The radius will thus be 6 units.

Answer:

1/x^2+2x

Step-by-step explanation:

Answer:

x = 4/5, and x = 3

Step-by-step explanation:

set both parts of the equation equal to 0

-5x+4 =0

-5x= -4

divide by -5

x= 4/5

x-3 = 0

x=3

Answer:

a) 2260 cm³

b) 3390 grams

Step-by-step explanation:

3.

a)The radius of the solid cylinder = 6cm

The height of the cylinder is =20 cm

The volume = π*r²*h

The volume = 3.14 * 6²*20 =2260 cm³

b) Density of the material = 1.5 g/cm³

  Volume of the cylinder = 2261 cm³

  Mass of the cylinder = Density * Volume

  Mass of the cylinder = 1.5 * 2261 = 3390 grams

Answer: 9.44 seconds

Step-by-step explanation:

A movement equation in the vertical axis is usually written as follows:

p(t) = (-g/2)*t^2 + v0*t + p0

where:

g is the gravitational acceleration, in this case is 32 ft/s^2, then -g/2 = -16ft/s^2

v0 is the initial velocity, in this case, 24 ft/s

p0 is the initial height, in this case, 1200ft

Then, when p(t)  = 0ft will mean that the pebble will hit the ground, then we need to calculate:

p(t) = -16t^2+24t+1200  = 0

and find the value of t, this is a quadratic equation, then we can use the Bhaskara equation to find the two solutions, these are:

[tex]t = \frac{-24 +- \sqrt{24^2 - 4*(-16)*1200} }{2*-16} = \frac{-24 +- 278.2}{-32}[/tex]

Then the two solutions are:

t = (-24  + 278.2)/-32 = -7.94 seconds (we can discard this one, because the negative time is not really defined)

t = (-24 - 278.2)/-32 = 9.44 seconds

Then the pebble needs 9.44 seconds to hit the ground

Answer:

out of 100

Step-by-step explanation:

Hey you’ve got it right on ur screen.

Total cost is $93.75

Answer:

The answer is $93.75

Step-by-step explanation:

Answer:

green

Step-by-step explanation:

green has a higher possible of being picked over blue

The conditions would be represented by the following set of inequalities:

An inequality can be defined as a mathematical relation for comparing two (2) or more integers or variables in an equation based on any of the following:

In this scenario, the ratio of fruit to nuts in the crunchy trail mix is equal to 1:3. Therefore, 1/4 of each bag contain fruits while 3/4 contain nuts.

Mathematically, these conditions would be represented by the following set of inequalities:

1/2 × (c + 5f) ≤ 30  ⇒ c + 5f ≤ 60.

1/2 × (3c + 3f) ≤ 50  ⇒ 3c + 3f ≤ 100.

c ≥ 0. f ≥ 0.

Read more on inequality here: https://brainly.com/question/24372553

#SPJ2

Answer:

qwertyu

Step-by-step explanation:

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rtyuytrtyuytrertytrertytretytrertytrerty

rertytrertytrtytrertytrertytrerty

rertrertrertrertytrertyrertr

ertrertrertretyretytr

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t

Answer:

8

Step-by-step explanation:

Its right on edge

Answer:8

Step-by-step explanation:

Answer:

i think its 10.71 i dont know if i got it right your welcome

Step-by-step explanation:

Answer:

$10.71

Step-by-step explanation:

Answer:

what

Step-by-step explanation:

Answer:

HAVE A FANTASTIC DAY!!!XD

Step-by-step explanation:

BRAINLIEST WOULD BE MUCH APPRECIATED!!!

Answer:

-log(3.2•10^-4)=pH

Step-by-step explanation:

The choice which shows a valid step in the process of calculating the pH of the substance is; Choice B. - log(3.2.10-⁴) = pH.

According to the question;

Therefore, when H = 0.00032

However; 0.00032 can be written in standard form as; 3.2.10-⁴

Therefore, Choice B is correct.

Read more:

https://brainly.com/question/17093969

Answer:

1. 1/4 cup of molasses.

2. 72 1/2 strips.

3. 7 1/2 hours.

Step-by-step explanation:

Answer:

A. 18°

Step-by-step explanation:

Using the cofunction identity

sin x = cos(90 - x)

Hence

sin72° = cos(90 - 72)° = cos18° ⇒ ∠Y = 18°

Answer:

The answer is 18.

Step-by-step explanation:

90-72=18

Answer: The blue dot is at -22

Step-by-step explanation:

The distance between two line is shown to be 6, so you subtract six from -16 to find the value of the dot.

Answer:

-22

Step-by-step explanation:

the distance between -10 and -16 is 6 and 6 divided by 2 is 3. I add -6 to -16 to get -22

Answer:

3x=4x+19 (extarior angels of parallel )

3x-4x=19

_1x=19

x=_19

Answer:

I'm dumb hwhsbdbshagebsvxv

Answer:

The length is 15 yards

Step-by-step explanation:

Given

Represent the width with W and length with L: So

[tex]Area = 135yd^2[/tex]

[tex]L=3W - 12[/tex]

Required

Determine the length of the rectangle:

Area is calculated as thus:

[tex]Area = L * W[/tex]

Substitute 3W - 12 for L and 135 for Area

[tex]135= (3W - 12) * W[/tex]

[tex]135= 3W^2 - 12W[/tex]

Reorder:

[tex]3W^2 - 12W - 135= 0[/tex]

Divide through by 3

[tex]W^2 - 4W - 45 = 0[/tex]

Expand:

[tex]W^2 - 9W + 5W - 45 = 0[/tex]

[tex]W(W - 9) + 5(W - 9) = 0[/tex]

[tex](W + 5)(W-9) = 0[/tex]

[tex]W + 5 = 0[/tex] or [tex]W - 9 = 0[/tex]

[tex]W = -5[/tex] or [tex]W = 9[/tex]

But width can't be negative

So:

[tex]W = 9[/tex]

Recall that: [tex]L=3W - 12[/tex]

[tex]L = 3 * 9 - 12[/tex]

[tex]L = 15[/tex]

Hence, the length 15 yards

Answer:

Congruent, ASA Congruency Theorem

Step-by-step explanation:

Answer:

11/5

Step-by-step explanation:

its 11/5

Answer:

[tex]m=\frac{11}{5} \\\\m=2\frac{1}{5}[/tex]

Step-by-step explanation:

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-9,\:-6\right),\:\\\left(x_2,\:y_2\right)=\left(-4,\:5\right)\\\\m=\frac{5-\left(-6\right)}{-4-\left(-9\right)}\\\\m = \frac{5+6}{-4+9}\\\\m=\frac{11}{5} \\\\m=2\frac{1}{5}[/tex]

Answer:

d. x=21

Step-by-step explanation:

x-4=17

x-4 +4=17+4

x=21

Answer:

A, B, D are true

Step-by-step explanation:

A)  Speed = Distance travelled ÷ time taken

                 = 112 ÷ 1.75

                  = 64 miles per hour

True

B) Cost of 6 pens = $7.74

   Cost of 1 pen    = 7.74 ÷ 6 = $ 1.29

   Cost of 7 pens = 1.29 * 7   = $ 9.03

TRUE

C) Speed = 57 miles per hour

4 hour 10 minutes = 250 minutes

Distance traveled in an hour  = 57

Distance traveled in 250 minutes = (57* 250)   ÷ 60 = 237.50 miles

FALSE

D) Cost of 17 cans = $ 38.59

   Cost of 1 can      = 38.59 ÷ 17 = $2.27

   Cost of 3 cans    = 2.27 * 3 = $ 6.81

TRUE

e) Cost of two dozen eggs = $ 8.40

    Cost of an egg                = 8.40 ÷  24  =   $ 0.35

FALSE

Answer:

4096π / 5

Step-by-step explanation:

∫∫∫ (x² + y² + z²) dV

In spherical coordinates, x² + y² + z² = r², and dV = r² sin φ dr dθ dφ.

E is the range 0 ≤ r ≤ 4, 0 ≤ φ ≤ π, 0 ≤ θ ≤ 2π.

∫₀ᵖⁱ∫₀²ᵖⁱ∫₀⁴ (r²) (r² sin φ dr dθ dφ)

∫₀ᵖⁱ∫₀²ᵖⁱ∫₀⁴ (r⁴ sin φ) dr dθ dφ

Evaluate the first integral.

∫₀ᵖⁱ∫₀²ᵖⁱ (⅕ r⁵ sin φ)|₀⁴ dθ dφ

∫₀ᵖⁱ∫₀²ᵖⁱ (¹⁰²⁴/₅ sin φ) dθ dφ

¹⁰²⁴/₅ ∫₀ᵖⁱ∫₀²ᵖⁱ (sin φ) dθ dφ

Evaluate the second integral.

¹⁰²⁴/₅ ∫₀ᵖⁱ (θ sin φ)|₀²ᵖⁱ dφ

¹⁰²⁴/₅ ∫₀ᵖⁱ (2π sin φ) dφ

²⁰⁴⁸/₅ π ∫₀ᵖⁱ sin φ dφ

Evaluate the third integral.

²⁰⁴⁸/₅ π (-cos φ)|₀ᵖⁱ

²⁰⁴⁸/₅ π (-cos π + cos 0)

²⁰⁴⁸/₅ π (1 + 1)

⁴⁰⁹⁶/₅ π

Answer:

[tex]\displaystyle \iiint_E {x^2 + y^2 + z^2} \, dV = \frac{4096 \pi}{5}[/tex]

General Formulas and Concepts:
Calculus

Integration

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Multivariable Calculus

Triple Integrals

Cylindrical Coordinate Conversions:

Spherical Coordinate Conversions:

Integral Conversion [Spherical Coordinates]:
[tex]\displaystyle \iiint_T {f( \rho, \phi, \theta )} \, dV = \iiint_T {\rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta[/tex]

Step-by-step explanation:

*Note:

Recall that φ is bounded by 0 ≤ φ ≤ 0.5π from the z-axis to the x-axis.

I will not show/explain any intermediate calculus steps as there isn't enough space.

Step 1: Define

Identify given.

[tex]\displaystyle \iiint_E {x^2 + y^2 + z^2} \, dV[/tex]

[tex]\displaystyle \text{Region E (Ball):} \ x^2 + y^2 + z^2 \leq 16[/tex]

Step 2: Integrate Pt. 1

Find ρ bounds.

Find θ bounds.

Find φ bounds.

Step 3: Integrate Pt. 2

We evaluate this spherical integral by using the integration rules, properties, and methods listed above:

[tex]\displaystyle \begin{aligned}\iiint_E {x^2 + y^2 + z^2} \, dV & = \int\limits^{2 \pi}_0 \int\limits^{\pi}_0 \int\limits^4_0 {\rho^4 \sin \phi} \, d\rho \, d\phi \, d\theta \\& = \int\limits^{2 \pi}_0 \int\limits^{\pi}_0 {\frac{\rho^5}{5} \sin \phi \bigg| \limits^{\rho = 4}_{\rho = 0}} \, d\phi \, d\theta \\& = \int\limits^{2 \pi}_0 \int\limits^{\pi}_0 {\frac{1024}{5} \sin \phi} \, d\phi \, d\theta\end{aligned}[/tex]

[tex]\displaystyle \begin{aligned}\iiint_E {x^2 + y^2 + z^2} \, dV & = \int\limits^{2 \pi}_0 {\frac{-1024}{5} \cos \phi \bigg| \limits^{\phi = \pi}_{\phi = 0}} \, d\theta \\& = \int\limits^{2 \pi}_0 {\frac{2048}{5}} \, d\theta \\& = \frac{2048}{5} \theta \bigg| \limits^{\theta = 2 \pi}_{\theta = 0} \\& = \frac{4096 \pi}{5}\end{aligned}[/tex]

∴ we have evaluated the given integral in spherical coordinates.

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Learn more about spherical coordinates: https://brainly.com/question/17166987

Learn more about multivariable calculus: https://brainly.com/question/4746216

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Topic: Multivariable Calculus

Unit: Triple Integrals Applications

It might help to draw out a probability tree. Check out the diagram below. The first two branches at the top represent bags A and B. The probability of picking either bag is 1/2 assuming each bag is equally likely to be picked.

If we go with bag A, then the probability of getting blue is 3/11 since there are 3 blue out of 8+3 = 11 total. The probability of getting bag A and a blue marble is (1/2)*(3/11) = 3/22 which I've marked in the diagram as well.

If we go with bag B, then the probability of getting blue is 7/12 since there are 7 blue out of 5+7 = 12 total. The probability of getting bag B and blue is (1/2)*(7/12) = 7/24

Add up the results found getting

P(blue) = P(blue & bag A) + P(blue & bag B)

P(blue) = 3/22 + 7/24

P(blue) = 36/264 + 77/264

P(blue) = 113/264

This is shown in the diagram as well.

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

Recall that conditional probability in general is defined as follows

P(A given B) = P(A and B)/P(B)

In this problem, we'll have

P(bag B given blue) = P(bag B and blue)/P(blue)

Therefore, we can say...

P(bag B given blue) = P(bag B and blue)/P(blue)

P(bag B given blue) = (7/24)/(113/264)

P(bag B given blue) = (7/24)*(264/113)

P(bag B given blue) = (7*264)/(24*113)

P(bag B given blue) = (7*24*11)/(24*113)

P(bag B given blue) = (7*11)/(113)

P(bag B given blue) = 77/113

In short, the probability of getting bag B, given the marble is blue, is 77/113.