Simplify: \(4\sqrt{12} - \sqrt{3} + 4 \sqrt{6} + 3 \sqrt{4}\)

// not C

Answer:

9.75

Step-by-step explanation:

-25 = -4p + 19

-25 - 19 = -4p

-39 ÷ -4 = p

9.75 = p

Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

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The solution of the equation by factoring is x = 6.645 and x = 1.355.

The breaking or breakdown of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics. An algebraic expression is factorised when it is written as the product of its factors. Certain variables, factors, or algebraic expressions might be present.

The given equation is:

x² - 8x + 16 = 7

x² - 8x + 16 - 7 = 0

x² - 8x + 9 = 0

Using the quadratic formula we have:

x = 8 ±√(8)² - 4(1)(9) /2(1)

x = 8 ± 5.29/2

x = 8 + 5.29/2 and x = 8 - 5.29/2

x = 6.645 and x = 1.355

Hence, the solution of the equation by factoring is x = 6.645 and x = 1.355.

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Answer:

y'=|x-5|-1

Step-by-step explanation:

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The average rate of change over is 1.

Given that;

the function is,

⇒ g (t) = - (t - 1)² + 5

Hence, We need to determine the average rate of change over the interval - 4 ≤ t ≤ 5.

The value of G(-4):

The value of G(-4) can be determined by substituting t = -4 in the function

⇒ g (t) = - (t - 1)² + 5

Thus, we have,

⇒ g (t) = - (-4 - 1)² + 5

⇒ g (t) = - 20

Thus, the value of G(-4) = -20

The value of G(5):

The value of G(5) can be determined by substituting t = 5 in the function , we get,

⇒ g (t) = - (t - 1)² + 5

⇒ g (t) = - (5 - 1)² + 5

⇒ g (t) = - 11

Thus, the value of G(5) is, -11

Now, Average rate of change:

The average rate of change can be determined using the formula,

⇒ G(b) - G (a) / (b - a)

where, a = - 4 and b = 5

Substituting the values, we get,

⇒ G(5) - G (-4) / (5 - (-4))

⇒ ( - 11 - (- 20)) / 9

⇒ 9/9

⇒ 1

Thus, the average rate of change over the interval is. 1.

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To determine the type of discontinuity that exists at f(20):

According to the graph,

There is no discontinuity that exists at f(20).

Hence, the correct option is the first one.

Complete question is;

The paraboloid z = 5 − x − x² − 2y² intersects the plane x = 1 in a parabola. Find parametric equations for the tangent line to this parabola at the point (1, 2, -4).

Answer:

x = 1

y = (2 + t)

z = (-4 - 8t)

Step-by-step explanation:

We are given the paraboloid z = 5 − x − x² − 2y²

That it intersects the plane x = 1 and tangent to the point (1, 2, -4).

Thus, the position of the tangent is;

r_o = (1, 2, -4).

Direction vector is; v = (x, y, z)

Let's put 1 for x into the paraboloid.

z = 5 − 1 − 1² − 2y²

z = 3 - 2y²

Now, let's use vectors to find the parametric equation, where;

x = 1

y = t

z = 3 - 2t²

Thus, the Directional vector is now;

v = (1, t, 3 - 2t²)

Derivative of this directional vector is;. v' = (0, 1, -4t)

Putting 2 for t gives;

v' = (0, 1, -4(2))

v' = (0, 1, -8)

Multiplying this derivative by T gjves;

tv' = (0, t, -8t)

The final direction vector will be;

r = r_o + tv'

r = (1, 2, -4) + (0, t, -8t)

r = (1, (2 + t), (-4 - 8t))

Thus our parametric equation is;

x = 1

y = (2 + t)

z = (-4 - 8t)

Answer:

sweefe

Step-by-step explanation:

EFEFEEa

9514 1404 393

Answer:

  x = -25/3

Step-by-step explanation:

Multiply by the inverse of the coefficient of x. Reduce the fraction.

  (-5/2)(10/3) = (-5/2)(x/(-5/2))

  -50/6 = x = -25/3

Answer:

-25/3

Step-by-step explanation:

the other person is also correct. khan said so

The combination shows that the different sets of three albums that she can choose will be 45.

The different sets of three albums that she can choose will be:

= 9C1 + 9C2

= 9 + 36

= 45

The number of sets that would not include the jazz album will be:

= 9C2

= 36

The sets that would include the jazz album will be:

= 9C1

= 9

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Answer:

it is 390

Step-by-step explanation:

Answer:

i agree with other guy

Step-by-step explanation:

The estimated probability of a success is 3/5 or 0.6

From the question, we have the following parameters that can be used in our computation:

Integers = 5

Success = 3

The probability of success is then calculated as

Probability = Success/Integrs

Substitute the known values in the above equation, so, we have the following representation

probability = 3/5 = 0.6

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Answer:

min: 56

lower quartile: 70

median: 74

upper quartile: 80

max: 86

Answer:

I think. . . sphere? SO SORRY IF IM WRONG!!

Step-by-step explanation:

Answer:

k ≥ -18

Step-by-step explanation:

-8 ≥ 2/5(k-2)

-8 ≥ 2/5k - 4/5

(-8 ≥ 2/5k - 4/5) 5

-40 ≥ 2k - 4

+4           +4

-36 ≥ 2k

-36 divided by 2

2 divided by 2

-18 ≥ k

flip the greater than or equal to sign to the k.

k ≥ -18

Answer:

16 hrs

Step-by-step explanation:

4 of them doing it in 32 hrs is the equivalent to 4/8hrs (32hrs) days 32÷ 4 = 8

8 of them doing it in 16hrs would be the equivalent to 2/8 hrs( 16hrs) days

Answer:

The smaller number in 0.01

Step-by-step explanation:

To find this answer, just take the fraction and find the quotient of both numbers.

1.789/178 = 0.01005056179

Now take the quotient and compare it to 0.05.

Is 0.01 larger or 0.05 - the answer is 0.01.

Answer:

90. ( was the full capacity of jug)

to solve this

firstly let the full capacity of jug

be. x

so,

4/5*x = 72

x = 72*5/4

x = 90

hope it helps

The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

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Answer:

6 is 100 times 0.06

Step-by-step explanation:

0.06 times 100 = 6

Answer:

26? im not sure wut u mean

Step-by-step explanation:

The volume of the squared pyramid is 9 cubic yards, so the correct option is D.

For a square pyramid of sidelength S (S is the sidelength of the square base), the volume is given by the formula:

V = (1/3)*S^3

Here we want to find the volume if S = 3 yards, so we just need to replace that in the formula above to get the volume of the sculpture, we will get:

V = (1/3)*(3 yd)^3

V = (1/3)*(27 yd^3)

V = 9 yd^3

The volume is 9 cubic yards, then the correct option is D.

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The negations of the given statements with the application of De Morgan's law and/or conditional law.

a) ∃x (¬P(x) ∨ ¬R(x))

De Morgan's law:

∃y ∀z(¬P(y) ∧ ¬Q(z))

b) ∃y ∀z(¬P(y) ∧ ¬Q(z))

The double negation:

∃y ¬∃z(P(y) ∨ Q(z))

c) ¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

The conditional law:

¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

Let's form the negation of the given statements and apply De Morgan's law and/or conditional law, when applicable:

a) ∀x (P(x) ∧ R(x))

The negation of this statement is:

∃x ¬(P(x) ∧ R(x))

Now let's apply De Morgan's law:

∃x (¬P(x) ∨ ¬R(x))

b) ∀y∃z(¬P(y) → Q(z))

The negation of this statement is:

∃y ¬∃z(¬P(y) → Q(z))

Using the conditional law, we can rewrite the negation as:

∃y ¬∃z(¬¬P(y) ∨ Q(z))

c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

The negation of this statement is:

¬∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

Using the conditional law, we can rewrite the negation as:

¬∃x (P(x) ∨ (∀z (R(z) ∨ ¬Q(z))))

Applying De Morgan's law:

¬∃x (P(x) ∨ (∀z ¬(¬R(z) ∧ Q(z))))

Simplifying the double negation:

¬∃x (P(x) ∨ (∀z ¬(R(z) ∧ Q(z))))

Using De Morgan's law again:

¬∃x (P(x) ∨ (∀z (¬R(z) ∨ ¬Q(z))))

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The expression (-3)0 has a value of 0 when evaluated because a number multiplied by 0 gives 0

From the question, we have the following parameters that can be used in our computation:

(-3)0

The above statement is a product expression that multiplies the values of -3 and 0

Also, there is no need to check if there are like terms in the expression or not

This is  because we are multiplying the factors

So, we have

(-3)0 = 0

This means that the value of the expression is 0 i.e a number multiplied by 0 gives 0

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Answer:

Here it is

Step-by-step explanation:

If you have any questions feel free to ask :)

Joey's actual speed is 143.59 mph, and his actual direction is slightly west of northwest.

Given that Joey's aircraft speed: 188 mph

Wind speed: 60 mph

Wind direction: 150 degrees (measured clockwise from due north)

We can consider the wind as a vector, which has both magnitude (speed) and direction.

The wind vector can be represented as follows:

Wind vector = 60 mph at 150 degrees

We convert the wind direction from degrees to a compass bearing.

Since 150 degrees is measured clockwise from due north, the compass bearing is 360 degrees - 150 degrees = 210 degrees.

Joey's aircraft speed vector = 188 mph at 0 degrees (due northwest)

Wind vector = 60 mph at 210 degrees

To find the resulting velocity vector, we add these two vectors together. This can be done using vector addition.

Converting the wind vector into its x and y components:

Wind vector (x component) = 60 mph × cos(210 degrees)

= -48.98 mph (negative because it opposes the aircraft's motion)

Wind vector (y component) = 60 mph×sin(210 degrees)

= -31.18 mph (negative because it opposes the aircraft's motion)

Now, we can add the x and y components of the two vectors to find the resulting velocity vector:

Resulting velocity (x component) = 188 mph + (-48.98 mph) = 139.02 mph

Resulting velocity (y component) = 0 mph + (-31.18 mph) = -31.18 mph

Magnitude (speed) = √((139.02 mph)² + (-31.18 mph)²)

= 143.59 mph

Direction = arctan((-31.18 mph) / 139.02 mph)

= -12.80 degrees

The magnitude of the resulting velocity vector represents Joey's actual speed, which is approximately 143.59 mph.

The direction is given as -12.80 degrees, which indicates the deviation from the original northwest direction.

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Mai travels abοut 4.2 feet per secοnd faster than Kiran.

Circumference is the distance arοund the οutside οf a circle. It is the length οf the bοundary that enclοses a circle. Tο find the circumference οf a circle, yοu can use the fοrmula C=2πr, where "C" represents the circumference, "π" is a mathematical cοnstant (apprοximately equal tο 3.14159), and "r" is the radius οf the circle (the distance frοm the center οf the circle tο its edge). Sο, the circumference οf a circle is directly prοpοrtiοnal tο its radius. This means that if yοu dοuble the radius οf a circle, its circumference will alsο dοuble.

The circumference οf Kiran's ring is:

C1 = 2πr1 = 2π(9 ft) ≈ 56.55 ft

The circumference οf Mai's ring is:

C2 = 2πr2 = 2π(r1 + 8 ft) = 2π(17 ft) ≈ 106.81 ft

Therefοre, Mai travels a distance οf 106.81 - 56.55 = 50.26 feet mοre than Kiran in οne rοtatiοn.

The time it takes fοr οne rοtatiοn is given as 12 secοnds. Therefοre, the speed οf Kiran in feet per secοnd is:

V1 = C1 / t = 56.55 ft / 12 s ≈ 4.71 ft/s

And the speed οf Mai in feet per secοnd is:

V2 = C2 / t = 106.81 ft / 12 s ≈ 8.90 ft/s

The difference in their speeds is:

V2 - V1 = 8.90 ft/s - 4.71 ft/s ≈ 4.2 ft/s

Therefοre, Mai travels abοut 4.2 feet per secοnd faster than Kiran.

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