all vectors are in . check the true statements below: a. a square matrix with orthonormal columns is invertible. b. if is an matrix with orthonormal columns, then , the identity matrix. c. every orthogonal set in is a linearly independent set. d. if a set has the property that whenever , then is an orthonormal set.

Answer:

1.8

Step-by-step explanation:

The equation we are given is \(\frac{n}{-1.5} = -1.2\). We can multiply both sides by -1.5 to get n = 1.8.

Answer:

N = 1.8

Step-by-step explanation:

You do cross multiplication

n*1 = -1.5 * -1.2

1n = 1.8

To check it, we plug in 1.8

1.8/-1.5 = -1.2

44 + 38 can be written in the form a(b + c) as:

44 + 38 = 2(22 + 19) = 2(41)

We may use the distributive property to factor 44 + 38 by first determining their greatest common factor (GCF), which is 2, and then writing the result as follows:

44 + 38 = 2(22) + 2(19)

By removing the second from the equation, we may further reduce it: 44 + 38 = 2(22 + 19).

Therefore, 44 + 38 can be written in the form a(b + c) as:

44 + 38 = 2(22 + 19) = 2(41)

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Answer:

see below

Step-by-step explanation:

P = 2l + 2w

Subtract 2w using the subtraction property of equality

P -2w = 2l+2w-2w

P -2w = 2l

Divide each side by 2, using the division property of equality

P/2 -2w/2 = 2l/2

1/2 P -w = l

Now we have P =40.2 and w = 6.7

l =1/2 (40.2) - 6.7

l =20.1-6.7

 =13.4

see the photos above given

Answer:

\($x^2=\frac{9}{4} \implies x=\pm \frac{3}{2} $\)

\($x^2=-2 \implies x=\pm\sqrt{-2} \implies x=\pm\sqrt{2i} $\)

The solutions are

\($\{-\frac{3}{2},\frac{3}{2}, -\sqrt{2i}, \sqrt{2i} \}$\)

The Real roots are

\($\{-\frac{3}{2},\frac{3}{2}\}$\)

Step-by-step explanation:

\($\frac{18}{x^4} +\frac{1}{x^2}=4$\)

Multiply both sides by \(x^4\)

\($x^4\frac{18}{x^4} +x^4\frac{1}{x^2}=4\cdot x^4$\)

\($18+x^2=4x^4$\)

\(4x^4-x^2-18=0\)

Substitute \(x^2=t\)

\(4t^2-t-18=0\)

Solving the quadratic equation using the quadratic formula:

\($t=\frac{-(-1)\pm \sqrt{(-1)^2-4\cdot 4(-18)}}{2\cdot 4}$\)

\($t=\frac{1\pm \sqrt{289}}{8}$\)

\($t=\frac{1\pm 17}{8}$\)

\($t_1=\frac{9}{4}$\)

\(t_2=-2\)

Now we have to solve for \(x^2=t\)

\($x^2=\frac{9}{4} \implies x=\pm \frac{3}{2} $\)

\($x^2=-2 \implies x=\pm\sqrt{-2} \implies x=\pm\sqrt{2i} $\)

Answer:

They are on opposite sides of the river ( the riddle never said that they were on the same side )

One simply uses the boat to cross the river and the other person gets into the boat and takes it back to where it started.

Step-by-step explanation:

Answer:

one person ues's the boat to get to the other side then when they get there come up with a srategy to get the boat back to the other person

Step-by-step explanation:

As a result, the solid's volume in the first octant, which is restricted by the paraboloid z = 4 + 2 x + 2 y, is 9.

We must determine the limits of integration for x, y, and z in order to determine the volume of the solid in the first octant bounded by the paraboloid z = 4 + 2x + 2y + 2 and the plane z = 10.

At z = 10, where the paraboloid and plane overlap, we put the two equations equal and find z:

4 + 2x^2 + 2y^2 = 10

2x^2 + 2y^2 = 6

x^2 + y^2 = 3

This is the equation for a circle in the xy plane with a radius of 3, centred at the origin. We just need to take into account the area of the circle where x and y are both positive as we are only interested in the first octant.

Integrating over the circle in the xy-plane, we may determine the limits of integration for x and y:

∫∫[x^2 + y^2 ≤ 3] dx dy

Switching to polar coordinates, we have:

∫[0,π/2]∫[0,√3] r dr dθ

Integrating with respect to r first gives:

∫[0,π/2] [(1/2)(√3)^2] dθ

= (3/2)π

So the volume of the solid is:

V = ∫∫[4 + 2x^2 + 2y^2 ≤ 10] dV

= (3/2)π(10-4)

= 9π

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The company has $41,463.52 in cash on hand and is prepared to purchase the equipment.

The formula is

Principal * (1 + r)^t =  Amount

12000 * (1 +0.055)⁵ = Amount

The 12,000 capitalize for 5 years

$15,638,52

15000 * (1+0.055)¹ = Amount

Capitalize for 1 year

$15,825

$10,000 This deposit is only used to finish and buy the equipment; it has no capitalizing effect.

$15,638.52 + $15,825 + $10,000 =  $41,463.52

Hence, The company named Howell corporation has $41,463.52 in cash on hand and is prepared to purchase the equipment.

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Let's start by substituting the right-hand side of the equation into the left-hand side:

What does the math equation mean?

Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.

4y - 3 = 4(y + 1)

4y - 3 = 4y + 4

Now, we can isolate y by subtracting 4y from both sides:

0 = y + 4

-4 = y

So, there is a solution to the equation: y = -4. This means that Dawson is incorrect in saying that the equation has no solution.

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Answer:

Step-by-step explanation:

60(70/100)

4200/100

42 empty seats

Answer:

−10ba+15ba^2

Step-by-step explanation:

The product of the given monomial and binomial is -10ab+15a²b.

The given expression is −5b(2a−3a²).

We need to simplify the polynomial using multiplication.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Binomials are also a kind of polynomials consisting of only two terms. A binomial is defined as an algebraic expression consisting of two terms that are separated by the arithmetic signs, either the addition sign (+) or the subtraction sign (-). When multiplying a monomial by a binomial, we follow the distributive law of multiplication.

Now, 2a×(−5b)−3a²×(−5b)

=-10ab+15a²b

Therefore, the product of the given monomial and binomial is -10ab+15a²b.

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Answer:

A

Step-by-step explanation:

It can only be a bc its the only one with -4 as b

The difference quotient of \(f(x) = x^2 - 6x + 5\) is is 2x - 6 + h.

To find the difference quotient for the function \(f(x) = x^2 - 6x + 5\), we need to evaluate

(f(x + h) - f(x)) / h, where h is not equal to 0.

First, let's find f(x + h):

\(f(x + h) = (x + h)^2 - 6(x + h) + 5\)

\(= x^2 + 2hx + h^2 - 6x - 6h + 5\)

\(= x^2 - 6x + 5 + 2hx - 6h + h^2\)

Now, we can substitute the values of f(x + h) and f(x) into the difference quotient:

\((f(x + h) - f(x)) / h = ((x^2 - 6x + 5 + 2hx - 6h + h^2) - (x^2 - 6x + 5)) / h\)

= (2hx - 6h + h^2) / h

= 2x - 6 + h

Therefore, the difference quotient of \(f(x) = x^2 - 6x + 5\) is 2x - 6 + h.

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Answer:

be sure the force is velocity and again vo ahead

Answer: 57.8

Step-by-step explanation:48.7 seconds + 49.3 seconds.= 57.8

Answer:

12*56-56+11=12

Step-by-step explanation:

12 for 56

The required area of the shaded region is 141.3  sq. in.

A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius. The square unit, such as m^2, cm^2, etc., is the unit of area. Area of a circle is equal to r2 or d2/4, where = 22/7 or 3.14.

inner radius = 6 in, outer radius= 9 in

are of small circle = πr^2

Area = π(6)^2 = 36π sq. in

Similarly

Area of big circle = πr^2

Area = π(9)^2 = 81π sq. in

So,

Area of shaded region =  81π - 36π

Area of shaded region = 45π

Area of shaded region = 141.3  sq. in

Thus, required area is 141.3  sq. in.

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To find the height of the kite above the ground, we need to use trigonometry. We know that the kite string is 89 ft long, and the angle between the kite and the ground is 47 degrees. Let's call the height of the kite "h".

We can use the tangent function, which relates the opposite side (height) and the adjacent side (distance from the kite to the observer on the ground):

tan(47 degrees) = h / x

where x is the distance from the kite to the observer on the ground. We can solve for h:

h = x * tan(47 degrees)

To find x, we can use the cosine function:

cos(47 degrees) = x / 89 ft

x = 89 ft * cos(47 degrees)

Now we can substitute x into the first equation and solve for h:

h = (89 ft * cos(47 degrees)) * tan(47 degrees)

h ≈ 66.7 ft

So the kite is about 66.7 ft above the ground.
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Answer:

see explanation

Step-by-step explanation:

(a)

x² - 2x - 4

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² - 2x

= x² + 2(- 1)x + 1 - 1 - 4

= (x - 1)² - 5

with c = - 1 and d = - 5

(b)

x² - 2x - 4 = 0 ← using result from (a) , that is

(x - 1)² - 5 = 0 ( add 5 to both sides )

(x - 1)² = 5 ( take the square root of both sides )

x - 1 = ± \(\sqrt{5}\) ( add 1 to both sides )

x = 1 ± \(\sqrt{5}\)

The statement that is true about whether A and B are independent events is D. A and B are not independent events because P(A∣B) = 0.375 and P(A) = 0.25.

Let A be the event that the person rides the bus to school, then:

P(A) = 75/300

P(A) = 0.25

Let B be the event that the person has 3 or more siblings, then:

P(B) = 24/300 = 0.25

P(A/B)=9/24

P(A/B)=0.375

Since P(A/B)=0.375 is different from P(A)=0.25 the events are not independent.

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To find the exact length of the curve `x=(1/8)y^4+1/(4y^2)` from `y=1` to `y=2`, we can use the formula for arc length:

`L = int_a^b sqrt(1+(dy/dx)^2) dx`
In this case, `dx/dy` is given by:
`dx/dy = 2y^3/8 - y^(-3)/2`
Thus, `dy/dx` is the reciprocal:
`dy/dx = 1/(dx/dy) = 2/y^3 - 4y`
Substituting this into the arc length formula, we get:
`L = int_1^2 sqrt(1+(2/y^3-4y)^2) dy`

This integral is not easy to solve analytically, so we can use numerical methods to approximate the value of `L`. One such method is the trapezoidal rule:
`L ≈ h/2 [f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]`
where `h = (b-a)/n` is the step size and `n` is the number of subintervals.
Applying this to our integral with `n = 10`, we get:
`L ≈ 1/20 [sqrt(17) + 2sqrt(10) + 2sqrt(5) + 2sqrt(2) + sqrt(13)]`
which is approximately `3.888`.

Therefore, the exact length of the curve is approximately `3.888` units.

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Answer:

The circumference vis 289

Step-by-step explanation:

17x17

= 289

Answer:

106.81m

Step-by-step explanation:

20 Characters.

A standard set of tab arranged name dice includes seven different dice. The number of different ways these dice can be arranged is calculated as follows

The number of different ways in which the seven tab arranged name dice can be arranged is given by the product of the number of ways each die can be arranged.

The number of different arrangements for each of the seven dice is given as follows: Die 1: Can be arranged in 6 ways Die 2: Can be arranged in 5 ways Die

3: Can be arranged in 4 ways Die 4: Can be arranged in 3 ways Die 5: Can be arranged in 2 ways Die 6: Can be arranged in 1 way Die 7: Can be arranged in 1 way Therefore, the number of different ways in which the seven dice can be arranged is:

6 × 5 × 4 × 3 × 2 × 1 × 1=720Therefore, the number of different ways the seven tab arranged name dice can be arranged is 720.

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\(-x^2 + 2xy - y^2\) can be written as the opposite of the square of the binomial (x-y), which is equal to \(-(x - y)^2.\)

\(-x^2 + 2xy - y^2\) can be composed as something contrary to the square of the binomial (x - y).

To check, you can utilize the character \((a-b)^2 = a^2 - 2ab + b^2\). On the off chance that you substitute a = x and b = y, you get:

\((x - y)^2 = x^2 - 2xy + y^2\)

Presently, assuming you take something contrary to this, you get:

\(-(x - y)^2 = - x^2 + 2xy - y^2\)

Thus,\(- x^2 + 2xy - y^2\) is something contrary to the square of the binomial (x - y).

The articulation \(- x^2 + 2xy - y^2\) can be composed as something contrary to the square of a binomial. To see as the binomial, we utilize the character \((a-b)^2 = a^2 - 2ab + b^2\), which is the recipe for figuring out a binomial. In the event that we substitute a = x and b = y, we get \((x-y)^2 = x^2 - 2xy + y^2\). Taking something contrary to this articulation gives us \(- x^2 + 2xy - y^2\), which is the articulation we began with. Hence, something contrary to the square of the binomial (x-y) is equivalent to - \(x^2 + 2xy - y^2\).

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The expression 22x + 19 is the simplified form of the given expression which is determined by the distributive property of multiplication.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given below as:

3(5x + 7) + 7x - 2

Apply the distributive property of multiplication,

3 × 5x + 3 × 7 + 7x - 2

15x + 21 + 7x - 2

Combine the likewise terms in the above expression,

22x + 19

Thus, the simplified expression is:

22x + 19

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1. The total distance covered to come to a stop is approximately 12.07 meters. 2. The target should be approximately 5.44 meters away from the base of the building when you release the tracker. 3. The correct answer for the baseball's horizontal distance traveled is D. 305.05 m.

To solve these problems, we'll use the appropriate equations of motion.

1. Total distance covered to come to a stop:

Reaction time (t) = 0.7 s

Acceleration (a) = 8 m/s²

Initial velocity (u) = 52 km/h = (52 * 1000) / 3600 m/s ≈ 14.44 m/s

We need to find the total distance covered (S).

We can use the equation: S = ut + (1/2)at²

Plugging in the values, we have:

S = (14.44 m/s)(0.7 s) + (1/2)(8 m/s²)(0.7 s)²

S ≈ 10.11 m + 1.96 m

S ≈ 12.07 m

Therefore, the total distance covered to come to a stop is approximately 12.07 meters.

2. Dropping the tracker on the target's head:

Given:

Height of the building (h) = 56.6 m

Target's height (H) = 1.72 m

Target's constant speed (v) = 1.60 m/s

To drop the tracker on the target's head, we need to calculate the time it takes for the tracker to fall from the top of the building to the ground. Then, we can calculate the horizontal distance the target would have covered during that time.

Using the equation for free fall:

h = (1/2)gt²

Solving for time (t):

56.6 m = (1/2)(9.8 m/s²)t²

t² = (2 * 56.6 m) / 9.8 m/s²

t² ≈ 11.55 s²

t ≈ √11.55 s ≈ 3.40 s

Now, we can calculate the horizontal distance covered by the target during that time:

Distance (D) = velocity (v) * time (t)

D = 1.60 m/s * 3.40 s ≈ 5.44 m

Therefore, the target should be approximately 5.44 meters away from the base of the building when you release the tracker.

3. Horizontal distance traveled by the baseball:

Angle of projection (θ) = 22.5°

Initial velocity (v₀) = 65 m/s

To find the horizontal distance traveled, we can use the equation:

Range (R) = (v₀² * sin(2θ)) / g

Plugging in the values, we have:

R = (65 m/s)² * sin(2 * 22.5°) / 9.8 m/s²

R = 4225 * sin(45°) / 9.8

R ≈ 4225 * 0.7071 / 9.8

R ≈ 305.05 m

Therefore, the baseball traveled approximately 305.05 meters horizontally when it hit the ground.

The correct answer for the baseball's horizontal distance traveled is D. 305.05 m.

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