The radius,R, of a sphere is8.2mm . Calculate the sphere's volume,V .
Use the value 3.14 for\(\pi\) , and round your answer to the nearest tenth. (Do not round any intermediate computations.)

This result demonstrates that the permutation matrix P0 does not change the basis vectors in the standard basis.

To show that P0(ei) = ei for the standard basis En = (e1, e2, ..., en) in Rⁿ, we need to apply the permutation matrix P0 to each basis vector ei and show that the result is equal to the original basis vector.

The permutation matrix P0 is defined as the matrix that corresponds to the permutation o in the n-permutation (1, 2, ..., n). Each row and column of the permutation matrix contains a single 1, and all other entries are 0.

Let's consider the action of P0 on the basis vector ei:

P0(ei) = [P0] * [ei]

Since P0 has a single 1 in each row and column, the product [P0] * [ei] selects the ith row of P0. This means that P0(ei) will be equal to the vector formed by the ith row of P0.

Since P0 corresponds to the permutation o in the n-permutation, the ith row of P0 will have a 1 in the o(i)th position and 0s elsewhere.

Therefore, P0(ei) will have a 1 in the o(i)th position and 0s elsewhere.

Since o(i) = i for the identity permutation, P0(ei) will have a 1 in the ith position and 0s elsewhere, which is exactly the same as the original basis vector ei.

Thus, we have shown that P0(ei) = ei for each basis vector ei in the standard basis En.

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Answer: | x - 2 | = 8

Answer:

Step-by-step explanation:

\(x_1 , y_1 = (3,3) \\

m= -1\)

Put information in Slope-intercept form :

\(y-y_1=m(x-x_1) \\ y - 3 = - 1(x - 3) \\ y - 3 = - x + 3\)

Collect like terms and simplify

\(y = - x + 3 + 3 \\ y = - x + 6\)

The equation of the tangent line to the curve at the given point is given by: y = x + 1.

Now,

Given:

To find: Equation of a tangent line through the given point.

Finding:

y = \(e^{x}\) cos(x)

By product rule of differentiation, y' = \(e^{x} sin(x) +e^{x} cos(x)\)

For x = 0, y' (0) = 1 (0) + 1( 1) = 1 = slope of the line

Now, we know: equation of a line is given by:

\((y-y_0)=m(x-x_0)\)

For \(x_0 = 0 And y_0 = 1\), The equation of the tangent line will be:

=> y - 1  = 1 (x - 0)

=> y - 1 = x

=> y = x + 1

Hence, The equation of the tangent line to the curve at the given point is given by: y = x + 1.

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The statement is true.

An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.

Given that,

From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.

Whether the claim is true or false must be determined.

The statement is true.

An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.

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Answer:

a part, share, or number considered in comparative relation to a whole.

Example:A rope's length and weight are in proportion. When 20m of rope weighs 1kg, then: 40m of that rope weighs 2kg. 200m of that rope weighs 10kg.

70.8 mins - 90 mins = 19.2  minutes

Answer:

Step-by-step explanation:

Answer:

It is a linear equation

solving by substitution method

x + y =6 ------ eqn 1

2x + 4y =20 -------- eqn 2

x = 6 - y ------ eqn 3

putting the value of x from eqn 3. into eqn 2.

2(6-y) +4y =20

12 - 2y + 4y =20

12 +2y =20

2y = 20-12

2y = 8

2y / 2 =8/2

y =4

put the value of y into eqn 3

x =6 - y

x = 6 - 4

x = 2

Therefore x = 2, y= 4

Answer:

D -6x + 2 = -15

Step-by-step explanation:

-4(3/2 x - 1/2) = -15

-4 × 3/2 x + (-4) × (-1/2) = -15

-6x + 2 = -15

Answer: D -6x + 2 = -15

Answer:

The second decrease is larger at 16 1/6% decrease

Step-by-step explanation:

175 to 150

Take the original price minus the new price divided by the original price

(175 -150) /175 =25/175 = 1/7 =.142857143 = 14.28 % decrease

150 to 125

Take the original price minus the new price divided by the original price

( 150-125)/150 = 25/150 = 1/6 =.16666 = 16 1/6 % decrease

The second decrease is larger at 16 1/6% decrease

Answer:

x = 1

Step-by-step explanation:

(4x/3) - 3x + 1 = 10

(4x/3) -3x = 9

4x - x = 3

3x = 3

x = 1

Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

Answer:

7.6

Step-by-step explanation:

We want to find the distance between (0,6) and (-3,-1)

We can find the distance between any two points using the distance formula

Distance between two points =

\( \sqrt{(x2 - x1)^{2} +(y2 - y1) {}^{2} } \)

Where the values of x and y are derived from the the two points. (x1,y1) and (x2,y2)

Here the two points are (0,6) and (-3,-1)

So we have (x1,y1) = (0,6) so x1 = 0 and y1 = 6

And we have (x2,y2) = (-3,1) so x2 = -3 and y2 = -1

Now we plug in the values of x and y into the formula and evaluate to get the distance.

Again recall distance = √(x2-x1)²+(y2-y1)²

==> plug in x2 = -3 , x1 = 0, y2 = -1 and y1 = 6

Distance = √(-3-0)²+(-1-6)

==> evaluate operations inside of parenthesis

Distance = √(-3)²+(-7)²

==> evaluate all exponents

Distance = √9+49

==> and 9 and 49

Distance = √58 = 7.6 (rounded)

Answer:

-3 / -5 = 0.6

Step-by-step explanation:

Answer:

the other candidate received 1875 votes

Step-by-step explanation:

if you add 50 and 25 percent you get 75 which leaves only 25 percent and to get the number or votes multiply 7500 by 0.25 or 7500 divided by 4

Answer:

she has 2 sisters; lucy simon and joanna simon

Step-by-step explanation:

The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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Answer:

x = 34

Step-by-step explanation:

-8 = dropped 8 degrees

26 = 26 degrees at midnight

x = temperature at 6

x - 8 = 26

(add 8 to both sides) x = 34

Answer:

C.

Step-by-step explanation:

The answer is C. The other questions you have stated are questions that have one definite answer or, one that requires one variable in the situation. With many stores distributing the books, it's a matter of finding the percentage of how many of been sold at each store. From this it reveals, it's a statistical question.

Answer:

0.8 lb rice/ 1qt water is a unit rate for the mix.

Using the unit rate, the cook should mix 10 pounds of rice with 12.5 quarts of water.

These two statements are true the rest are false.

Step-by-step explanation:

Figuring out which statements are true and which statements are false.

If you can please make my answer the brainliest that would be much appreciated. Thanks!

Translation is one of the four types of mathematical transformations that may be applied to a function graph.

(x, y) = (x + a, y + b)

In mathematics, a translation is the up, down, left, or right movement of a form. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more routes have been altered. There is no change in the form because it is just being moved from one location to another.

When the shape is moved towards the left by k units, then replace x with x - k.

When the shape is moved towards the right by k units, then replace x with x + k.

When the shape is moved up by k units, then replace y with y + k.

When the shape is moved down by k units, then replace y with y - k.

Example: What are the new coordinates when the translation (x, y) → (x - 2, y + 3) is applied to the point (2, 5).

Solution:

The coordinates of old point (preimage) are (x, y) = (2, 5). Now, applying the given translation to this point,

x - 2 = 2 - 2 = 0

y + 3 = 5 + 3 = 8

Thus, the coordinates of the translated point (image) are (0, 8).

This was the example of translation.

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Answer:

4/3

Step-by-step explanation:

Rise over run of 2 known points

Hope this helps!

Answer:

6, 11, 16, 21

Step-by-step explanation:

To obtain the first 4 terms add the common difference 5 to the previous term, that is

a₁ = 6

a₂ = a₁ + 5 = 6 + 5 = 11

a₃ = a₂ + 5 = 11 + 5 = 16

a₄ = a₃ + 5 = 16 + 5 = 21

There are 775 three-digit numbers with at least one even digit.

To find the number of three-digit numbers with at least one even digit, we can use the principle of inclusion-exclusion.

There are 9 choices for the first digit (it can't be 0), and 10 choices for each of the second and third digits.

9 × 10 × 10 = 900

possible three-digit numbers in total.

Now, we need to count the number of three-digit numbers with no even digits.

There are 5 odd digits (1, 3, 5, 7, 9), so there are:

5 × 5 × 5 = 125

three-digit numbers with no even digits.

Therefore, the number of three-digit numbers with at least one even digit is:

900 - 125 = 775

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Answer:

hundredths place

Step-by-step explanation:

hope this helps

Answer:

hundredths' place

Step-by-step explanation:

The first digit after the decimal represents the tenths place. (In this case, it's 9) The next digit after the decimal represents the hundredths place. In this case, it's 8 !

Answer:

Can I see an attachment if there is a graph or something???

The solid D is a tetrahedron located in the first octant and can be visualized as a triangular pyramid with vertices at (0,0,0), (3,0,0), (0,2,0), and (0,0,3).

First, we need to determine the limits of integration for each variable. Since D is bounded by the coordinate planes, the limits for x, y, and z are all from 0 to the corresponding values on the plane 2x + 3y + 2z = 6.

To find the limits for z, we set z = 0 and solve for x and y. We get 2x + 3y = 6, which implies y = (6 - 2x)/3. So the limits for z are from 0 to (6 - 2x)/3.

For y, we set y = 0 and solve for x and z. We get 2x + 2z = 6, which implies z = (6 - 2x)/2 = 3 - x. So the limits for y are from 0 to (6 - 2x)/3.

Finally, the limits for x are from 0 to the intersection point of the plane with the x-axis, which is found by setting y = z = 0 in 2x + 3y + 2z = 6. Solving for x, we get x = 3.

The integral becomes ∭D f(x, y, z) dV = ∫[0,3] ∫[0,(6 - 2x)/3] ∫[0,(6 - 2x)/2] f(x, y, z) dz dy dx.

The solid D is a tetrahedron located in the first octant and bounded by the coordinate planes and the plane 2x + 3y + 2z = 6. It can be visualized as a triangular pyramid with vertices at (0,0,0), (3,0,0), (0,2,0), and (0,0,3).

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