MATHEMATICS COLLEGE

Round 3.83991676655 to the nearest hundred-thousandth.

Answers

Answer 1

Answer:

Rounding 3.83991676655 to nearest hundred = 3.83991677

Rounding 3.83991676655 to nearest -thousandth will result to 3.8399168

Given, number to be rounded off 3.83991676655 .

Concept of rounding off:

When the digit after decimal is greater than 5 than it will be rounded up.

When the digit after decimal is less than 5 than it will be rounded down.

Number : 3.83991676655

Rounding number to nearest tenth = 3.8

Rounding number to nearest hundred = 3.83991677

Rounding number to nearest thousandth = 3.8399168

Know more about rounding off,

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Answer 2

Answer:

Answer:

3.83992

Step-by-step explanation:

3.8399_676655

676655=1000000

3.83991+1000000=3.83992

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This holiday season, Ms. Bastarache organized to give each 9th grader a $10 Dunkin Donuts gift card. Because she bought a lot of cards, Ms. Bastarache tipped the Dunkin Donuts employee $20.This function represents the relationship between the number of gift cards, c, and T(c), the total cost of the cards.T(c) = 10c + 20Be sure to answer BOTH questions below.1. Determine the total cost, in dollars, for Ms. Bastarache to give out 93 gift cards.2. Last year, Ms. Bastarache spent $820, how many cards did she purchase?need help asap plzzzzzz

Graph the equation x= -7/2 by plotting points

Answers

Answer: the dot is right at the -5

hope it helped

Let S be the sphere of radius 1 centered at (2, 4, 6). Find the distance from S to the plane x + y + z = 0.

Answers

Answer:

5.928

Step-by-step explanation:

Given that:

The relation of the plane x+y+z= 0

Suppose (x,y,z) is any point on the plane.

Then the difference between (2,4,6) to (x,y,z) is:

$d^2 = (x-2)^2 + (y -4)^2 + ( z -6)^2 \n \n d^2 = (x^2 -4x+4) + ( y^2-8y +16) +(z^2 -12z + 36)$

$d^2 = x^2 + y^2 +z^2 -4x -8y -12z +4 +16 +36$

$d^2 = x^2 +y^2 + z^2 -4x -8y -12z +56$

∴

$f(x,y,z) =d^2 = x^2 + y^2 + z^2 - 4x -8y - 12 z +56 - - - (1)$

To estimate the maximum and minimum values of the function f(x,y,z) subject to the constraint g(x,y,z) = x+y+z =0

By applying Lagrane multipliers;

If we differentiate equation (1) with respect to x; we have:

f(x,y,z) = 2x -4

If we differentiate equation (1) with respect to y; we have:

f(x,y,z) = 2y - 8

If we differentiate equation (1) with respect to z; we have:

f(x,y,z) = 2z - 12

Differentiating g(x,y,z) with respect to x, we have:

$g_x(x,y,z) = 1$

Differentiating g(x,y,z) with respect to y, we have:

$g_y(x,y,z) = 1$

Differentiating g(x,y,z) with respect to z, we have:

$g_z(x,y,z) = 1$

Calculating the equations $\bigtriangledown f = \lambda \bigtriangleup g \ \ \ \& \ \ \ g(x,y,z) =0$

$f_x = \lambda g_x\n$

$2x - 4 = \lambda (1)$

$2x= 4 + \lambda$

$x= 2 + (\lambda )/(2) --- (2)$

$f_y = \lambda g_y$

$2x -8 = \lambda(1)$

$2x = 8+ \lambda$

$x = 4+(\lambda)/(2) --- (3)$

$f_z = \lambda g_z$

$2x -12 = \lambda (1)$

$x = 6 + (\lambda )/(2) --- (4)$

x+y+z = 0 - - - (5)

replacing x, y, z values in the given constraint

x + y + z = 0

$2+(\lambda)/(2)+4+(\lambda)/(2)+6+(\lambda)/(2)=0$

$12 + (3 \lambda )/(2)=0$

$(3 \lambda )/(2)=-12$

$3 \lambda=-12 * 2$

$3 \lambda=-24$

$\lambda=(-24)/(3)$

$\lambda=-8$

Therefore, from equation (2)

$x=2 +( \lambda )/(2)$

$x=2 +( -8 )/(2)$

x = 2 - 4

x = - 2

From equation (3)

$x=4 +( \lambda )/(2)$

$x=4 +( -8 )/(2)$

x = 4 - 4

x = 0

From equation (3)

$x=6 +( \lambda )/(2)$

$x=6 +( -8 )/(2)$

x = 6 -4

x = 2

i.e (x,y,z) = (-2, 0, 2)

∴

$d^2 = (x-2)^2 +(y-4)^2 + (z -6)^2$

$d^2 = (-2-2)^2 +(0-4)^2 + (2 -6)^2$

$d^2 = 16 +16 + 16$

$d^2 =48$

$d =√(48)$

$d= \pm 6.928$

since we are taking only the positive integer because distance cannot be negative, then:

The distance from the center of the sphere to the plane is 6.928.

However, the distance from the surface S to the plane is:

6.928 - radius of the sphere.

where;

the radius of the sphere is given as 1

Then:

the distance from the surface S to the plane is:

6.928 - 1

= 5.928

I NEED HELP, PLEASE!!Two numbers have a distance of 6 units from 0 on a number line. The numbers can be graphed on the number line as points A and B.

Drag and drop the labels to the correct positions on the number line.

Answers

Answer:

You have to put A on -6 and b on 6.

Step-by-step explanation:

IN order to solve tis you just have to take one of the markers, lets say A and move it 6 units to the left all the way to -6, then you just have to move the B marker 6 units to the right from 0 all the way to the 6, that is how you get the two numbers that have a distanceof 6 units from 0 on the number line.

Answer:

See attached image.

Step-by-step explanation:

Start at 0 and count to the right. When you get to 6, place EITHER marker on the point. It doesn't look like it matters whether you use A or B.

Start at 0 and count to the left. When you get to 6, place the other marker on the point.

H3lp pl34ssssssssssssssssssssssssss

Answers

Answer:

Step-by-step explanation:

Find the surface area and volume of a rectangular solid with length 10, width 7, height 12surface area______square inches
volume_____cubic inches

Answers

Answer:

Surface area is =548

Volume = 840 in³

Step-by-step explanation:

l × w, l × w, w × h, w × h, l × h, l × h

70 + 70 + 84 + 84 + 120 + 120 = 548

l × w × h = 840

A lightning bolt is graphed on the coordinate plane below. A rotation of this lightning bolt 270° clockwise would place it in which quadrant?A. Quadrant I (x, y)B. Quadrant II (-x, y)C. Quadrant III (-x, -y)D. Quadrant IV (x, -y)

Answers

Explanation

From the image, it can be seen that the initial position of the lightning bolt is in the first quadrant.

After it has been rotated 270 degrees clockwise, it moves by three quadrants and stays in the second quadrant

Answer: Option B

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