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3 years ago

a 96 inch board has to be cut into two pieces , one piece 8 inches longer than the other. How long should each piece be?

Mathematics

2 answers:

Savatey [412]3 years ago

6 0

X+x+8=96
2x=88
x=44. the other board is 52

S_A_V [24]3 years ago

4 0

This situation can be written as x+(x+8)=96
2x+8=96
2x=88
x=44cm
To check, 44 + (44+8)=96
44+8=52 so the second cut of board is 52cm long

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A container is shaped like a cylinder with half spheres on each end. The cylinder has a length of 30 centimeters and a radius is

Crank

The cubic centimeter one container can hold is 2,878.33 cm³.

<h3>What is the cubic centimeter one container can hold ?</h3>

In order to determine the cubic centimeter one container can hold, the volume of the container has to be determined.

Volume of the container = volume of the cylinder + (2 x volume of the hemisphere)

Volume of the cylinder = πr²h

Where:

π = 3.14
r = radius
h = height

3.14 x 5² x 30 = 2355 cm³

Volume of a hemisphere = (2/3) x π x r³

2 x (2/3 x 3.14 x 5³) = 523.33 cm³

Volume of the container = 523.33 cm³ + 2355 cm³ = 2,878.33 cm³

To learn more about the volume of a hemisphere, please check: brainly.com/question/26840364

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7 0

2 years ago

Danielle wants to know if a new dresser will fit next to her bed. The dresser she would like to buy is 73 centimeters wide. She

zhannawk [14.2K]

Answer:

No.

The dresser's width(28.74in) is greater than the remaining free width(10in) in the room.

Step-by-step explanation:

First, convert the chest width into inches, $73cm=28.74 \ in$

To find the excess width after fitting the bed in her room, we subtract the bed width from the room's width:

$Width_R=86 \ in\\Width_B=76 \ in\\\\Width_{excess}=Width_R-Width_B\\\\=86\ in -76\ in\\\\=10\ in$

Since 10in is less than 28.74in, the dresser will not fit next to her bed.

5 0

3 years ago

I need help with the 3rd one if appreciate it.

igor_vitrenko [27]

Answer:

skp

Step-by-step explanation:

5 0

3 years ago

Two particles travel along the space curves r1(t) = t, t2, t3 r2(t) = 1 + 2t, 1 + 6t, 1 + 14t . Find the points at which their p

GuDViN [60]

Answer:

A) points at which paths intersect : (1,1,1) ; (2,4,8)

B) DNE

Step-by-step explanation:

A) To find the points in which the particle paths intersect, it is necessary to find the values of t for which the three components of both vectors are equal:

$t_1=1+2t_2\\\\t_1^2=1+6t_2\\\\t_1^3=1+14t_2$

you replace t1 from the first equation in the second equation:

$(1+2t_2)^2=1+6t_2\\\\1+4t_2+4t_2^2=1+6t_2\\\\4t_2^2-2t_2=0\\\\t_2(2t_2-1)=0\\\\t_2=0\\\\t_2=\frac{1}{2}$

Then, for t2 = 0 and t2=1/2 you obtain for t1:

$t_1=1+2(0)=1\\\\t_1=1+2(\frac{1}{2})=2$

Hence, for t1=1 and t2=0 the paths intersect. Furthermore, for t1=2 and t2=1/2 the paths also intersect.

The points at which the paths intersect are:

$r_1(1)=(1,1,1)=r_2(0)=(1,1,1)\\\\r_1(2)=(2,4,8)=r_2(\frac{1}{2})=(2,4,8)$

B) You have the following two trajectories of two independent particles:

$r_1(t)=(t,t^2,t^3)\\\\r_2(t)=(1+2t,1+6t,1+14t)$

To find the time in which the particles collide, it is necessary that both particles are in the same position on the same time. That is, each component of the vectors must coincide:

$t=1+2t\\\\t^2=1+6t\\\\t^3=1+14t$

From the first equation you have:

$t=1+2t\\\\t=-1$

This values does not have a physical meaning, then, the particle do not collide

answer: DNE

5 0

3 years ago

What are the roots of the function f(x) = x2 + 2x – 1? a. x = ± √ _ 2 b. x = − 1 ± √ _ 2 c. x = 2 ± √ _ 2 d. x = 1 ± √ _ 2

Masteriza [31]

Step-by-step explanation:

Root of the function, where y = 0

f(x) = x² + 2x - 1

0 = x² + 2x - 1

x² + 2x - 1 = 0

x² + 2x = 1

x² + 2x + 1 = 1 + 1

(x + 1)² = 2

x + 1 = ±√2

x = -1 ± √2

Roots → x = -1 ± √2

7 0

2 years ago