MATHEMATICS COLLEGE

Which equation can be used to find the value of h?A.
135 – 60 = h

B.
135 + h = 60

C.
60 + 135 = h

D.
60 – h = 135

Answers

Answer 1
Answer: I think that the answer is A

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Find the components of the vertical force Bold Upper FFequals=left angle 0 comma negative 4 right angle0,−4 in the directions parallel to and normal to the plane that makes an angle of StartFraction pi Over 3 EndFraction π 3 with the positive​ x-axis. Show that the total force is the sum of the two component forces.

Answers

Answer:

F_p = < - √(3) , -3 >\n\nF_o = < √(3) , -1 >

Step-by-step explanation:

- A plane is oriented in a Cartesian coordinate system such that it makes an angle of ( π / 3 ) with the positive x - axis.

- A force ( F ) is directed along the y-axis as a vector < 0 , - 4 >

- We are to determine the the components of force ( F ) parallel and normal to the defined plane.

- We will denote two unit vectors: ( u_p ) parallel to plane and ( u_o ) orthogonal to the defined plane. We will define the two unit vectors in ( x - y ) plane as follows:

- The unit vector ( u_p ) parallel to the defined plane makes an angle of ( 30° ) with the positive y-axis and an angle of ( π / 3 = 60° ) with the x-axis. We will find the projection of the vector onto the x and y axes as follows:

                         u_o = < cos ( 60° ) , cos ( 30° ) >

                         u_o = < (1)/(2) , (√(3) )/(2) >

- Similarly, the unit vector ( u_o ) orthogonal to plane makes an angle of ( π / 3 ) with the positive x - axis and angle of ( π / 6 ) with the y-axis in negative direction. We will find the projection of the vector onto the x and y axes as follows:

                        u_p = < cos ( (\pi )/(6) ) , - cos ( (\pi )/(3) ) >\n\nu_p = < (√(3) )/(2) , -(1)/(2) >\n

- To find the projection of force ( F ) along and normal to the plane we will apply the dot product formulation:

- The Force vector parallel to the plane ( F_p ) would be:

                          F_p = u_p(F . u_p)\n\nF_p = < (1)/(2) , (√(3) )/(2) > [ < 0 , - 4 > . < (1)/(2) , (√(3) )/(2) > ]\n\nF_p = < (1)/(2) , (√(3) )/(2) > [ -2√(3) ]\n\nF_p = < -√(3) , -3 >\n

- Similarly, to find the projection of force ( F_o ) normal to the plane we again employ the dot product formulation with normal unit vector (  u_o  ) as follows:

                         F_o = u_o ( F . u_o )\n\nF_o = < (√(3) )/(2) , - (1)/(2) > [ < 0 , - 4 > . < (√(3) )/(2) , - (1)/(2) > ] \n\nF_o = < (√(3) )/(2) , - (1)/(2) > [ 2 ] \n\nF_o = < √(3) , - 1 >

- To prove that the projected forces ( F_o ) and ( F_p ) are correct we will apply the vector summation of the two orthogonal vector which must equal to the original vector < 0 , - 4 >

                       F = F_o + F_p\n\n< 0 , - 4 > = < √(3), -1 > + < -√(3), -3 > \n\n< 0 , - 4 > = < √(3) - √(3) , -1 - 3 > \n\n< 0 , - 4 > = < 0 , - 4 >  .. proven                    

Need to be able to check my work with this problem.

Answers

Answer:

You are correct

Step-by-step explanation:

Hi,

(f+g)(x)=6x-12+3x+8=9x-4\n\n(f-g)(x)=6x-12-3x-8=3x-20

Thanks

The expression below is a sum of cubes. 125x3 + 169

Answers

Answer:

\text{The expression }125x^3+169\text{ is not the sum of cube}

Step-by-step explanation:

Given the expression

125x^3+169

we have to tell the above expression is the sum of cube

The sum of cube is of the form

a^3+b^3   →  (1)

Expression: 125x^3+169

125 is the cube of 5 and 169 is the square of 13

125x^3+169

(5x)^3+13^2

Comparing above with equation (1), we see the given expression is not the sum of cube
125x^3 = (5x)^3
125x^3 is the cube of 5x.

169 = 13^2
169 is the square of 13, but not the cube of a rational number.

The statement is false.

Select the correct answer.What is the current value of a future sum of money called?
А.
current value
B.
present value
С. .
future value

Answers

Answer:

b. present money

Step-by-step explanation:

the concept that States an amount of money today is worth more than that sum amount in the future. future money is not worth much then the amount received today.

Answer is B, Present Value

99 POINT PROJECT -- ACTUALLY DO IT, DONT TELL ME HOW! 99 POINTS.Search your home for a rectangular prism. Some examples are a cereal box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet.

Complete the following. Show all work for calculations.

List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).

Describe the shape of the cross section when the box is cut parallel to the base.

What is the surface area of the box?

What is the surface area of the box if it is scaled up by a factor of 10?

What is the volume of the box?

What is the volume of the box if it is scaled down by a factor of 1/10?

Answers

Final Answers are in "Shaded box"

Hope this helps!

Answer:

Rectangular prism

I chose a box of cereal.

Part 1)List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).

Length: 20 cm

Width: 8 cm

Height: 32 cm

Part 2).

 Describe the shape of the cross-section when the box is cut parallel to the base.

The shape of the cross-section would be a rectangle in dimensions.

20 cm x 8 cm

Part 3)

What is the surface area of the box? 

surface area=2*area of the base + perimeter of the base*height

area of the base=20*8=160 cm²

perimeter of the base=2*[20+8]-----> 56 cm

height=32 cm

surface area=2*160+56*32------> 2,112 cm²

the answer part 3) is

2,112 cm²

Part 4)

What is the surface area of the box if it is scaled up by a factor of 10?

we know that

surface area of the larger box =[scale factor]²*surface area original box

scale factor=10

surface area original box=2,112 cm²

so

surface area of the larger box=10²*2,112-----> 211,200 cm²

the answer part 4) is

211,200 cm²

Part 5) 

What is the volume of the box?

volume of the box = L*W*H 20*8*32-5,120 cm³

the answer Part 5) is

5,120 cm³

Part 6) 

What is the volume of the box if it is scaled down by a factor of 1/10?

we know that

the volume of the smaller box =[scale factor]³volume original box

scale factor=1/10

volume original box=5,120 cm³

so

volume of the smaller box =[1/10]³*5,120 5.12 cm³

the answer part 6) is

5.12 cm³

The length is 6 in., the width is 2 in., and the height is 16 in.

The tree diagram represents anexperiment consisting of two trials.
.4
.5
.6
D
.3
С
.5
.7
D
Þ(B and D) = [?]
ter

Answers

Answer:

0.35

Step-by-step explanation:

.5x.7
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