1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
rodikova [14]
3 years ago
8

What is the longest line segment that can be drawn in a right rectangular prism that is 13 cm long,

Mathematics
2 answers:
Ganezh [65]3 years ago
7 0

Step-by-step explanation:

The line segment (or chord) AB (in the figure), which passes through the foci (F1, F2) and terminates on the ellipse, is called the major axis. This axis is the longest segment that can be obtained by joining two points on the ellipse. The two points at which the major axis intersects the curve are called the vertices.

givi [52]3 years ago
5 0

Answer:

15.81 cm

Step-by-step explanation:

The diagonal line that links the 13 cm and 9 cm sides will be longest.

Use the Pyth Theorem to find it:

13^2 + 9^2 = c^2

169 + 81 = c^2

250 = c^2

15.81 = c

You might be interested in
A school wishes to enclose its rectangular playground using 480 meters of fencing.
Harlamova29_29 [7]

Answer:

Part a) A(x)=(-x^2+240x)\ m^2

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

P=2(L+W)

we have

P=480\ m\\L=x\ m

substitute

480=2(x+W)

solve for W

240=x+W\\W=(240-x)\ m

<u><em>Find the area of the rectangular playground</em></u>

The area is given by

A=LW

we have

L=x\ m\\W=(240-x)\ m

substitute

A=x(240-x)\\A=-x^2+240x

Convert to function notation

A(x)=(-x^2+240x)\ m^2

Part b) What side length x gives the maximum area that the playground can have?

we have

A(x)=-x^2+240x

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

A(x)=-x^2+240x

Factor -1

A(x)=-(x^2-240x)

Complete the square

A(x)=-(x^2-240x+120^2)+120^2

A(x)=-(x^2-240x+14,400)+14,400

A(x)=-(x-120)^2+14,400

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

x=120\ m

W=(240-120)=120\ m

The playground is a square

A=120^2=14,400\ m^2

8 0
3 years ago
Light travels about 180 million kilometers in 10 minutes. How far does it travel in one minute? How far does it travel in one se
astraxan [27]

Answer:

18 million kilometers in one min. and 0.3 million kilometers in one second

Step-by-step explanation:

so the one min. is easy because all you have to do is take 180 and divide it by 10 and you get 18 million kilometers in one min. and then you would take 18 and divide it by 60 and you would get 0.3 million kilometers in one second

8 0
3 years ago
Read 2 more answers
What's -9 x 7 plssssssssss answerrrrr quicklyyyy
NNADVOKAT [17]
It’s -63 all you would be multiple like normal 63 which then you put a negative symbol on front
6 0
3 years ago
Read 2 more answers
Solve the given equation. State the number and type of roots. x² + 3x- 4
sesenic [268]

Answer:

x=1, x=-4

Two distinct real roots

Step-by-step explanation:

x² + 3x- 4 = (x - 1)(x + 4)

x=1, x=-4

Two distinct real roots

4 0
3 years ago
Read 2 more answers
Differentiate Functions of Other Bases In Exercise, find the derivative of the function.
WARRIOR [948]

Answer:

\dfrac{dy}{dx} =\dfrac{2 x + 6}{ \log{\left (10 \right )}\left(x^{2} + 6 x\right)}

Step-by-step explanation:

given

y = \log_{10}{(x^2+6x)}

using the property of log \log_ab=\frac{log_cb}{log_ca}, and if c =e,\log_ab=\frac{ln{b}}{ln{a}}, we can rewrite our function as:

y = \dfrac{\ln{\left (x^{2} + 6 x \right )}}{\ln{\left (10 \right )}}

now we can easily differentiate:

\dfrac{dy}{dx} = \dfrac{1}{\ln{10}}\left(\dfrac{d}{dx}(\ln{(x^{2} + 6x)})\right)

\dfrac{dy}{dx} = \dfrac{1}{\ln{10}}\left(\dfrac{2x+6}{x^{2} + 6x}\right)

\dfrac{dy}{dx} =\dfrac{2 x + 6}{ \log{\left (10 \right )}\left(x^{2} + 6 x\right)}

This is our answer!

3 0
3 years ago
Read 2 more answers
Other questions:
  • A professor's son, having made the wise decision to drop out of college, has been finding his way in life taking one job or anot
    6·2 answers
  • I don't understand how to the problem
    5·1 answer
  • Evaluate each expression if m = 2, n = 16, and g = 1/5.
    15·1 answer
  • A basketball coach asks half of his players to stretch before each game; the other players do not stretch. After a month of game
    8·1 answer
  • The angles below are supplementary. What is the value of x?
    9·2 answers
  • Help plz thank you so so much
    11·1 answer
  • The Econo Motel charges 260 for 4 nights. At that rate, how many would 7 nights cost?
    9·1 answer
  • A triangle has two angle measures of 20 degrees and 30 degrees. Find the third angle. This triangle is a(n) ________ triangle
    11·2 answers
  • Select the story problem that this division problem represents 1/2 divided by 2/5
    9·1 answer
  • Four points are always coplanar if they: check all that apply.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!