The radius of a sphere is 6 inches. Find the length of a chord connecting two perpendicular radii. x = inches

Answers

Answer 1

Answer:

6√2 ≈ 8.485 inches

Step-by-step explanation:

The radii and the chord together make an isosceles right triangle with legs 6 inches long. The hypotenuse of such a triangle is √2 times the leg length. So, the chord will be 6√2 in long.

_____

Comment on isosceles right triangle

It is worth remembering that the hypotenuse of an isosceles right triangle is √2 times the leg length. This is easily found using the Pythagorean theorem:

... c² = a² + b²

... c² = 1² + 1² = 2 . . . . for legs of length 1

... c = √2 . . . . . . . . . . take the square root.

Scale this result as needed for any particular problem. Here, the scale factor is 6 inches.

Related Questions

Lita,Kala, and Rose entered a typing competition. Lita typed 2 times as fast as Kala. The ratio of the number of words Kala typed to the number of words Rose typed was 4:1. If Rose typed 48 words, how many words did Lita type?

Answers

If the ratio from Kala to Rose is 4:1, then for the 48 words Rose typed Kala typed 192 words. 48*4=192
Then Lita types twice as fast so 192*2=384.
It should be 384 words.

The Bureau of Justice Statistics reports that the number of Americans on probation increased 76% from 1980 to 1995 and that 3.09 million Americans were on probation in 1995. If the rate of increase continues in the same way for the next 15-year period, what might be the number of Americans on probation in 2010?

Answers

For this case, what we are going to do is first define variables.
x: current number of Americans.
y: number of Americans after the next 15 years.
We now write the expression to model the problem, assuming:
"the rate of increase continues in the same way for the next 15-year period".
We have then:
y = 1.76 * x
y = 1.76 * (3.09)
y = 5.44 million Americans
Answer:
the number of Americans on probation in 2010 might be:
y = 5.44 million Americans

how to do this 24:96 = 5:?

Answers

Um... I think you meant 24:96 = 5:x

In that case, x=20

A slice is made perpendicular to the base of a right rectangular prism as shown.
What is the area of the resulting two-dimensional cross section?
Drag and drop the answer into the box.

mm²
48
28
84
144
16

Answers

Answer:

The correct option is 1. The area of cross section area is 48 mm².

Step-by-step explanation:

From the find it is noticed that the cross section is a rectangle with length 4 mm and width is 12 mm.

The area of a rectangle is the product of its dimensions.

[tex]A=l\times w[/tex]

Where, l is length of the rectangle and w is width of the rectangle.

The area of cross section is

[tex]A=4\times 12[/tex]

[tex]A=48[/tex]

Therefore the area of cross section area is 48 mm². Option 1 is correct.

Please help me with this question

Answers

Try this option:
1. S=12²-10²=44 sq. ft.
2. S=10*12-6*8=120-48=72 sq. ft.

answers: 1-C; 2-C.

how much difference is there between investing $5,000 at 4% simple interest for 5 years and investing that same amount at 4% compounded quarterly

Answers

To find the difference between the tow investments we are going to use tow formulas. Simple interest formula for our simple interest investment, and compound interest formula for our compound interest investment.
- Simple interest formula: [tex]A=P(1+rt)[/tex]
where
  [tex]A[/tex] is the final investment value
  [tex]P[/tex] is the initial investment
  [tex]r[/tex] is the interest rate in decimal form
  [tex]t[/tex] is the time in years
For our problem we know that [tex]P=5000[/tex], [tex]r= \frac{4}{100} =0.04[/tex], and [tex]t=5[/tex], so lets replace those values in our simple interest formula to find [tex]A[/tex]:
[tex]A=5000(1+(0.04)(5))[/tex]
[tex]A=5000(1.2)[/tex]
[tex]A=6000[/tex]

Now that we know the final investment value of our simple interest investment, lets use the compound interest formula to find the final investment value of the other one:
- Compound interest formula: [tex]A=P(1+ \frac{r}{n})^{nt} [/tex]
where
  [tex]A[/tex] is the final investment value
  [tex]P[/tex] is the initial investment
  [tex]r[/tex] is the interest rate in decimal form
  [tex]n[/tex] is the number of times the interest is compounded per year
  [tex]t[/tex] is the time in years
For our problem we know that [tex]P=5000[/tex], [tex]r= \frac{4}{100} =0.04[/tex], and [tex]t=5[/tex]. Since we know that the interest is compounded quarterly (each 4 months), it mean that is compounded [tex] \frac{12months}{4months} =3[/tex] times per year, so [tex]n=3[/tex]. Now that we have all the vales, lets replace them in our formula:
[tex]A=5000(1+ \frac{0.04}{3} )^{(3)(5)} [/tex]
[tex]A=5000(1+ \frac{0.04}{3} )^{15} [/tex]
[tex]A=6098.95[/tex]

now that we know the final amounts of our investments, lets find how much difference is between them:
[tex]6098.95-6000=98.95[/tex]

We can conclude that the difference between invest $5000 in a compound interest investment vs a simple interest investment is $98.95.

The region r is bounded by the parabola y = x2 and the line y = 4. set up definite integrals to find the moment mx of r about the x-axis and the area a of the region r. then find (x, y )

Answers

Consider this option:
Volume is 256π/5, area is 32/3.
Details are in the attachment.
P.S. intersection points are (-2;4) and (2;4).

Alicia buys a 5 pound bag of rocks for fish tank. She uses 1 1/8 pounds for a small fish bowl. How much is left

Answers

Hello,

Here is your answer:

The proper answer to this question is "4".

Here is how:

First convert the mix number into a fraction:

1 1/8=9/8

5*8=40
1*8=8
-
9*1=9
8*1=8

40-8=32

32/8=4
8/8=1

Which means your answer is 4/1 or 4!

If you need anymore help feel free to ask me!

Hope this helps!

3^2•3^n simplifies to 3^20 what is the value of the exponent n?

Answers

Given that:
[tex]3^2 \times 3^n = 3^20 [/tex]
Solving for n.
Divide both sides by 3²
[tex] \frac{3^2 \times 3^n}{3^2} = \frac{3^{20}}{3^2} [/tex]
Simplify
[tex]3^n= 3^{20-2} \\ 3^n=3^{18} \\[/tex]
[tex]if \ a^{f(x)}=a^{g(x)} , \ then \ f(x)=g(x)[/tex]
So, n=18

Answer: n=18

Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Answers

The direction and magnitude can be found by summing the x- and y-components of each force.
It is best presented in the form of a table, where
x-component = Fcos(theta)
y-component = Fsin(theta)
For F=25 pounds, angle = 30
25cos(30)=21.65

Force angle x-component y-component
25 30 25cos(30)=21.65 25sin(30)=12.5
30 100 30cos(100)=-5.21 30sin(100)=29.54
Total Fx=16.44 Fy=42.04
Therefore angle = tan^(-1)(Fy/Fx)=tan^(-1)(42.04/16.44) = 68.64 °
magnitude = sqrt(Fx^2+Fy^2)=sqrt(16.44^2+42.04^2)=45.15 pounds

plz help ill give u branlist

Answers

Remember complementary sum is 90
so...
48 + 7(x + 1) = 90
7(x + 1) = 42
x + 1 = 6
x = 5

A square playground has an area of 175 m2. What is the approximate length of each side of the playground? Round your answer to the nearest meter

Answers

We know that the area of a square = side ²

Therefore, for a known area A, the side length is
side = √ (area)
= √ (175)
= 13.2288 (to 4 places of decimals).

If the area of a square playground is 175 [tex]m^{2}[/tex] then the approximate length is 13 meters.

What is square?

A square is a two dimensional figure having four vertices, four edges, four angles and all the sides are equal to each other. The perimeter is equal is equal to 4*side and the area is side*side.

How to find side of square?

We have been given the area of the square playground equal to 175 meter square. We know that the area of a square is side*side means [tex]side^{2}[/tex].

Put the value of 175 equal to side square and we will get the value of slide.

Area =[tex]side^{2}[/tex]

175=[tex]side^{2}[/tex]

side=[tex]\sqrt{175}[/tex]

Side=13.22m

If we round to nearest meter then it will be equal to 13m.

Hence if the area of a square playground is 175 meter square then the side will be equal to 13m.

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A math test took 50 minutes to complete. The test ended at 3:55. What time did the test begin?

Answers

The test started at 3:05 if it ended 50 minutes later at 3:55

A math test ended at 3:55 and it took 50 minutes to complete. What time did the math test start?

The math test started at 3:05.

If we know that the math test ended at 3:55 and lasted 50 minutes, we can subtract 50 minutes from 3:55 and we will get an answer of 3:05.

Therefore, the math test started at 3:05.

The prism is completely filled with 1750 cubes that have edge length of 1/5 feet. What is the volume of the prism,

Answers

we know that
the volume one cube=(1/5)*(1/5)*(1/5)=(1/125) ft³
the volume of prism=1750*(1/125)=14 ft³

the answer is 14 ft³

Find a vector equation and parametric equations for the line segment that joins p to q. p(1, −1, 7), q(7, 6, 1) vector equation r(t) = <1+6t,−1+7t,7−6t> parametric equations (x(t), y(t), z(t)) =

Answers

Answers:

- vector equation: r(t) = <1 + 6t, -1 + 7t, 7 - 6t>
- parametric equations:
x = 1 + 6t
y = -1 + 7t
z = 7 - 6t

Explanation:

To obtain the vector equation, we first get a vector v that is parallel to the line. To get the vector v, we subtract p from q. So,

v = q - p
= (7,6,1) - (1,-1,7)
v = (6, 7, -6)

The vector equation of the line is given by

[tex]r(t) = v_0 + tv[/tex]

Where

[tex]v_0[/tex] = a point in the line (we choose point p(1,-1,7))

So, the equation of the line joining p and q is given by

[tex]r(t) = v_0 + tv \\ \indent = \left \langle 1, -1, 7 \right \rangle + t\left \langle 6, 7, -6 \right \rangle \\ \indent = \left \langle 1, -1, 7 \right \rangle + \left \langle 6t, 7t, -6t \right \rangle \\ \indent \boxed{r(t) = \left \langle 1 + 6t, 1 + 7t, 7 - 6t \right \rangle }[/tex]

In the parametric equation of the line, we just need to get the x, y and z coordinates in the vector equation.

Since the vector equation is given by

[tex]r(t) = \left \langle 1 + 6t, 1 + 7t, 7 - 6t \right \rangle[/tex]

The parametric equations of the line are given by:

[tex]x(t) = 1 + 6t \\y(t) = 1 + 7t \\z(t) = 7 - 6t[/tex]

Final answer:

The vector equation for the line segment joining the points p(1, -1, 7) and q(7, 6, 1) is r(t) = <1+6t, -1+7t, 7-6t> and the corresponding parametric equations are x(t) = 1 + 6t, y(t) = -1 + 7t, z(t) = 7 - 6t.

Explanation:

To find the vector and parametric equations for the line segment joining two points p(1, -1, 7) and q(7, 6, 1), we first need to understand that the vector equation for a line segment in space is given by r(t) = p + t (q - p), where 0 ≤ t ≤ 1, and p and q are the coordinates of the points. The parametric equations are obtained by expressing the x, y, and z coordinates of r(t) as individual functions of t.

Substituting the given points into the vector equation we get: r(t) = <1+6t, -1+7t, 7-6t>. Then, the corresponding parametric equations will be x(t) = 1 + 6t, y(t) = -1 + 7t, and z(t) = 7 - 6t.

Learn more about Vector and Parametric Equations here:

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How many different possible outcomes are there when Jillana spins the spinner below and then flips the coin?

The spinner is from 1-6.

Answers

the answer is 12 because for each number on the spinner you have 2 options which the coin may land, heads or tails, so 6x2 is 12

Answer:

There are total 12 outcomes

Step-by-step explanation:

The number of outcomes in spinning a spinner is 6 (getting a number from 1 to 6)

The number of outcomes in flipping a coin=2 (head or tail)

Hence, total 12 outcomes are possible which are:

(1,H) (2,H) (3,H) (4,H) (5,H) (6,H)

(1,T) (2,T) (3,T) (4,T) (5,T) (6,T)

EXPERTS/ACE/GENIUSES

Answers

the answer would be D

Can somebody please help me out ?

Answers

The area of a triangle is:
A = (1/2) * b * h
Where
b: base
h: height.
For the lower triangle we have:
A = (1/2) * (10) * (root ((8) ^ 2- (5) ^ 2))
A = 31 in ^ 2
We add this area with the area of the upper triangle:
31 in ^ 2 + 17 in ^ 2 = 48 in ^ 2
Answer:
The quadrilateral area will be:
48 in ^ 2 (option 3)

simplify the complex fraction

Answers

pl see the attachment
the final answer is (y+z)/(y-z)

find the product 3012 and 4

Answers

product is multiplying, so it is 3012*4 which equals 12048

753. Its hard to show long division with out a paper, but if you remember divide, multiply and subtract, bring it all down and bring it all back, you'll be good. There is a really good video online to help remember it, but with this specific problem, 4 ends up going into 3012, 753 times.

can someone please help me with this equation? thank you.

Answers

I found it simplest to start with the given line in standard form. That is
.. x +2y = 3 . . . . . . . . divide the given equation by 3

Now, the perpendicular line is easily written as
.. 2(x -(-4)) -(y -2) = 0 . . . . . swap x, y coefficients, negate one. Translate to the given point

Simplifying, we have
.. 2x -y +10 = 0
Solving for y gives
.. y = 2x +10 . . . . . . . . . . . . corresponds to selection B

A zoo has three panda bears and five giraffes. What is the ratio of panda bears to giraffes at that zoo?

Answers

Hey there! :D

This is a ratio:

x:y

The ratio asks for panda bears to giraffes.

panda bears= 3

giraffes= 5

3:5 <== the ratio

I hope this helps!
~kaikers

Hey there!

The answer is 3:5

Hope this helps!

Always remember, you are a Work Of Art!
- Nicole <3 :)

Why do clouds tend to form around 3:00 pm and 6:00 am

Answers

During daytime, the sun heats the land and warms the air that rises. That lowers the pressure, causing a gradient force to bring air from the colder sea. The wind is then onshore. Small cumulus clouds form over the land, often following the coastline very closely

and are similar. Find the value of x. A. 5 B. 15 C. 60 D. 240

Answers

Dude we need to actualy see the question all we see is find the value of x but we don't know our other value?

53b−7b−6b+1 if b=25
Please help me with this problem! And what is the simplified expression?

Answers

Answer: 1001

B/c i said so

What is 3^2/3 equal to? A.3√9 B.2√9 C.3√27 D.2√27

Answers

[tex] a^{\frac{m}{n}} = \sqrt[n] {a^m} [/tex]

[tex] 3^{\frac{2}{3}} = \sqrt[3] {3^2} = \sqrt[3] {9} [/tex]

6 Bands were going to play at a concert. How many ways can the concert manager send them on stage?

Answers

Try this option:
there are two ways to resolve this task:
1. the 1st in this sequence is for 6 bands, the 2d in this sequence is for 5 rest bands, the 3d in this sequence is for 4 rest bands, the 4th in this sequence is for rest 3 bands, the 5th in this sequence is for rest 2 bands and the 6th in this sequence is for the last 1 band. Using the logical rule 'AND': A=6*5*4*3*2*1=720.
2. According to arrangement rules it is the formula: A=n!, where n - number of bands.
A=6!=720.

answer: 720.

Rob cuts a 15-foot wire into 8 equal pieces. about how long is each piece?

Answers

Divide 15 with 8

15/8 = 1.875

Each piece is 1.875 foot long

hope this helps

To find out how long each piece is, you would need to divide 15 by 8 to get an answer of 1.875 feet.
I hope this helped! :-)

Shelly has a photo that is 7 1/3 inches tall. she wants to shrink it down to fit in a picture frame that is only 5 1/3 inches tall. the photo shop can only reduce photos by certin fractions. they can reduce it to 2/3 the original size, 3/4 the original size, or 5/9 the original size. which reduction should she use so the picture fills as much of the frame as possible, without being too large?

Answers

we know that

the photo is 7 1/3 inches tall-----> 7 1/3=(7*3+1)/3=22/3 in ----- > (7.33 in)
the picture frame is 5 1/3 inches tall--> 5 1/3=(5*3+1)/3=16/3 in----> (5.33 in)

a) case A reduce 2/3 the original size------> (22/3)*(2/3)=44/9 in-----> (4.89 in)

b) case B reduce 3/4 the original size---> (22/3)*(3/4)=66/12 in-----> (5.5 in)
this is not solution because 66/12 (5.5 ) in >16/3 (5.33) in ( picture frame)

c) case C reduce 5/9 the original size---> (22/3)*(5/9)=110/27 in-----> (4.07 in)

the answer is the case A reduce 2/3 the original size----> 44/9 in (4.89 in)

At noon, ship a is 60 km west of ship
b. ship a is sailing south at 15 km/h and ship b is sailing north at 5 km/h. how fast is the distance between the ships changing at 4:00 pm?

Answers

dA/dt=15 km/h and dB/dt=5 km/h
base of our triangle if drawn is 60 km
to find dD/dt when t=4 hours we shall have:

(A+B)²+60²=D²
d/dt[(A+B)²+60²]=d/dt(D²)
[d(A+B)]/dt*2(A+B)(2)=dD/dt*2D
B=5km/h*4hr=20km
A=15km/hr*4=60km
20²+60²=D²
D=√4000

(15+5)*(2)*80*(2)=2*√4000*dD/dt
dD/dt=6400/√4000=101.192 km/hr

The two ships are sailing in opposite sides, Hence, the resultant speed is given by 15+5 = 20 km/hr.

Therefore, from the below triangle, we have

[tex]\frac{dx}{dt} = 20 \text{ km/hr}[/tex]

Let the distance between the ships is y. On applying Pythagorous theorem, we have

[tex]y^2=x^2+60^2\\ \text{On differentiating, we get}\\ 2y\frac{dy}{dt} =2x\frac{dx}{dt}\\\frac{dy}{dt}= \frac{x}{y} \frac{dx}{dt}[/tex]

On substituting the value of y as [tex]y=\sqrt{60^2+x^2}[/tex]

[tex]\frac{dy}{dt} =\frac{x}{\sqrt{60^2+x^2}} \frac{dx}{dt}[/tex]

Since, the at noon the ship is 60 km to each other. Hence, for 4 PM, i.e. t=4, we have

[tex]x=4 \times \frac{dx}{dt} \\ x= 4 \times 20 \\x=80[/tex]

On substituting the value in above, we get

[tex]\frac{dy}{dt} =\frac{80}{\sqrt{60^2+80^2}} (20[/tex]

[tex]\frac{dy}{dt} = 16.0 \text{ km/hr}[/tex]

Therefore, the distance between the ships changing at a rate of 16 km/hr at 4:00 pm

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What two events made it possible for Christianity to grow rapidly? Select all that apply. A. Theodosius I made it the official religion of the Persian Empire. B.The Edict of Milan came into being. C.The Roman Empire split. D.Theodosius I made it the official religion of the Roman Empire. Do butterfly get food by eating other organisms Of all the houses on kermit lane, 20 have front porches, 20 have front yards, and 40 have back yards. how many houses are on kermit lane? Express the complex number in trigonometric form. 3 The death penalty does not deter crime and should therefore be abolished in the United StatesThis is an example of which type of claim?A- Claim of definition B- Claim of fact C- Claim of policy D- Claim of value Which phrase describes an unknown or changeable quantity? A.60 seconds multiplied by 5 B.2 times the number of pages in the book C.15 years of schooling D.3 dollars and 76 cents Divide 3x^2 -2x^2 -61x -20 by x -5 The sun is wonderful source of energy. It is renewable and natural with few dangers. Solar cells rely on the sun for energy. These cells would be more practical to use if they were ________. A) larger B) Nonrenewable C) Pollution-free D) less expensive Preterito de oir, leer, creer y destruir Quiz 1. Which of the following countries borders Uruguay?1. Panama2. Chile3. Brazil4. Peru2. Uruguay has suffered a series of which kind of natural disaster?1. droughts2. cyclones3. tsunamis4. forest fires3. Which of the following is a reason the residents of Montevideo might be glad about the reopening of el Observatrio Meterorologico del Colegia Pio?1. it provides another school for sudents to attend2. it may provide education about meteorites3. it provides a safe location to be during earthquakes4. it provides acurate weather info and training in meteorology 4. In the event of un incendio, whom should you call first?1. los bomberos2. los paramedicos3. los heridos4. los reporteros5. Atillio Pelossi is best remembered for beng1. asustado2. muerto3. valliente4. vivo6. which of the following options includes two natural disasters?1. la lluvia, investigar2. escapar, la tormenta3. el terremoto, la tormenta4. el noticerio, la inundacion7. He read the newspaper. What is the best way to write "He read" in Spanis?1. Leyo2. Leio3. Leyeron4. Lee8. "Yo trabajaba en esa empresa" is best translated as1. i am working for that company2. once i worked for that company3. i never worked for that company4. i used to work for that company9. which of the following options is the best to complete the sentence? Cuando eelos llegaron, Maria ______1. hablo por telefono2. hablaron por telefono3. hablaba por telefono4. hablaban por telefono Strong cultures can have powerful effects on employee behavior. how does this create inadvertent control mechanisms? Of the following terms, the one that includes all others isa)Oxidation b)Respirationc)Metabolism d)PolinationPlz give the correct answer with reason Which one of the following statements best describes the just world hypothesis?A.People deserve what happens to them, whether good or bad.B.The world is just, but some people don't think it is.C.People who work hard are superior to those who are lazy.D.If people act with integrity, they contribute to a just world. Why did Churchill believe the Munich Pact was the "beginning of the reckoning"? In close relationships: 1. positive events have greater psychological impact than negative events do. 2. positive and negative events have roughly the same impact. 3. negative events have greater psychological impact than positive events do. 4. positive events have greater impact in the early stages of relationships, but negative events have greater impact later on. Benjamin rush, a physician who also signed the declaration of independence, was the first to: When you play melody in D minor, which finger would you use to play the note on the staff? the number 0.4 can be written as 4/10 so it is a rational number Which condition would most likely result in an increase in the phenotypic variation within a population?Question 4 options:The variety of food available in the habitat decreasesA mutation leads to individuals with genetic differencesCompetition is reduced for all individuals during the winter Which group made up the largest percentage of Californias population in 1840 Anhydrous calcium chloride removes water vapor from the air inside a container having an air-tight seal called a desiccator. Explain