Answer:Circumference = 2 \pi r
circumference = 2 \pi (1.5)
circumference = 9.42 feet
The circumference is 9.42 feet, so we need to get fencing for 10 feet (assuming the fence comes in feet, i.e. you cant buy half a foot)
1 feet = $.075
10 feet = $0.75 x 10 = $7.50
Select TWO equivalent expression to the function 3x^2−12x−36.
Question 1 options:
3(x+6)(x−2)
3(x−6)(x+2)
(3x+6)(x−6)
(3x−6)(x+6)
Answer:
3(x-6)(x+2) and (3x+6)(x-6)
Step-by-step explanation:
The other two answers are wrong because the value for their x will be positive.
In a lilac paint mixture 40% of the mixture is white paint 20% is blue and the rest is red there are four cups of blue paint used in a batch of lilac paint how many cups of white paint is used
Answer: 8 cups of white paint is used.
Step-by-step explanation:
In a lilac paint mixture 40% of the mixture is white paint 20% is blue and the rest is red. This means that the percentage of red paint in the mixture is 100 - (40 + 20) = 40%
There are four cups of blue paint used in a batch of lilac paint. This means that 20% of the total number of cups of paint used in a batch of lilac paint is 4.
Assuming that the total number of cups of paint in the mixture is x, then,
20/100 × x = 4
0.2x = 4
x = 4/0.2 = 20
Therefore, the number of cups of white paint used is
40/100 × 20 = 0.4 × 20
= 8 cups
Final answer:
In the lilac paint mixture, for every 4 cups of blue paint, which accounts for 20% of the mixture, there are 8 cups of white paint, corresponding to 40% of the mixture.
Explanation:
The question involves determining the amount of white paint used in a batch of lilac paint given that 40% of the paint mixture is white, 20% is blue, and the remainder is red. We're told that 4 cups of blue paint are used. Since blue paint represents 20% of the mixture, we can use this information to find out the total amount of the paint mixture and then calculate the amount of white paint needed.
First, find the total amount of the paint mixture by calculating the full 100% that the 4 cups of blue paint (20%) contribute to. This calculation is as follows:
Total Paint = 4 cups (20%) / 0.20Total Paint = 20 cupsNow that we know the total paint mixture is 20 cups, we can determine the amount of white paint, which is 40% of the total mixture:
White Paint = Total Paint x 40%White Paint = 20 cups x 0.40White Paint = 8 cupsTherefore, 8 cups of white paint are used in the mixture.
what are the values of c and d in the matrix [[6,8],[-11,15]]-[[c+2,3],[-5,d-4]]=[[22,5],[-6,17]]
Answer:
c = -18
d = 2
Step-by-step explanation:
[[6,8],[-11,15]]-[[c+2,3],[-5,d-4]]=[[22,5],[-6,17]]
First we arrange the subtraction to clear the unknowns
- [[c+2,3],[-5,d-4]] = [[22,5],[-6,17]] - [[6,8],[-11,15]]
[[c+2,3],[-5,d-4]] = [[6,8],[-11,15]] - [[22,5],[-6,17]]
Now we solve what can be done
[[c+2,3],[-5,d-4]] = [[6-22 , 8-5],[-11+6 , 15-17]]
[[c+2,3],[-5,d-4]] = [[-16 , 3] , [-5 , -2]
we match each term with its corresponding one and we will obtain
c + 2 = -16 d - 4 = -2
c = -16 - 2 d = -2 + 4
c = -18 d = 2
which of the following terms is not a monomial a)6x b)1/3x^2 c)13 d) 3x^-3
Answer:
The answer is D.
Step-by-step explanation: A monomial is an algebraic expression that consists of one term. D consists of 2 terms and is considered a binomial.
Identify the triangle that contains an acute angle for which the sine and cosine ratios are equal. 1. Triangle A B C has angle measures 50 degrees, 40 degrees, and 90 degrees. 2. Triangle A B C has angle measures 45 degrees, 45 degrees, 90 degrees. 3. The lengths of sides A C and C B are congruent. 4. Triangle A B C has angle measures 68 degrees, 22 degrees, and 90 degrees. 5. Triangle A B C has angle measures 60 degrees, 30 degrees, and 90 degrees.
Answer:
The correct option: (2) Triangle ABC that has angle measures 45°, 45° and 90°.
Step-by-step explanation:
It is provided that a triangle ABC has an acute angle for which the sine and cosine ratios are equal to 1.
Let the acute angle be m∠A.
For the sine and cosine ratio of m∠A to be equal to 1, the value of Sine of m∠A should be same as value of Cosine of m∠A.
The above predicament is possible for only one acute angle, i.e. 45°, since the value of Sin 45° and Cos 45° is,
[tex]Sin\ 45^{o} =Cos\ 45^{o} = \frac{1}{\sqrt{2} }[/tex]
So for acute angle 45° the ratio of Sin 45° and Cos 45° is:
[tex]\frac{Sin\ 45^{o}}{Cos\ 45^{o}} = \frac{\frac{1}{\sqrt{2} } }{\frac{1}{\sqrt{2} } } = 1[/tex]
Hence one of the angles of a triangle is, m∠A = 45°.
Comparing with the options provided the triangle is,
Triangle ABC that has angle measures 45°, 45° and 90°.
Thus, the provided triangle is a right angled isosceles triangle, since it has two similar angles.
Answer:
IT'S the second option
Step-by-step explanation:
We have three fair coins, each of which has probability 1/2 of having a heads outcome and a tails outcome. The experiment is to flip all three coins and observe the sequence of heads and tails. For example, outcome HTH means coin 1 was heads, coin 2 was tails, coin 3 was heads. Note that there are 8 total outcomes, and we assume that each one is equally likely. What is the probability that the outcome has at least two consecutive heads in the sequence?
Answer: 3/8
Step-by-step explanation:
Firstly, let's look at the possible outcome when 3 coins are tossed.
If two coins are first tossed, the possible outcome will be,
{HH, HT, TH, TT}
if one more coin is tossed together with the two to make it 3coins, the possible outcome will be gotten by matching the H and T of the third coin with the set of sample space above to give us,
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
This gives a total sample space of 8.
Outcomes that has at least two consecutive heads in the sequence are {HHH, HHT, THH} which is the possible outcome i.e 3
Probability that the outcome has at least two consecutive heads in the sequence will be;
Possible outcome/total outcome
= 3/8
26,) If y varies inversely as x, and y = 5 as x = 6, find y for the x-value of 10.
Answer:
3
Step-by-step explanation:
the initial statement is
y ∝ 1 /x
to convert to an equation multiply by k the constant
of variation
y = k × 1 /x = k /x
to find k use the given condition
y = 5 when x = 6
y = k/ x ⇒ k = y x = 5 × 6 = 30
y = 30 /x
when
x = 10
then
y = 30 /10 = 3
Answer: y = 3
Step-by-step explanation:
In inverse variation, as one variable increases, the other variable decreases and as one variable decreases, the other increases.
We would introduce a constant of proportionality, k. Therefore,
y = k/x
When y = 5 , x = 6
Therefore,
5 = k/6
Cross multiplying by 6, it becomes
k = 6 × 5 = 30
The expression becomes
y = 30/x
Therefore, when x is 10,
y = 30/10
y = 3
Lisa picked some berries. She used 2/8 of the berries to make a pie she gave 5/7 of the berries to her friend. What fraction of the berries did she give her friend?
Answer:
15/28
Step-by-step explanation:
Let the number of berries Lisa picked be y
Number of berries she used to make pie = 2y/8 = y/4
Number of berries left = y - y/4 = 3y/4
Number of berries she gave her friend = 5/7 × 3y/4 = 15y/28
Fraction of the berries she gave her friend = 15/28
Write the function as a set of ordered pairs.
Give the domain and range of f.
f(1)=10, f(2)=-3, f(3)=3
Answer:
1. (1,10) 2. (2,-3) 3. (3,3)
The reequired ordered pair of the given function is (1, 10), (2, -3), and (3, 3).
Given that,
To determine the function as a set of ordered pairs.
f(1)=10, f(2)=-3, f(3)=3
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.
Here,
Since order pair of function f(x) = y is given as (x, y)
Similarly ordered pair of the function given is,
f(1) = 10
ordered pair = (1, 10)
f(2) = 3
ordered pair = (2, -3)
f(3) = 3
ordered pair = (3, 3)
Thus, the reequired ordered pair of the given function is (1, 10), (2, -3), and (3, 3).
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Suppose the age of people in a certain population are distributed normally with a mean of 37.5 years and standard deviation of 6.2 years. What is the probability of randomly selecting a person who is over 45 years old given that they are older than 40.
Answer:
[tex] P(X>45 | X>40)= \frac{P(X>45 \cap X>40)}{P(X>40)}= \frac{P(X>45)}{P(X>40)}= \frac{0.113}{0.343}= 0.329[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the age of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(37.5,6.2)[/tex]
Where [tex]\mu=37.5[/tex] and [tex]\sigma=6.2[/tex]
We are interested on this probability:
[tex] P(X>45 | X>40)= \frac{P(X>45 \cap X>40)}{P(X>40)}= \frac{P(X>45)}{P(X>40)}[/tex]
We can begin finding [tex] P(X>40)[/tex] using the z score formula given by:
[tex] z = \frac{a-\mu}{\sigma}[/tex]
Using this formula we have:
[tex] P(X>40)= P(Z>\frac{40-37.5}{6.2}) = P(Z>0.403)[/tex]
And using the complement rule and the normal standard table or excel we have this:
[tex]P(Z>0.403)=1-P(Z<0.403)= 1-0.657= 0.343[/tex]
Now we can find [tex] P(X>45)[/tex] using the z score formula given by:
[tex] z = \frac{a-\mu}{\sigma}[/tex]
Using this formula we have:
[tex] P(X>45)= P(Z>\frac{45-37.5}{6.2}) = P(Z>1.210)[/tex]
And using the complement rule and the normal standard table or excel we have this:
[tex]P(Z>1.210)=1-P(Z<1.210)= 1-0.887= 0.113[/tex]
And replacing into our original probability we got:
[tex] P(X>45 | X>40)= \frac{P(X>45 \cap X>40)}{P(X>40)}= \frac{P(X>45)}{P(X>40)}= \frac{0.113}{0.343}= 0.329[/tex]
Which of the following functions are solutions of the differential equation y'' + y = sin(x)?a) y= sinx
b) y= cosx
c) y=1/2sinx
d) -1/2xcosx
Answer:
Option (d)
Step-by-step explanation:
Given,
y" +y=sin x ...........(1)
The particular solution
[tex]y_p=A x sinx +Bx cosx[/tex]
[tex]y'_p=Axcosx+Asinx+B cosx-Bxsinx[/tex]
[tex]y"_p=Acosx-Axsinx+Acosx-Bsinx-Bsinx-Bxcosx[/tex]
[tex]y"_p=2Acosx-Axsinx-2Bsinx-Bxcosx[/tex]
Putting the value of y" and y in equation (1)
[tex]2Acosx-Axsinx-2Bsinx-Bxcosx+Axsinx+Bxcosx = sinx[/tex]
[tex]\Rightarrow 2Acosx-2Bsinx=sinx[/tex]
Therefore 2A =0 -2B=1
⇒A=0 [tex]\rightarrow B=-\frac{1}{2}[/tex]
Therefore [tex]y_p=-\frac{1}{2} x cosx[/tex]
The solutions of the differential equation y'' + y = sin(x) are y = cos(x), y = (1/2)sin(x), and y = -(1/2)xcos(x).
Explanation:To determine which of the given functions are solutions of the differential equation y'' + y = sin(x), we can substitute each function into the equation and check if it satisfies the equation. Let's go through each option:
Substituting y = sin(x) into the equation, we get -sin(x) + sin(x) = sin(x), which is not true. So, y = sin(x) is not a solution.Therefore, the solutions of the differential equation y'' + y = sin(x) are y = cos(x), y = (1/2)sin(x), and y = -(1/2)xcos(x).
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-----40 POINTS--------
Provide the missing reasons for the proof of part of the triangle midsegment theorem.
Proof
Provide the missing reasons for the proof of part of the triangle midsegment theorem.
Given: K is the midpoint of MJ.
L is the midpoint of NJ.
Prove: MN = 2KL
The complete answer is attached in the diagram below.
The complete answer for the missing reasons is attached below in the diagram.
Please check the figure.
Keywords: statement, proof, reason
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58x176 equals what.... will make brainliest
Answer:
10208
Step-by-step explanation:
just 58x176
Peter answered 15 questions on a quiz and obtained 29 points. If 3 points were given for each correct answer and one point deducted for each wrong answer, how many questions did Peter answer correctly?
Final answer:
By setting up an equation with x representing the number of correct answers, we find that Peter answered 11 questions correctly on his quiz.
Explanation:
To determine how many questions Peter answered correctly on his quiz, we first need to set up an equation to represent the situation. Let's let x be the number of questions Peter got right, and since he answered 15 questions in total, it means he got (15 - x) questions wrong. Since he gets 3 points for each correct answer and loses 1 point for each wrong answer, we can write the equation as:
3x - (15 - x) = 29
Now, we will solve for x:
3x - 15 + x = 29
4x - 15 = 29
4x = 29 + 15
4x = 44
x = 44 / 4
x = 11
So, Peter answered 11 questions correctly.
The apparent brightness of a star if it were viewed from a distance of 10 parsecs (32.6 light- years) is called ________.
Answer:
Absolute magnitude
Step-by-step explanation: Astronomy deals with the study of stars and other heavenly bodies. Astronomers use apparent magnitude to define how bright a star appears and shines from the earth.
A local Walmart sells sweatpants ($7) and jackets ($14). If total sales were $6,160 and customers bought 8 times as many sweatpants as jackets, what would be the number of jackets sold?
A. 880
B. 8
C. 88
D. 8,880
E. None of these
Answer:
Option C) 88
Step-by-step explanation:
We are given the following in the question:
Unit cost of sweatpants = $7
Unit cost of jackets = $14
Let x be the number of sweatpants sold and y be the number of jackets sold.
Customers bought 8 times as many sweatpants as jackets
Then, we can write,
[tex]x = 8y[/tex]
Total sales = $6,160
[tex]7x + 14y = 6160[/tex]
Substituting the values, we get,
[tex]7(8y) + 14y = 6160\\70y = 6160\\y = 88\\x = 704[/tex]
Thus, 88 jackets were sold.
Option C) 88
A silicon (Φ = 7.77 × 10-19 J) surface is irradiated with UV radiation with a wavelength of 235 nm. Assume an electron was a mass of 9.11 x 10-31 kg. What is the kinetic energy of the emitted electrons?
Since a silicon (Φ = 7.77 × 10-19 J) surface is irradiated with UV radiation with a wavelength of 235 nm. Assume an electron was a mass of 9.11 x 10-31 kg, the kinetic energy of the emitted electrons is 6.9 × 10⁻²⁰ J
What is kinetic energy of emitted electron in photoelectroic effect?The kinetic energy of emitted electron in photoelectric effect is given by
K = hc/λ - Φ where
h = Planck's constant = 6.63 × 10⁻³⁴ Jsc = speed of light = 3 × 10⁸ m/s λ = wavelength of light andΦ = work function of metalSince a silicon (Φ = 7.77 × 10-19 J) surface is irradiated with UV radiation with a wavelength of 235 nm. Assume an electron was a mass of 9.11 x 10-31 kg. To determine the kinetic energy of the emitted electrons, we proceed as follows
Since the kinetic energy of the emitted electrons is
K = hc/λ - Φ
Given that
λ = 235 nm = 235 × 10⁻⁹ m andΦ = 7.77 × 10⁻¹⁹ JSo, substituting the values of the variables into the equation, we have that
K = hc/λ - Φ
K = (6.63 × 10⁻³⁴ Js × 3 × 10⁸ m/s)/235 × 10⁻⁹ m - 7.77 × 10⁻¹⁹ J
K = (19.89 × 10⁻²⁶ Jm)/235 × 10⁻⁹ m - 7.77 × 10⁻¹⁹ J
K = 0.0846 × 10⁻¹⁷ J - 7.77 × 10⁻¹⁹ J
K = 8.46 × 10⁻¹⁹ J - 7.77 × 10⁻¹⁹ J
K = 0.69 × 10⁻¹⁹ J
K = 6.9 × 10⁻²⁰ J
So, the kinetic energy is K = 6.9 × 10⁻²⁰ J
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The probability you'll see a falling star in the sky over the course of one hour is 0.44. What's the probability you'll see one over half an hour?
Answer:
Probability so see one falling star over half an hour is 0.25
Step-by-step explanation:
An hour can be taken as two half hours so we can write the probability to see a falling star as
(1-P)*(1-P) = 1 - 0.44
( 1 - P )² = 0.56
1 - P = [tex]\sqrt{0.56}[/tex]
P = 1 - [tex]\sqrt{0.56}[/tex]
P = 0.25
The area of the base of the prism is 360 square centimetres and the height of the prism 19 centimeters what is the volume in cubic centimeters of the rectangular
Answer:
6,840cm³
Step-by-step explanation:
V = 360 * 19
V = 6,840cm³
The cylinder coffee cup has a radius of 1.8 inches and a height of 4 inches. Find the surface area of the coffee cup, not including the handle. Round to the nearest tenth
Answer:
Step-by-step explanation:
The formula for determining the total surface area of a cylinder is expressed as
Total surface area = 2πr² + 2πrh
Where
r represents the radius of the cylinder.
h represents the height of the cylinder.
π is a constant whose value is 3.14
Assuming that the cylindrical cup is open at the top, the formula becomes
Area = πr² + 2πrh
From the information given,
Radius = 1.8 inches
Height = 4 inches
Therefore, the surface area of the coffee cup is
(3.14 × 1.8²) + (2 × 3.14 × 1.8 × 4)
= 10.1736 + 45.216
= 55.4 inches² to the nearest tenth.
Answer:
55.4 :))
Step-by-step explanation:
Use the graph that shows the solution to
f(x)=g(x) .
f(x)=−3/4x^2+3x+1
g(x)=2x
Graph A is the correct representation, as it aligns with the functions f(x) and g(x), resulting in the accurate intersection point (2, 4). Graph B does not accurately represent the functions based on the reported intersection point (4, 1).
The correct graph can be determined by analyzing the given functions and the specified intersection points. The functions are f(x) = -3/4 * x^2 + 3x + 1 and g(x) = 2x, and the reported intersection points are (2, 4) for graph A and (4, 1) for graph B.
To verify the accuracy, substitute the x-values into both functions:
Graph A (Intersection at (2, 4)):
f(2) = -3/4 * (2)^2 + 3 * 2 + 1 = 4
g(2) = 2 * 2 = 4
Both functions align, confirming the correctness of the reported intersection point.
Graph B (Intersection at (4, 1)):
f(4) = -3/4 * (4)^2 + 3 * 4 + 1 = 1
g(4) = 2 * 4 = 8
There is a discrepancy here, as the y-values do not match. Therefore, graph B does not accurately represent the functions f(x) and g(x).
In conclusion, graph A is correct since it accurately reflects the given functions and results in the reported intersection point (2, 4).
Need help ASAP
Simplify using only positive exponents
1.) 3^2•3^4
2.) (2x^2)^-4
3.) 2x^4y^-4z^-3
————————-
3x^2y^-3z^4
Part (1) : The solution is [tex]729[/tex]
Part (2): The solution is [tex]$\frac{1}{16 x^{8}}$[/tex]
Part (3): The solution is [tex]$\frac{2 x^{2}}{3 y z^{7}}$[/tex]
Explanation:
Part (1): The expression is [tex]3^{2} \cdot3^{4}[/tex]
Applying the exponent rule, [tex]$a^{b} \cdot a^{c}=a^{b+c}$[/tex], we get,
[tex]$3^{2} \cdot 3^{4}=3^{2+4}$[/tex]
Adding the exponent, we get,
[tex]3^{2} \cdot3^{4}=3^6=729[/tex]
Thus, the simplified value of the expression is [tex]729[/tex]
Part (2): The expression is [tex]$\left(2 x^{2}\right)^{-4}$[/tex]
Applying the exponent rule, [tex]$a^{-b}=\frac{1}{a^{b}}$[/tex], we have,
[tex]$\left(2 x^{2}\right)^{-4}=\frac{1}{\left(2 x^{2}\right)^{4}}$[/tex]
Simplifying the expression, we have,
[tex]\frac{1}{2^4x^8}[/tex]
Thus, we have,
[tex]$\frac{1}{16 x^{8}}$[/tex]
Thus, the value of the expression is [tex]$\frac{1}{16 x^{8}}$[/tex]
Part (3): The expression is [tex]$\frac{2 x^{4} y^{-4} z^{-3}}{3 x^{2} y^{-3} z^{4}}$[/tex]
Applying the exponent rule, [tex]$\frac{x^{a}}{x^{b}}=x^{a-b}$[/tex], we have,
[tex]\frac{2x^{4-2}y^{-4+3}z^{-3-4}}{3}[/tex]
Adding the powers, we get,
[tex]\frac{2x^{2}y^{-1}z^{-7}}{3}[/tex]
Applying the exponent rule, [tex]$a^{-b}=\frac{1}{a^{b}}$[/tex], we have,
[tex]$\frac{2 x^{2}}{3 y z^{7}}$[/tex]
Thus, the value of the expression is [tex]$\frac{2 x^{2}}{3 y z^{7}}$[/tex]
Hank and debra each own two milking cows. One day, they milked their cows and compared the amount of milk the cows prodyce in that one day. How many more gallons of milk did debras two cowsbprodyce on that day compared to hanls two cows?
Debra's cows produced [tex] 2 \frac{7}{24}[/tex] more gallons than Hank's cows.
Hank's cows :
4¾ + 4⅛ = 8⅞Debra's Cows :
5½ + 5⅔ = 11⅙The difference in amount of Milk produced :
Sum of Debra's cow - Sum of Hank's cows
Now we have:
11⅙ - 8⅞
67/6 - 71/8 = (536 - 426) / 48
67/6 - 71/8 = 110/48
110/48 = [tex] 2 \frac{7}{24}[/tex]
Hence, Debra's cows produced [tex] 2 \frac{7}{24}[/tex] more gallons than Hank's cows.
The golden state bridge is 8980 feet long .For a science project , garbriel built a scale model of the bridge . How long is the model if he used the scale.1 millimeters equals 20 feet/
Answer:
449 millimeters.
Step-by-step explanation:
Each millimeter corresponds to 20 feet.
Therefore the length of the model = 8980 / 20 = 449 millimeters.
Answer:
HI! I'VE DONE THIS B4, IT IS 449 MILLIMETERS. DOES ANYONE KNOW HOW TO TURN THE CAPS BUTTON OFF? ANYWAYS, PLZ MARK BRAINLIEST
Step-by-step explanation:
A cube of mass m 1 = 7.0 kg is sitting on top of a second cube of the same size and mass m 2 = 0.7 kg while both are in free fall. Ignoring any air resistance, what is the magnitude of the normal force with which the bottom cube is acting on the top cube?
Answer:
0 N
Step-by-step explanation:
We are given that
[tex]m_1=7 kg[/tex]
[tex]m_2=0.7 kg[/tex]
Total mass =[tex]m_1+m_2=7+0.7=7.7 Kg[/tex]
We have to find the magnitude of the normal force with which the bottom cube is acting on the top cube.
When both cube are fall freely then
g=[tex]0m/s^2[/tex]
Then, the weight=[tex]mg=7.7\times 0=0 N[/tex]
The direction of weight is downward.
We know that
Normal force is equal to weight and act in opposite direction of weight.
When the weight is zero N then
The magnitude of the normal force with which the bottom cube is acting on the top cube=0 N
The radius of the earth is 4000 miles. How fast is someone on the equator moving compared to someone at the north pole due to daily rotation of the Earth (in miles per hour)?
Answer: speed at the equator =
1047.33 miles per hour
Step-by-step explanation:
The radius of earth is 4000miles
The earth rotates on its axis, hence we calculate the circumference at the equator
Circumference, C = 2 π R
C = 2 x 3.142 x 4000miles
C = 25,136 miles
Since the total time of one complete rotation about it's axis is 24hours
Hence, the speed at the equator is
speed = 25,136/24 = 1047.33 miles per hour
The speed of the person on the equator due to daily rotation of the earth is;
Speed = 1047.221 miles per hour
We are told that the radius of the earth is; R = 4000 miles.Formula for circumference is;
C = 2πR
Thus;
C = 2 × π × 4000miles
C = 25,132.74 miles
C ≈ 25133 miles
Now, the time it takes for the earth to complete one full rotation about it's axis is 24 hours.
We know that formula for speed is;
speed = distance/time
Thus;
Speed on the equator is;
speed = 25133/24 = 1047.221 mph
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Janay is constructing a triangle using wire an art project.She has 3 inches of purple wire and 7 inches of pink wire.Janay is going to buy some blue wire for the third side of her triangle
For Janay's art project, the blue wire must be longer than 4 inches and shorter than 10 inches to create a triangle. This is based on the Triangle Inequality Theorem, which states that the length of any side of a triangle should be less than the sum of the lengths of the other two sides, but more than the difference of the two sides' lengths.
Explanation:To determine how long the blue wire should be for Janay's art project, we need to understand a rule in geometry related to triangles, specifically the Triangle Inequality Theorem. This theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides.
Here, we have side lengths of 3 inches (purple wire) and 7 inches (pink wire), so the blue wire can be any length that is less than 3+7=10 inches, and more than |7-3|=4 inches. So the blue wire should be more than 4 inches and less than 10 inches to form a triangle.
This ensures that Janay will be able to form a valid triangle for her art project. If the length of the blue wire is less than 4 inches or greater than 10 inches, a triangle cannot be formed.
Learn more about Triangle Inequality Theorem here:https://brainly.com/question/1163433
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The temperature is 71 °F at 2:00 in the afternoon. If the temperature drops 8 °F every hour after that, what is the temperature at 6:00 in the evening?
Answer = _____ F
Answer:
The answer is 39 degrees by 6:00 in the evening.
Step-by-step explanation:
Since it is 2:00 in the afternoon and there is 4 hours, with 8 degrees dropping every hour, 8 times 4 equals 32, so 71 degrees minus 32 degrees is 39 degrees.
Answer: the temperature at 6:00 in the evening is 39°F
Step-by-step explanation:
If the temperature drops 8 °F every hour after that, then the rate is linear and the rate at which the temperature is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
From the information given,
a = 71 °F
d = - 8 °F (since it is decreasing)
n = 5 (2pm to 6pm)
We want to determine the value of the 5th term, T5. Therefore,
T5 = 71 - 8(5 - 1)
T5 = 71 - 32 = 39
Let V be a vector space and assume that T, U, W are sub spaces of V. Show that if T cup U W is a sub space of V, then two of these subspaces must be contained in the other one?
Answer: T⊂U⊂W are subspaces of V
Step-by-step explanation:
Proof: This is the easier direction.
If T⊂U⊂W or W⊂U⊂T then we have U⊂T⊂W = T or T⊂U⊂W = U
orT⊂U⊂W=W respectively.
SoT⊂U⊂W is a subspace as T, U and W are subspaces.
1st case :T⊂U⊂W is true Then the disjunction W⊂U⊂T or U⊂T⊂W is trivially true.
Let x∈W1 and y∈W2−W1.
By the definition of the union, we have x∈W∪T∪C and y∈T⊂U⊂W
As T∪U∪W is a subspace, x+y∈T∪C∪W which, again by the definition of the union, means that x+y∈W∪T∪C
V∈W∪T∪C
As V was arbitrary, as desired.
Final answer:
If T ∪ U ∪ W is a subspace of V, then two of the subspaces must be contained in the other one.
Explanation:
If T ∪ U ∪ W is a subspace of V, then two of the subspaces must be contained in the other one. We can prove this by contradiction. Assume that none of the subspaces is contained in the other. This means that there is an element in T that is not in U ∪ W, an element in U that is not in T ∪ W, and an element in W that is not in T ∪ U. If we take any two of these elements, one from each subspace, and add them together, the result will not be in T ∪ U ∪ W, which contradicts the assumption.
Therefore, two of the subspaces must be contained in the other one.
The sun subtend an angle at 35degree from the centre of the earth whose distant from the centre of the earth is 382,100km. Find the diameter of the sun
Study the figure attached below:
Answer:
240951.33km
Step-by-step explanation:
For this type of question first we need to draw the figure as shown in the attached file (Figure.1).
Looking at the figure, we can see that triangle ABC is formed by bisecting the angle 35 degree (i.e. if the angle is bisected, it will divide into two equal parts, so 35 degree will divide into two equal parts of 17.5 degree).
As the triangle ABC is a right triangle, so we can use the trigonometric ratios to find the diameter of the sun.
[tex]tan(\theta )= \frac{perpendicular}{Base}[/tex]
In the triangle ABC, perpendicular (opposite side to [tex]\theta[/tex] ) is BC and base (Adjacent side) is AC
[tex]tan(\theta)=\frac{BC}{AC}[/tex]
[tex]\theta[/tex]=17.5 degree
AC=382100km
Putting the values, we get
[tex]tan(17.5)=\frac{BC}{382100}\\ \\BC=tan(17.5)*382100km\\\\BC=0.315*382100km\\\\BC=120475.66km[/tex]
Diameter=d=2*Radius
As BC is the distance from center of the sun, it is the radius, so we can find the diameter if we multiply it by 2.
Diameter of the sun=d=2*120475.66km
[tex]The\ diameter\ of\ the\ sun\ = 240951.33km[/tex]
Final answer:
To find the diameter of the Sun based on its angular diameter and distance from Earth, use the trigonometric function tan to calculate the true diameter, resulting in an approximate value of 865,373 miles.
Explanation:
To find the diameter of the Sun:
Given: Angular diameter = 0.5°, Distance from Earth = 93,000,000 milesCalculate the true diameter using the formula: True Diameter = 2 * Distance * tan(Angular diameter)Plug in the values: True Diameter = 2 * 93,000,000 * tan(0.5°)After calculation, the diameter of the Sun is approximately 865,373 miles.