To find the number of years it takes for an investment to grow to a certain value at a certain interest rate, you can use the formula:
n = (future value - principal) / (principal * interest rate)
Where:
n = number of years
future value = the final value of the investment
principal = the initial amount invested
interest rate = the annual interest rate as a decimal
Plugging in the given values:
n = (21150 - 5000) / (5000 * 0.17)
n = 16.65
Rounding to the nearest whole number, it would take approximately 17 years for the investment to be worth $21,150.00.
The bill is 19.37 find the amount of a 15% tip
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 19.37}}{\left( \cfrac{15}{100} \right)19.37} ~~ \approx ~~ 2.91[/tex]
there is an angle $\theta$ in the range $0^\circ < \theta < 45^\circ$ which satisfies \[\tan \theta \tan 2 \theta \tan 3 \theta
The solution of the below trignometric equation are θ= mπ , θ= nπ/3
Given tan θ + tan 2θ = tan 3θ
=> tan θ + tan 2θ - tan 3θ = 0
(tanθ + tan2θ)−(tanθ + tan2θ)/(1 - tanθ tan2θ) =0
or (tanθ + tan2θ)(1 − tanθ tan2θ−1)=0
or tanθ tan2θ(tanθ + tan2θ) = 0
tanθ = 0
∴θ=nπ, tan2θ=0,
∴2θ=nπ or θ=nπ/2
tanθ + tan2θ=0
or sin(θ+2θ)=0
∴θ=nπ/3
However, the values of given by =n/2 for odd values of n do not fulfill the preceding equation as it will result in ∞ = ∞
Hence the required solution is:
θ= 2mπ/2=mπ
θ= nπ/3
where m and n is an integer
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Complete question:
Find the general solution of the equation tan θ + tan 2θ = tan 3θ
Part A
In a major league baseball park, the pitching rubber, where the pitcher stands, is always 60.5 feet from home plate, where the batter stands. In Widget Stadium, the distance from home plate to the wall in center field is 450 feet.
A major league baseball pitcher throws a baseball with a horizontal velocity of 132 feet/second. The batter then hits the ball with a horizontal velocity of 141 feet/second, which results in a home run when the baseball passes over the center field fence. The ball passes over the pitching rubber on its way out of the stadium
Ignoring gravity and the air resistance that would slow the baseball down, create an equation to model the distance that the baseball is from the pitching rubber once it is thrown. (Hint: distance = velocity × time.)
Answer:
The distance that the baseball is from the pitching rubber, D, can be modeled using the equation:
D = V*t + 60.5
Where V is the horizontal velocity of the baseball in feet per second and t is the time in seconds that the baseball is in the air.
In this scenario, the baseball is thrown by the pitcher with a horizontal velocity of 132 feet/second, and then hit by the batter with a horizontal velocity of 141 feet/second. The baseball passes over the pitching rubber on its way out of the stadium and eventually passes over the center field fence, 450 feet away. So, the equation will be
D = (132+141) * t + 60.5
given: ab=bc, ae=fc
prove m < aec=m < afc
rsm problem pls help
∆AEC ≅ ∆AFC by reason of SAS. Thus, using CPCTC, we can prove that <AEC ≅ <AFC.
How to Write a Congruence Proof?With the given information and the image attached below, we can state that the two triangles are congruent by SAS, and then go ahead to use the CPCTC to show that any of their corresponding parts are congruent as well.
The proof is given as:
Statement Reason
1. AB ≅ BC, AE ≅ FC 1. Given
2. AC ≅ AC 2. Reflexive property of congruence
3. <BAC ≅ <BCA 3. Base angles of isosceles ∆BAC
4. ∆AEC ≅ ∆AFC. 4. SAS
5. <AEC ≅ <AFC. 5. CPCTC
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substituting this back into the equation for f(x, y), we can now conclude that the potential function for f is
The potential function for f(x,y) is given by f(x,y) = x^2 + y^2 + 2xy.
The potential function can be used to find the maximum value of f by taking the partial derivatives with respect to x and y, setting them equal to zero, and solving for the x and y values that correspond to the maximum. This will give the x and y values that will produce the maximum value of f.
To prove this, we can start by taking the partial derivatives of f(x,y), which are given by:
f_x = 2x + 2y
f_y = 2y + 2x
Therefore, the potential function for f(x,y) is equal to the integral of the partial derivatives with respect to x and y:
∫f_xdx + ∫f_ydy = x^2 + y^2 + 2xy
This shows that the potential function for f(x,y) is given by f(x,y) = x^2 + y^2 + 2xy.
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Complete question: What is the potential function for the function f(x, y) = x + y + xy?
Can someone help me with this?
Answer:
9
Step-by-step explanation:
parenthesis
exponents
multiply
división
add
Subtract
do it in this order and it makes it 10 times easier
Classify these events. Selecting a king from a deck of cards, replacing it and selecting a queen from the same deck. These events would be considered:
Group of answer choices
A) Subjective
B) Empirical
C) Independent
D) Dependent
Picking a king from a deck of cards, swapping it out for a queen, then continuing. These occurrences would constitute Dependent events.
'What is dependent probability?'
A dependent variable is precisely what it sounds like, just like an independent variable. It is something on which other elements depend.
A test score, for instance, may be a dependent variable because it could vary based on a number of variables, including how much you studied, how much sleep you got the night before the test, and even how hungry you were. Typically, when attempting to establish a connection between two variables, the goal is to determine what causes the dependant variable to vary in the manner that it does.
Many people struggle to recall which variable is the independent variable and which variable is the dependent variable.
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Suppose that h(x) is a continuous function and is defined for all x greater than or equal to 1. You are given that h(x) has critical points at x = 1, x = 3, and x = 5. If h'(x) is negative on the interval 1 < x < 3, positive on the interval 3 < x < 5, and positive on the interval x > 5, what can be said about the point (3, h(3))? O (3, h(3)) is an absolute maximum.O (3, h(3)) is an absolute minimum. O (3, h(3)) is neither an absolute maximum nor an absolute minimum. O Nothing can be determined about the point (3, h(3)).
An absolute maximum point is where the function reaches its highest value.
What is the difference between absolute maximum and absolute minimum?A function may have more than one location (x values) or point (ordered pairs) where these values occur, but there can be only one absolute minimum value and one absolute maximum value (in a given closed interval).
A point where the function achieves its highest value is known as an absolute maximum point. Similar to this, an absolute minimum point is the location at which the function's maximum value is obtained.
Minimum refers to the bare minimum that can be done. For instance, if anything requires seven dollars as the minimum payment, you cannot make a payment of six or less (you must pay at least seven). More than the bare minimum is acceptable, but not less. Maximum refers to the greatest quantity of anything.
Therefore, the correct answer is option C) (3, h(3)) is neither an absolute maximum nor an absolute minimum.
The complete question is:
Suppose that h(x) is a continuous function and is defined for all x greater than or equal to 1. You are given that h(x) has critical points at x = 1, x = 3, and x = 5. If h'(x) is negative on the interval 1 < x < 3, positive on the interval 3 < x < 5, and positive on the interval x > 5, what can be said about the point (3, h(3))?
A) (3, h(3)) is an absolute maximum.
B) (3, h(3)) is an absolute minimum.
C) (3, h(3)) is neither an absolute maximum nor an absolute minimum.
d) Nothing can be determined about the point (3, h(3)).
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Prove divisability
will mark the brainliest!
Step-by-step explanation:
We can prove without use of calculator.
Use exponent product rule:
[tex]a^{n+m} = a^{n}*a^{m}[/tex]
Rewrite with exponent power rule:
[tex](9*9*9*9)-(3^{2}*3^{2}*3^{2}*3)[/tex]
Since [tex]3^{2}=9[/tex], we can eliminate 3 pairs via subtraction, leaving us with:
[tex]9-3=6[/tex]
6 is divisible by 6.
Easy without calculator :)
Hope this helps.
The sum of a number k and t is 11
The mathematical sentence can be written as the equation below,
k + t = 11
How to write the sentence as an equation?Here we want to write the the mathematical sentence below:
"The sum of a number k and t is 11"
As an algebraic equation, so let's analyze each part of the mathematical sentence.
"sum" refers to an addition, in this case between two numbers represented by k and t, then we can write:
k + t
And that is equal to 11, then the equation will just be:
k + t = 11
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The gate code at your apartment complex is three numerical digits followed by the "#" sign. If each code
contains non-repeating digits, how many possible gate codes does your apartment complex have
If each code contains non-repeating digits there would be 720 possible gate codes.
What is a combination in mathematics?
Combination in mathematics is a way of selecting items from a set, without regard to the order in which they were chosen.
In your example, there are 10 possible digits (0-9) that can be used for each of the three numerical digits, but since the digits cannot repeat, the total number of possible gate codes is 1098 = 720. Since the "#" sign is not included in this calculation, the final answer is 720 possible gate codes.
Hence, If each code contains non-repeating digits there would be 720 possible gate codes.
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Translate the sentence into a mathematical equation-
The total revenue derived from selling x refrigerators is $160 per refrigerator times the number of refrigerators sold.
Let R represent the revenue and x the number of refrigerator sold.
The sentence into a mathematical equation is R = 160x
How to translate the sentence into a mathematical equation?The sentence "The difference between a number and ten is four" can be translated into a mathematical equation as:
x - 10 = 4
To solve for x, we can add 10 to both sides of the equation. This will give us:
x - 10 + 10 = 4 + 10
x = 14
Therefore, the number is 14.
More generally speaking, we can say that the equation for this sentence is x - a = b, where a is the number we are subtracting (in this case 10) and b is the result of the subtraction (in this case 4). To solve for x, we add a to both sides of the equation, giving us x = a + b.
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khalil is working two summer jobs, making $18 per hour tutoring and $9 per hour landscaping. last week khalil worked a total of 14 hours and earned a total of $180. graphically solve a system of equations in order to determine the number of hours khalil worked tutoring last week, x,x, and the number of hours khalil worked landscaping last week, yy.
10 number of hours khalil worked tutoring last week and 3 the number of hours khalil worked landscaping last week
given that
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a b indicates that an is smaller than b.
When a > b is used, it indicates that an is bigger than b.
A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.
khalil is working two summer jobs, making $18 per hour tutoring
$9 per hour landscaping
last week khalil worked a total of 14 hours and earned a total of $180.
let x be number of hours khalil worked tutoring last week
y be the number of hours khalil worked landscaping last week
we can form equation by given information
x + y [tex]\leq[/tex] 13 - (1)
18x + 9y > 180 - (2)
the numbers that satisfy the above equations is (10,3)
10 number of hours khalil worked tutoring last week and 3 the number of hours khalil worked landscaping last week
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Steven wants to buy some candy with his birthday money. He can choose from Jelly Belly jelly beans that sell for $5.99 per pound and Brach's variety that sells
for $3.99 per pound. He likes to have twice the amount of Jelly Belly jelly beans as Brach's variety. If he spent a total of $63.88 how many pounds of each type of candy did he buy?
Part 1 of 2
Steven bought (blank) lb of Jelly Belly jelly beans
Part 2 of 2
Steven bought (blank) lb of Brach's variety.
Answer:
Jelly bean is 8 pound
Brach's variety is 4 pound
Step-by-step explanation:
jelly belly = x
brach's variety = y
5.99x + 3.99y = 63.88 _______(1)
x = 2y ______(2)
5.99x + 3.99y = 63.88
5.99(2y) + 3.99y = 63.88
11.98y + 3.99y = 63.88
15.97y = 63.88
15.97y/15.97 = 63.88/15.97
y = 4
Substitute y = 4 into equ 2
x = 2y
x = 2(4)
x = 8
Therefore, Steven bought 8 lb of jellybean and 4 lb of brach variety
the general solution to a linear system is given. express this solution as a linear combination of vectors. x1
The linear combination of the general solution of system of equations is.
[tex]X=(7,-3,0)+S1(-2,0,1)\\[/tex].
A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. A linear system in three variables determines a collection of planes The intersection point is the solution.
A linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results.
Write vector form of the equations, then the vector with variable can expressed as a linear combination of vectors on right sides.
[tex](x1,x2,x3)=(7-2S1,-3,S1)\\=(7,-3,0)+(-2S1,0,S1)\\\\=(7,-3,0)+S1(-2,0,1)[/tex]
So, the linear combination of vectors is.
[tex]X=(7,-3,0)+S1(-2,0,1)\\[/tex]
The complete question is,
the general solution to a linear system is given. express this solution as a linear combination of vectors.
x1=7-2S1
X2=-3
X3=S1.
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2c-10<3c-9 solve the following inequality
Answer:
[tex]c > -1[/tex]
Step-by-step explanation:
[tex]2c-10 < 3c-9\\-10 < c-9\\-1 < c\\c > -1[/tex]
the first part of the problem asks them to calculate the work done on the gas when the gas goes from the initial state to the final state shown. here is part of their dialogue: nora: the gas is compressed because the volume decreases. that means that there is work done on the gas, and the work is positive. bob: ok. that's right because we're using the first law with q w. we need to use that area thing to find the work. nora: yeah. we want the area under the line between the dots. bob: that line shows the process, right? nora: yup, that's the one. so the area is one-half times base times height. it's the area of that triangle. bob: but you have to add the area of that skinny rectangle below it, don't you? nora: i don't think so. that bottom dot for the final state tells you where the bottom of the area is. bob: why don't we ever agree? tell you what. we'll each try our own way and let webassign tell us who's right. nora: hmmm... i hope i get the big, green check mark!
To determine how much effort the gas undergoes as it changes from its original condition to its final one, Nora and Bob utilize the area underneath the line separating the two states and the first rule of thermodynamics.
When a gas changes from its initial condition to its final state, Nora and Bob explain how to compute the work that is done. They talk about compressing gas, thus something is being done to the gas.
You suggest using the area under the line separating the final and initial states to calculate the work done as well as the application of the first equation of thermodynamics, q=w.
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The depth , in inches, of snow in my yard hours after it started snowing this morning given by =1.4+3. If the depth of snow is 9 inches now, what will the depth be one hour from now?
The depth of snow in the yard one hour after the snow depth was 9 inches, obtained using the linear function used for finding the snow depth, D = 1.4·t + 3 is; 10.4
What is a linear function?A linear function is a function that produces a straight line graph when plotted.
The function that can be used to calculate the depth of the snow D in inches is; D = 1.4·t + 3
Where;
D = The snow depth in inches
t = The time duration (hours)
The present depth of the snow = 9 inches
The depth of the snow one hour from now can be found as follows;
The function for the depth of the snow; D = 1.4·t + 3 is a linear function
Therefore, the slope, which is the coefficient of the input variable, t, when the coefficient of the output variable, D, is 1
Therefore, the slope = 1.4
The slope is the rate of change of the output variable D when the input variable increases by one unit
The slope therefore, indicates that the depth of the snow in the yard, increases by 1,4 inches per hour
If the depth of the snow is presently 9 inches, the depth of the snow 1 hour later is therefore; D = 9 inches + 1.4 inches = 10.4 inches
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Jack spins a fair six-sided spinner 240 times. What is the probability that he will score more than 45 sixes?
Give your answer to 2 d.p.
The probability that Jack will score more than 45 sixes in 240 spins of the spinner is about 0.13%.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain.
The probability of getting a six on one spin of a fair six-sided spinner is 1/6. If Jack spins the spinner 240 times, the expected number of sixes he will get is 240 * 1/6 = 40.
We can use a normal approximation to the binomial distribution to find the probability that Jack will get more than 45 sixes. The mean of the distribution is 40 and the standard deviation is the square root of the variance, which is the product of the number of spins and the probability of getting a six on each spin, divided by the number of trials:
Standard deviation = sqrt(240 * 1/6 * 5/6 / 240) = sqrt(40/240) = sqrt(1/6)
Using the normal approximation, the probability that Jack will get more than 45 sixes is equal to the probability that a standard normal random variable is greater than (45 - 40) / sqrt(1/6) = 5 / sqrt(1/6) = 5 * sqrt(6).
Using a standard normal table or a calculator, this probability can be found to be approximately 0.0013, or 0.13%.
Hence, the probability that Jack will score more than 45 sixes in 240 spins of the spinner is about 0.13%.
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scientist do not accept a nutrition or scientific hypothesis until it has been thoroughly tested using the
The scientific method is a systematic set of method that scientists follow to gain information. we will explore how the scientific method is used in the study of nutrition.
To make the things simple, you might want to think of the scientific method as a pro way to ask questions and find answers. With this in mind, it makes sense that the stride of the scientific method starts when researchers ask questions.
For example, a research scientist might awe whether people who eat an apple a day visit their family doctor hardly times a year than those who do not eat apples.
The scientific method is a nice tool for analyzing nutrition. It has been used to set nutrition advice, understand how nutrients support health and learn how nutrition supports athletic account.
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What quantity of 60% chlorine solution must be mixed with a 18% chlorine solution to produce 542.5 mL of 42% solution?
Answer: ___mL
The quantity of chlorine that has a 60% concentration is 310 ml.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given that, 60% chlorine solution must be mixed with an 18% chlorine solution to produce 542.5 mL of 42% solution
Let "x" be the quantity of chlorine that has a 60% concentration
So, the quantity of chlorine that has 18% concentration = 542.5 - x
thus, As per the given data expression formed as given below:
0.6 * x + 0.18 (542.5 - x) = 542.5 * 0.42
0.6x - 0.18x + 0.18 *542.5 = 542.5 *0.42
0.42x = 130.20
x = 310
therefore, the quantity of chlorine that has a 60% concentration is 310 ml.
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There are three consecutive even integers. If twice the first integer added to the second is 268,220 . Find all three integers
The three integers are 89,406, 89408 and 89410.
What are integers?
The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
Let 'm' be a positive integer.
Then, 2m is an even integer ( as multiplying by 2 makes the number even)
So, 2m+2 is the next integer and 2m+4 is the next.
Now, we have three consecutive integers as 2m, 2m+2 and 2m+4.
We are given that twice the first integer added to the second is 2,68,220, this means
⇒2(2m) + (2m+2) = 2,68,220
⇒4m + 2m + 2 = 2,68,220
⇒6m + 2 = 2,68,220
⇒6m = 2,68,218
⇒m = 44,703
So, 2m = 89,406
2m+2 = 89408
2m+4 = 89410
Hence, the three integers are 89,406, 89408 and 89410.
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HELP ASAP TIMED FAST
The value of the missing length is 44.
Properties of similar triangles.Two or more triangles will be similar if on comparing their corresponding sides or measure of angles, some common properties can be observed. But when two or more shapes are similar, it do not imply that they are equal.
To find the value of the missing length, let the length LV be represented by s.
So that;
VN/ LN = NU/ MN
11/ (11 + s) = 8/ (24 + 8)
11/ (11 + s) = 8/ 32
cross multiply to have;
8(11 + s) = 11 *32
88 + 8s = 352
8s = 352 - 88
= 264
s = 264/8
= 33
Therefore, the missing length = 11 + 33
= 44
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Find the degree measure of each interior angle of quadrilateral PQRS.
Note: Figure not to scale.
angle s= 2yº
angle p= 3yº
angle q= 4y°
angle r= y°
S=72, P=108, Q=144, and R=36 are the degree measures for each quadrilateral angel.
Calculating the angles:Since the sum of all angles is 360.
∠S+∠P+∠Q+∠R=360
2y+3y+4y+y=360
10y=360
y=36.
Hence, we get ∠S=72, ∠P=108, ∠Q=144 and ∠R=36.
Name some of the properties of the quadrilateral and explain what it is?A polygon with four sides, four vertices, and four angles is called a closed quadrilateral. It is made by joining four non-collinear points together. In all cases, the inner angles of quadrilaterals add up to 360 degrees.
Do the interior angles of all quadrilaterals add up to 360?The fact that the sum of the interior angles is always equal to 360 degrees is a property shared by all of the above four-sided shapes. Each interior angle of a regular quadrilateral, such as a square, will be equal to: 90 degrees is 360/4.
Are there four equal angles in every quadrilateral?They split in two directions. There are both regular and irregular quadrilaterals. The diagonals of a regular quadrilateral must cross each other and have four equal sides and angles. The only quadrilateral that meets all of these requirements is square
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The sum of four consecutive integers is 105. What are the integers?
The following data show the amount (in ounces) of beverage in randomly selected 16-ounce beverage cans. Create a Stem-Leaf plot for these data.
15.8
16.1
15.2
14.8
15.8
15.9
16.0
15.5
16.1
15.7
Fill in the blanks of table below to complete the Stem-Leaf plot for these data. The key is 15|2 = 15.2. Sort the values for Leaf in increasing order and do not keep spaces or commas between leaves.
Stem
Leaf
14
15
16
(a)
(b)
(c)
The 5th value is 15.5, and the 6th value is 15.7. The median is then (15.5 + 15.7)/2 = 15.6.
A Stem-Leaf plot is a graphical way to organize and summarize numerical data. It is composed of two columns, the stem and the leaf. The stem column contains the leading digits of the data values, while the leaf column contains the remaining digits.
For the given data set, the stem-leaf plot looks like this:
Stem Leaf
14 8
15 2 8 5 7 9
16 0 1
To create this stem-leaf plot, the data values were first sorted in ascending order, and then the leading digits were placed in the stem column. The remaining digits were then placed in the leaf column, in increasing order. The key, 15|2=15.2, is an example of a data value from the set.
To calculate the median of the data set, we first need to find the number of values in the set. Since there are 10 values, the median will be the average of the 5th and 6th values.
The 5th value is 15.5, and the 6th value is 15.7. The median is then (15.5 + 15.7)/2 = 15.6.
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Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. Y=30(0.95)t
y = 30 ( 0.95 ) t y=30(0.95)^t y=30(0.95)t is an exponential decay function. Because 0.95 < 1 0.95<1 0.95<1. Therefore, 0.95 0.95 0.95 is the decay factor 1 − r 1-r 1−r.
What is meant by function ?
Functional refers to an object's operation or usefulness. It also denotes that it relates to how it performs or operates.A mathematical machine known as a function accepts one or more numbers as inputs and outputs another number.One or more functions may be inputs to a functional, which outputs a number. A Functional is a function of Functions, then.All biological activities, including digestion, elimination, respiration, and others, can be performed by a cell.The functional unit of life is referred to be such for this reason. Each and every living thing is made up of cells, which are the smallest unit of life.To learn more about function refer to
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Identify whether the statement represents an exponential function. Explain.A population of bacteria decreases by a factor of 18 every 24 hours.Yes, the statement is an exponential function because the population decreases daily by a proportional rate.Yes, the statement is an exponential function because the population decreases daily by a constant rate.No, the statement is not an exponential function because the population decreases daily by a proportional rate.No, the statement is not an exponential function because the population decreases daily by a constant rate.No, the statement is not an exponential function because it is a quadratic function.
Option A is correct i.e., Yes, the statement is an exponential function because the population decreases daily by a proportional rate.
Exponents in mathematics are usually defined as when a number or an expression is given a specific power. The number to which the power is assigned is multiplied power times itself to get the final value. It is depicted by raised symbol written beside the number or expression.
It is written as a∧b where a is the base and b is the power and is called b to the base a or a raised to bth power. An example of the same can be 2∧3= 2x2x2=8, [tex]a^{3}[/tex]=axaxa, etc.
There are some properties of exponents like
[tex]a^{b}[/tex] + [tex]a^{c}[/tex]= a∧bc E.g., [tex]2^{3}[/tex]+[tex]2^{4}[/tex]=[tex]2^{3.4}[/tex] =[tex]2^{12}[/tex][tex]a^{0}[/tex]=1 E.g., [tex]2^{0}[/tex]=1[tex]a^{(-3)}[/tex]=1/[tex]a^{3}[/tex] = [tex]3^{(-4)}[/tex]=1/[tex]3^{4}[/tex]To know more about exponents visit
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what is the width of an rectangle with a length of 3/7 ft and a area of 2ft²? write an equation to show your work.
Width of the rectangle is 14/3 feet.
What is Rectangle?Rectangle is a two dimensional figure which has four sides and four angles and all the angles are right angles.
Area of a rectangle = Length × Width
Length = 3/7 feet
Area = 2 feet²
Substituting in the equation for the area,
2 = 3/7 × Width
Width = (2 × 7) / 3
= 14/3 feet
Hence the measure of width of the rectangle is 14/3 feet.
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The quarter circle of radius R in the first quadrant (x' + y' = R2 for x ) 0 and
y > 0) is revolved about the x-axis to produce a hemisphere. Find the volume of the hemisphere in the following three ways:
a. Apply the disk method and integrate with respect to x.
b. Apply the shell method and integrate with respect to y.
c. Apply the general slicing method and integrate with respect to y.
The volumes of the hemisphere are (π/12)R³, 2π/3(R³) and π/3(R³)
How to determine the volumes of the hemisphereFrom the question, we have the following parameters that can be used in our computation:
x' + y' = R²
Using the disk method
Start by calculating the area of a single disk is given by the quarter circle of radius R in the first quadrant.
The area of the single disk is:
Area = π(R/2)²
The volume of the hemisphere using the disk method is given by:
V = ∫(π(R/2)² dx from 0 to R
This gives
V = (π/4) * ∫R^2 dx from 0 to R
Differentiate
V = (π/12)R³
Using the shell methodHere, we first need to find the area of a single shell.
The area of the single shell is:
Area = 2πx * dx
The volume of the hemisphere using the single shell method is given by:
V = ∫(2π x * dx)dy from 0 to R
So, we have
V = 2π * ∫xdy*dx from 0 to R
Differentiate
V = 2π/3(R³)
Using the general slicing methodHere, we can use any slicing method, such as slicing the hemisphere parallel to the y-axis.
The volume of the hemisphere using the general slicing method is given by:
V = ∫(π * (x^2) * dy) from 0 to R
So, we have
V = π * ∫(y^2)dy from 0 to R
Differentiate
V = π/3(R³)
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