Step-by-step explanation:
TSA of cylinder = 2πr (h + r)
according to the question
height = radius
then,
TSA = 2πr (r + r)
2464=2 × 3.1415×r ×2r
2464/4 ×3.1415 = r×r
196.08 = r^2
r = 14.00
r = 1 4 cm
We know,
volume = 2πr ^2 ×h
=2×3.1415×14×14×14 (h=r)
=17240.552 cm^3
Answer:
8620.5 cm³
Step-by-step explanation:
h = r
SA = 2πrh + 2πr²
Since h = r, we can substitute h with r.
SA = 2πr² + 2πr² = 4πr²
4πr² = 2464 cm²
r = 14 cm
V = πr²h
r = h = 14 cm
V = π(14 cm)²(14 cm)
V = 8620.5 cm³
using a number line, find both the intersection and the union of following intervals: [1,5] and (0,8]
How many nonzero terms of the maclaurin series for ln(1 x) do you need to use to estimate ln(1. 4) to within 0. 0001?
We need at least 7 terms of the Maclaurin series for ln(1 + x) to estimate ln 1.4 to within 0.0001
For given question,
We have been given a function f(x) = ln(1 + x)
We need to find the estimate of In(1.4) within 0.001 by applying the function of the Maclaurin series for f(x) = In (1 + x)
The expansion of ln(1 + x) about zero is:
[tex]ln(1+x)=x-\frac{x^2}{2} + \frac{x^3}{3} -\frac{x^4}{4} +\frac{x^5}{5} -\frac{x^6}{6} +.~.~.[/tex]
where -1 ≤ x ≤ 1
To estimate the value of In(1.4), let's replace x with 0.4
[tex]\Rightarrow ln(1+0.4)=0.4-\frac{0.4^2}{2} + \frac{0.4^3}{3} -\frac{0.4^4}{4} +\frac{0.4^5}{5} -\frac{0.4^6}{6} +.~.~.[/tex]
From the above calculations, we will realize that the value of [tex]\frac{0.4^5}{5}=0.002048[/tex] and [tex]\frac{0.4^6}{6}=0.000683[/tex] which are approximately equal to 0.001
Hence, the estimate of In(1.4) to the term [tex]\frac{0.4^6}{6}[/tex] is enough to justify our claim.
Therefore, we need at least 7 terms of the Maclaurin series for function ln(1 + x) to estimate ln 1.4 to within 0.0001
Learn more about the Maclaurin series here:
https://brainly.com/question/16523296
#SPJ4
Write the equation of the line in point slope form given the information below slope =-1/5 Y-intercept =-3
Answer:
y = 1/5x -3
Step-by-step explanation:
Use y = mx +b as your model. We plug in our slope for me and our y-intercept for b.
A label on an empty sample container reads 10.000 g. You add in a sample of a compound and mass the sample container obtaining 13.54 g. What should the mass of the sample be reported as?
The mass of the sample should be reported as 3.54 g
The amount of matter in an object is expressed in terms of mass.
The most frequent way to determine mass is to weigh something.
The units of mass are grams, kilograms, tonnes (in metric units), or ounces and pounds (US units).
According to the question,
A label on an empty sample container reads 10.000 g
A sample of a compound is added and the mass of the sample container is found to be 13.54 g.
The mass of the sample should thus be reported as,
= 13.54 - 10.000
= 3.54 g
Learn more about mass here:
https://brainly.com/question/19385703
#SPJ1
NASA launched another space probe, Voyager 2 on August 20, 1977. Voyager 2 is a bit slower than Voyager 1 only traveling 15.4 km/s (34,449 miles per hour). Voyager 2 is 19.3 billion kilometers or 1.93 x 10^10 km (1.2 billion miles) away from the Earth. How many years will it take Voyager 2 from its location to travel to the second closest star (Proxima Centauri) which is 4.24 light years away from Earth? Include all your calculations in your answer. Recall that a light year is 9.5 x 10^12 kilometers.
Using proportions, it is found that it will take Voyager 2 82,900 years from its location to travel to the second closest star.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In this problem, the Voyager 2 travels 15.4 km/s. In kilometers per year, considering that one hour has 3600 seconds, the measure is given by:
15.4 x 365 x 24 x 3600 = 485,654,400 km/year.
The distance to Proxima Centauri in km is given by:
d = |1.93 x 10^10 km - 4.24 x 9.5 x 10^12 km| = 4.02607 x 10^13 km.
Hence the time in years is given by:
t = d/v = 4.02607 x 10^13/485,654,400 = 82,900.
It will take Voyager 2 82,900 years from its location to travel to the second closest star.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
How do I write a comment on the data following the completion of the box plot
We can comment that the maximum value of the given data is 0.2, maximum value is 42. The interquartile range is 15 to 37, first and third quartile values are 15 and 37 respectively. It can also be inferred from the box plot that there are no outliers. The median of the given data, as shown in the box plot, is 28.
What is a box plot?
A box and whisker plot, often known as a box plot, shows a data set's five-number summary. A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box. The five-number summary of a box plot includes the following:
Minimum Value Maximum ValueFirst quartileThird quartileMedianIt also tells if there are any outliers in the data.
Learn more about a box plot here:
https://brainly.com/question/1523909
#SPJ1
Find the length of AN given the figure below:
Answer:
21
Step-by-step explanation:
In the diagram, the three tangents (segment touching a circle at one point) have equal length.
6y - 3 = 29 - 2y
8y = 32
y = 4
Since the lengths of segments AM and AN are equivalent, we can substitute the value of y into the expression, 6y - 3, to find AN.
6y - 3 = 6*4 - 3 = 24 - 3 = 21
SOLVE 4x-6<-2
Help solve
The answer is x < 1.
Bring the constant to the other side.
4x - 6 < 24x < 4Divide by 4 on both sides.
4x ÷ 4 < 4 ÷ 4x < 1[tex]\Large\texttt{Answer}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad\space\space\qquad\qquad\qquad}}[/tex]
[tex]\Large\texttt{Process}[/tex]
[tex]\rm{4x-6 < -2}[/tex]
Do you remember that we need to get x by itself to find its value?
We should do this:
⇨ Add 6 to both sides
[tex]\rm{4x-6+6 < -2+6}[/tex]
On the left hand side (lhs), the 6s add up to zero; on the right hand side (rhs), the -2 and 6 result in 4. Hence
[tex]\rm{4x < 4}[/tex]
Now divide both sides by 4
[tex]\rm{\cfrac{4x}{4} < \cfrac{4}{4}}[/tex]
Simplifying fractions gives us
[tex]\rm{x < 1}[/tex]
* what this means is: numbers less than 1 will make the statement true
[tex]\Large\texttt{Verification}[/tex]
Substitute 1 into the original inequality [tex]\boxed{4x-6 < -2}[/tex]
[tex]\rm{4(1)-6 < -2}[/tex]
[tex]\rm{4-6 < -2}[/tex]
Do the arithmetic
[tex]\rm{-2 < -2}[/tex]
Hope that helped
At a football game
number of men : number of women : number of children = 13:5:7
There are 4152 more men then women.
Work out the number of children at the game
Answer:
Step-by-step explanation:
let the ratio of men women and children be 13x 5x and 7x
now
13x + 5x + 7x = 4152
25x = 4152
x = 4152/25
x = 166.08
A random sample has 49 values. The sample mean is 8.5 and the sample standard deviation is 1.5. Use a level of significance of 0.01 to conduct a left-tailed test of the claim that the population mean is 9.2. Compute the sample test statistic t. 0.005 0.0005 -2.267 -3.267
No,the population mean is not equal to 9.2 and the value in t statistic is -1.02.
Given sample size of 49,sample mean of 8.5,standard deviation of 1.5, significance level of 0.01.
We are required to find out whether the population mean is equal to 9.2 and the value of t in test statistic.
We have to first make the hypothesis for this.
[tex]H_{0}[/tex]:μ≠9.2
[tex]H_{1}[/tex]:μ=9.2
We have to use z statistic because the sample size is more than 30.
Z=(X-μ)/σ
We have been given sample mean but we require population mean in the formula so we will use sample mean.
Z=(8.5-9.2)/1.5
=-0.7/1.5
=-0.467
P value of -0.467 is 0.67975.
P value is greater than 0.01 so we will accept the hypothesis means population mean is not equal to 9.2.
t=(X-μ)/s/[tex]\sqrt{n}[/tex]
=(8.5-9.2)/1.5/[tex]\sqrt{49}[/tex]
=-0.7/0.21
=-1.02
Hence it is concluded that no,the population mean is not equal to 9.2 and the value in t statistic is -1.02.
Learn more about t test at https://brainly.com/question/6589776
#SPJ1
PLEASE I NEED HELP PLEASE
Answer:
i'll give you answer.Dont worry. Since i came back from school
A triangular garden is to be split so that the angle at vertex B is bisected. This diagram was supplied by the landscape architect, but you do not have a way to measure the angles at B. You do have the given side lengths, so what is the length of side that will allow the angle at B to be bisected?
A diagram shows a triangle ABC. BD is a line drawn to the base AC. The length of AB is 5 m, BC is 7 m, AD is x m, DC is 4 m, and AC is 12 m.
The AD's length of 3m will enable the angle at B to be divided in half.
Angle Bisector Theorem: What is it?
The angle bisector of a triangle divides the opposing side into two portions that are proportional to the other two sides, according to the angle bisector theorem, in simpler words the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.
The triangle has sides of 5, 7, and (x+4) m.
Angle B's angle bisector will only be the BD if
x/4 = 5/7
x = 5 *4 / 7
x = 20/7 = 2.85 ≈ 3m
Thus if AD has length of 3m then it will enable the angle at B to be divided in half.
Learn more about Angle Bisector Theorem here :
https://brainly.com/question/26036278
#SPJ1
Answer:
AD = 3m
Hope this helps!
Step-by-step explanation:
What is the step that comes after 3x(x+1)-5(x+1) when factoring by grouping?
Answer:
Separating the 3x and -5 apart from the (x+1)
Step-by-step explanation:
It would turn out to be (3x-5)(x+1) !
Factor out x+1 from the expression
(x+1) x (3x-5)
The area of inner total surface of acubical water tank is 54m². How m3 many of water does it hold?
Answer:
0
Step-by-step explanation:
54m² - 54m² = 0
Water is 0
someone help me out please
Answer:
[tex]\displaystyle x=\frac{5}{4},\;\;1\frac{1}{4}, \;\; or \;\; 1.25[/tex]
Step-by-step explanation:
To solve for x, we need to isolate the x variable.
Given:
[tex]\displaystyle x+\frac{1}{2} =\frac{7}{4}[/tex]
Subtract [tex]\frac{1}{2}[/tex] from both sides of the equation:
[tex]\displaystyle (x+\frac{1}{2})-\frac{1}{2} =(\frac{7}{4})-\frac{1}{2}[/tex]
[tex]\displaystyle x=\frac{7}{4}-\frac{1}{2}[/tex]
Now, we will create common denominators to simplify.
[tex]\displaystyle x=\frac{7}{4}-\frac{2}{4}[/tex]
[tex]\displaystyle x=\frac{5}{4}[/tex]
Find the number of integral solutions of x+y +z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and
z ≥ 3.
The total number of integral solutions of x + y + z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and z ≥ 3 is; 59 integer solutions
How to find the number of Integral Solutions?We are given the condition that;
−3 ≤ x ≤ 4
Thus, we will use x values of -3, -2, -1, 0, 1, 2, 3, 4
When;
x = -3 and y = 2, in x + y + z = 12, solving for z gives z = 13
x = -3 and y = 3, in x + y + z = 12, solving for z gives z = 12
x = -3 and y = 4, in x + y + z = 12, solving for z gives z =11
x = -3 and y = 5, in x + y + z = 12, solving for z gives z = 10
x = -3 and y = 6, in x + y + z = 12, solving for z gives z = 9
x = -3 and y = 7, in x + y + z = 12, solving for z gives z = 8
x = -3 and y = 8, in x + y + z = 12, solving for z gives z = 7
x = -3 and y = 9, in x + y + z = 12, solving for z gives z = 6
x = -3 and y = 10, in x + y + z = 12, solving for z gives z = 5
x = -3 and y = 11, in x + y + z = 12, solving for z gives z = 4
Thus, there are 10 solutions with x =-3
Repeating the above with x = -2, we will have 10 solutions
Similarly, with x = -1, we will have 9 more solutions
Similarly, with x = 0, we will have 8 more solutions.
Similarly, with x = 1, we will have 7 more solutions.
Similarly with x = 2, we will have 6 more solutions.
Similarly with x = 3, we will have 5 more solutions.
Similarly with x = 4, we will have 4 more solutions.
Thus,
Total number of solutions = 4 + 5 + 6 + 7 + 8 + 9 + 10 + 10
= 59 integer solutions
Read more about Number of Integral Solutions at; https://brainly.com/question/251701
#SPJ1
1. If x = 1 and y = 7, evaluate x+y/4
Answer:
2
Step-by-step explanation:
given x=1 and y=7
now, given expression ,
x+y/4
by putting the values of the x and y ,we get
x+y/4
= 1+7/4
= 8/4
= 2 (Ans.)
Solve the system of equations.
\begin{aligned} &-5x-3y - 9=0 \\\\ &4x-18y-54=0 \end{aligned}
−5x−3y−9=0
4x−18y−54=0
Answer:
(0, - 3 )
Step-by-step explanation:
- 5x - 3y - 9 = 0 → (1)
4x - 18y - 54 = 0 → (2)
multiplying (1) by - 6 and adding to (2) will eliminate y
30x + 18y + 54 = 0 → (3)
add (2) and (3) term by term to eliminate y
34x + 0 + 0 = 0
34x = 0 ⇒ x = 0
substitute x = 0 into either of the 2 equations and solve for y
substituting into (2)
4(0) - 18y - 54 = 0
- 18y - 54 = 0 ( add 54 to both sides )
- 18y = 54 ( divide both sides by - 18 )
y = - 3
solution is (0, - 3 )
Answer:
(0, -3)
Step-by-step explanation:
This system of equations consists of two equations. There are 3 main ways to solve a system of equations:
Graphing (The solution is the point where the two lines intersect)Substitution EliminationFirst, start by having the variables on one side.
[tex]-5x-3y-9=0 \Rightarrow \text{Add 9 to both sides} \Rightarrow -5x-3y=9\\4x-18y-54=0 \Rightarrow \text{Add 54 to both sides} \Rightarrow 4x-18y=54 \Rightarrow \text{Simplify} \Rightarrow 2x-9y=27[/tex]
Solve Using EliminationThis method is the easiest to use in this situation.
In this method, we increase equations by a certain factor in order to eliminate one variable.
We can see that 3y in the first equation can be multiplied by 6 in order to obtain the 18y in the second equation. Therefore, we can multiply the whole first equation by 6:
[tex]-30x-18y=54\\4x-18y=54[/tex]
Now, subtract the two equations to eliminate y.
[tex]-34x=0\\x=0[/tex]
Plug in 0 to x in either of the equations to solve for y:
[tex]-5(0)-3y=9\\0-3y=9\\-3y=9\\ \text{Divide both sides by -3}\\y=-3[/tex]
OR
[tex]4(0)-18y=54\\0-18y=54\\-18y=54\\\text{Divide both sides by -18}\\y=-3[/tex]
Therefore:
(x, y) = (0, -3)
An airplane covers 3500 km in three hours. What would be the distance covered by the plane in 4.5 hours if it flies at the same constant speed. ( I need the proportion equation please help ASAP.)
Answer:
5,250 km
Step-by-step explanation:
[tex]\frac{hours}{miles}[/tex] = [tex]\frac{hours}{miles}[/tex]
[tex]\frac{3}{3500}[/tex] = [tex]\frac{4.5}{x}[/tex] Cross Multiply
3x = (4.5)(3500)
3x = 15750 Divide both sides of the equation by 3
x = 5,250
Help me pleaseeeeeeeee
The value of the function g(-3) from the given piecewise function is 1
What are piecewise function?A piecewise-defined function is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain.
From the given piecewise function, we are to find the value of the function when x is -3 that is g(-3)
In order to determine the equivalent function, we need to determine the function where x = -3
The equivalent function is g(x) = x+ 4
Substitute x = -3 into the resulting function
g(x) = x + 4
g(-3) = -3 + 4
g(-3) = 1
Hence the value of the function g(-3) from the given piecewise function is 1
Learn more on piecewise function here: https://brainly.com/question/1848520
#SPJ1
Evaluate the integral, show all steps please!
Answer:
[tex]\dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given indefinite integral:
[tex]\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x[/tex]
Take partial fractions of the given fraction by writing out the fraction as an identity:
[tex]\begin{aligned}\dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A}{x-4}+\dfrac{B}{x+2}\\\\\implies \dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A(x+2)}{(x-4)(x+2)}+\dfrac{B(x-4)}{(x-4)(x+2)}\\\\\implies x+5 & \equiv A(x+2)+B(x-4)\end{aligned}[/tex]
Calculate the values of A and B using substitution:
[tex]\textsf{when }x=4 \implies 9 = A(6)+B(0) \implies A=\dfrac{3}{2}[/tex]
[tex]\textsf{when }x=-2 \implies 3 = A(0)+B(-6) \implies B=-\dfrac{1}{2}[/tex]
Substitute the found values of A and B:
[tex]\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x = \int \dfrac{3}{2(x-4)}-\dfrac{1}{2(x+2)}\:\:\text{d}x[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ax^n\:\text{d}x=a \int x^n \:\text{d}x$\end{minipage}}[/tex]
If the terms are multiplied by constants, take them outside the integral:
[tex]\implies \displaystyle \dfrac{3}{2} \int \dfrac{1}{x-4}- \dfrac{1}{2} \int \dfrac{1}{x+2}\:\:\text{d}x[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating}\\\\$\displaystyle \int \dfrac{f'(x)}{f(x)}\:\text{d}x=\ln |f(x)| \:\:(+\text{C})$\end{minipage}}[/tex]
[tex]\implies \dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}[/tex]
Learn more about integration here:
https://brainly.com/question/27805589
https://brainly.com/question/28155016
For an alternative approach, expand and complete the square in the denominator to write
[tex](x-4)(x+2) = x^2 - 2x - 8 = (x - 1)^2 - 9[/tex]
In the integral, substitute [tex]x - 1 = 3 \sin(u)[/tex] and [tex]dx=3\cos(u)\,du[/tex] to transform it to
[tex]\displaystyle \int \frac{x+5}{(x - 1)^2 - 9} \, dx = \int \frac{3\sin(u) + 6}{9 \sin^2(u) - 9} 3\cos(u) \, du \\\\ ~~~~~~~~~~~~ = - \int \frac{\sin(u) + 2}{\cos(u)} \, du \\\\ ~~~~~~~~~~~~ = - \int (\tan(u) + 2 \sec(u)) \, du[/tex]
Using the known antiderivatives
[tex]\displaystyle \int \tan(x) \, dx = - \ln|\cos(x)| + C[/tex]
[tex]\displaystyle \int \sec(x) \, dx = \ln|\sec(x) + \tan(x)| + C[/tex]
we get
[tex]\displaystyle \int \frac{x+5}{(x - 1)^2 - 9} \, dx = \ln|\cos(u)| - 2 \ln|\sec(u) + \tan(u)| + C \\\\ ~~~~~~~~~~~~ = - \ln\left|\frac{(\sec(u) + \tan(u))^2}{\cos(u)}\right|[/tex]
Now, for [tex]n\in\Bbb Z[/tex],
[tex]\sin(u) = \dfrac{x-1}3 \implies u = \sin^{-1}\left(\dfrac{x-1}3\right) + 2n\pi[/tex]
so that
[tex]\cos(u) = \sqrt{1 - \dfrac{(x-1)^2}9} = \dfrac{\sqrt{-(x-4)(x+2)}}3 \implies \sec(u) = \dfrac3{\sqrt{-(x-4)(x+2)}}[/tex]
and
[tex]\tan(u) = \dfrac{\sin(u)}{\cos(u)} = -\dfrac{x-1}{\sqrt{-(x-4)(x+2)}}[/tex]
Then the antiderivative we found is equivalent to
[tex]\displaystyle - \int \frac{x+5}{(x - 1)^2 - 9} \, dx = - \ln\left|-\frac{3(x+2)}{(x-4) \sqrt{-(x-4)(x+2)}}\right| + C[/tex]
and can be expanded as
[tex]\displaystyle - \int \frac{x+5}{(x - 1)^2 - 9} \, dx = -\ln\left| \frac{3(x+2)^{1/2}}{(x-4)^{3/2}}\right| + C \\\\ ~~~~~~~~~~~~ = - \ln\left|(x+2)^{1/2}\right| + \ln\left|(x-4)^{3/2}\right| + C \\\\ ~~~~~~~~~~~~ = \boxed{\frac32 \ln|x-4| - \frac12 \ln|x+2| + C}[/tex]
To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create an inequality in standard form that represents the restaurant owner’s desired revenue.
Type the correct answer in each box. Use numerals instead of words.
The inequality in the box has to be written as
x² + 2x - 80 ≤ - 65
How to solve the inequalityWe have
(10 + x)1 * (16-2x) ≥ 130
Next we would have to open the bracket
160 + 16x - 20x - 2x² ≥ 130
Then we would have to arrange the equation
- 2x² - 4x + 160 ≥ 130
Divide the equation by two
- x² - 2x + 80 ≥ 65
This is arranged as
x² + 2x - 80 ≤ - 65
Read more on inequalities here:
https://brainly.com/question/24372553
#SPJ1
The total mass of 2 similar clay pots and 2 similar metal pots was 13.2 kg. The mass of 1 such clay pot was 3 times the mass of a metal pot. What was the mass of a clay pot?
Answer:
mass of a clay pot = 4.95 kg
Kindly award branliest
Step-by-step explanation:
Let the mass of a clay pot be x
Let the mass of a metal pot be y
Thus; 2x + 2y = 13.2
And ;
x = 3 times y
x = 3y
2x + 2y = 13.2
2(3y) + 2y = 13.2
6y + 2y = 13.2
8y = 13.2
y = 13.2/8 = 1.65
x = 3y = 3(1.65) = 4.95
mass of a clay pot = 4.95 kg
Peanuts cost 6.40 per kg what is the cost of 400 g peanuts
Answer:
$25.60
Step-by-step explanation:
1 kg = 1000 grams
peanuts = 6.40 per kg = 0.064 per grams
0.064*400 = 25.6
PLEASE HELP, I REALLY NEED IT!!!
The number which is express in each of the models as given in the image attached to the task content are as follows;
a). 1.37
b). 1.37
c). 1.37.
What numbers are expressed according to the given models in the task content?It follows from the task content that the models describe that One flat represents 1 whole, One rod represents 1 tenth and one unit represents 1 hundredth.
It therefore follows from the task content that in each of the models, the algebraic sum of flat(s), rods and units as the case may be results in the value; 1.37 as the utmost number represented by the models.
Read more on place values;
https://brainly.com/question/2041524
#SPJ1
A sampling method is _________ when the individuals selected for one sample are used to determine the individuals in the second sample.
a sampling method is dependent when the individuals selected for one sample are used to determine the individuals in the second sample
What is sampling?Sampling can be defined as a technique of selecting a subset of the population or individual members in order to make statistical inferences from them and estimate the entire characteristics of the whole population.
Sampling methods are used by researchers in market research to reduce the workload and also to research the entire population
It is time-friendly, cost-effective method and forms the basis of research design.
Some sampling methods are;
Simple random samplingSystematic samplingStratified samplingClustered samplingQuota samplingPurposive samplingIt can be said to be dependent when selecting from one sample affects another sample.
Thus, a sampling method is dependent when the individuals selected for one sample are used to determine the individuals in the second sample.
Learn more about sampling methods here:
https://brainly.com/question/16587013
#SPJ1
Use the figure to the right to find the value of PT. T is the midpoint of PQ
PT=3x+3 TQ=7x-9
If T is the midpoint of PQ and PT = 3x+3, TQ = 7x-9, then PT = 12 units.
Determining the Value of PT
It is given that,
T is the midpoint of PQ ........ (1)
PT=3x+3 ......... (2)
TQ=7x-9 .......... (3)
From (1), the distance from P to T and the distance from T to Q will be equal.
⇒ PT = TQ [Since, a midpoint divides a line into two equal segments]
Hence, equating the equations of PT and TQ given in (2) and (3) respectively, equal, we get the following,
3x + 3 = 7x - 9
or 7x - 9 = 3x + 3
or 7x - 3x = 9 + 3
or 4x = 12
or x = 12/4
⇒ x = 3
Substitute this obtained value of x in equation (2)
PT = 3(3) + 3
PT = 9 + 3
PT = 12 units
Thus, if T is the midpoint of PQ, then the measure of PT and TQ is equal to 12 units.
Learn more about midpoint here:
https://brainly.com/question/5127660
#SPJ1
Let f(x) = [infinity] xn n2 n = 1. find the intervals of convergence for f. (enter your answers using interval notation. ) find the intervals of convergence for f '. find the intervals of convergence for f ''
Best guess for the function is
[tex]\displaystyle f(x) = \sum_{n=1}^\infty \frac{x^n}{n^2}[/tex]
By the ratio test, the series converges for
[tex]\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{(n+1)^2} \cdot \frac{n^2}{x^n}\right| = |x| \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = |x| < 1[/tex]
When [tex]x=1[/tex], [tex]f(x)[/tex] is a convergent [tex]p[/tex]-series.
When [tex]x=-1[/tex], [tex]f(x)[/tex] is a convergent alternating series.
So, the interval of convergence for [tex]f(x)[/tex] is the closed interval [tex]\boxed{-1 \le x \le 1}[/tex].
The derivative of [tex]f[/tex] is the series
[tex]\displaystyle f'(x) = \sum_{n=1}^\infty \frac{nx^{n-1}}{n^2} = \frac1x \sum_{n=1}^\infty \frac{x^n}n[/tex]
which also converges for [tex]|x|<1[/tex] by the ratio test:
[tex]\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{n+1} \cdot \frac n{x^n}\right| = |x| \lim_{n\to\infty} \frac{n}{n+1} = |x| < 1[/tex]
When [tex]x=1[/tex], [tex]f'(x)[/tex] becomes the divergent harmonic series.
When [tex]x=-1[/tex], [tex]f'(x)[/tex] is a convergent alternating series.
The interval of convergence for [tex]f'(x)[/tex] is then the closed-open interval [tex]\boxed{-1 \le x < 1}[/tex].
Differentiating [tex]f[/tex] once more gives the series
[tex]\displaystyle f''(x) = \sum_{n=1}^\infty \frac{n(n-1)x^{n-2}}{n^2} = \frac1{x^2} \sum_{n=1}^\infty \frac{(n-1)x^n}{n} = \frac1{x^2} \left(\sum_{n=1}^\infty x^n - \sum_{n=1}^\infty \frac{x^n}n\right)[/tex]
The first series is geometric and converges for [tex]|x|<1[/tex], endpoints not included.
The second series is [tex]f'(x)[/tex], which we know converges for [tex]-1\le x<1[/tex].
Putting these intervals together, we see that [tex]f''(x)[/tex] converges only on the open interval [tex]\boxed{-1 < x < 1}[/tex].
If tan theta = 2ab / a2-b2 then find all other trigonometric ratios
Answer:
[tex]\displaystyle{\sin \theta = \dfrac{2ab}{a^2+b^2}}\\\\\displaystyle{\cos \theta = \dfrac{a^2-b^2}{a^2+b^2}}\\\\\displaystyle{\csc \theta = \dfrac{a^2+b^2}{2ab}}\\\\\displaystyle{\sec \theta = \dfrac{a^2+b^2}{a^2-b^2}}\\\\\displaystyle{\cot \theta = \dfrac{a^2-b^2}{2ab}}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle{\tan \theta = \dfrac{2ab}{a^2-b^2}}[/tex]
To find other trigonometric ratios, first, we have to know that there are total 6 trigonometric ratios:
[tex]\displaystyle{\sin \theta = \sf \dfrac{opposite}{hypotenuse} = \dfrac{y}{r}}\\\\\displaystyle{\cos \theta = \sf \dfrac{adjacent}{hypotenuse} = \dfrac{x}{r}}\\\\\displaystyle{\tan \theta = \sf \dfrac{opposite}{adjacent} = \dfrac{y}{x}}\\\\\displaystyle{\csc \theta = \sf \dfrac{hypotenuse}{opposite} = \dfrac{r}{y}}\\\\\displaystyle{\sec \theta = \sf \dfrac{hypotenuse}{adjacent} = \dfrac{r}{x}}\\\\\displaystyle{\cot \theta = \sf \dfrac{adjacent}{opposite} = \dfrac{x}{y}}[/tex]
Since we are given tangent relation, we know that [tex]\displaystyle{y = 2ab}[/tex] and [tex]\displaystyle{x = a^2-b^2}[/tex], all we have to do is to find hypotenuse or radius (r) which you can find by applying Pythagoras Theorem.
[tex]\displaystyle{r=\sqrt{x^2+y^2}}[/tex]
Therefore:
[tex]\displaystyle{r=\sqrt{(a^2-b^2)^2+(2ab)^2}}\\\\\displaystyle{r=\sqrt{a^4-2a^2b^2+b^4+4a^2b^2}}\\\\\displaystyle{r=\sqrt{a^4+2a^2b^2+b^4}}\\\\\displaystyle{r=\sqrt{(a^2+b^2)^2}}\\\\\displaystyle{r=a^2+b^2}[/tex]
Now we can find other trigonometric ratios by simply substituting the given information below:
[tex]\displaystyle{x = a^2-b^2}[/tex][tex]\displaystyle{y = 2ab}[/tex][tex]\displaystyle{r = a^2+b^2}[/tex]Hence:
[tex]\displaystyle{\sin \theta = \dfrac{y}{r} = \dfrac{2ab}{a^2+b^2}}\\\\\displaystyle{\cos \theta = \dfrac{x}{r} = \dfrac{a^2-b^2}{a^2+b^2}}\\\\\displaystyle{\csc \theta = \dfrac{r}{y} = \dfrac{a^2+b^2}{2ab}}\\\\\displaystyle{\sec \theta = \dfrac{r}{x} = \dfrac{a^2+b^2}{a^2-b^2}}\\\\\displaystyle{\cot \theta = \dfrac{x}{y} = \dfrac{a^2-b^2}{2ab}}[/tex]
will be other trigonometric ratios.
Simplify.
√75
OA. 3√5
OB. 15√5
OC. 25√3
OD. 5√3
Answer:
Option D
Step-by-step explanation:
Using the surd law :
[tex]\sqrt{ab} = \sqrt{a}\sqrt{b}[/tex]
We can find the largest square number that goes into 75 :
Let's write the multiples of 75 :
1 , 75
3 , 25
5 , 15
The only square number is 25
So using the law mentioned above we split √75 into :
√25√3
The square root of 25 is 5
Now we have our final answer of 5√3
Hope this helped and have a good day
The simplified form of expression √75 is 5√3.
Option D is the correct answer.
We have,
To simplify √75, we can factor it into its prime factors and then take the square root:
√75 = √(3 * 5 * 5)
= √(3 x 5²)
Take out the perfect square factor from under the square root:
= √3 x √5²
= √3 x 5
= 5√3
Thus,
The simplified form of expression √75 is 5√3 which is option D.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ7