9514 1404 393
Answer:
as written: the limit does not existsin(x-1)/(x-1) has a limit of sin(1) ≈ 0.841 at x=0Step-by-step explanation:
The expression written is interpreted according to the order of operations as ...
sin(x) -(1/x) -1
As x approaches 0 from the left, this approaches +∞. As x approaches 0 from the right, this approaches -∞. These values are different, so the limit does not exist.
__
Maybe you intend ...
sin(x -1)/(x -1)
This can be evaluated directly at x=0 to give sin(-1)/-1 = sin(1). The argument is interpreted to be radians, so sin(1) ≈ 0.84147098...
The limit is about 0.841 at x=0.
Mrs. Gomez has two kinds of flowers in her garden. The ratio of lilies to daisies in the garden is 5:2
If there are 20 lilies, what is the total number of flowers in her garden?
Answer:
28
Step-by-step explanation:
5 : 2
since this is a simplified ratio, they have a common factor. let's say it is 'x'
so now :
5x : 2x
we know that 5x is lilies, and we also know that she has 20 lilies, so:
5x = 20
x = 4
the daisies would be 2x so 2*4 = 8
total flowers is 20 + 8
28
A triangle has base of 7 1/8 feet and height 6 1/4 feet. Find the area of a triangle as a mixed number.
Answer: The area is 22 17/64.
Step-by-step explanation:
base = 7 1/8 = 57/8
height = 6 1/4 = 25/4
area = 1/2*b*h
= 1/2*57/8*25/4
= 1425/64
= 22 17/64
Write the equation of the line that passes through the points (0, 4) and (- 4, - 5) . Put your answer in fully reduced slope intercept form , unless it is a vertical or horizontal line
Answer:
y=9/4x+4
Step-by-step explanation:
Start by finding the slope
m=(-5-4)/(-4-0)
m=-9/-4 = 9/4
next plug the slope and the point (-4,-5) into point slope formula
y-y1=m(x-x1)
y1=-5
x1= -4
m=9/4
y- -5 = 9/4(x - -4)
y+5=9/4(x+4)
Distribute 9/4 first
y+5=9/4x + 9
subtract 5 on both sides
y=9/4x+4
What is the measure of 7 shown in the diagram below?
110°
O A. 74.5°
B. 32°
X
O C. 71°
Z
D. 35.5°
Answer:
c
Step-by-step explanation:
Answer:
the correct choice is B
Step-by-step explanation:
If a and b are positive numbers, find the maximum value of f(x) = x^a(2 − x)^b on the interval 0 ≤ x ≤ 2.
Answer:
The maximum value of f(x) occurs at:
[tex]\displaystyle x = \frac{2a}{a+b}[/tex]
And is given by:
[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
We are given the function:
[tex]\displaystyle f(x) = x^a (2-x)^b \text{ where } a, b >0[/tex]
And we want to find the maximum value of f(x) on the interval [0, 2].
First, let's evaluate the endpoints of the interval:
[tex]\displaystyle f(0) = (0)^a(2-(0))^b = 0[/tex]
And:
[tex]\displaystyle f(2) = (2)^a(2-(2))^b = 0[/tex]
Recall that extrema occurs at a function's critical points. The critical points of a function at the points where its derivative is either zero or undefined. Thus, find the derivative of the function:
[tex]\displaystyle f'(x) = \frac{d}{dx} \left[ x^a\left(2-x\right)^b\right][/tex]
By the Product Rule:
[tex]\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[x^a\right] (2-x)^b + x^a\frac{d}{dx}\left[(2-x)^b\right]\\ \\ &=\left(ax^{a-1}\right)\left(2-x\right)^b + x^a\left(b(2-x)^{b-1}\cdot -1\right) \\ \\ &= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right] \end{aligned}[/tex]
Set the derivative equal to zero and solve for x:
[tex]\displaystyle 0= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right][/tex]
By the Zero Product Property:
[tex]\displaystyle x^a (2-x)^b = 0\text{ or } \frac{a}{x} - \frac{b}{2-x} = 0[/tex]
The solutions to the first equation are x = 0 and x = 2.
First, for the second equation, note that it is undefined when x = 0 and x = 2.
To solve for x, we can multiply both sides by the denominators.
[tex]\displaystyle\left( \frac{a}{x} - \frac{b}{2-x} \right)\left((x(2-x)\right) = 0(x(2-x))[/tex]
Simplify:
[tex]\displaystyle a(2-x) - b(x) = 0[/tex]
And solve for x:
[tex]\displaystyle \begin{aligned} 2a-ax-bx &= 0 \\ 2a &= ax+bx \\ 2a&= x(a+b) \\ \frac{2a}{a+b} &= x \end{aligned}[/tex]
So, our critical points are:
[tex]\displaystyle x = 0 , 2 , \text{ and } \frac{2a}{a+b}[/tex]
We already know that f(0) = f(2) = 0.
For the third point, we can see that:
[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(2- \frac{2a}{a+b}\right)^b[/tex]
This can be simplified to:
[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Since a and b > 0, both factors must be positive. Thus, f(2a / (a + b)) > 0. So, this must be the maximum value.
To confirm that this is indeed a maximum, we can select values to test. Let a = 2 and b = 3. Then:
[tex]\displaystyle f'(x) = x^2(2-x)^3\left(\frac{2}{x} - \frac{3}{2-x}\right)[/tex]
The critical point will be at:
[tex]\displaystyle x= \frac{2(2)}{(2)+(3)} = \frac{4}{5}=0.8[/tex]
Testing x = 0.5 and x = 1 yields that:
[tex]\displaystyle f'(0.5) >0\text{ and } f'(1) <0[/tex]
Since the derivative is positive and then negative, we can conclude that the point is indeed a maximum.
Therefore, the maximum value of f(x) occurs at:
[tex]\displaystyle x = \frac{2a}{a+b}[/tex]
And is given by:
[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
could anyone help me solve this? I’ve had several questions like this and I don’t understand how to solve it. I’ll give brainliest:)
Answer:
-2, - 1, - 2 and - 3
Step-by-step explanation:
As the graph depicts an odd function, it will follow the rule f(-x) = - f(x)
Solve the following formula for a.
Answer:
B is correct .trust me
Step-by-step explanation:
Clue is a board game in which you must deduce three details surrounding a murder. In the original game of Clue, the guilty person can be chosen from 66 people, and there are 66 different possible weapons and 99 possible rooms. At one point in the game, you have narrowed the possibilities down to 44 people, 55 weapons, and 77 rooms. What is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices, and the guess being correct
Answer:
The probability of making a correct random guess is 0.00053%.
Step-by-step explanation:
Since Clue is a board game in which you must deduce three details surrounding a murder, and in the original game of Clue, the guilty person can be chosen from 66 people, and there are 66 different possible weapons and 99 possible rooms, and at one point in the game, you have narrowed the possibilities down to 44 people, 55 weapons, and 77 rooms, to determine what is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices , and the guess being correct, the following calculation must be performed:
(1 / (44x55x77)) x 100 = X
(1 / 186,340) x 100 = X
0.0005366 = X
Therefore, the probability of making a correct random guess is 0.00053%.
Write the quadratic equation whose roots are 2 and -4 and whose leading coefficient is 2
Answer:
2x^2+4x-16
Step-by-step explanation:
The quadratic can be written as
f(x) = a(x-z1)(x-z2) where z1 and z2 are the roots
f(x) = a (x-2)(x- -4)
a is the leading coefficient
f(x) = 2(x-2)(x+4)
= 2(x^2 -2x+4x-8)
= 2(x^2 +2x-8)
= 2x^2 +4x-16
Will give brainliest answer
4. Lynn can walk two miles intenta
24 minutes. At this rate, how long will
it take her to walk 6 miles?
What is the measure of m?
Answer:
√245
Step-by-step explanation:
altitude on hypotenuse theorem:
m^2=7*35
m^2=245
m=√245
Triangle DEF has sides of length x, x+3, and x−1. What are all the possible types of DEF?
Triangle DEF is scalene
Must click thanks and mark brainliest
The triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.
What is a scalene triangle?A scalene triangle is a type of triangle which have all the sides to be unequal and similarly, all the angles will also be unequal to each other.
Given that:-
Triangle DEF has sides of length x, x+3, and x−1it is given that all the sides of the triangle are x, x+3, and x−1 we can clearly see that for any value of x all the three sides will have different values. we can conclude from this that the triangle DEF is a scalene triangle.
Therefore triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.
To know more about the scalene triangle follow
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I need to know the answer please
Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.
g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]
Option C
Hope this helps!
find the value of the trigonometric ratio. make sure to simplify the fraction if needed.
Answer:
36/39
Step-by-step explanation:
Cos(theta) = Base/Hypotenuse
Cos(X) = 36/39
It is estimated that t months from now, the population of a certain town will be changing at the rate of 4+ 5t^2/3 people per month. If the current population is 10,000, what will the population be 8 months from now?
Answer:
240000
Step-by-step explanation:
Represent the exponential equation.
[tex]10000 (5 {t}^{ \frac{2}{3} } + 4) = [/tex]
Replace 8 with t
[tex]10000(5(8) {}^{ \frac{2}{3} } + 4)[/tex]
[tex]10000(5 \times 4 + 4) [/tex]
[tex]10000(24) = 240000[/tex]
The population of the town after 8 month will be 2,40,000.
What is exponential growth?
Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.
Let P be the population of the town after 8 months
According to the given question
The current population of the town = 10,000.
Also, the population of the town is changing at the rate of [tex]4+5t^{\frac{2}{3} }[/tex].
Therefore, the population of the town after 8 month is given by the exponential function
[tex]P = 10000(4+5t^{\frac{2}{3} } )[/tex]
Substitute t =8 in the above equation
⇒[tex]P = 10000(4 + 5(8)^{\frac{2}{3} } )[/tex]
⇒[tex]P = 10000(4 + 5(2^{3}) ^{\frac{2}{3} } )[/tex]
⇒[tex]P = 10000(4+5(4))[/tex]
⇒[tex]P = 10000(24)[/tex]
⇒[tex]P = 240000[/tex]
Hence, the population of the town after 8 month will be 2,40,000.
Find out more information about exponential growth here:
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find the maximum number of children to whom 30 sweaters and 45 trousers can be equally divided. also how many sweaters and trousers will each get?
Answer:
five kids .each 6 sweaters and 9 trousers
Step-by-step explanation:
fGiven FE=23.5, find BD.
Answer:
11.75
Step-by-step explanation:
The required triangle is attached below :
The triangle AFE has it's by the mid segment as BD ;as B is the mid-point of line EA ; and D is the mid-point of line FA ;
HENCE, The Length of the midsegment BD = 1/2FE
Hence, BD =. 1/2 * 23.5
BD = 23.5 / 2 = 11.75
If two bags of popcorn and three drinks cost $14,
and four bags of popcorn and one drink costs
$18, how much does a drink cost?
Answer:
2dollars
Step-by-step explanation:
one bag of popcorn is 4 dollars so 4 bags of popcorn is 16 plus 1 drink which is 2 dollars equal 18.
The cost of each popcorn is $4 and the cost of each drink will be $2.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
If two bags of popcorn and three drinks cost $14, and four bags of popcorn and one drink costs $18.
Let the cost of each popcorn be 'x' and the cost of each drink be 'y'. Then the equations are given as,
2x + 3y = 14 ...1
4x + y = 18 ...2
From equations 1 and 2, then we have
2x + 3(18 - 4x) = 14
2x + 54 - 12x = 14
10x = 40
x = $4
Then the value of the variable 'y' is calculated as,
y = 18 - 4(4)
y = 18 - 16
y = $2
The cost of each popcorn is $4 and the cost of each drink will be $2.
More about the solution of the equation link is given below.
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what is an example of a quintic bionomial?
Scientists have steadily increased the amount of grain that farms can produce each year. The yield for farms in France is given by y=−2.73x2+11000x−11000000 where x is the year and y is the grain yield in kilograms per hectare (kg/ha).
What does the y-intercept of this function represent?
9514 1404 393
Answer:
the yield in year 0
Step-by-step explanation:
The y-value is the yield for farms in France in year x. The y-value when x=0 is the yield for farms in France in year 0.
_____
Additional comment
The reasonable domain for this function is approximately 1843 ≤ x ≤ 2186. The function is effectively undefined for values of x outside this domain, so the y-intercept is meaningless by itself.
please explain it step by step
I need help on this problem
9514 1404 393
Answer:
see attached
Step-by-step explanation:
(a) The graph is scaled by a factor of 2, and shifted up 1 unit. The scaling moves each point away from the x-axis by a factor of 2. The points on the x-axis stay there. The translation moves that scaled figure up 1 unit.
__
(b) The graph is reflected across the x-axis and shifted right 4 units. The point on the x-axis stays on the x-axis.
Is u=−12 a solution of 8u−1=6u?
Answer:
No, -12 is not a solution.
Step-by-step explanation:
8u-1=6u
8(-12)-1=6(-12)
-96-1=-72
-97=-72
Untrue, to it’s not a solution
Help me out!! Anyone
Answer:
4:10
Step-by-step explanation:
if they have to wait for plane B and it arrives every 10 mins then 4:10 is the anser
Gant Accounting performs two types of services, Audit and Tax. Gant’s overhead costs consist of computer support, $267000; and legal support, $133500. Information on the two services is:
(See screenshot)
Answer:
$240,300
Step-by-step explanation:
Given :
Overhead cost :
Computer support = $267000
legal support = $133500
Overheads applied to audit services = (Number of CPU minutes used by Audit services * activity rate per CPU minute)
+
(number of legal hours used by Audit services * activity rate per legal hour)
The overhead applied to audit is thus :
40,000 * (267,000 / (40,000 + 10,000)) +
200 * (133500 / (200 + 800)
(40000 * 5.34) + (200 * 133.5)
= $240,300
Hãy tìm hàm gốc f(t) có hàm ảnh Laplace như dưới đây:
F(p)=6/p(2p^2+4p +10)
It looks like we're given the Laplace transform of f(t),
[tex]F(p) = L_p\left\{f(t)\right\} = \dfrac6{p(2p^2+4p+10)} = \dfrac3{p(p^2+2p+5)}[/tex]
Start by splitting up F(p) into partial fractions:
[tex]\dfrac3{p(p^2+2p+5)} = \dfrac ap + \dfrac{bp+c}{p^2+2p+5} \\\\ 3 = a(p^2+2p+5) + (bp+c)p \\\\ 3 = (a+b)p^2 + (2a+c)p + 5a \\\\ \implies \begin{cases}a+b=0 \\ 2a+c=0 \\ 5a=3\end{cases} \implies a=\dfrac35,b=-\dfrac35, c=-\dfrac65[/tex]
[tex]F(p) = \dfrac3{5p} - \dfrac{3p+6}{5(p^2+2p+5)}[/tex]
Complete the square in the denominator,
[tex]p^2+2p+5 = p^2+2p+1+4 = (p+1)^2+4[/tex]
and rewrite the numerator in terms of p + 1,
[tex]3p+6 = 3(p+1) + 3[/tex]
Then splitting up the second term gives
[tex]F(p) = \dfrac3{5p} - \dfrac{3(p+1)}{5((p+1)^2+4)} - \dfrac3{5((p+1)^2+4)}[/tex]
Now take the inverse transform:
[tex]L^{-1}_t\left\{F(p)\right\} = \dfrac35 L^{-1}_t\left\{\dfrac1p\right\} - \dfrac35 L^{-1}_t\left\{\dfrac{p+1}{(p+1)^2+2^2}\right\} - \dfrac3{5\times2} L^{-1}_t\left\{\dfrac2{(p+1)^2+2^2}\right\} \\\\ L^{-1}_t\left\{F(p)\right\} = \dfrac35 - \dfrac35 e^{-t} L^{-1}_t\left\{\dfrac p{p^2+2^2}\right\} - \dfrac3{10} e^{-t} L^{-1}_t\left\{\dfrac2{p^2+2^2}\right\} \\\\ \implies \boxed{f(t) = \dfrac35 - \dfrac35 e^{-t} \cos(2t) - \dfrac3{10} e^{-t} \sin(2t)}[/tex]
Three numbers are in the ratio of 1:2:4. If 3 is added to the first and 8 is subtracted from the third, the new numbers will be the first and third terms of an A.P., whose second term is the second number. Find the original numbers.
9514 1404 393
Answer:
5, 10, 20
Step-by-step explanation:
Suppose the three numbers are x, 2x, and 4x. Then they have the required ratios. After the transformation, we have ...
((x+3) +(4x -8))/2 = 2x . . . . . 2nd term is average of 1st and 3rd
5x -5 = 4x ⇒ x = 5
The original numbers are 5, 10, 20.
_____
After the adjustment, the arithmetic sequence is 8, 10, 12.
Been stuck on this since yesterday !!?!?
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
I have uploaded a graph for you. The x axis is the number of years. The y axis is the salary multiplied by 1000. I should have made the multiplication factor 10000 but 1000 will do.
The 5 given points are plotted in red. The blue line is the function.
The function is y = 5x + 35. That means for every year you add 5 times the year onto the salary.
No years is 35000
1 year is 1 * 5000 + 35000
2 years is 2 * 5000 + 35000 = 45000
6 years is 5 * 5000 * 35000 = 65000
and so on.
The point you want is x = 12
12 years is 12 * 5000 + 35000 = 95000
Forgot the graph
Answer by formula please
Answer:
Step-by-step explanation:
I honestly have no idea what you mean by answer by formula, but I'm going to give it my best. I began by squaring both sides to get:
(a² - b²) tan²θ = b² and then distributed to get:
a² tan²θ - b² tan²θ = b² and then got the b terms on the side to get:
a² tan²θ = b² + b² tan²θ and then changed the tans to sin/cos to get:
[tex]\frac{a^2sin^2\theta}{cos^2\theta}=b^2+\frac{b^2sin^2\theta}{cos^2\theta}[/tex] and isolated the sin-squared on the left to get:
[tex]a^2sin^2\theta=cos^2\theta(b^2+\frac{b^2sin^2\theta}{cos^2\theta})[/tex] and distributed to get:
***[tex]a^2sin^2\theta=b^2cos^2\theta+b^2sin^2\theta[/tex]*** and factored the right side to get:
[tex]a^2sin^2\theta=b^2(sin^2\theta+cos^2\theta)[/tex] and utilized a trig Pythagorean identity to get:
[tex]a^2sin^2\theta=b^2(1)[/tex] and then solved for sinθ in the following way:
[tex]sin^2\theta=\frac{b^2}{a^2}[/tex] so
[tex]sin\theta=\frac{b}{a}[/tex] This, along with the *** expression above will be important. I'm picking up at the *** to solve for cosθ:
[tex]a^2sin^2\theta=b^2cos^2\theta+b^2sin^2\theta[/tex] and get the cos²θ alone on the right by subtracting to get:
[tex]a^2sin^2\theta-b^2sin^2\theta=b^2cos^2\theta[/tex] and divide by b² to get:
[tex]\frac{a^2sin^2\theta}{b^2}-sin^2\theta=cos^2\theta[/tex] and factor on the left to get:
[tex]sin^2\theta(\frac{a^2}{b^2}-1)=cos^2\theta[/tex] and take the square root of both sides to get:
[tex]\sqrt{sin^2\theta(\frac{a^2}{b^2}-1) }=cos\theta[/tex] and simplify to get:
[tex]\frac{sin\theta}{b}\sqrt{a^2-b^2}=cos\theta[/tex] and go back to the identity we found for sinθ and sub it in to get:
[tex]\frac{\frac{b}{a} }{b}\sqrt{a^2-b^2}=cos\theta[/tex] and simplifying a bit gives us:
[tex]\frac{1}{a}\sqrt{a^2-b^2}=cos\theta[/tex]
That's my spin on things....not sure if it's what you were looking for. If not.....YIKES