Answers
[tex]Area= \frac{16}{3}=2*( k*\sqrt{k}- \int\limits^{\sqrt{k}}_{0} {x^2} \, dx )\\\\ \dfrac{8}{3}=k ^\frac{3}{2}- \frac{1}{3}* [x^3]^{\sqrt{^k}}_0\\\\ 2* k ^\frac{3}{2}=8\\\\ k = \sqrt[3]{16}\\ [/tex]
Related Questions
Jovan bought a bond with a face value of 15,000 and a coupon rate of 8.5%. The bond will mature in 15 years. How much interest will he receive semiannually
Answers
19,125
Explanation
The value of bond has an interest of 8.5% annually. Monthly it will be 8.5/2%=4.25%
The initial value of bond is 15,000.
The formula for calculating the interest is;
Interest=PRT
Where p is the money deposited, R is the interest rate and T is the period.
Since the interest semiannually for 15 years, the interest period is (15×2) = 30.
Interest=15,000×0.045×30
=19,125.
I need to write these description into the new function but I keep getting the wrong thing -.-
1.The function f(x)=(1/2)^x is translated 4 units right, reflected across the x-axis, and vertically stretched by a factor of 1.5
2.The function f(x)=ln x is translated 3 units left, horizontally compressed by a factor of 1/4 and translated 0.5 units down.
3. The function f(x)=e^x is horizontally stretched by a factor of 3, reflected across the y-axis, and translated 1 unit right.
Answers
.. translation right by k units: f(x) ⇒ f(x-k)
.. translation up by k units: f(x) ⇒ f(x) +k
.. horizontal stretch by a factor of k: f(x) ⇒ f(x/k) . . . . same as compressed by 1/k
.. vertical stretch by a factor of k: f(x) ⇒ k*f(x)
.. reflection across the x-axis: f(x) ⇒ -f(x)
.. reflection across the y-axis: f(x) ⇒ f(-x)
The sequence in which these are done is important.
1. f(x) = (1/2)^x
.. translated 4 units right: f(x) = (1/2)^(x -4)
.. reflected across the x-axis: f(x) = -(1/2)^(x -4)
.. vertically stretched by a factor of 1.5: f(x = -1.5(1/2)^(x -4)
2. f(x) = ln(x)
.. translated 3 units left: f(x) = ln(x +3)
.. horizontally compressed by a factor of 1/4: f(x) = ln(x/4 +3)
.. translated down 0.5 units: f(x) = -0.5 +ln(x/4 +3)
3. f(x) = e^x
.. horizontally stretched by a factor of 3: f(x) = e^(x/3)
.. reflected across the y-axis: f(x) = e^(-x/3)
.. translated 1 unit right: f(x) = e^(-(x -1)/3)
The transformed equations for each of your base functions according to given changes are f(x) = -1.5*(1/2)ˣ⁻⁴, f(x) = ln(4×(x+3))-0.5, and f(x)=e⁻³×(x-1) respectively.
Explanation:1. The transformed function for your first one, namely f(x)= (1/2)ˣ, after being translated 4 units right, reflected across the x-axis, and vertically stretched by a factor of 1.5 would be f(x) = -1.5×(1/2)⁽ˣ⁻⁴⁾.
2. Your second function, f(x) = ln(x), after being translated 3 units left, horizontally compressed by a factor of 1/4, and translated 0.5 units down becomes:
f(x) = ln(4×(x+3))-0.5.
3. Your final function, f(x)=e^x, when it's horizontally stretched by a factor of 3, reflected across the y-axis, and translated 1 unit right, would transform into: f(x)=e⁻³×(x-1).
Learn more about Function Transformation here:https://brainly.com/question/37849754
#SPJ3
What is the second term when 3+2x^2-3x^4+x3
Answers
I can explain if you want.
1. Vertex (1,2), Point (2,-5)
2. Vertex (-3,6), Point (1,-2)
3. Vertex (0,5), Point (1,-2)
4. Vertex (1/4, -3/2), Point (1.3)
Answers
he difficulty of graphing a quadratic function varies depending on the form you find it in. We'll start things off relatively easily.
f(x) = a(x – h)2 + k
No, we're not lying to you; that is a quadratic function. Go ahead, multiply it out.
f(x) = ax2 + (-2ah)x + (ah2 + k)
The h and k are constants, so (-2ah) and (ah2 + k) are also constants, which we could call, say, b and c. See, you can trust us, it's totally quadratic.
When you have a parabola written out like f(x) = a(x – h)2 + k, it's in vertex form. With vertex form, you have several pieces of important information thrown at you right away. When you first meet someone, your first impression tends to stick with you. It's the same with this equation.
The sign of a tells you if the parabola opens up or down. If a is positive, it opens up. If a is being a Negative Nancy, the parabola opens down. You also know that the vertex of the parabola is at the point (h, k). Be careful with the sign of h, though.
Is (a-3) a factor of (a^3-6a^2+29)?
Answers
f(3) = 8 - 6*9 + 29
f(3) = 8 - 54 + 29
f(3) = - 17
As further "proof", here is the graph. Notice that the graph cuts the x axis around -2 , 2.5 and 4.2 (These are rough guesses). The factors are
(a+2)(a - 2.5)(a - 4.2)
By what percent will a fraction decrease if its numerator is decreased by 50% and its denominator is decreased by 25%?
AND NO, it is not 33, 33.3, 66, or 66.6 percent.
Answers
[tex] \frac{N}{D} [/tex]
if its numerator is decreased by 50%
[tex] N - \frac{50}{100}N [/tex] ==> (this will be the numerator part)
if its denominator is decreased by 25%
[tex] D - \frac{25}{100}D [/tex] ==> (this will be the denominator part)
I try to separate them out, so it's easier to see the problem.
[tex] N - \frac{50}{100}N = \frac{100N}{100} - \frac{50N}{100} = \frac{50N}{100} [/tex]
[tex] D - \frac{25}{100}D = \frac{100D}{100} - \frac{25D}{100} = \frac{75D}{100}[/tex]
[tex] \frac{\frac{50N}{100}}{\frac{75D}{100}} = \frac{50N}{100} * \frac{100}{75D}[/tex]
[tex] \frac{50N}{75D} = \frac{2}{3}(\frac{N}{D})[/tex] by this, you can understand that
[tex] \frac{2}{3}(\frac{N}{D})[/tex] as 66.6% of N/D because 2/3 is 0.666666.... The answer should be 66.7% if you round them up.
PLEASE HELP MATH WILL MARK BRAINLY ASAP PICTURE ATTACHED
Answers
So for x we have 540 - 83 - 89 - 119 - 90 = 159° left
A coin is tossed and a number cube is rolled. What is the probability that the coin shows heads and the number cube shows 5? A. start fraction 1 over 6 end fraction B. start fraction 1 over 12 end fraction C. start fraction 2 over 3 end fraction D. one-fourth
Answers
Answer:
i got 1/4
Step-by-step explanation:
me sorry in wrong
Jenny has saved $3,800 over the last 12 months. She saved either $250 or $350 a month. During the 12 month period, how many times did Jenny save $250 for the month? A) 3 B) 4 C) 5
Answers
Here is your answer:
The proper answer to the question is option A "3".
Here is how:
There is only two options 250 and 350 and there is 12 months which means there can only be three for both.
Your answer is A.
If you need anymore help feel free to ask me!
Hope this helps!
Answer:
the answer is actually 4
Step-by-step explanation:
(Please help, urgent).
What is the value of r?
Round your final answer to the nearest whole number.
Answers
[tex] Heya \: ! \: \\ \\ We \: know \: that \\ \\ \: \sin( \alpha ) = \frac{perpendicular}{hypotenuse} \\ \\ \sin(67.4) = \frac{12}{r} \\ \\ \\ also \: , \\ \\ \sin(67.4) = 0.9231 \\ \\ comparing \: both \: ,\\ \\ \frac{12}{r} = 0.9231 \\ \\ r = \frac{12}{0.9231} \\ \\ r = 13 \: \: \: \: \: ans.[/tex]
You have decided to buy a new car, but you are concerned about the value of the car depreciating over time. You do some research on the model you are looking at and obtain the following information:
Suggested retail price - $18,790
Depreciation per year - $1385 (It is assumed that this value is constant.)
The following table represents the value of the car after n years of ownership.
Answers
3125 = 3200*(d)^3
3125/3200 = d^3
3-root (3125/3200) = d
d = 0.992125657...
1 - d = 0.007874...
Therefore it depreciates at about 0.8% monthly
To find the depreciation 6 months from now, or 9 months from the beginning:
v = 3200 (d)^9
= 2980.232239...
So after 9 months the car would be about $2980.23
Answer: D on edge
Step-by-step explanation:
True or false the fraction 9/21 is in lowest terms
Answers
9/12 in it's lowest terms is 3/7.
3\7 in decimal is 0.42857142 or 0.43
3\7 in percent 42.857143% or 43 %
use math way . c o m
What is the median of the data set?
42 55 27 31 17 24 65 47 39 18
A. 21
B. 35
C. 17
D. 24
Answers
Y᷉᷈o᷉᷈u᷉᷈ p᷉᷈l᷉᷈a᷉᷈c᷉᷈e᷉᷈ t᷉᷈h᷉᷈e᷉᷈m᷉᷈ i᷉᷈n᷉᷈ n᷉᷈u᷉᷈m᷉᷈e᷉᷈r᷉᷈i᷉᷈c᷉᷈a᷉᷈l᷉᷈ o᷉᷈r᷉᷈d᷉᷈e᷉᷈r᷉᷈
T᷉᷈h᷉᷈e᷉᷈n᷉᷈ f᷉᷈i᷉᷈n᷉᷈d᷉᷈ t᷉᷈h᷉᷈e᷉᷈ m᷉᷈i᷉᷈d᷉᷈d᷉᷈l᷉᷈e᷉᷈ n᷉᷈u᷉᷈m᷉᷈b᷉᷈e᷉᷈r᷉᷈
Find the greatest common factor : 25p^2q^3, 15p^2q^2 and 35pq^4
Answers
Answer:
The greatest common factor is [tex]5pq^2[/tex].
Step-by-step explanation:
The given expressions are [tex]25p^2q^3[/tex], [tex]15p^2q^2[/tex] and [tex]35pq^4[/tex].
Greatest common factor of two numbers is the greatest number that divides both numbers completely.
Find factors of each expression.
[tex]25p^2q^3=5\times 5\times p\times p\times q\times q\times q[/tex]
[tex]15p^2q^2=3\times 5\times p\times p\times q\times q[/tex]
[tex]35pq^4=5\times 7\times p\times q\times q\times q\times q[/tex]
The common factors are 5,p,q and q. So, the greatest common factor of given expressions is
[tex]G.C.F.=5\times p\times q\times q[/tex]
[tex]G.C.F.=5pq^2[/tex]
Therefore the greatest common factor is [tex]5pq^2[/tex].
Please help and show work. 15 points.
Answers
the x satys the same, the Y reverses positive/negative
Factor completely x^2 − 36.
(x + 6)(x − 6)
(x + 6)(x + 6)
(x − 6)(x − 6)
Prime
Answers
[tex](First \ step) \\ \\ Factoring: (x2-36) \\ \\ \boxed{ A^2 - B^2 \ can \ be \ factored \ into \ (A+B) * (A-B)} \\ \\\ \left[\begin{array}{ccc}Proof : (A+B) * (A-B) = \\ A2 - AB + BA - B2 = \\ A2 - AB + AB - B2 = \\ A2 - B2\end{array}\right] \\ \\ \\ Factorization is : (x + 6) * (x - 6) \\ \\ \boxed{FINAL \ ANSWER} \\ \\ \boxed{\boxed{ (x + 6) * (x - 6)}}[/tex]
Your correct answer would be (option a) the first option.
I hope this helps you!
Which of the following pairs of organisms compete with each other for food?
A. squirrels and owls
B. mice and owls
C. rabbits and green plants
D. mice and rabbits
Answers
In a given amount of time , Nijah drove twice as far as Jared. Altogether they drove 135 miles. Find the number of miles driven by Nijah
Answers
3x = 135
x = 135 /3
x = 45
Nijah = 2*45 = 90 miles
brainliest for best answer
Answers
Answer:
Step-by-step explanation:
________
Good evening ,
_______________
-4x+3y=-12
-2x+3y=-18
This system is the same as
y = (4/3)x - 4
y = (2/3)x - 6
We note that the two coefficients 4/3 and 2/3 are positives
So the right answer is C (graph 2).
___
:)
PLEASE HELP ME OUT PLEASE!!
EXPLAIN IT PLEASE SO I CAN UNDERSTAND IT BETTER
THX
Answers
Someone Please Help!!!
Find the radian measure of an angle of -280 degrees
Answers
Answer:-14pi/9
Step-by-step explanation:
The function f(x) is defined as follows:
f(x)= 3x+1 if x is less than or equal to 0
2x^2 if 0
4 if c is greater than or equal to 2
determine the following values of the function
f(-3)= __
f(2)= ___
Answers
[tex]f(x)=3x+1[/tex]
[tex]f(-3)=3(-3)+1[/tex]
[tex]f(-3)=-9+1[/tex]
[tex]f(-3)=-8[/tex]
Similarly, when you are evaluating the function at 2, you are saying that [tex]x=2[/tex]. Since [tex]2 \geq 2[/tex], we are going to use our second rule to evaluate our function:
[tex]f(x)=2 x^{2} [/tex]
[tex]f(2)=2(2^{2} )[/tex]
[tex]f(2)=2(4)[/tex]
[tex]f(2)=8[/tex]
We can conclude that [tex]f(-3)=-8[/tex] and [tex]f(2)=8[/tex].
To determine the values of the function f(x) at specific points, we need to look at the different cases given in the definition of f(x).
Explanation:To determine the values of the function f(x) at specific points, we need to look at the different cases given in the definition of f(x).
If x is less than or equal to 0, then f(x) = 3x + 1. So, f(-3) = 3(-3) + 1 = -8.If x is greater than 0 and less than 2, then f(x) = 2x^2. So, f(2) = 2(2^2) = 8.If x is greater than or equal to 2, then f(x) = 4. So, f(2) = 4.Therefore, f(-3) = -8 and f(2) = 4.
Learn more about Determining values of a function here:https://brainly.com/question/32738253
#SPJ11
Factor completely 2x3 + x2 - 18x - 9
A. (x2-9)(2x+1)
B. (x-3)(x+3)(2x-1)
C. (x-3)(x+3)(2x+1)
D. (2x-3)(2x+3)(x-1)
Answers
2 x^3 + x^2 - 18 x - 9
Factor terms by grouping. 2 x^3 + x^2 - 18 x - 9 = (2 x^3 + x^2) + (-18 x - 9) = x^2 (2 x + 1) - 9 (2 x + 1):
x^2 (2 x + 1) - 9 (2 x + 1)
Factor 2 x + 1 from x^2 (2 x + 1) - 9 (2 x + 1):
(2 x + 1) (x^2 - 9)
x^2 - 9 = x^2 - 3^2:
(2 x + 1) (x^2 - 3^2)
Factor the difference of two squares. x^2 - 3^2 = (x - 3) (x + 3):
Answer: (x - 3) (x + 3) (2 x + 1) thus the Answer is C.
The factorization of the given polynomial 2x3 + x2 - 18x - 9 is (x-3)(x+3)(2x+1) and we achieve this by factoring common terms and applying the formula for difference of squares.
Explanation:To factor the polynomial 2x3 + x2 - 18x - 9, you would first tie together similar terms (if any), then check for any common factors in all the terms. In this case, we can factor this expression in two steps:
First step: Looking for common factors, we can rewrite the expression as x2(2x) - 9(2x) + x2 - 9.Second step: Then, factor using the formula for the difference of squares and you will find that the fully factored expression is (x-3)(x+3)(2x+1).Learn more about Factoring Polynomials here:https://brainly.com/question/35418869
#SPJ11
Which step will get you closest to the solution of this equation? 5⋅(x−2)=7
Answers
The points (15, 10), (25, 20), (30, 22), (40, 32), (55, 53), (60, 55) represent the time, x, it takes 6 people to travel y miles. The scatterplot below represents the situation.
(Graph Below)
A. 32 miles
B. 42 miles
C. 48 miles
D. 54 miles
Answers
Answer:IT IS B
Step-by-step explanation:
I GOT A 100 ON MY TEST YOUR WELCOME :D
4x^3+2x^2+3x+4 divided by x+4
Answers
= 4x^2 -14x +59 -232/(x+4)
The remainder is f(-4) = -232.
Simplify: 4x^4+2x^3+3x^2+4x+4/x
Point D is on segment BC. Segment BC measures 8x units in length.What is the length of segment BC?units
Answers
helppppppppppppppppppppppp
Answers
Jesse wants to write a function to represent the graph. He says that the period of the graph is triple that of sin x and that the equation of the graph is f(x)=3sin x. Why is he incorrect?
a. The period of the graph is twice that of sin x.
b. The frequency of the graph is triple that of sin x.
c. The equation of the graph should be f(x)=sin x/3.
d. The equation of the graph should be f(x)=3sin x.
Answers
Answer C
the value of sin(pi/2) =1
the value of sin(pi) = 0
according to the graph sin(3pi/2) = 1 and sin(3pi) =0
so the correct equation for the graph must be f(x) = sin(x/3)
Jesse is incorrect, because the equation of the graph should be [tex]f(x) = \sin(\frac{x}{3})[/tex]
From the question, we understand that the period is 3 times sin x.
The above claim is wrong.
Given that, the period (B) is 3.
i.e B = 3
The function is represented as:
[tex]f(x) = \sin(\frac{2\pi}{B})[/tex]
So, we have:
[tex]f(x) = \sin(\frac{2\pi}{3})[/tex]
Represent [tex]2\pi[/tex] with x
[tex]f(x) = \sin(\frac{x}{3})[/tex]
Hence, the equation of the graph should be [tex]f(x) = \sin(\frac{x}{3})[/tex]
Read more about sine functions at:
https://brainly.com/question/9565966
I Will Mark it the brainiest
A bouncy ball is dropped such that the height of its first bounce is 3.5 feet and each successive bounce is 75% of the previous bounce's height. What would be the height of the 9th bounce of the ball? Round to the nearest tenth (if necessary).
Answers
y = A * (b) ^ x
Where,
A: initial height
b: decrease rate of initial height
x: number of bounces.
We have then:
y = 3.5 * (0.75) ^ x
For the ninth bounce:
y = 3.5 * (0.75) ^ x
y = 0.26
Answer:
The height of the 9th bounce of the ball is:
y = 0.26 feet.