Which value, to the nearest tenth, is the smallest solution of f(x) = g(x) if f(x) = ln(x + 5) – 1 and g(x) = x3 – 2x + 1?
Answers
Answer:
There are two possibilities of determine which solution is the smallest one:
(i) The smallest solution is the value of [tex]x[/tex] has the smallest distance with respect to origin: [tex](x_{2},y_{2}) = (0.18,0)[/tex]
(ii) The smallest solution is the most negative value: [tex](x_{1},y_{1}) = (-1.577,0)[/tex]
Step-by-step explanation:
Let [tex]f(x) = g(x)[/tex], [tex]f(x) = \ln (x+5)-1[/tex] and [tex]g(x) = x^{3}-2\cdot x + 1[/tex], then we have the following implicit equation:
[tex]\ln (x+5)-x^{3}+2\cdot x -2 = 0[/tex] (1)
This equation cannot be solved by analytical means. There are two different strategies to solve this expression: (i) Numerical methods, (ii) Graphical methods. We decide to use the second method:
Let suppose that we use this function [tex]h(x) = \ln (x+5) -x^{3}+2\cdot x - 2[/tex]. By the help of a graphing tool, we find the smallest solution such that [tex]h(x) = 0[/tex]. There are three possible solutions: [tex](x_{1},y_{1}) = (-1.577,0)[/tex], [tex](x_{2},y_{2}) = (0.18,0)[/tex], [tex](x_{3}, y_{3}) = (1.376, 0)[/tex]
There are two possibilities of determine which solution is the smallest one:
(i) The smallest solution is the value of [tex]x[/tex] has the smallest distance with respect to origin: [tex](x_{2},y_{2}) = (0.18,0)[/tex]
(ii) The smallest solution is the most negative value: [tex](x_{1},y_{1}) = (-1.577,0)[/tex]
The smallest smallest solution of f(x) = g(x) will be [tex]\rm \left(-1.577,0.223\right)[/tex]
What exactly is a function?A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.
Given functions;
f(x) = ln(x + 5) – 1
g(x) = x³ – 2x + 1
After graphing both the function, we get the three solutions of the given equation,
[tex]\rm \left(-1.577,0.223\right)[/tex]
[tex]\left(0.18,0.645\right)[/tex]
[tex]\left(1.376,0.853\right)[/tex]
Hence,the smallest smallest solution of f(x) = g(x) will be [tex]\rm \left(-1.577,0.223\right)[/tex]
To learn more about the function, refer to:
https://brainly.com/question/5245372
#SPJ5
Related Questions
Hansen won the raffle At the zoo and gets to feed the dolphins! The dolphin trainer gives Hansen a bucket of fish to divide evenly among five dolphins. Each dolphin gets four fish. Which equation can you use to find the number of fish F in the bucket before hansen feeds them
Answers
Answer:
Number of dolphins in zoo * number of fish per dolphin.
Step-by-step explanation:
Hansen won the raffle At the zoo and gets to feed the dolphins! The dolphin trainer gives Hansen a bucket of fish to divide evenly among five dolphins. Each dolphin gets four fish. Which equation can you use to find the number of fish F in the bucket before hansen feeds them
Given that:
Number of dolphins = 5
Fish in bucket is distributed equally ; hence, Number of fish per dolphin = 4
To obtain the initial number of fish in bucket before hansen began to feed the fishes :
Number of fish in bucket before hansen feeds then :
Number of dolphins in zoo * number of fish per dolphin.
5 * 4 = 20
How do I solve for an answer for this?
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Answers
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Answer:
60 degrees
Step-by-step explanation:
set up like 240-120
240-120=120
120 divided by 2 equals 60
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Answers
Answer: 6
Step-by-step explanation:
Collin is building a deck on the back of his family's house. He has enough lumber for the deck to be 75
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A. 15
B. -5
C. -15
D. 5
Answers
Answer:
A. 15
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
The value of y is directly proportional to the value of x If y=81 when x=54, what is the value of y when x=38
Answers
Answer:
y = 57
Step-by-step explanation:
y α x
y = kx ; k = Constant of proportionality
81 = k* 54
k = 81/54
k = 1.5
Value of y when x = 38
y = kx
y = 1.5 * 38
y = 57
Hence, y = 57 when x = 38
A loan requires that the 4% interest be compounded monthly for five years find the number of compounding periods
Answers
Answer:
60 compounding periods
Step-by-step explanation:
The proper formula for compound interest is A = P(1 + r/n)^(nt), where r is the interest rate as a decimal fraction, n is the number of times that interest is compounded in 1 year, and t is the number of years.
In this problem, we don't need to calculate the Amount, but only the number of compounding periods. That is nt, which here is 12*5, or 60.
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Answers
Answer:
640
Step-by-step explanation:
8^2 = 64
10*64 = 640
Answer:
640
Step-by-step explanation:
b = 8
10b^2 = (10)(8^2) = (10)(64) = 640
Help Me, Now! A. What equation represents the amount of money in Kade's account as a function of weeks passed?
Answers
Answer:
Step-by-step explanation:
Watch rep
Jayden invested $1,500 in an account in the year 2005, and the value has been
growing exponentially at a constant rate. The value of the account reached $1, 800 in
the year 2011. Determine the value of the account, to the nearest dollar, in the year
2019.
0
Submit ADC
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AnCTOR
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נ
11
Type here to search
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Answers
Something happened when you copy and pasted the question, was it important to the question?
Combine like terms to create an equivalent expression.
- 4/7p + (-2/7p) + 1/7
Answers
Answer:
-6/7p+1/7
Step-by-step explanation:
-4/7p+(-2/7)+1/7
-4/7p-2/7p+1/7
-6/7p+1/7
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Answers
Which ordered pair is a solution of y = x - 4?
A: (3,-7)
B: (-3,-7)
C: (3,7)
D: (-3,7)
Answers
Answer:
The correct answer is (-3,-7). This is because you can plug it in and the two sides are equal to each other. When you plug -3 in for x, you subtract for from it and get -7 since the y term is -7 the answer is -7=-7, thus (-3, -7) is the answer.
Step-by-step explanation:
Hope this helps :)
If PQ = 2v and PS = 6v - 52, find the value of v in parallelogram QRST.
Answers
Answer:
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
find the value of given expression
[tex] \sqrt{200 \div 2} [/tex]
Answers
Answer:
10 Ans.......
Step-by-step explanation:
Given:
=√200÷ 2
Solution:
= √200÷2
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A construction company wants to hire x carpenters for $220 a day and y plumbers for $260 a day. the company wants to hire at least 18 workers. it wants to pay no more than $4500 each day.
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Answers
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Step-by-step explanation:
$220 × 6 = $1320 this is how much it cost to pay 6 carpenters for one day. Now lets find how much it cost to 12 plumbers at $260 a day. $260 × 12 = $3120 this is how much it costs to pay 12 plumbers a day.
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
5. B, C and E
6. C
7. None
8. A and D
9. F and G
Step-by-step explanation:
See attachment for complete question
5. B, C and E
B, C and E are not parallelogram because they do not have 2 pairs of parallel sides
B and E are trapeziums while C is just a quadrilateral.
6. C
In (5) above, we established that B and E are trapeziums while C is not. This implies that only C is a quadrilateral.
7. None
A square is a parallelogram. So, it is not possible for a shape to be a square and not be a parallelogram.
8. A and D
A is a rhombus. D is a square and will be treated as a rhombus because all sides are equal.
9. F and G
These shapes have 2 pairs of parallel lines but all 4 sides are not equal; only the opposite sides are equal.
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Answers
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Answers
Answer:
∆WUV⁓∆SRT
Step-by-step explanation:
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Step-by-step explanation:
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0.9
Step-by-step explanation:
Basic angle =
[tex]cos { }^{ - 1} ( \frac{4}{5} ) = 36.870 \: degrees \\ [/tex]
Therefore,
[tex]theta = 180 + 36.870 = 216.87 \: degrees[/tex]
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[tex] \sin( \frac{theta}{2} ) = \sin(108.435 ) = 0.9[/tex]
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Answers
Answer:
no name and function
Step-by-step explanation:
Emila bought 3 2/3 kilogram of sugar on wednesday she bought 3/10 kilograms of sugar less on Thursday. How uch sugar did she buy on Thursday?
Answers
Answer:
[tex]1\frac{7}{10}[/tex] kg of sugar
Step-by-step explanation:
Amount of sugar on Wednesday: [tex]3\frac{2}{3}[/tex] kg
Convert the mixed number fraction to an improper fraction (multiply the whole number by the numerator)
[tex]3\frac{2}{3}[/tex] ⇒ [tex]\frac{6}{3}[/tex] ⇒ [tex]2[/tex]
Therefore, Emila bought 2 kg of sugar on Wednesday.
Because Emila bought [tex]\frac{3}{10}[/tex] kg less sugar on Thursday, subtract [tex]\frac{3}{10}[/tex] from [tex]2[/tex].
[tex]2-\frac{3}{10}[/tex]
Convert 2 into a fraction with 10 as the denominator
[tex]=\frac{20}{10} -\frac{3}{10}\\=\frac{17}{10}[/tex]
Convert the fraction into a mixed number
[tex]= 1\frac{7}{10}[/tex]
Therefore, Emila bought [tex]1\frac{7}{10}[/tex] kg of sugar on Thursday.
I hope this helps!
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Answers
Answer:
10
Step-by-step explanation:
from -5 to 5 is a complete period. So the period is 10.
What's the value of
[tex] \sqrt{3 \times 3} [/tex]
Answers
Answer:
3.
Step-by-step explanation:
Square root is the opposite of power. Simplify:
[tex]\sqrt{3 * 3 } = \sqrt{3^2} = 3[/tex]
3 is your answer.
~
Answer:
√{3×3}=√3²=±3 is your answer
Solving Quadratic Equations
Directions: Solve the following quadratic equations using the quadratic formula. Show your work
and all answers must be in simplest radical form.
I
a. x2 - 2x - 15 =0
b. x2 + 8x - 10 =0
Answers
Answer:
a) x= 5 or x= -3
b) x = -4 + [tex]\sqrt{26}[/tex] or -4 - [tex]\sqrt{26}[/tex]
Step-by-step explanation:
a) [tex]x^{2}[/tex] - 2x - 15 =0
x = [tex]\frac{-(-2) +\sqrt{(-2)^{2} - 4(1)(-15)}}{2(1)}[/tex] or [tex]\frac{-(-2) -\sqrt{(-2)^{2} - 4(1)(-15)}}{2(1)}[/tex]
x= 5 or x=-3
b) [tex]x^{2}[/tex] + 8x - 10 =0
x = [tex]\frac{-(8) +\sqrt{(8)^{2} - 4(1)(-10)}}{2(1)}[/tex] or [tex]\frac{-(8) -\sqrt{(8)^{2} - 4(1)(-10)}}{2(1)}[/tex]
x = -4 + [tex]\sqrt{26}[/tex] or -4 - [tex]\sqrt{26}[/tex]