Answer:
acdc
Step-by-step explanation:
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?
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]
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solve this equation x-24/8 = 2x+ 1/2
x =
Answer:
x= - 7/2
Step-by-step explanation:
Decimal Form: -3.5
Mixed Number Form: -3 1/2
Michael brought 2 gallons of lemonade for his class party. How many 1 cup servings does he have for his class? (1 gallon = 16 cups) *
Write the fifteenth term of the binomial expansion of (a^2+b)^20
Answer:
The fifteenth term of the binomial expansion of [tex](a+b)^{20}[/tex] is [tex]38760\cdot a^{6}\cdot b^{14}[/tex].
Step-by-step explanation:
Let be a binomial of the form [tex](a+b)^{n}[/tex], where [tex]a, b\in \mathbb{R}[/tex] and [tex]n\,\in\mathbb{N}^{+}[/tex]. The expansion of this polynomial is defined below:
[tex](a+b)^{n} = \Sigma\limits_{k=0}^{n}\,\frac{n!}{k!\cdot (n-k)!}\cdot (a^{n-k}\cdot b^{k})[/tex] (1)
Where:
[tex]n[/tex] - Number of terms of the expanded polynomial.
[tex]k[/tex] - Index associated to [tex]k[/tex]-th term of the expanded polynomial.
For all [tex]n[/tex]-th binomial, we a sum of [tex]n+1[/tex] terms. If the given binomial has a term of [tex]20[/tex], then we have 21 terms and the fifteenth term of the polynomial corresponds to the [tex]14[/tex]-th term. Then, the fifteenth term of the binomial is:
[tex]c_{14} = \frac{20!}{14!\cdot 6!}\cdot (a^{6}\cdot b^{14})[/tex]
[tex]c_{14} = 38760\cdot a^{6}\cdot b^{14}[/tex]
The fifteenth term of the binomial expansion of [tex](a+b)^{20}[/tex] is [tex]38760\cdot a^{6}\cdot b^{14}[/tex].
In 2011 a sweatshirt cost $20 and in 2012 the price increase to 25 what is the percent change
A windshield wiper is 50 cm long. In one sweep it turns through an angle of 115°. Calculate the distance (length) it covers in one sweep. Round to the nearest whole number.
Answer:
The distance in one sweep is 100 cm approximately
Step-by-step explanation:
Here, we want to calculate the distance the wiper covers in one sweep
Mathematically;
we have a structure like an arc of a circle. It is the length of this arc we want to calculate.
The formula for the length of an arc is;
theta/360 * 2 * pi * r
r is the radius which in this case is 50 cm
We have ;
115/360 * 2 * 3.1412 * 50 = 100 cm approximately
Solve system by substitution.
−5x−7y=3
x+6y=−19
Bobo and the Bouncing Ball Math Problem
Please help me solve it. There are 3 questions, question 1, 2, and the Einstein problem.
WORTH 20 POINTS!
This doesn’t include the Einstein problem cause I didn’t have that one.
Answer:
1)0.125
2)127.825
Step-by-step explanation:
True or false ??????
Jackson invested $140 in an account paying an interest rate of 3 3/4% compounded
quarterly. Lucy invested $140 in an account paying an interest rate of 3 1/2%
compounded daily. After 10 years, how much more money would Jackson have in his
account than Lucy, to the nearest dollar?
Answer: $5
Step-by-step explanation:
Mickey has $4,500 in a college savings account, and he will need to 0
contribute $6,000 each year towards his college tuition. Mickey wants to
save enough in 3 years to cover his first 2 years of tuition. According to
the table, what is the minimum monthly deposit that Mickey should make
in order to meet his goal
Answer:
200
Step-by-step explanation:
you would need to do 6,000 times 2 to find out how much he will need to cover and 6,000 times 2=12000 so the answer is b 200
1 flower has 10 petals how many petals do 5 flowers have?
Answer:
50 :)
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
Can someone help me with one of these? Factor using the X method please!
Answer:
Step-by-step explanation:
6. x² + 8x + 7
= x² + 7x + x + 7
= x (x + 7) + 1 (x + 7)
= (x + 1) (x + 7)
Option D is the answer.
7. x² - x - 72
= x² - 9x + 8x - 72
= x(x - 9) + 8(x - 9)
Option B is the answer.
8. x² - 49
= (x - 7) (x + 7) [formula used a² - b² = (a-b)]
Option D is the answer.
9. 9x² - 54x + 72
= 9(x² - 6x + 8)
= 9(x² - 4x - 2x + 8)
= 9[x(x-4) -2 (x-4)]
= 9[(x - 2) (x - 4)]
= Option A is the answer.
10. x⁴ - 3x³ - 10x²
= x² (x² - 3x - 10)
= x² (x² - 5x + 2x - 10)
= x² [x (x-5) + 2 (x-5)]
= x² (x+2) (x-5)
Option A is the answer.
Laura borrowed $40,500 at 3% for 10 years. what was the total interest?
Answer:
$12,150
Step-by-step explanation:
I = Prt
I = (40500)(0.03)(10)
I = 12150
if there 3 cats and 3 dogs how mush would be together
Answer:
6
Step-by-step explanation:
3+3 = 6
Answer:
There is 1 cat for each dog so the ratio would be 1:1 together.
Step-by-step explanation:
This means there are twice as many cats as dogs, or half as ... The ratio of 6:3 reduces to the ratio of 1:1
Leslie has a black and purple marker. She can
use either of them to write on either a white, pink
or yellow sticky note, is this a simple event or compound event?
Answer:
Compound
Step-by-step explanation:
A number b is increased by 6, and then the sum is doubled.
Answer:
2(b+6)
Step-by-step explanation:
Nick plans to start a home-based business producing and selling gourmet dog treats. He figures it will cost $20 in operating costs per week plus $0.50 to produce each treat. He plans to see each treat for $1.50. Graph y=0.5x+20 and y=1.5x to represent the situation
Answer: Nick needs to sell 20 treats to break even.
Carter has a piece of rope that is of a meter long. He
ties knots in the rope to divide it into 3 equal sections.
Use the expression
to find the length of each
section.
Each section of rope is meter long.
Answer:
1 foot
Step-by-step explanation:
1 meter = 3 feet
3 feet divided by 3 = 1 foot
The length of each section of the rope is 1 foot.
What is an expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.Many authors make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects.Solution -The piece of rope is 1m long.
Carter divided the ropes into three equal parts by tying up the knot.
1 meter = 3 foot.
Therefore, divide 3 by 3.
[tex]\frac{3}{3} =1[/tex] foot.
Therefore, each section is 1 foot long.
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Find the greatest common factor of 10, 3, and 6.
Answer:10
Step-by-step explanation:u have to see how many time can a number go into it
Hello do any no how to do this .If so can you tell me step by step please. It is called Solving Equations Puzzle.
I'm pretty sure you have to write how much they are
Pink heart is 2
Green square is 2
Blue moon 1
Answer:
Pink Heart = 2 Green Square = 6 Blue Moon = 4
Step-by-step explanation:
h ( h x g) = (b x g) = 24 left side of table
2 (2 x 3) = (4 x 6) = 24 right side of table
h(h x g ) = 2(2 x 3) = (4 x 6) = (b x g) = 24 equivalent outcomes
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?
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!
I WILL MAKE YOU BRAINLIEST FOR THE FIRST ONE TO SOLVE THIS FOR ME!!!
Which number is larger, A or B? Write more than a sentence to explain your reasoning.
(A) 9.675 x 10^24
(B) 1.109 x 10^28
Answer:
the answer is B
Step-by-step explanation:
when you take the first answer and subtract the second answer from it you get a negitive number of -1.1080325x10+28
HELP I NEEEEEEEEEEEEEEEED HELP
Answer:
It's B
Step-by-step explanation:
What is the volume of a rectangular prism that measures 2 & 2/6 inches by 3 & 3/7 inches by 2 inches.
Answer:
16 inch³
Step-by-step explanation:
Given that :
Length = 2 2/6 = 14/6 inches
Width = 3 3/7 = 24 /7 inches
Height = 2
The volume of a rectangular prism is given by :
Volume = Length * width * height
Volume = (14/6) * (24/7) * 2
Volume = 16 inch³
Please I need help with this it’s due at 3:30
Answer:
The y intercept is added to the new parent function.
Step-by-step explanation:
The parent function changed because the y intercept (SLOPE) was added into the new parent function. In order to prove that the change took place with the y intercept being added to the function, you can use any value from 2 and up.
Completion of substitution for X:
Original parent function: Plug in 2 for x
(2)^3 = 8
Completion of substitution for X with NEW parent function: plug in 2 for x
(2)^3 + 2 = 10
What 3-dimensional solid has a circular cross section when cut parallel to the base and a rectangular cross section when cut perpendicular to the base? A) cylinder B) sphere C) Triangular Prism D) Square Pyramid
Answer:
Option A ) Cylinder is correct.
Step-by-step explanation:
The important information need to consider is
1. Circular cross section when cut parallel to the base
2. Rectangular cross section when cut perpendicular to the base.
Let's consider each options.
Cylinder would have circular cross section when parallel to base and rectangle when it cut perpendicular to the base.
Yes! The cylinder works.
what is the mean .median ,mode of 2,3,4,3,2
Answer:
Step-by-step explanation:
mean = total / amount of numbers
= 15/5 = 3
median = 4 middle number
mode = most common numbers = 3,2
A pounds of apples and b pounds of plums were packed into n boxes. How many pounds of fruit are there in each box?
Answer:
(a + b) / n
Step-by-step explanation:
Pounds of apple in box = a
Pounds of plum in box = b
Number of boxes used in packing = n
The amount fruit in pounds that are in each box :
Total pound of fruits / number of boxes used
Total pounds of fruit = a + b
Number of boxes used = n
Hence, we have ;
(a + b) / n
Find the value of x
Answer:
x=23
Step-by-step explanation:
set them equal to each other since its not same sides
these are alternative exterior
8x-77=3x=38
5x=115
x=23
Answer:
23
Step-by-step explanation:
8x-77=3x+38 > 8x=3x+115 > 5x=115 > x=23