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]

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

The slope of the line below is-2. Which of the following is the point-slope
form of the line?
10-
10
10
(4-8)
10-
A. y + 8 = -2(x-4)
B. y - 8 = -2(x + 4)
c. y - 4 = -2(x+8)
a
D. y+ 4 = -2(x-8)

Expand to write an equivalent expression: −14(8x+12y)
Factor to write an equivalent expression: 36a−6
Pls solve these quick

Given: m∠B = 46°; m∠C = 45°; m∠R = 46°;
m∠T = 89°

Prove: △ABC ~ △TRS

Triangles A B C and T R S are shown. Angles A B C and T R S are 46 degrees. Angle B C A is 45 degrees. Angle R T S is 89 degrees.

Melissa believes that the AA similarity theorem can prove that the triangles are similar. Which fact would be necessary in the proof?

△ABC is an acute triangle.
△TRS is larger than △ABC.
The sum of the measures of the interior angles of a triangle is 180°.
The sum of the side lengths of two sides of a triangle is greater than the third side length

Lin opened a lemonade stand during the summer. She
noticed that she sold more lemonade on warmer days.
For each day she sold lemonade, she plotted the point
(t,c), where t represents high temperature and c
represents cups of lemonade sold.
b. A computer program found that the line c= 2t - 89
is a good fit for the data. Use this equation to predict
how many cups of lemonade Lin might sell on a day
when the high temperature is 74 degrees.
Use the sketch pad to show or explain your thinking.

find the nth term - 8,14,20,26

NEED HELP ASAP! TY IN ADVANCE <3 DO THE TABLE OF VALUES AS WELL!

Order the steps to solve the equation log(x2 - 15) = log(2x) form 1 to 5.
x² – 2x - 15=0
Potential solutions are -3 and 5
x² – 15 = 2x
X-5 = 0 or x + 3 = 0
(x - 5)(x + 3) = 0

What is the best measure of center for this data set?
{101, 2, 108, 104, 102, 107, 109, 102}

A.mean because there is an outlier

B.median because there is an outlier

C.mean or median because there is no outlier

D.mode because there is an outlier

b) Select all expressions that can be used to find 85% of 280.
A. O
8.5
10
280
B.
0.85
100
280
c. O
85
100
• 280

Find The Volume (nearest integer):*

what is the positive solution to this equation?
4x²+12x=135

HURRY I NEED HELPPPPP !!!!
Write each expression as a single power of 10 .

A. 10^(−3) ⋅ 10^(−2)

B. 10^4 ⋅ 10^(−1)

C. 10^5/10^7

D. (10^(−4))^5

E. 10^(−3) ⋅ 10^2

F. 10^y / 10^5

Jonas wants to paint the walls of his bedroom and the
ceiling. The dimensions of his room are 7 feet by 12 feet
by 8 feet
What statements about calculating the surface area of
the walls to be painted are correct? Select all that
apply.
Include the areas of all six faces.
Include the areas of five faces.
7 ft
Include the areas of four faces.
The surface area that will be painted is 376 ft?.
The surface area that will be painted is 472 ft2.
8 ft
12 ft

Zach wants to buy a skateboard that costs $85. He currently has $15 saved. Zach plans to save d, dollars to have enough to buy the skateboard. Which equation represents the amount of money Zach still needs to buy the skateboard? *

Henry's height is 3 inches more than one-half of Charlie's height. If Henry is 24 inches tall, how tall is Charlie?

How many times will a circle's diameter fit around that circle?​

The exponential function h, whose graph is given below, can be written as h(x) = a•b^x


Complete the equation for h(x).

I AM BEGGING, PLEASE HELP ME. CAN SOMEONE PLEASE HELP ME!

I NEED IT QUICK:
WHAT IS THE VALUE OF X - YOU DONT HAVE TO EXPLAIN YOUR ANSWER I JUST NEED THE VALUE OF X

(x^7 + 3x^6 - x^2 + 4) + (3x^7 - x^4 + 3x^2 - 9) add

In a certain country the heights of adult men are normally distributed with a mean of 69 inches and a standard deviation of 2.2 inches. The country's military requires that men have heights between 64.6 inches and 73.4 inches.

The slope of the tangent to a curve at any point (x, y) on the curve is negative x divided by y . Find the equation of the curve if the point (2, -2) is on the curve.

x + y = 0
x^2 - y^2 = -2
x^2 + y^2 = 16
x^2 + y^2 = 8

Expand (- 3a - 5x) (- 2b - 4y).​

1
Which is an equation of the line with slope 2 that contains the point (6,4)?
a.y= 22 - 8
1
y =
+1
b.
х
1
2
2 +4
C С.
1
y =
2
Question 2
Which is the equation of a line that passes through the point (5, 6) and has a slope of O?
a.y = 5
b.y=6
X cx=5
d. x = 6
Okoo

PLEASE HELP ME THANK YOU IF U DO

PLEASE SHOW WORK AND EXPLAIN IM AM VERY CONFUSED ASAP WILL GIVE BRAINLIEST 10 MINUTES TILL ITS DUE

Jack correctly wrote another expression, 100−2t 100 - 2 t , to find the number of tickets Kate has now. Use the drop-down menus to explain what each part of Kate's and Jack's expressions mean.

somebody help me fast pleaseee 5 rate

At work, Mr. Grinnell receives 20 phone calls every 60 minutes. How many calls should he expect to receive in 180 minutes?
60
80
100
40

One angle of an isosceles triangle measures 48°. Which other angles could be in that isosceles triangle? Choose all that apply.

Ahmad went on a bicycle tour. In the first two hours , he averaged 12 km/h; but in the next three hours he averaged 8 km/h;. A)Calculate the total distance covered b) , calculate his average speed for the whole journey