Answer:
[tex]x \approx 2.740646096[/tex]
Step-by-step explanation:
Given:
[tex]x\log_{10}x=1.2[/tex]
Rewrite so that it's equal to zero:
[tex]\implies x\log_{10}x-1.2=0[/tex]
Therefore:
[tex]\implies f(x)=x\log_{10}(x)-1.2[/tex]
Differentiate the function:
Use the product rule to differentiate [tex]x\log_{10}(x)[/tex]:
[tex]\textsf{Let }u=x \implies \dfrac{du}{dx}=1[/tex]
[tex]\textsf{Let }v=\log_{10}(x) \implies \dfrac{dv}{dx}=\dfrac{1}{x \ln 10}[/tex]
[tex]\begin{aligned}\implies \dfrac{dy}{dx} & = u\dfrac{dv}{dx}+v \dfrac{du}{dx}\\& = \dfrac{x}{x \ln 10}+\log_{10}(x)\\& = \dfrac{1}{\ln 10}+\log_{10}(x)\end{aligned}[/tex]
[tex]\implies f'(x)=\dfrac{1}{\ln 10}+\log_{10}(x)[/tex]
[tex]\implies f'(x)=\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}[/tex]
Newton-Rhapson iteration formula
[tex]x_{n+1}=x_n-\dfrac{f(x_n)}{f'(x_n)}[/tex]
Substitute the function and its derivative into the formula, replacing x with [tex]x_n[/tex]:
[tex]\implies x_{n+1}=x_n-\dfrac{x_n\log_{10}(x_n)-1.2}{\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}}[/tex]
[tex]\implies x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]
Therefore, the iteration formula is:
[tex]x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]
Let [tex]x_0=3[/tex]
Substitute this into the formula and carry out 3 iterations:
[tex]\implies x_{1}=3-\dfrac{3\ln 10\log_{10}(3)-1.2\ln 10}{1+\ln 10 \log_{10}(3)}=2.746149035[/tex]
[tex]\implies x_2=2.740648841[/tex]
[tex]\implies x_3= 2.740646096[/tex]
Find the original price of a pair of shoes if the sale price is 9$ after a 75% discount
Answer:
Original price=$12
Step-by-step explanation:
First set that up as an equation
9/a=75/100
Now cross multiply
75a=900
Then divide 75 from both sides for original price
75a/75=900/75
a=12
There's your answer
Hope this helped :)
Help please
A.-3
B.-1/3
C.1/3
D.3
(-4,3)
-5-4-3
24
5
432
-14
-2
-3-
A
(0,1)
1 2
(4,-1)
Which linear function is represented by the graph?
Of(x) = -2x + 1
Of(x)=x+1
O f(x) = x+1
Of(x)=2x+1
Answer:
f(x) = -2x+1
Step-by-step explanation:
See attached image
The equation of line will be;
⇒ f (x) = - 1/2x + x
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (- 4, 3) and (4, -1).
Now,
Since, The equation of line passes through the points (- 4, 3) and (4, -1).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 1 - (3)) / (4 + 4)
m = - 4 / 8
m = - 1/2
Thus, The equation of line with slope - 1/2 is,
⇒ y - (3) = - 1/2 (x + 4)
⇒ y - 3 = - 1/2x - 2
⇒ y = - 1/2x + x
Therefore, The equation of line will be;
⇒ f (x) = - 1/2x + x
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A rectangular tank measures 1.2m by 0.8m by 0.5m.
(a) Water flows from the full tank into a cylinder at a rate of 0.3m3
/min.
Calculate the time it takes for the full tank to empty.
Give your answer in minutes and seconds.
By knowing that water outflow is stable and the known geometry, the draining time of the rectangular tank is equal to a time of a minute and 36 seconds.
How to determine the draining time of a rectangular tank
In this question we must determine the draining time of a tank whose dimensions are known and whose water outflow is stable. The draining time is equal to the volume of the rectangular tank divided by outflow rate:
V = (1.2 m) · (0.8 m) · (0.5 m)/(0.3 m³/min)
V = 1.6 min
By knowing that water outflow is stable and the known geometry, the draining time of the rectangular tank is equal to a time of a minute and 36 seconds.
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Write the equation of the line that is parallel to the line y = -x - 2 through the
point (4,-2)
Answer:
y = -x +2
Step-by-step explanation:
Equation of a line in slope-intercept form :
y = mx + b where m = slope and 'b' is the y-axis intercept
y = -x-2 is in this form..... slope m = -1 b = -2
the parallel line will have the same slope = -1 and will look like
y = -x + b
to calculate the value of 'b' for this line, substitute in the point given:
-2 = - (4) + b shows b = 2
so your line becomes y = -x + 2
Answer:
y =-x + 2
Step-by-step explanation:
Equation of line:Parallel lines have same slope.
y = -x - 2
Compare with the equation of the line in slope y-intercept form: y =mx + b
Slope = m = -1
So, equation of line: y = -x + b
Point(4 ,-2) is going through this line. so, substitute x = 4 & y = -2 in the above equation.
-2 = -4 + b
-2 + 4 = b
[tex]\sf \boxed{b = 2}[/tex]
Equation of the required line:
[tex]\sf \boxed{\bf y = -x + 2}[/tex]
What is the square root of 48 simplified?
Please help me smart peeps
Determine if the two triangles below are similar and state how you know.
The first and foremost rule for determining if 2 triangles are similar is checking if their angles are the same. Obviously, in this example, the angles are completely different, so the triangles are not similar.
Have a nice day!
And good luck on the assignment!
Which of the lines below is a line of symmetry?
O A. Red
•
B. Yellow
C. Neither
• D. Both
Both the Red and Yellow lines are lines of symmetry, Option D is correct.
What is Coordinate system?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
Lines of symmetry in a figure are lines that divide the figure into equal parts.
The given figure is a square as we observe the four sides are equal in the given shape.
In a square, there are four lines of symmetry, each of which divides it into two identical parts.
The symmetry lines of a square are both its diagonals and the lines joining the midpoints of its opposite sides (bisectors).
In the given Figure, the Red lines cuts the shape into 2 equal halves vertically and the Yellow line cuts the shape into 2 equal halves diagonally.
Hence, both the Red and Yellow lines are lines of symmetry, Option D is correct.
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In which direction must the graph of f(x) = x be shifted to produce the graph of g(x) = x − 6?
Answer:
f(x) must be shifted 6 units down in order to produce the graph of g(x).
PLEASE HELP FAST!!!
By trigonometric functions and law of cosines, the value of x associated with a missing angle in the geometric system is between 7.701 and 7.856.
How to find a missing variable associated to an angle by trigonometry
In this question we have a geometric system that includes a right triangle, whose missing angle is determined by the following trigonometric function:
sin (7 · x + 4) = 12/14
7 · x + 4 = sin⁻¹ (12/14)
7 · x + 4 ≈ 58.997°
7 · x = 54.997°
x ≈ 7.856
In addition, the geometric system also includes a obtuse-angle triangle and that angle can be also found by the law of the cosine:
7² = 8² + 6² - 2 · (8) · (6) · cos (7 · x + 4)
17/32 = cos (7 · x + 4)
7 · x + 4 = cos⁻¹ (17/32)
7 · x + 4 ≈ 57.910°
7 · x ≈ 53.910°
x ≈ 7.701
Hence, we conclude that the value of x associated with a missing angle in the geometric system is between 7.701 and 7.856.
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Answer two questions about system a and b
Answer:
Question 1: A. Replace one equation with a multiple of the other equation
Question 2: B. No
Step-by-step explanation:
1) How can we get System B from System A?
Choose 1 answer:
A. Replace one equation with a multiple of the other equation
B. Replace one equation with a multiple of itself
C. Swap the left-hand sides of both equations
D. Swap the order of the equations
2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
Choose 1 answer:
A. Yes
B. No
The answer to both questions is in bold and in the "Answer" section.
Hope this helps!
If not, I am sorry.
Mrs. Cooper hosts an annual art contest for kids. She has records of the number of entries for the last 9 years. She received 30 entries in the first year. Over the next 3 years, the number of entries increased by 10 kids per year. In the next 2 years after that, there were 60 entries each year, and in the last 3 years, the number of entries increased by 15 kids per year. Which graph models the piecewise function for the given situation, where x represents time after the first year and y represents the number of entries in that year?
To graph this situation we must take into account the data and the organization of each of them on the X axis and Y axis.
How to graph this situation?To graph this situation we must take into account the data we have:
YearsTicketsBased on these data, we assign the horizontal axis to count years and the vertical axis to count tickets per year. We must continue the pattern of increased attendance over the years.
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How do i graph those
The graph of (2x - 1) / (x + 2) have intercepts at (0.5, 0) and (0, -0.5), The graph of (1 - 4x) / (1 - x) have intercepts at (0, 1) and (0.25, 0) and The graph of (-3x - 4) / (x + 2) have intercepts at (-1.33, 0) and (0, -2).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Plotting the graph using geogebra online graphing tool.
The graph of (2x - 1) / (x + 2) have intercepts at (0.5, 0) and (0, -0.5), The graph of (1 - 4x) / (1 - x) have intercepts at (0, 1) and (0.25, 0) and The graph of (-3x - 4) / (x + 2) have intercepts at (-1.33, 0) and (0, -2).
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Find the mean of the following group of numbers: 6. 1, 5. 9, 4. 2, 5. 9, and 10. 7. Round your answer to the nearest tenth
Answer:
6.6
Step-by-step explanation:
the "mean" of a data set is what we commonly refer to as the average. We find this estimate of values by adding up all of the values of the data set, and then dividing by the number of values we added together.
{for example: the mean [average] of 1, 5, 6:
1 + 5 + 6 = 12
12 ÷ 3 [we have 3 numbers] = 4}
our values:
6.1 ; 5.9 ; 4.2 ; 5.9 ; 10.7
> 6.1 + 5.9 + 4.2 + 5.9 + 10.7 = 32.8
[we have 5 numbers]
32.8 / 5 = 6.56
when rounding a number, we look to the digit one place to the right. If it is greater than or equal to 5, we "round up" our digit [we move it up to the next digit]
if it is less than 5, we keep our digit the same
(the tenths place = _ . _ _ _ ones. tenths)
so if we round 6.56 to the nearest tenth:
6.56
[6 > 5]
6.6
So, the mean of this data set rounded to the nearest tenth is 6.6
hope this helps!!
A health food store has launched a new pack of vitamins for children. The store records the number of packs ordered by a random sample of 100 online customers and the number of packs ordered by a random sample of 100 walk-in customers.
Two dot plots are shown one below the other. The title for the top dot plot is Online Customers and the title for the bottom plot is Walk In Customers. Below the line for each dot plot is written Number of Packs. There are markings from 1 to 5 on each line at intervals of one. For the top line there are 0, 0, 1, 4, 5 dots respectively for marks from 1 to 5. For the bottom line there are 3, 6, 1, 0, 0 dots respectively for marks from 1 to 5. On the right side, towards the middle of the two plots is shown a dot symbol equal to 10 customers.
Which inference can be drawn about the buying pattern of the online customers versus that of the walk-in customers?
Online customers buy an average of 4 packs compared with walk-in customers, who buy an average of 1 pack.
Online customers buy an average of 5 packs compared with walk-in customers, who buy an average of 2 packs.
Online customers buy an average of 4 packs compared with walk-in customers, who buy an average of 2 packs.
Online customers buy an average of 5 packs compared with walk-in customers, who buy an average of 1 pack.
Answer:
Online customers buy an average of 4 packs compared with walk-in customers, who buy an average of 2 packs.
Step-by-step explanation:
Create the dot plots (see attached diagrams)
Online customers: blue dots
Walk-in customers: red dots
To calculate the average packs both groups of customers buy, sum all data values and divide by the total number of data values.
[tex]\textsf{Average of Online customers}=\dfrac{ 1 \times 3+ 4 \times 4+ 5\times 5}{10}=4.4[/tex]
[tex]\textsf{Average of Walk-in customers}=\dfrac{ 3 \times 1+ 6\times 2+ 1\times 3}{10}=1.8[/tex]
Online: 4.4 rounds down to 4
Walk-in: 1.8 rounds up to 2
Therefore, online customers buy an average of 4 packs compared with walk-in customers, who buy an average of 2 packs.
Find average of both customers
Online :-
3+4(4)+5(5)/103+16+25/1044/104.44Offline
3+6(2)+3/106+12/1018/101.82option C
On a map 1/4 inch between represnts an actual distance of 2 miles between the location what is the actual distance in miles between two cities that are 3 3/4 inch apart on the map
Answer:
30 miles is the actual distance.
Step-by-step explanation:
3 3/4 = 15/4
15*2=30
Which statements accurately describe the function f(x) = 3(16) superscript three-fourths x? select three options.
Range for the given Exponential function [tex]f(x) = 3(16)^{{\frac{3}{4}x}[/tex] is f(x) > 0.
the correction option is a). f(x) > 0
The function given in, the question is exponential function is given by
[tex]f(x) = 3(16)^{{\frac{3}{4}x}[/tex] Which is an exponential function. The domain of the give function is (-∞, ∞).
The function which is in format f(x) = [tex]a^{x}[/tex] where, a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
the Question seems to be incomplete. And options could be
a) f(x) > 0 c) f(x) ≤ 0
b) f(x) < 0 d) f(x) ≥ 0
Simplification of the given equation
[tex]f(x) = 3(16)^{{\frac{3}{4}x}[/tex]
[tex]f(x) = 3(2^4)^{{\frac{3}{4}x}[/tex]
[tex]f(x) = 3(8)^{x}[/tex]
clearly, the range of the exponential function is f(x) > 0.
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work out 6z - 4z .what is the answer?
Answer:
4 is the answer
Step-by-step explanation:
you can - or + the equation only then when the letter is same z and z both are same so you can - them and get the answer.
An airline claims that it rarely loses a passenger's checked luggage, and, if checked luggage is lost, 90% of the luggage is recovered and returned to the owner within 24 hours. A consumer group believes the 24-hour recovery rate of lost luggage is actually lower (worse) than the airline's claim. They surveyed a large random sample of the airline's customers and found that 103 of 122 people who had lost luggage were reunited with the missing items within 24 hours. Is this enough evidence to claim the proportion of people who lost luggage with this airline a
The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.
What is a null hypothesis?Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.
It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.
The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.
In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.
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The side length of a square is 3x^2 . Find The area of the square
Answer: A=9x^4
Step-by-step explanation:
Hii, do you need to find the area of a square with a side length of 3x^2? Let me help you out! (:
AreaTo find the area of a square, you need to square its side length.
Sounds strange, right?
The formula is shown below.
[tex]\LARGE\boldsymbol{A=a^2}[/tex]
Here "A' (capital A) denotes the area
"a" (lower-case a) denotes the side length
The 2 above the a tells us that we need to multiply the side length times itself.
Alright, now it's just a matter of sticking in the known values...
[tex]\sf A=(3x^2)^2[/tex]
Simplify
[tex]\sf A=9x^4[/tex]
Voila! There's our answer, cheers! (;
_________Hope I helped! Best wishes! (:
Reach far. Aim high. Dream big.
________[tex]\underbrace[/tex]
help pls i’ll do anything D:
Answer:
search it up ok that's all you can do
The slope of a line perpendicular to the line containing (0,3)and (-2,0) is: The slope of a line perpendicular to the line containing ( 0,3 ) and ( -2,0 ) is :
Answer:
Step-by-step explanation:
The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation y = −0.4x2 + 3x, where y is the height above water and x is the horizontal distance in feet. If a beam of light is shone upward at an angle modeled by the equation x + y = 10, at what height from the water's surface will the beam of light hit the dolphin?
Answer:
5 feet
The graphs intersect at x = 5.
Pretest: Manipulating and Interpreting Expressions
Drag each expression to the correct location on the table.
Place each algebraic expressions next to its corresponding verbal description.
5³-²-1 (5-4)³
the difference of 5 times the cube of x cubed and
the quotient of 4 times x and 3
5 times the cube of x divided by 4 times x
the quotient of the difference of 5 times x cubed and 4 and x
the cube of the difference of 5 times x and 4
Submit
Answer:
9
Step-by-step explanation:
0
An organization supports 125 villages financially. This figure is only 11% as compared to the organization's worldwide support. How many villages does the organization support worldwide?
If organisation supports 125 villages financially and it is 11% of world wide then the total villages in world wide that needs help is 1136.36 villages.
Given An organization supports 125 villages financially. This figure is only 11% as compared to the organization's worldwide support.
If 125 villages are 11% of worldwide villages who need help financially then we have to find 100% value according to organisation figure which can be calculated as under:
if 125 is 11% then 1% will be 125/11
then 100% will be 125/11*100
=12500/11
=1136.36
=1136 Approx
Hence 1136 villages are totally present worldwide which need help financially.
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Given √b6.
What is the rational exponent form of this expression?
O b1/3
0 b3
O b6
O b3/2
The rational exponent form of the given expression is b³. The correct option is the second option b³
Evaluating an expressionFrom the question, we are to determine the rational exponent form of the given expression
The given expression is
[tex]\sqrt{b^{6} }[/tex]
From one of the laws of indices, we have that
[tex]\sqrt[n]{x^{m} } = x^{\frac{m}{n} }[/tex]
Thus,
[tex]\sqrt{b^{6} } = b^{\frac{6}{2} }[/tex]
= [tex]b^{3}[/tex]
∴√b⁶ = b³
Hence, the rational exponent form of the given expression is b³. The correct option is the second option b³
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I will give brainiest to the first person who responds BUT only if the answer is correct
Answer:
70 cm2??
Step-by-step explanation:
The area of the rectangle: 50 cm2
The area of the triangle: About 20 cm2
50 cm2 + 20 cm2 +
What shift will occur to the graph given the following equation?
y≤ |x + 2|
Graph will shift 2 units to the left.
Graph will shift 2 units to the right.
Graph will shift 2 units down.
Graph will shift 2 units up
Answer:
Graph will shift 2 units to the left
OVER DUED HOMEWORK pls help!! T-T
Answer:
see explanation
Step-by-step explanation:
(9m + 4)² - (9m - 4)² ← expand both factors using FOIL
= 81m² + 72m + 16 - (81m² - 72m + 16) ← distribute parenthesis by - 1
= 81m² + 72m + 16 - 81m² + 72m - 16 ← collect like terms
= 144m
= 72(2m)
which is divisible by 72 for all m
7 times 36 = 21 times ?
help needed asap :)
Answer:
7*36=21*x
252=21x
x=12
Hope it helps!
Answer:
12
Step-by-step explanation:
Let x be the unknown number.
Method 1
[tex]\implies \sf 7 \times 36 = 21 \times x[/tex]
[tex]\implies \sf 252 = 21x[/tex]
[tex]\implies \sf \dfrac{252}{21} = \dfrac{21x}{21}[/tex]
[tex]\implies \sf 12=x[/tex]
[tex]\implies \sf x=12[/tex]
Method 2 (using mental arithmetic)
[tex]\implies \sf 7 \times 36 = 21 \times x[/tex]
As 7 and 21 are both multiples of 7, divide both sides by 7:
[tex]\implies \sf 36=3x[/tex]
Divide both sides by 3:
[tex]\implies \sf 12=x[/tex]
[tex]\implies \sf x=12[/tex]
