please help soon, i can't seem to figure this one out!!
Consider the following equation. -2x + 6 = -(2/3)^x + 5. Approximate the solution to the equation above using three iterations of successive approximation. Use the graph below as a starting point.
A. x = 3/4
B. x = 13/16
C. x = 7/8
D. x = 15/16
Answers
The required solution after three successive iterations is near x = 7/8. Option c is correct.
Equation is -2x + 6 = -(2/3)^x + 5. Approximate the solution to the equation above using three iterations of successive approximation.
The equation is the values of two expressions that are equal.
Here,
[tex]-2x + 6 = -(2/3)^x + 5[/tex]
Arranging the equation
[tex]-2x + 6 +(2/3)^x - 5 = 0\\(2/3)^x-2x+1=0[/tex]
Since the solution of the equation is when f(x) = 0 at near to x = 0.8
[tex]f(x) = (2/3)^x-2x+1\\[/tex]
First iteration at x =0.8
[tex]f(0.8) = (2/3)^x-2x+1\\ = (2/3)^{0.8}-2*0.8+1\\ = 0.123[/tex]
It will go up more to get exact zero, so
Second iteration at x = 0.9
[tex]f(0.9) = (2/3)^{0.9}-2*0.9+1\\f(0.9) = -0.106[/tex]
It seems that zero is near 0.9 so will go down
The third iteration at x = 0.87
[tex]f(0.87) = (2/3)^{0.87}-2*0.87+1\\f(0.87) = -0.037[/tex]
Here , solution is much near to x = 0.87 or x =7/8.
Thus, the required solution after three successive iterations is near x = 7/8.
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Related Questions
find the midpoint of Line ac
Answers
Answer:
-28
Step-by-step explanation:
-2-13=-15
-13-15=-28
Answer:
-28
Step-by-step explanation:
according to a survey, the population of a city doubled in 12 years.
The annual rate of increase of the population of this city is approximately _____. The population will grow to three times its current size in approximately ______.
First box of answers: 2.50, 5.78, 12.0, 50.0
Second box of answers: 18, 19, 23, 24.
Answers
Answer:
5.78
19
Step-by-step explanation:
Let original population be, P = x
Growth in 12 years, A = 2x
Rate be = r
Time = 12years
Find the rate :
[tex]A = P(1 + \frac{r}{100})^t[/tex]
[tex]2x = x(1 + \frac{r}{100})^{12}\\\\\frac{2x}{x} =(1 + \frac{r}{100})^{12}\\\\2 = (1 + \frac{r}{100})^{12}\\\\ \sqrt[12]{2} = (1 + \frac{r}{100})\\\\\sqrt[12]{2} - 1 = \frac{r}{100}\\\\2^{0.08} - 1 = \frac{r}{100}\\\\1.057 - 1 = \frac{r}{100}\\\\0.057 \times 100 = r\\\\r = 5.7 \%[/tex]
The annual rate of increase of the population of this city is approximately 5.78.
Find time in which the population becomes 3 times.
That is A = 3x
P = x
R= 5.78%
[tex]A = P( 1 + \frac{r}{100})^t\\\\3x = x ( 1 + \frac{5.78}{100})^t\\\\3 = (1.0578)^t\\\\log \ 3 = t \times log \ 1.0578 \\\\t = \frac{log \ 3}{ log \ 1.0578 }\\\\t = 19.55[/tex]
The population will grow to three times its current size in approximately 19years .
5.78% ,19 years are the answers.
2=(1+r)^12
r=(2)^(1÷12)−1
R=0.0578*100=5.78%
3=(1+0.0595)^t
t=log(3)÷log(1.0595)
t=19 years
What is an exponential growth model?
Exponential growth and exponential decay are two of the most common uses of exponential functions. Systems with exponential growth follow a model of the form y = y0ekt. In exponential growth, the growth rate is proportional to the amount present. In other words, for y'= ky
exponential function, multiply a by x to produce y. The exponential graph looks like a curve that starts with a very flat slope and becomes steep over time.
The exponential model, like the sphere model, starts at the origin and operates linearly near it. However, the increasing slope of the curve is less than the slope of the spherical model.
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|48+(-6)|+|-35+7|
Please help me with this! Thank you!
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{|48 - 6| + |- 35 + 7|}[/tex]
[tex]\mathsf{|48 - 6| = \boxed{\bf 42}}[/tex]
[tex]\mathsf{= 42 +| -35 + 7|}[/tex]
[tex]\mathsf{|-35 + 7| = \boxed{\bf -28}}[/tex]
[tex]\mathsf{= 42 + |- 28|}[/tex]
[tex]\mathsf{= 42 + 28}[/tex]
[tex]\boxed{\mathsf{= \bf 70}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf 70}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Use the properties of logs to determine how many more times severe was the San Francisco earthquake? The severity is equal to the ratio below:
Answers
Answer:
The answer is "158.489"
Step-by-step explanation:
for san francisco earthquake:
[tex]\log(\frac{a_1}{T}) + B = 7.8\\\\\log(\frac{a_1}{T})+\log(10^{B}) = 7.8\\\\\log(\frac{a_1}{T} \times 10^{B})=7.8\\\\(\frac{a_1}{T} \times 10^B=10^{7.8}...............(i)[/tex]
similarly , for coloumbia earthquake:
[tex]\frac{a_2}{T}\times 10^B = 10^{5.6}.................(ii)[/tex]
divide equation (i) and (ii):
[tex]\frac{a_1}{a_2}=\frac{10^{7.8}}{10^{5.6}}\\\\\frac{a_1}{a_2}=10^{2.2}\approx 158.489[/tex]
Jackson's cupcake recipe calls for 1 3/4 cups of sugar. He plans to make 3 1/2 times the recipe. How much sugar, in
cups, will Jackson need?
Answers
Answer:
6 1/8 cups
Step-by-step explanation:
multiply both numbers together
what are the step for distributive property to find the product for (a+8) (a-3)?
Answers
Answer:
---
Step-by-step explanation:
(a+8)(a-3)
You multiply a*a and a*-3 first.
a²-3a
Then you multiply 8*a and 8*-3.
8a-24
Then combine.
a²-3a+8a-24
Combine like terms.
a²+5a-24
So dat the answer.
---
hope it helps
Answer:
See below
Step-by-step explanation:
(a+8)(a-3)
See image for extra explanation.
a * a = a^2
a * -3 = -3a
8 * a = 8a
8 * -3 = -24
a^2 - 3a + 8a - 24
a^2 + 5a - 24
2x+1>
[tex]2x + 1 \geqslant 5 - x[/tex]
5-x
Answers
A study of a population of 102
parrakeets revealed that 4 out
of every 12 parakeets in the
population are blue.
Based on the results of this
study, how many parakeets in
the population are NOT blue?
Answers
Answer:
68
Step-by-step explanation:
4 out of 12 are blue.
Then 8 out 12 are not blue.
8 out of 12 is the same as the fraction 8/12 which can be reduced to 2/3.
2/3 of the birds are not blue.
2/3 of 102 = 2/3 * 102 = 68
Answer: 68
2) find the volume of the trapezoid prism 7in 6in 4in 12in
Answers
Answer: 228 in3 (sorry I don’t know how to do the mini number at the top)
Solve for x.
Please helpppp!
Answers
Answer:
Pythagoreas Theorem
Step-by-step explanation:
a^2+b^2=c^2
4^2+b^2=15^2
16+b^2=225
b^2= 209
14.45=b
Solve the equation y - 2.7 = -2.0 + 2y
Answers
Answer:
y = -0.7
Step-by-step explanation:
Reorder the terms:
-2.7 + y = -2.0 + 2y
Solving
-2.7 + y = -2.0 + 2y
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-2y' to each side of the equation.
-2.7 + y + -2y = -2.0 + 2y + -2y
Combine like terms: y + -2y = -1y
-2.7 + -1y = -2.0 + 2y + -2y
Combine like terms: 2y + -2y = 0
-2.7 + -1y = -2.0 + 0
-2.7 + -1y = -2.0
Add '2.7' to each side of the equation.
-2.7 + 2.7 + -1y = -2.0 + 2.7
Combine like terms: -2.7 + 2.7 = 0.0
0.0 + -1y = -2.0 + 2.7
-1y = -2.0 + 2.7
Combine like terms: -2.0 + 2.7 = 0.7
-1y = 0.7
Divide each side by '-1'.
y = -0.7
Simplifying
y = -0.7
Need help on this please ASAP ????? DUE SOON
Answers
Answer:
[tex]33.5\:\mathrm{ft^3}[/tex]
Step-by-step explanation:
The volume of a cone is given by [tex]V=\frac{1}{3}\cdot r^2\pi\cdot h[/tex], where [tex]r[/tex] is the radius of the cone and [tex]h[/tex] is its height.
What we're given:
[tex]r[/tex] of 2 [tex]h[/tex] of 8Solving, we get:
[tex]V=\frac{1}{3}\cdot 2^2\pi\cdot 8\approx\boxed{33.5}[/tex]
Answer:
The volume of cone is 33.5ft ³.
Step-by-step explanation:
Using Formula,
Volume of cone = 1/3 × π × r ² × h
Where, r is the radius and h is the height of the cone.
We have givenRadius of cone, r = 2 ft
Height of cone , h = 8 ft
substitute the values into the formula
Volume of cone = 1/3 × 3.14 × ( 2ft ) ² × 8ft
Volume of cone = 1/3 = 3.14 × 4 ft ²× 8ft
multiply
Volume of cone = 1/3 × 100.8 ft ³
divide, we get
Volume of cone = 33.50 ft ³.
Therefore,the volume of cone is 33.50 ft³.
A supermarket sells various brands of peanut butter.
• Brand A costs $1.92 per jar, and each jar contains 12 ounces.
• Brand B costs $2.40 per jar, and each jar contains 16 ounces.
Which brand costs less per ounce
Answers
there is a population of 100,000 bacteria in a colony . if the number of bacteria doubles every 3 hours what will be 6 hours from now
Answers
Answer:
400,000 bacteria
Step-by-step explanation:
If we start at 100,000 and double every three hours until 6 hours, to colony will be at 400,000 bacteria.
First find out how many times it will double by dividing 6/3=2. It will double twice in 6 hours. Next double 100,000 once, to get 200,000. Then, double it once more to get to the final answer of 400,000 bacteria.
Hope this helps!
If y = 100 when x = 15, which equation could you use to find the value
of k?
Answers
Answer:
y+x=k
Step-by-step explanation:
ABC was dilated to create A' B' C'. What is the center of dilation? And what is the scale factor of the dilation?
Answers
Given:
In the given figure the vertices of triangle ABC are A(-2,2), B(4,2), C(-2,-2).
The vertices of triangle A'B'C' are A'(-4,4), B'(8,4), C'(-4,-4).
To find:
The center of dilation and the scale factor.
Solution:
In the given graph, draw the lines AA', BB' and CC'. The intersection point of these lines is the center of dilation.
From the below graph, it is clear that the lines AA', BB' and CC' intersect each other at (0,0).
Therefore, the center of dilation is (0,0).
If a figure is dilated by factor k and the center of dilation is origin, then
[tex](x,y)\to (kx,ky)[/tex]
[tex]A(-2,2)\to A'(k(-2),k(2))[/tex]
[tex]A(-2,2)\to A'(-2k,2k)[/tex]
It is given that A'(-4,4). So,
[tex](-2k,2k)=(-4,4)[/tex]
On comparing both sides, we get
[tex]-2k=-4[/tex]
[tex]2k=4[/tex]
[tex]k=\dfrac{4}{2}[/tex]
[tex]k=2[/tex]
Therefore, the scale factor is 2.
What is the measure of the angles? (Help pls)
Answers
Answer:
13 degrees
Step-by-step explanation:
working out is attached
hope it helps:)
A school has two photocopiers. On any given day, machine A has an 8% chance of malfunctioning
and machine B has a 12% chance of malfunctioning. Determine the probability that on any given
day, both machines will: malfunction
Answers
probability they both malfunction = 0.08 x 0.12 = 0.0096
Find the circumference of a circle whose area is /. A. B. C. D. Please select the best answer from the choices provided A B C D
Answers
Answer:
Circumference of circle = (15.5)π cm
Step-by-step explanation:
Missing information:
Area of circle = 60π cm²
Find:
Circumference of circle
Computation:
Area of circle = πr²
Area of given circle = π(Radius of circle)²
60π = πr²
60 = r²
Radius of circle = 7.75 cm (Approx)
Circumference of circle = 2πr
Circumference of circle = 2(π)(7.75)
Circumference of circle = (15.5)π cm
Describe the relationship between ∠2 and ∠8
Answers
Answer:
Alternate Interior Angles
Step-by-step explanation:
Angles can be corresponding; alternate or same side; or interior or exterior. The angles 2 and 8 are on opposite sides of the transversal; this means that they must be alternate angles. Additionally, they are both within the parallel lines, so they are interior. Alternate interior angles are always congruent. Therefore, their measurements must be equal.
Answer:
They are alternate interior angles
Step-by-step explanation:
<2 and <8 are inside the parallel lines and on opposite sides of the transversal
They are alternate interior angles
[tex]\huge\mathfrak\green{please \: help...} \\ \\ \huge\mathfrak\red{5 {}^{2} + 6 {}^{2} = {?} ...}[/tex]
Answers
61 is a required answer.
Answer:
[tex]\boxed{5²+6²=5*5+6*6=25+36=61}[/tex]
Find the missing angle measurements
Answers
Answer:
look at picture.
Step-by-step explanation:
every angle in a triangle equals 180° and every straight line equals 180°. So you just take the angles given in each triangle and subtract from 180° to get the total of the 3rd angle.
How to solve a+52/3=9
Answers
Answer:
-25/3
Step-by-step explanation:
Answer:
a+52/3=9
a + 52/3 - 52/3 = 9 - 53/3
a=[tex]\frac{27- 53}{3}[/tex]
a= [tex]\frac{26}{3}[/tex]
Step-by-step explanation:
Given the function g(x) = 2x2 - 3
Is this statement true or false? g(2) = g(-2)
Answers
g(2)=5 but g(-2)= -11
And I don't know if what I analyzed is true or not...!!!
Which Statement About The Data Is True? 52 56 60 64 68 72 76 80 A. The difference between the medians is about 4 times the range. B. The difference between the medians is about 4 times the IQR. C. The difference between the medians is about 2 times the range. D. The difference between the medians is about 2 times the IQR.
Answers
Answer:
The answer is "Option B".
Step-by-step explanation:
IQR for the first boxplot [tex]= Q_3 - Q_1 = 77-73 = 4[/tex]
IQR for the first boxplot [tex]= Q_3 - Q_1 = 63-59 = 4[/tex]
Calculating the median for the first boxplot [tex]= 76[/tex]
Calculating the median for the second boxplot [tex]= 60[/tex]
Calculating the difference:
[tex]\to 76-60 = 16[/tex]
therefore, the difference between medians is about 4 times the IQR.
Answer:
B
Step-by-step explanation:
did the test
Twice the complement of an angle is 25 less than 3 times the angle. Find the measure of both angles.
Answers
Answer:
Step-by-step explanation:
Let the angles size = x
The complement of the angle is 90 - x
Two times the compliment is 2*(90 - x)
Three times the angle is 3x
25 less than 3 times the angle = 3x - 25
Now you have to equate the two bolded pieces of information.
3x - 25 = 2(90 - x) Remove the brackets
3x - 25 = 180 - 2x Add 25 to both sides
25 25
3x = 205 - 2x Add 2x to both sides.
2x 2x
5x = 205 Divide by 5
5x/5 = 205/5
x = 41
The compliment of x = 90 - 41 = 49
The angle itself = 41
True or False? The blue radius is perpendicular to the green cord.
Answers
Answer:
true
Step-by-step explanation:
Answer:
False. if it was perpendicular than the segments would be equal
Step-by-step explanation:
pls help me ill give brainliest and no links pls ty!:)
Answers
Given : GH bisects ∠FGI
It means : ∠FGH and ∠HGI are equal
Given :
∠FGH = (5x - 8)°
∠HGI = (6x - 15)°
⇒ 5x - 8 = 6x - 15
⇒ 6x - 5x = 15 - 8
⇒ x = 7°
Substituting the value of x, We get :
∠FGH = 5(7) - 8 = (35 - 8) = 27°
∠HGI = 6(7) - 15 = (42 - 15) = 27°
∠FGI = ∠FGH + ∠HGI = (27 + 27) = 54°
A flower bed is in the shape of a triangle, with a base of 11 feet and a height of 7 feet. What is the area of the flower bed?
a. 38.5 square feet
b. 42.5 square feet
c. 72 square feet
d. 77 square feet
Answers
Answer:
a. 38.5 square feet.
Step-by-step explanation:
11*7 = 77
77/2 = 38.5
Hope this helps! Good luck with your work.
Mark as brainliest if you'd like :D
Helppppppppp meeeeeeeeeeee