Answer:
x ∈ [-0.369, 0.678]
Step-by-step explanation:
To prove - [tex]\sqrt[4]{1 + 2x}[/tex] ≈ 1 + [tex]\frac{1}{2}[/tex] x
As given , f(x) = [tex]\sqrt[4]{1 + 2x}[/tex]
As we know that the linear approximation can be defined as :
L(x) = f(a) + f'(a)(x-a) .........(1)
Now,
We have to show that at a = 0 , equation (1) satisfies
Now,
f(0) = [tex]\sqrt[4]{1 + 0}[/tex] = 1
Also,
f'(x) =
[tex]\frac{d}{dx} (\sqrt[4]{1 + 2x} ) = \frac{1}{4}(1 + 2x)^{\frac{1}{4} - 1}\frac{d}{dx}(1 + 2x) ) \\ = \frac{1}{4}(1 + 2x)^{\frac{-3}{4} } (2)\\ = \frac{1}{2}(1 + 2x)^{\frac{-3}{4} }\\[/tex]
∴ we get
f'(x) = [tex]\frac{1}{2}(1 + 2x)^{-\frac{3}{4} }[/tex]
⇒f'(0) = [tex]\frac{1}{2}[/tex]
Now, equation (1) becomes
L(x) = f(0) + f'(0)(x-0)
= 1 + [tex]\frac{1}{2}[/tex] (x)
⇒ [tex]\sqrt[4]{1 + 2x}[/tex] ≈ 1 + [tex]\frac{1}{2}[/tex] x
Hence verified.
Now,
|[tex]\sqrt[4]{1 + 2x}[/tex] - (1 + [tex]\frac{1}{2}[/tex] x ) | ≤ 0.1
⇒ -0.36893 ≤ x ≤ 0.67766
⇒x ∈ [-0.369, 0.678]
Melkon travels 8/11 miles to the grocery store. Tamar travels 12 miles to the grocery store. Write the ratio of the distance Tamar travels to the distance Melkon travels as a fraction in simplest form. Write the ratio of the distance Melkon travels to the distance Tamar travels as a fraction in simplest form.
Answer: 33/2 and 96/11.
Step-by-step explanation:
The ratio of the distance Tamar travels to the distance Melkon travels:
[tex]\dfrac{12}{\frac{8}{11} } =\dfrac{12 \cdot 11}{8} =\dfrac{132}{8} =\dfrac{33 \cdot 4}{2 \cdot 4} =\dfrac{33}{2}[/tex]
The ratio of the distance Melkon travels to the distance Tamar travels:
[tex]\dfrac{\frac{8}{11} }{12} =\dfrac{8 \cdot 12}{11} =\dfrac{96}{11}[/tex]
A bake sale sells cupcakes for $.75 and brownies for $.50 Billy spends $10 at the sale using C for cupcakes and beef or brownies write a linear equation for the amount spent by Billy for cookies and brownies
Answer:
Stuck on it
Step-by-step explanation:
solve for y.
-13=4y+3
Answer:
-13=4y+3 -3
-16=4y ÷4
-4=y
Step-by-step explanation:
hope it helps ^^
Answer:
y = -4
explenation in picture
Can anyone solve this?
Answer:
x = 35°
∠Q = 127°
∠R = 35°
∠P = 18°
Step-by-step explanation:
x + 2x + 57 + x - 17 = 180 {Angle sum property of triangle}
x + 2x + x +57 -17 = 180 {Combine like terms}
4x + 40 = 180
4x = 180 - 40
4x = 140
x = 140/4
x = 35
∠Q = 2x + 57 = 2*35 + 57 = 70 +57 = 127°
∠R = x = 35°
∠P = x - 17 = 35 - 17 = 18°
The price of a 7-minute phone call is $1.05. What is the price of a 19-minute phone call
Answer:
19.95
Step-by-step explanation:
if you take 1.05 times it by 19 you get your answer
3 : 7 = 300 : x fill in the x for the equivalent ratios
Answer: 300:700
Step-by-step explanation:
If you have a 3:7 ratio and you multiply the 3 by 100, you would also have to multiply the 7 by 100, giving you a 300:700 ratio. Plz note I could be wrong but I believe that is the answer you are looking for
HELP PLEASE...........
Answer:
1. 9
2. 12
3. 26
Step-by-step explanation:
Answer:
1. 9
2. 12
3. 26
Step-by-step explanation:
An easy way to solve problems like this is to convert the percentage into a decimal, then multiply that decimal by the whole. For example, if I had the question "What is 10% of 100?", I would first convert the 10% to a decimal. 10% is the same as 10/100, which in decimal form is 0.1. I would then multiply 0.1 by 100 to find out how much 10% of 100 is. I get 10, so my answer is 10. Hope this helps!
A +3178 equals 6000 evaluate
Answer:
A=2822
Step-by-step explanation:
A+3178=6000
A=6000-3178
A=2822
Steph Curry scored 62 points in 36 minutes of playing time. What was the unit rate? (points per minute)
A. 9
B. 1 13/18
C. 25.3
D. 6
Answer:
b
Step-by-step explanation:
it is
Answer:
B. 1 13/18
Step-by-step explanation:
1 13/18 x 36 = 62
Write in lowest terms:
9/(15x)
Answer:
Step-by-step explanation:
3x - 25
———————
5
Should be something similar to that, sorry If i couldn't help much.
I will give brainliest please help
Answer:
2.5
Step-by-step explanation:
[tex] \frac{u}{11} = \frac{3}{13} \\ \\ u = \frac{3 \times 11}{13} \\ \\ \\ \\ u = \frac{33}{13} \\ \\ u = 2.53846154 \\ \\ u \approx2.5[/tex]
Enter the product in simplest form 8/12 x 3/8
Answer:
1/4
Step-by-step explanation:
I simplified before multiplying
8/12=2/3
2/3*3/8
Cross simplilify and get
1*1/4
1/4
solve the equation 1/2x+7=18
Answer: 22
Step-by-step explanation:
Solve for x
1/2x + 7 = 18
Combine 1/2 and x.
x/2+ 7 = 18
Move all terms not containing x to the right side of the equation.
Subtract 7 from both sides of the equation.
x/2= 18 − 7
x/2 = 11
Multiply both sides of the equation by 2.
2 ⋅ x/2 = 2 ⋅ 11
Simplify both sides of the equation.
Cancel the common factor of 2.
x = 2 ⋅ 11
Multiply 2 by 11.
x = 22
if I was 15 ft tall and I grew 17 yards how much have I grown
Answer:
66 ft or 22 yards
Step-by-step explanation:
1 yard = 3 ft.
Convert 15 ft to yards (multiply by 3) and add 17.
(3x + 4) (1 - 1)
Evaluate the limit lim
a.-3
b. 3
c. 1
d limit does not exist
could anyone help me find the area of this please :)
Answer:
40
Step-by-step explanation:
if you cute the shape into 2 triangles and move them to make a square you'll get 5 and 8, then multiply them together and you'll get 40
my question is on the image it would mean the world to me if you could help
Answer:
a. Slope of f(x) is greater than g(x)
b. y-intercept of f(x) is less than the y-intercept of g
Step-by-step explanation:
Function f(x)
Given the function f(x)
x f(x)
-3 -0.5
-2 0
-1 0.5
0 1
Finding the slope between any two points
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-3,\:-0.5\right),\:\left(x_2,\:y_2\right)=\left(-2,\:0\right)[/tex]
[tex]m=\frac{0-\left(-0.5\right)}{-2-\left(-3\right)}[/tex]
[tex]m=0.5[/tex]
Thus,
The slope of f(x) = 0.5
We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
From the given point (0, 1), we can easily observe that at x = 0, the value of y = 1.
Thus, the y-intercept of f(x) = 1
Function g(x)
Taking two points from the given graph of g(x)
(1, 0)(0, 2)Finding the slope between (1, 0) and (0, 2)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(1,\:0\right),\:\left(x_2,\:y_2\right)=\left(0,\:2\right)[/tex]
[tex]m=\frac{2-0}{0-1}[/tex]
Refine
[tex]m=-2[/tex]
Thus,
The slope of g(x) = -2
We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
From the given point (0, 2), we can easily observe that at x = 0, the value of y = 2.
Thus, the y-intercept of g(x) = 2
Conclusion:
FOR function f(x)
The slope of f(x) = 0.5
The y-intercept of f(x) = 1
FOR function gx)
The slope of g(x) = -2
The y-intercept of g(x) = 2
Thus:
a. Slope of f(x) is greater than g(x)
b. y-intercept of f(x) is less than the y-intercept of g
1. 42
2.70
3.35
4.84
Helpppppppppp
Angles in a triangle
Answer
1=62
2=45
3=24
Angle 1
1 plus 118 equals 180 degrees (because both of the angles combined creates a straight angle).
1+118=180
180-118=1
1=62
Angle 2
The angles in a triangle add up to 180 degrees.
You know that angle 1 is 62 degrees.
And the other angle is 73 degrees.
You can now find angle 2.
62+73+2=180
2=180-62-73
2=45
Angle 3
Angle three is in a different triangle.
You already know that the angles in a triangle added up are 180 degrees.
The other missing angle in the triangle can be found by subtracting 73 from 180.
180-73=107
Now you know that two of the angles in the triangle are 107 and 49.
You can now find angle 3.
107+49+3=180
3=180-107-49
3=24
You are playing the game "Hidden Treasure" and your hint is that the treasure is 9 spaces away from the point (0, 0). Which of the following points could contain the treasure?
Answer:
(9, 0)
(-9, 0)
(0, 9)
(0, -9)
Step-by-step explanation:
Someone answer this for me. I will give u branily whoever right.
Step-by-step explanation:
21x+72+105+78=360
21x=105
x=5
The total number of seats in an auditorium is modeled by the function
f(x) = 2x2 - 6x, where x represents the number of rows of seats.
How many rows are there in the auditorium if it has a total of 416 seats?
What is the volume of the following rectangular prism?
2 units
3
3- units?
Plssss help ASAP!!!
Answer:
13.5
Step-by-step explanation:
ngl i asked siri
Jaden and Dani are both travelling by train.
Jaden's train travels 130 km in 75 minutes.
Dani's train travels 312 km.
It leaves at 15:15 and arrives at 18:30.
Work out the difference, in km/h, between the average speed of their trains.
Answer: 28.765957 km/hour
This value is approximate. Round it however you need to.
==============================================
Explanation:
Let's convert 75 minutes to hours.
75 min = (75 min)*(1 hr/60 min) = (75/60) hr = 1.25 hr
So Jaden's train takes 1.25 hours to travel 130 km. Her train's speed is
speed = distance/time
speed = (130 km)/(1.25 hrs)
speed = (130/1.25) km per hour
speed = 104 km per hour
Let A = 104, so we can use it later.
------------------------------------
Dani's train leaves at 15:15 and arrives at 18:30. We need to calculate the duration of elapsed time here.
From 15:15 to 16:00, this is a difference of 00:45, aka 45 minutes or 45/60 = 3/4 = 0.75 hours.From 16:00 to 18:00, this is a time gap of 2 hours. From 18:00 to 18:30, this is a gap of 30/60 = 0.5 hoursOverall, the length of time from 15:15 to 18:30 is 0.75+2+0.5 = 3.25 hours.
Dani's train travels 312 km in 3.25 hours.
That train's speed is...
speed = distance/time
speed = (312 km)/(3.25 hours)
speed = (312/2.35) km per hour
speed = 132.765957 km per hour, approximately
Let B = 132.765957 so we can use it later.
------------------------------------
Lastly, we subtract the values of A and B to get the final answer
C = difference in train speeds.
C = B - A
C = 132.765957 - 104
C = 28.765957 km/hour
This value is approximate. This says that Dani's train is approximately 28.765957 km/hour faster compared to Jaden's train.
FAST PLEASE A school assembly had 98 students in attendance, and 50% of them were first-graders. How
many first-graders were at the assembly?
Answer:
49
Step-by-step explanation:
50% is basically half so divide 98 by 2
Question 8 of 11
Simplify the following expression:
V-16 + V-25+5
O A. 14+01
O B. 5+9i
O C. 9-51
O D. 5 + 5411
Answer: 5+ 9i
Step-by-step explanation:
3x + 1 = -2 (solve for x)
Answer:
x = -1
Step-by-step explanation:
3x + 1 = -2
Subtract 1 from both sides.
3x = -2 - 1
Simplify -2 - 1 to 3.
3x = -3
Divide both sides by 3.
x = -1
PLEASE HELP ASAP! WILL GIVE BRAINLIEST!
Which statements below are ALWAYS TRUE about Rectangles? Choose ALL THAT APPLY.
- Diagonals are perpendicular
- Diagonals bisect each other in diagonals are equal in length
- Diagonals bisect each other, but they are NOT equal in length
- Opposite sides are congruent
- All four sides are congruent
- Diagonals bisect 90° angles
- Diagonals DO NOT bisect 90° angles
3 Answers:
B) Diagonals bisect each other and diagonals are equal in lengthD) The opposite sides are congruentG) Diagonals do not bisect the 90 degree angles==========================================================
Explanation:
Let's go through the answer choices one by one
A) This is false. If the diagonals were perpendicular, then we would have a square. The diagonals are also perpendicular for any rhombus and for any kite. For any non-square rectangle, the diagonals are not perpendicular.B) This is true. The diagonals bisect each other because we're dealing with a parallelogram. Any rectangle is a parallelogram. For any rectangle, the diagonals are equal in length as well. We can use SAS congruence theorem to prove this.C) This is false. The first part is true, but the second part contradicts what choice B is saying.D) This is true. The opposite sides of any rectangle are congruent, and they are parallel. E) This is false. Imagine a really stretched out or elongated rectangle. So not all four sides of a rectangle are the same length. If they were, then we would have a square.F) This is false. The diagonals do not bisect the angles unless we're dealing with a square. Again imagine stretching out a rectangle to make it very elongated. G) This is true since choice F was false.The statements always true about rectangles are Diagonals bisect each other in diagonals are equal in length, Opposite sides are congruent, Diagonals DO NOT bisect 90° angles.
What is Rectangle?Rectangle is a two dimensional figure which has four sides and four angles and all the angles are right angles.
Diagonals are not perpendicular in rectangles. So first statement is wrong.
Diagonals bisect each other in rectangles and the length of the diagonals are equal.
Since the length of diagonals are equal, third statement is wrong.
Opposite sides of a rectangle are equal and are thus congruent.
In a rectangle, only opposite sides are congruent and equal. All the four sides are not equal and are thus not congruent.
Diagonals of a rectangle does not bisect 90° angles.
Hence the correct statements are shown.
Learn more about Rectangles here :
https://brainly.com/question/18983839
#SPJ6
PLEASE HELP Bill receives a monthly stipend of $800. He also works at a bookstore making $8 an hour. He wants a monthly income of $1,200.
How many hours does he need to work each month?
Answer:
Bill will need to work 50 hours every month.
Step-by-step explanation:
First, we subtract the stipend from the total income he wants to have since he will already recieve it.
[tex]1200 - 800 = 400[/tex]
From this 400 dollars, we can divide it by 8, or his hourly rate to find the rest of the time he needs to work.
[tex]\frac{400}{8}=50[/tex]
Bill needs to work 50 hours to make his total income of 1200.
Hope it helped!
I need help with this one
Answer:
Yes they are similar
Step-by-step explanation:
They have the same measurements adding up to 180.
Triangle RST angles are 120, 20, and 40
Triangle JKL angles are 120, 40, 20
Those are the same numbers.