Answer:
Show that if [tex]f(a) = f(b) = 0[/tex] for some [tex]a,\, b \in [-2,\, 2][/tex] where [tex]a \ne b[/tex], then by Rolle's Theorem [tex]f^{\prime}(x) = 0[/tex] for some [tex]x \in (-2,\, 2)[/tex]. However, no such [tex]x[/tex] exists since [tex]f^{\prime}(x) < 0[/tex] for all [tex]x \in (-2,\, 2)\![/tex].
Note that Rolle's Theorem alone does not give the exact value of the root. Neither does this theorem guarantee that a root exists in this interval.
Step-by-step explanation:
The function [tex]f(x) = x^{3} - 12\, x + 11[/tex] is continuous and differentiable over [tex][-2,\, 2][/tex]. By Rolle's Theorem. if [tex]f(a) = f(b)[/tex] for some [tex]a,\, b \in [2,\, -2][/tex] where [tex]a \ne b[/tex], then there would exist [tex]x \in (a,\, b)[/tex] such that [tex]f^{\prime}(x) = 0[/tex].
Assume by contradiction [tex]f(x)[/tex] does have more than one roots over [tex][-2,\, 2][/tex]. Let [tex]a[/tex] and [tex]b[/tex] be (two of the) roots, such that [tex]a \ne b[/tex]. Notice that [tex]f(a) = 0 = f(b)[/tex] just as Rolle's Theorem requires. Thus- by Rolle's Theorem- there would exist [tex]x \in (a,\, b)[/tex] such that [tex]f^{\prime}(x) = 0[/tex].
However, no such [tex]x \in (a,\, b)[/tex] could exist. Notice that [tex]f^{\prime}(x) = 3\, x^{2} - 12[/tex], which is a parabola opening upwards. The only zeros of [tex]f^{\prime}(x)[/tex] are [tex]x = (-2)[/tex] and [tex]x = 2[/tex].
However, neither [tex]x = (-2)[/tex] nor [tex]x = 2[/tex] are included in the open interval [tex](-2,\, 2)[/tex]. Additionally, [tex]a,\, b \in [-2,\, 2][/tex], meaning that [tex](a,\, b)[/tex] is a subset of the open interval [tex](-2,\, 2)[/tex]. Thus, neither zero would be in the subset [tex](a,\, b)[/tex]. In other words, there is no [tex]x \in (a,\, b)[/tex] such that [tex]f^{\prime}(x) = 0[/tex]. Contradiction.
Hence, [tex]f(x) = x^{3} - 12\, x + 11[/tex] has at most one root over the interval [tex][-2,\, 2][/tex].
{2700,-900,300…}is the sequence geometric
Answer:
Yes, the sequence is geometric.
Step-by-step explanation:
The rule is divide by -3
Multiplying or dividing is a geometric sequence
Sam hiked 4.5 km along a straight bush track, and then turned 40° and walked a further 3.8 km in a straight line.
How far was he from his starting point?
Answer correct to 1 decimal place.
What is the volume of the right rectangular prism? Enter your answer in the box.
Answer:
1000 cm²
Step-by-step explanation:
Given:
Length = 10 cmWidth = 12.5 cmHeight = 8 cmFormula:
[tex]\text{Volume = Length} \times \text{Width} \times \text{Height}[/tex]
Substitute the length, width, and the height of the prism to determine the volume of the prism.
[tex]\implies \text{Volume = 10} \times 12.5 \times 8[/tex]
Simplify the right hand side of the equation, as needed;
[tex]\implies \text{Volume = 10} \times 12.5 \times 8[/tex]
[tex]\implies \text{Volume =}\ 125 \times 8[/tex]
[tex]\implies \boxed{\text{Volume =}\ 1000 \ \text{cm}^{2} }[/tex]
Therefore, the volume of the prism is 1000 cm².
Find tаn Ө.
A. 15/17
B.15/8
C.8/15
D.8/17
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
[tex] \tan(\theta) = \frac{perpendicular}{base} \\ [/tex]
we can see we aren't provided with the perpendicular , so let's find it using Pythagoras Theorem !
[tex]H {}^{2} = P {}^{2} + B {}^{2} \\ \\ \dashrightarrow 17 {}^{2} = P {}^{2} + 8 {}^{2} \\ \\ \dashrightarrow \: P {}^{2} = 17 {}^{2} - 8 {}^{2} \\ \\ \dashrightarrow \: P {}^{2} = 289 - 64 \\ \\ \dashrightarrow \: P { }^{2} = 225 \\ \\ \dashrightarrow \: P = \sqrt{225} \\ \\ \dashrightarrow \: P = 15[/tex]
substituting the value of P in the formula
[tex] \tan(\theta) = \frac{15}{8} \\ [/tex]
therefore , option ( B ) is correct !
hope helpful ~
Can someone help me with this question please
Answer:
∠A≅∠Y AB≅YX
∠B≅∠X AC≅YZ
∠C≅∠Z BC≅XZ
ΔACB ≅ ΔYZX
Step-by-step explanation:
congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle
HELP ASAP PLS GUVING BRAINEST
Answer:
In order for the shapes to be in the same category, we need the following: 2 triangles and 1 quadrilateral with 2 sets of parallel lines.
Step-by-step explanation:
Remember Generalization is like an inference.
You need to write a statement that is based on the given information about Anna's shapes.
_______________________________________________________
If we look at Anna's shapes we have 2 quadrilaterals and 1 triangle.
Then, the "following" shapes have the same properties meaning 2 quads and 1 triangle.
We can go straightforwardly by saying the shapes that Anna chose are 2 quadrilaterals and 1 triangle.
Parallel sides are only shown on 2 of the shapes (the square and the parallelogram).
There are 3 triangles: 1 right, 1 obtuse, and 1 equilateral or acute.
______________________________________________________
Here's my generalization:
If we look at the shapes that Anna chose, we can identify 2 quadrilaterals and 1 triangle. The following shapes don't belong with the ones she chose because there are 2 triangles (equilateral and one right triangle). Then, we have a square with 2 sets of parallel lines which the parallelogram has. The other quadrilateral doesn't have any parallel lines which can't be a trapezoid either. In order for the shapes to be in the same category, we need the following: 2 triangles and 1 quadrilateral with 2 sets of parallel lines.
Can someone help me prove 1 and 2. I will reward brainliest if done asap.
Answer:
Here is your answer, this is how you prove it
helpppppp asapppppppppppp
Answer:
2,000
4,000
7,000
put points on (2, 2,000) - (4, 4,000) - and (7, 7,000)
Step-by-step explanation:
What is Limit of StartFraction x squared minus 4 Over x + 2 EndFraction as x approaches negative 2?
–4
0
4
DNE
Using perfect squares simplification, it is found that the value of the desired limit is of -4.
When is a limit?It is the value of a function as x approach
In this problem, the limit we want to find is given by:
[tex]\lim_{x \rightarrow -2} \frac{x^2 - 4}{x + 2}[/tex]
If we just replace x by -2, we end with an undetermined limit, as we have 0/0.
However, the perfect square simplification states that:
a² - b² = (a - b)(a + b).
Hence:
x² - 4 = (x + 2)(x - 2).
Then:
[tex]\lim_{x \rightarrow -2} \frac{x^2 - 4}{x + 2} = \lim_{x \rightarrow -2} \frac{(x + 2)(x - 2)}{x + 2} = \lim_{x \rightarrow -2} x - 2 = -2 - 2 = -4[/tex]
Hence, the value of the desired limit is of -4.
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Before his shopping spree, Jim owned 133
bracelets. Then he bought 138 more
bracelets. What is the ratio of bracelets
purchased to resulting total number of
bracelets?
Answer:
271
Step-by-step explanation:
Add 138 and 133 then you get 271 at the end
Mary had 80 fliers to post around town. Last week, she posted 1/5 of them. This week, she posted 1/4 of the remaining fliers. How many fliers has she still not posted?
Answer:
48 fliers
Step-by-step explanation:
Last week, Mary posted 1/5 of 80, or 16 fliers. There were 80 - 16, or 64 fliers left. This week, Mary posted 1/4 of 64, or 16 fliers. There are 64 - 16, or 48 fliers left.
Urgent! Find the length of the tangent segment AC given circle B below
Answer:
AC ≈ 12
Step-by-step explanation:
the angle between the tangent AC and the radius BC is 90°
then Δ ABC is right
note that BC = 9 ( radius of circle )
using Pythagoras' identity in the right triangle
AC² + BC² = AB²
AC² + 9² = (9 + 6)² = 15²
AC² + 81 = 225 ( subtract 81 from both sides )
AC² = 144 ( take square root of both sides )
AC = [tex]\sqrt{144}[/tex] = 12
In DEF what is the measurement of DF? HELP PLEASSE and thank you
Answer:
The measure of arc DEF is 204° ⇒ answer C
Step-by-step explanation:
If you raised $400,000 in a stock sale and gave up 12% of your company, what was the implied valuation of the company?
When you write an interpretive literary analysis using a quotation, why should you discuss literature that you have read in the analysis? it serves as a prompt for the interpretive literary analysis. it provides evidence to support the interpretation of the quotation. it determines the meaning of the quotation that is used. it offers an entertaining viewpoint for the reader.
You should discuss the literature that you have read in the analysis is to provide evidence to support the interpretation of the quotation.
What is interpretive literary analysis?The skill of interpretive literary analysis helps us to relate one work of literature to another and thereby be able to draw meaning especially from a quoted text.
The reason why you should discuss the literature that you have read in the analysis is to provide evidence to support the interpretation of the quotation.
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give two coterminal angles (one positive and one negative) and the reference angle -4 pi/5
The coterminal angle for the -4π/5 are -14π/5 , 6π/5 and reference angle is π/5 respectively.
What is coterminal angles?Two different angles that have the identical starting and ending edges termed coterminal angles however, since one angle measured clockwise and the other determined counterclockwise, the angles' terminal sides have completed distinct entire rotations.
We have an angle:
-4π/5
To find the coterminal angle, add and subtract by 2π in the angle -4π/5
Coterminal angle:
= -4π/5 - 2π
= -14π/5
= -4π/5 + 2π
= 6π/5
Reference angle:
= π - 4π/5 (as the angle lies in the second quadrant)
= π/5
Thus, the coterminal angle for the -4π/5 are -14π/5 , 6π/5 and reference angle is π/5 respectively.
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PLEASE HELP MEEE!!!!!! I WILL GIVE BRAINLIEST
Answer:
30/45 or 2/3
Step-by-step explanation:
If you factor out a 10 from the numerator and a 9 from the denominator, you should get the following:
Numerator = 10 (a + b)
Denominator = 9 (x - y)
Since we know that (a + b) = 3 and (x - y) = 5, we can rewrite it as:
Numerator = 10(3)
Denominator = 9(5)
Therefore, the answer is 30/45, or 2/3.
Hope this helps!
BRAINLIST IF CORRECT WORTH 100POINTS
Frank opens several pea pods and counts the number of peas in each pod. He records the number.
Written as a percent, what is the experimental probability that the pea pod has 9 peas in it?
Question 4 options:
12.5%
48.8%
45%
18%
Answer:
45%
Explanation:
According to the question, we can get:
[tex]N=1+4+18+15+2=4D[/tex]
[tex]P=\frac{18}{40}[/tex]
[tex]=0.45[/tex]
[tex]=45[/tex]%
Therefore, Written as a percent, the experimental probability that the pea pod has 9 peas in it is 45%
Answer:
Hi! The answer is 45%
Step-by-step explanation:
I just took the review and got the answer.
here is proof.
Hope this helps!
Brainliest please!
Please fully rate!
Have a great day!
The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 70.3% of their carbon-14. How old were the bones at the time they were discovered?
The bones at the time they were discovered when the radioactive element carbon-14 has a half-life of total 5750 years are 10062.5-year-old.
What is half-lives?Half lives is the time interval which is need to decay the atomic nuclei of a radioactive sample.
There is a scientist who determined that the bones from a mastodon had lost 70.3% of their carbon-14. Thus, the fraction remaining is,
f=1-(70.3/100)=1-0.703
f=1-(70.3/100)=0.297
Now the fraction remaining can be given as,
f=(1/2)ⁿ
Here, n is the half life elapsed. Put the value of fraction remaining.
0.297=(1/2)ⁿ
n=1.75
The radioactive element carbon-14 has a half-life of total 5750 years. Thus,
Years=1.75*5750
Years=10062.5
Thus, the bones at the time they were discovered when the radioactive element carbon-14 has a half-life of total 5750 years are 10062.5-year-old.
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You start at (0, 0). You move up 3 units. Where do you end?
Answer:
(0,3)
Step-by-step explanation:
Since you're moving up, you add to y the y-intercept.
hope this helps
have a good day
Answer:
0,3 it on the 0 so if you move up 3 it would go to the second number so 0,3
You are designing a new container for powdered laundry detergent. You are considering a cylindrical container with a diameter of 18 inches and a height of 20 inches. Find the volume of this container to the nearest cubic unit. Use a calculator.
Step-by-step explanation:
the volume of a cylinder is
base area × height.
and the base is a circle, and the area of a circle is
pi×r²
remember, the radius is half the diameter.
so, in our case, the volume is
pi×(18/2)²×20 = pi×9²×20 = pi×81×20 = pi×1620 =
= 5,089.380099... in³ ≈ 5,089 in³
The Dunnan family pays a rate of 37.5 mills in property tax. The assessed value of the home is $85,000. What is their property tax?
The property tax paid by the Dunnan family based on their millls and the assessed value of the home is $31,875.
What is the property tax?Property tax is the tax that is paid on property that is owned. Tax is a form of complusory payment made to the government.
Property tax = (mills /100) x assessed value
(37.5/100) x 85000 = $31,875
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3 m
3 m
3 m
6 m
Area:
Answer:
The area is 27m.
Step-by-step explanation:
We can first seperate this shape into two shapes. I seperated the 3x6 rectangle and the 3x3 square. Now we can find the area of these individual shapes. 3x3=9 and 3x6=18. We can now add these two numbers together to get the area of this shape. 9+18=27m. Therefore, the area of this shape is 27m.
State all the total value
(Canadian money)
Please i will give you 23 points\
Answer:
x ≈ 45.6°
Step-by-step explanation:
using the Cosine rule in the triangle
cos x = [tex]\frac{8^2+15^2-11^2}{2(8)(15)}[/tex] = [tex]\frac{64+225-121}{240}[/tex] = [tex]\frac{168}{240}[/tex] , then
x = [tex]cos^{-1}[/tex] ( [tex]\frac{168}{240}[/tex] ) ≈ 45.6° ( to 1 dec. place )
A street is 250 m long. It is represented by a distance of 5 cm on a map. Express the scale of the map in the form 1 : r.
Answer:
1 : 5000
Step-by-step explanation:
Firstly align the unit
Map 5cm represent 250m = 250x100cm = 25000cm
scale = 5 : 25000 = 1 : 5000
gsddsgaddsgdsggdsgsd
Answer:
?
Step-by-step explanation:
Answer:
rt4564564fr5646
Step-by-step explanation:
x = ………………………….°
Give reason for your answer.
…………………………………………………………………………………………
Answer:109
Step-by-step explanation:
71 degree and x make a linear pair
71 + x = 180
x= 180- 71
x= 109
I have no idea what to do for this question somebody please help
Answer:
405π
Step-by-step explanation:
Use the formula for Volume Of Cylinder (V=πr²h) where "V" represents the volume, "r" represents the radius, and "h" represents the height
The volume and the radius are given. (V=45π, r=3)
1. Solve for height
V=πr²h
45π=π3²h
45π/π=3²h
45=3²h
45=9h
45/9=h
h=5
2. Plug the new radius (3*3=9) into this formula and solve for "V"
V=π9²5
V=π81*5
V=405π
NEW VOLUME AFTER A TRIPLED RADIUS IS 405π
Here are two circles, Circle A and Circle D. Segment AD connects the two centers and is 10 inches long. Segment AD is a side to square ABCD. What is the area of the shaded region.
Answer:
the answer is, area of the square - a half of area of the circle
C=circle and S =square
radius of C is 10
so Area Of C is =
[tex]\pi r^{2} = \pi{10}^{2} = 100\pi[/tex]
area of S = 10×10 = 100
so the answer is
[tex]s - \frac{c}{2} = 100 - \frac{100\pi}{2} = 100 - 50\pi[/tex]
