Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) F(x) = sin(x/2) , [π/2,3π/2]

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Answer:

35 cm

Step-by-step explanation:

is the correct answer

Answer:

Step-by-step explanation:

[tex]\frac{a(b+c)}{bc} ,\frac{b(c+a)}{ca} ,\frac{c(a+b)}{ab} ~are~in~A.P.\\if~\frac{ab+ca}{bc} ,\frac{bc+ab}{ca} ,\frac{ca+bc}{ab} ~are~in~A.P.\\add~1~to~each~term\\if~\frac{ab+ca}{bc} +1,\frac{bc+ab}{ca} +1,\frac{ca+bc}{ab} +1~are~in~A.P.\\if~\frac{ab+ca+bc}{bc} ,\frac{bc+ab+ca}{ca} ,\frac{ca+bc+ab\\}{ab} ~are~in~A.P.\\\\divide~each~by~ab+bc+ca\\if~\frac{1}{bc} ,\frac{1}{ca} ,\frac{1}{ab} ~are ~in~A.P.\\if~\frac{a}{abc} ,\frac{b}{abc} ,\frac{c}{abc} ~are~in~A.P.\\if~a,b,c~are~in~A.P.\\which~is~true.[/tex]

You have to find the slope .

How?

Take 2points

[tex]\\ \rm\Rrightarrow \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Step-by-step explanation:

What the Slope Means A positive slope means that two variables are positively related—that is, when x increases, so does y, and when x decreases, y also decreases. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises.

Answer:

F statistic = 2.124

Pvalue = 0.0546

A. Fail to reject the null hypothesis. There is insufficient evidence to to support the claim that those given a sham treatment have reductions that vary more than those treated with magnets

Step-by-step explanation:

H0 : pain reduction is the same

H1 : pain reduction is varies more with sham.

Sham n= 20 x=0.41 s=1.37

Magnet n= 20 x =0.46 s= 0.94

α - level = 0.05

Using the Ftest statistic

Ftest = larger sample variance / smaller sample variance

Ftest = s1² / s2² = 1.37² / 0.94² = 1.8769 / 0.8836 = 2.124

The degree of freedom :

Numerator = n - 1 = 20 - 1 = 19

Denominator = n - 1 = 20 - 1 = 19

Pvalue(2.124, 19, 19) = 0.0546

Since ;

Pvalue > α ; WE fail to reject the Null ; Result is not significant

Answer:

x = -1

Step-by-step explanation:

1/3(6x-3)+2(x-1) = -7

Distribute

2x-1 +2x-2 = -7

Combine like terms

4x -3 = -7

Add 3 to each side

4x-3+3 = -7+3

4x = -4

Divide by 4

4x/4 = -4/4

x = -1

[tex] \frak{ \frac{1}{3}(6x - 3) + 2(x - 1) = - 7}[/tex]

[tex]\twoheadrightarrow \frak{2x - 1 + 2x - 2 = - 7}[/tex]

[tex]\twoheadrightarrow \frak{4x - 3 = - 7}[/tex]

[tex] \twoheadrightarrow \frak{4x = - 7 + 3}[/tex]

[tex]\twoheadrightarrow \frak{4x = - 4}[/tex]

[tex]\star \: \underline{ \boxed{ \frak \green{{x = - 1}}}}[/tex]

[tex]\\ \sf\longmapsto 2(3x-7)+4(3x+2)=6(5x+9)+3[/tex]

[tex]\\ \sf\longmapsto 6x-14+12x+8=30x+54+3[/tex]

[tex]\\ \sf\longmapsto 6x+12x-14+8=30x+57[/tex]

[tex]\\ \sf\longmapsto 18x+6=30x+57[/tex]

[tex]\\ \sf\longmapsto 30x-18x=6-57[/tex]

[tex]\\ \sf\longmapsto 12x=51[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{51}{12}[/tex]

Answer:

The hottest month for the northern hemisphere is August.

The hottest month for the southern hemisphere is January and February (these top two might be the opposite)

It's globally warmer during the months of June July and August

During april and november, the southern hemisphere and northern hemisphere are the same, or very close.

During July and August the southern and northern hemispheres have the largest difference in temperature

Answer:

Step-by-step explanation:

Our friend asking what the actual function is has a point. I completed this under the assumption that what we have is:

[tex]f(x)=\frac{e^{3x}}{5x-2}[/tex] and used the quotient rule to find the derivative, as follows:

[tex]f'(x)=\frac{e^{3x}(5)-[(5x-2)(3e^{3x})]}{(5x-2)^2}[/tex] and simplifying a bit:

[tex]f'(x)=\frac{5e^{3x}-[15xe^{3x}-6e^{3x}]}{(5x-2)^2}[/tex]and a bit more to:

[tex]f'(x)=\frac{5e^{3x}-15xe^{3x}+6e^{3x}}{(5x-2)^2}[/tex] and combining like terms:

[tex]f'(x)=\frac{11e^{3x}-15xe^{3x}}{(5x-2)^2}[/tex] and factor out the GFC in the numerator to get:

[tex]f'(x)=\frac{e^{3x}(11-15x)}{(5x-2)^2}[/tex]  That's the derivative simplified. If we want f'(0), we sub in 0's for the x's in there and get the value of the derivative at x = 0:

[tex]f'(0)=\frac{e^0(11-15(0))}{(5(0)-2)^2}[/tex] which simplifies to

[tex]f'(0)=\frac{11}{4}[/tex] which translates to

The slope of the function is 11/4 at the point (0, -1/2)

Answer: 17 feet

Step-by-step explanation:

51/48 = x/16

(51)(16)/48

The statute is 17 feet tall.

Similar triangles are the triangles that have the same shape, but different sizes. The corresponding angles are congruent and the sides are in proportion.

The ratio of any corresponding sides in two equiangular triangles is always the same.

Let's visualize the situation according to the given question.

AB is the building ,whose height is 51f

BC is the shadow of the building AB, whose length is 48ft.

QR is the shadow of the tower statue, whose length is 16feet.

Let the height of the statue PR be h feet.

In triangle ACB and triangle PRQ

∠ACB = ∠PRQ = 90 degrees  

( the objects and shadows are perpendicular to each other)

∠BAC = ∠QPR

( sunray falls on the pole and tower at the same angle, at the same time )

⇒ΔACB similar to ΔPRQ   ( AA criterion)

Therefore, the ratio of any two corresponding sides in equiangular triangles is always same.

⇒ AC/CB = PR/RQ

⇒[tex]\frac{51}{48} =\frac{h}{16}[/tex]

⇒ h = [tex]\frac{(51)(16)}{48}[/tex]

⇒ h = 17 feet.

Hence, the statute is 17 feet tall.    

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Answer:

y=5x-1 I think because the snd option doesn't make sense but you should try y =5x-1

Answer:

Step-by-step explanation:

Find GCF of 45 and 60:

GCF(45,60) = 3*5 = 15

Find Greatest common multiple or GCF

[tex]\\ \sf\longmapsto 45=3\times 3\times 5[/tex]

[tex]\\ \sf\longmapsto 60=2\times 2\times 3\times 5[/tex]

Now

[tex]\\ \sf\longmapsto GCF=3\times 5=15[/tex]

Answer:

B

Step-by-step explanation:

A function is a relation in which each input, x, has only one output, y.

There are two ways to determine if a relation is a function:

1. If each x-input has only one, unique y-output, then it's a function. If some x-inputs share the same y-outputs, it's not a function.

2. Vertical Line Test on Graphs:

To determine whether y is a function of x, when given a graph of relation, use the  following criterion: if every vertical line you can draw goes though only 1 point, the relation can be a function. If you can draw a vertical line that goes though more than 1 point, the relation cannot be a function.

Since we're given a graph relation, let's test both of the answers out.

If I were to draw a vertical line in a specific place on the first graph, I'd be hitting more than one point in the coordinate plane.

If I were to draw a vertical line in a specific place on the second graph, I'd only be hitting one point in the coordinate plane.

Therefore, choice B is a function.

Answer:

1. coefficient of 3rd term = 1

2. constant term= 0

The coefficient of the third term is 1 while the constant term is 0 for the given expression.

An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.

For example 3x +5y

As per the given polynomial,

(1/2)a⁴ + 3a³ + a

Here a is a variable.

(1)

The third term is a and its coefficient is 1 as (1)a.

(2)

All terms have variable "a" thus none of the terms is constant so the constant term is 0.

Hence "For the following statement, the constant term has a coefficient of 0 and the third term has a coefficient of 1".

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6 minutes / 30 minutes

Divide the top and bottom by 6.

1 minute / 5 minutes

Fraction in lowest terms: 1/5

Hope this helps!

Answer:

The dimensions of the rectangle are length 25 feet and width 15.92 feet

Step-by-step explanation:

Let L be the length of the rectangle and w be the width.

The area of the rectangular part of the shape is Lw while the area of the two semi-circular ends which have a diameter which equals the width of the rectangle is 2 × πw²/8 = πw²/4. The area of each semi-circle is πw²/4 ÷ 2 = πw²/8

So, the area of the shape A = Lw + πw²/4.

The perimeter of the shape, P equals the length of the semi-circular sides plus twice its length. The length of a semi-circular side is πw/2. So, both sides is 2 × πw/2 = πw

P = πw + 2L

Since the perimeter, P = 100 feet, we have

πw + 2L = 100

From this L = (100 - πw)/2

Substituting L into A, we have

A = Lw + πw²/4.

A = [(100 - πw)/2]w + πw²/4.

A = 50w - πw²/2 + πw²/4.

A = 50w - πw²/2

Now differentiating A with respect to w and equating it to zero to find the value of w which maximizes A.

So

dA/dw = d[50w - πw²/2]/dw

dA/dw = 50 - πw

50 - πw = 0

πw = 50

w = 50/π = 15.92 feet

differentiating A twice to get d²A/dw² =  - π indicating that w = 50/π is a value at which A is maximum since d²A/dw² < 0.

So, substituting w = 50/π into L, we have

L = (100 - πw)/2

L = 50 - π(50/π)/2

L = 50 - 50/2

L = 50 - 25

L = 25 feet

So, the dimensions of the rectangle are length 25 feet and width 15.92 feet

Step-by-step explanation:

yah language mujhe samajh mein nahin a rahi hai kya karu aapki is bataiye

Answer:

I think you can go with:

The margin of error is equal to half the width of the entire confidence interval.

so  try .74 ±   =   [ .724 , .756] as the confidence interval

Step-by-step explanation:

Answer:

Step-by-step explanation:

The combinations are:

Total number of combinations:

Correct choice is B

there are 8different combinations are modeled by the diagram.

Answer:

Solution given:

orange:2

grape:2

apple:2

grapefruit:2

no of term:4

now

total no. of combination ia 4*2=8

Answer:

None

Step-by-step explanation:

The given angles aren't equal which is needed for the polygon to be similar

No, the following polygons are not similar.

Used the concept of a similar figure that states,

In terms of Maths, when two figures have the same shape but their sizes are different, then such figures are called similar figures.

Given that,

Two polygons EFGH and JKLM are shown in the image.

Now the corresponding sides of both figures are,

EF = 27

JK = 63

And, EH  = 27

JM = 63

Hence, the ratio of corresponding sides is,

EF/JK = 27/63

= 9/21

= 3/7

EH/JM = 27/63

= 3/7

So their corresponding sides are equal in ratio.

But their corresponding angles are not the same.

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Answer:

0.85 in²

Step-by-step explanation:

really ? you need help with that ? you could not find the formula for the area of a circle on the internet and type it into your calculator ? I can't do anything else here.

a circle area is

A = pi×r²

r being the radius.

and pi being, well, pi (3.1415....)

r = 0.52 in

so,

A = pi×0.52² = pi×0.2704 = 0.849486654... in²

the area of one side of the coin is 0.85 in²

Answer:

the answer is d

Step-by-step explanation:

9514 1404 393

Answer:

  B. 11.000

Step-by-step explanation:

The function looks like a reflected and translated exponential function with a horizontal asymptote near y = 11.000. The rate of change is decreasing so fast that the next value is expected to be very near 10.994. The closest one among the answer choices is 11.000.

_____

First differences are 0.811 and 0.011. The latter is about 0.0136 times the former. At that rate of change, we expect the next first difference to be about 0.000149, which would make the next number in sequence be about 10.9941—very little change from 10.994.

Clearly, first differences are not constant, so the function is not linear. Ratios of the numbers are not constant, so this is not an exponential (geometric) sequence. A reflected exponential function of the type described is a good fit.

With only 3 points given, the rule is not at all obvious. The next term could legitimately be anything you like, and a rule could be made that would fit it.

Hence the time that the ball will be height than 12 feet off the ground is 4secs

Given the expression for calculating the height in  feet as;

h(t) = -4t²+16t

If the ball is higher than 12feet, h(t) > 12

Substituting h = 12 into the expression

-4t²+16t > 12

-4t²+16t - 12 > 0

4t²- 16t + 12 > 0

t²- 4t + 3 > 0

Factorize

(t²- 3t)-(t + 3) > 0

t(t-3)-1(t-3) > 0

(t-1)(t-3)>0

t > 1 and 3secs

Hence the time that the ball will be height than 12 feet off the ground is 4secs

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Answer:

First Choice: As the number of hours spent on homework increases, the tests scores increase.

Step-by-step explanation:

The definition of a positive correlation  is a relationship between two given variables, in which both variables are moving in the same direction. This can mean when one variable increases and the other variable increases, too, or one variable decreases and the other decreases as well.

The first choice is a positive correlation because both variables are changing (increasing) in the same direction. As you spend more time on homework, you're likely to get a higher test score.

The second choice cannot be a positive correlation because only one variable is having some kind of change (increasing). The doctor visits amount remains the same, so we can call this a zero-correlation relationship because the number of apples eaten yearly doesn't affect the amount of doctor visits. An apple a day keeps the doctor a way is just a proverb, not to be taken literally.

The third choice cannot be a positive correlation because the two variables are going different directions. Even though the number of times going to bed early is increasing, the number of times waking up late decreases, which is not moving in the same direction as the other variable.

The fourth choice cannot be a positive correlation because, similarly to the third choice, the two variables are going different directions. One variable is increasing, which is the amount of practice time. Meanwhile, the other variable is decreasing (going in the opposite direction), which is the number of games lost in a season.

Answer:

a + b = ⟨-4, -9, 0⟩

a - b = ⟨6, 1, 4⟩

2a = ⟨2, -8, 4⟩

3a + 4b = ⟨-17, -32, -2⟩

|a| = √21

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Pre-Calculus

Vectors

Step-by-step explanation:

Adding and subtracting vectors are follow the similar pattern of normal order of operations:

a + b = ⟨1 - 5, -4 - 5, 2 - 2⟩ = ⟨-4, -9, 0⟩

a - b = ⟨1 + 5, -4 + 5, 2 + 2⟩ = ⟨6, 1, 4⟩

Scalar multiplication multiplies each component:

2a = ⟨2(1), 2(-4), 2(2)⟩ = ⟨2, -8, 4⟩

Remember to multiply in the scalar before doing basic operations:

3a + 4b = ⟨3(1), 3(-4), 3(2)⟩ + ⟨4(-5), 4(-5), 4(-2)⟩ = ⟨3, -12, 6⟩ + ⟨-20, -20, -8⟩ = ⟨-17, -32, -2⟩

Absolute values surrounding a vector signifies magnitude of a vector. Follow the formula:

|a| = √[1² + (-4)² + 2²] = √21

Answer:

0.33362176

Step-by-step explanation:

Probability is the ratio of the number of possible outcomes to the number of total outcomes.

Given that a football team has a probability of 0.76 of winning when playing any of the other four teams in its conference, the probability that the team wins all its conference games

= 0.76 * 0.76 * 0.76 * 0.76

= 0.33362176

This is the probability that the teams wins the 4 matches played against the other teams in the conference.

Answer: 10m, 33m, and 29m

Step-by-step explanation:

n + 3n+3 + 3n-1 = 72m

7n+2=72m

7n = 72-2

n = 70/7

n = 10

Answer:

y =7

x =14

Step-by-step explanation:

Since this is a right triangle we can use trig functions

tan 30 = opp /adj

tan 30 = y/ 7 sqrt(3)

7 sqrt(3)  tan 30 = y

7 sqrt(3) * 1/ sqrt(3) =t

7 =y

sin 30 = opp/ hyp

sin 30 = 7/x

x sin 30 =7

x = 7/ sin 30

x = 7 / 1/2

x = 14