Select the correct answer. Vincent wants to construct a regular hexagon inscribed in a circle. He draws a circle on a piece of paper. He then folds the paper circle three times to create three folds representing diameters of the circle. He labels the ends the diameters A, B, C, D, E, and F, and he uses a straightedge to draw the chords that form a hexagon. Which statement is true? A. Vincent’s construction method produces a hexagon that must be regular. B. Vincent’s construction method produces a hexagon that must be equilateral but may not be equiangular. C. Vincent’s construction method produces a hexagon that must be equiangular but may not be equilateral. D. Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular.

Answers

Answer 1

Answer:

B.

Step-by-step explanation:

Answer 2

Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular. The correct option is D.

What is a regular polygon?

A regular polygon is a polygon that is equiangular and equilateral. Therefore, the measure of all the internal angles and the measure of all the sides of the polygon are equal to each other.

Given that Vincent wants to construct a regular hexagon inscribed in a circle. He draws a circle on a piece of paper. He then folds the paper circle three times to create three folds representing the diameters of the circle.

Now as it can be seen as the paper is folded as shown in the below image but it does not create a hexagon that is equilateral and equiangular.

Hence, Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular.

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Select The Correct Answer. Vincent Wants To Construct A Regular Hexagon Inscribed In A Circle. He Draws

Related Questions

The first and last term of an AP are 1 and 121 respectively. If the sum of the series is 671,find a) the number of terms (n) in the AP b) the common
difference between them​

Answers

Answer:

(a)11

(b)12

Step-by-step explanation:

The first term, a = 1

The last term, l=121

Sum of the series, [tex]S_n=671[/tex]

Given an arithmetic series where the first and last term is known, its sum is calculated using the formula:

[tex]S_n=\dfrac{n}{2}(a+l)[/tex]

Substituting the given values, we have:

[tex]671=\dfrac{n}{2}(1+121)\\671=\dfrac{n}{2} \times 122\\671=61n\\$Divide both sides by 61\\n=11[/tex]

(a)There are 11 terms in the arithmetic progression.

(b)We know that the 11th term is 121

The nth term of an arithmetic progression is derived using the formula:

[tex]a_n=a+(n-1)d[/tex]

[tex]a_{11}=121\\a=1\\n=11[/tex]

Therefore:

121=1+(11-1)d

121-1=10d

120=10d

d=12

The common  difference between them​ is 12.

Heights for teenage boys and girls were calculated. The mean height for the sample of 46 boys was 195 cm and the variance was 58. For the sample of 66 girls, the mean was 165 cm and the variance was 75. Estimate how much taller teenage boys are using a 85% confidence level. Round answers to the nearest hundredth and provide the point estimate together with the margin of error.

Answers

Answer:

With a 85% confidence level you'd expect the teenage boys to be on average between [29.217; 30.783]cm taller than the girls.

Step-by-step explanation:

Hello!

Given the variables:

X₁: height of a teenage boy.

n₁= 46

[tex]\frac{}{X}[/tex]₁= 195cm

S₁²= 58cm²

X₂= height of a teenage girl

n₂= 66

[tex]\frac{}{X}[/tex]₂= 165cm

S₂²= 75cm²

If the boys are taller than the girls then you'd expect μ₁ > μ₂ or expressed as a difference between the two population means: μ₁ - μ₂ > 0

To estimate the difference between both populations you have to calculate the following interval:

([tex]\frac{}{X}[/tex]₁- [tex]\frac{}{X}[/tex]₂) + [tex]t_{n_1+n_2-2; 1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S_1}{n_1} +\frac{S_2}{n_2} }[/tex]

[tex]t_{n_1+n_2-2; 1-\alpha /2}= t_{110; 0.925}= 1.450[/tex]

Point estimate: ([tex]\frac{}{X}[/tex]₁- [tex]\frac{}{X}[/tex]₂) = (195-165)= 30

Margin of error:[tex]t_{n_1+n_2-2; 1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S_1}{n_1} +\frac{S_2}{n_2} }[/tex]= 1.450*0.54= 0.783

30 ± 0.783

[29.217; 30.783]

With a 85% confidence level you'd expect the teenage boys to be on average between [29.217; 30.783]cm taller than the girls.

I hope this helps!

Find the limit L for the given function​ f, the point x 0​, and the positive number epsilon. Then find a number delta ​> 0 such​ that, for all​ x, 0less thanStartAbsoluteValue x minus x 0 EndAbsoluteValueless thandelta double right arrow StartAbsoluteValue f (x )minus Upper L EndAbsoluteValueless thanepsilon.

Answers

Answer:

L = -25 and  δ = 0.02

Step-by-step explanation:

The function f, point [tex]x_0[/tex] and ε is missing in the question.

The function, f is f(x) = - 4x - 9

           point,  [tex]x_0[/tex] = 4

        epsilon, ε = 0.08

So by the definition of limit,

      [tex]\lim_{x \rightarrow x_0} f(x)= L[/tex]

Therefore,

[tex]\lim_{x \rightarrow 4} (-4x-9)[/tex]

L= -4(4)-9

L= -16-9

L= -25

So, for every ε > 0, for all δ > 0 such that

|f(x) - L| < ε   [tex](0<|x-x_0|< \delta)[/tex]

[tex]|f(x)-L|<\epsilon \\|(-4x-9)-(-25)|<0.08\\|-4x+16|<0.08\\|-4(x-4)|<0.08\\|-4||x-4|<0.08\\4|x-4|<0.08\\|x-4|<\frac{0.08}{4}\\|x-4|<0.02\\0<|x-4|<0.02 \ \ \ \ \text{ comparing with}\ 0<|x-x_0|< \delta \\ \therefore \delta = 0.02[/tex]      

The quotient of a number and -5 has a result of 2. What is the number?
Type the correct answer in the box. Use numerals instead of words.

Answers

Answer:

-10

-5 * 2 = -10

Hope this is right

Find the measure of the indicated angle to the nearest degree.

PLEASE HELP ASAP

Answers


A. 26
B. 42
C. 64
D. 48

Answers

Answer:

The answer is option C

Step-by-step explanation:

To find the indicated angle we use sine

sin ∅ = opposite / hypotenuse

From the question

The opposite is 37

The hypotenuse is 41

So we have

sin ? = 37/41

? = sin-¹ 37/41

? = 64.4805

? = 64° to the nearest degree

Hope this helps you

Answer:

C.) 64

Step-by-step explanation:

I got it correct on founders edtell

Enter a range of vaules for x

Answers

A range for the values of x:

-2, -1, 0, 1, 2,

Happy to help! You can certainly extend this range

resultado de
x²-3x=0

Answers

Answer:

x = 3,0

Step-by-step explanation:

x²-3x=0

1- x(x - 3) = 0

2- x = 0 , x = 3

Answer:

X1=0    X2=3

Step-by-step explanation:

Factorize x²-3x=x*(x-3)=0

So x=0  or  x-3=0

SO x1=0 x2-3=0

x2=3

The area of a triangle is 14 square inches. The base is 28 inches. What is the height in inches? Do not include units in your answer.

Answers

Answer:

Hey there!

A=1/2bh

14=1/2(28)h

14=14h

h=1

Hope this helps :)

Answer:

the height is 1 inch

Step-by-step explanation:

Area of a triangle is

[tex] \frac{1}{2} \times b \times h[/tex]

where b is the base

h is the height

From the question

Area = 14in²

b = 14 inches

So we have

[tex]14 = \frac{1}{2} \times 28 \times h[/tex]

which is

[tex]14 = 14h[/tex]

Divide both sides by 14

That's

[tex] \frac{14}{14} = \frac{14h}{14} [/tex]

We have the final answer as

h = 1

Therefore the height is 1 inch

Hope this helps you

Find the centroid of the quarter of the unit circle lying in the fourth quadrant.

Answers

Step-by-step explanation:

In the fourth quadrant, the equation of the unit circle is:

y = -√(1 − x²), 0 ≤ x ≤ 1

The x and y coordinates of the centroid are:

cₓ = (∫ x dA) / A = (∫ xy dx) / A

cᵧ = (∫ y dA) / A = (∫ ½ y² dx) / A

For a quarter circle in the fourth quadrant, A = -π/4.

Solving each integral:

∫₀¹ xy dx

= ∫₀¹ -x √(1 − x²) dx

= ½ ∫₀¹ -2x √(1 − x²) dx

If u = 1 − x², then du = -2x dx.

When x = 0, u = 1.  When x = 1, u = 0.

= ½ ∫₁⁰ √u du

= ½ ∫₁⁰ u^½ du

= ½ (⅔ u^³/₂) |₁⁰

= (⅓ u√u) |₁⁰

= 0 − ⅓

= -⅓

∫₀¹ ½ y² dx

= ½ ∫₀¹ (1 − x²) dx

= ½ (x − ⅓ x³) |₀¹

= ½ [(1 − ⅓) − (0 − 0)]

= ⅓

Therefore, the x and y coordinates of the centroid are:

cₓ = (-⅓) / (-π/4) = 4/(3π)

cᵧ = (⅓) / (-π/4) = -4/(3π)

x−15≤−6 solve for x pls help

Answers

Answer:

x≤9  

Step-by-step explanation:

x−15≤−6

Add 15 to each side

x−15+15≤−6+15

x≤9  

Answer:

[tex]\boxed{x\leq 9}[/tex]

Step-by-step explanation:

[tex]x-15 \leq -6[/tex]

[tex]\sf Add \ 15 \ to \ both \ parts.[/tex]

[tex]x-15 +15 \leq -6+15[/tex]

[tex]x\leq 9[/tex]

What decimal is equivalent to 10/3?

Answers

Answer:

3.33333333 . . .

Step-by-step explanation:

Answer:

3.33333333

Step-by-step explanation:

Its a forever number, i forgot the term i think its called a terminal number, or nonterminal i forget. You divide 10 / 3 and get 3.33333333333333333333 forever

Find the area of the triangle. Round the answer to the nearest tenth. A. 4.4 square units B. 5.2 square units C. 6.8 square units D. 8.8 square units

Answers

Answer:

A. 4.4 units²

Step-by-step explanation:

Area of a Triangle: A = 1/2bh

sin∅ = opposite/hypotenuse

cos∅ = adjacent/hypotenuse

Step 1: Draw the altitude down the center of the triangle

- We should get a perpendicular bisector that creates 90° ∠ and JM = KM

- We should also see that we use sin∅ to find the h height of the triangle and that we use cos∅ to find length of JM to find b base of the triangle

Step 2: Find h

sin70° = h/3.7

3.7sin70° = h

h = 3.47686

Step 3: Find b

cos70° = JM/3.7

3.7cos70° = JM

JM = 1.26547

Step 4: Find entire length base JK

JM + KM = JK

JM = KM (Definition of Perpendicular bisector)

2(JM) = JK

2(1.26547) = 2.53095

b = 2.53095

Step 5: Find area

A = 1/2(3.47686)(2.53095)

A = 4.39988

A ≈ 4.4

experts, geniuses, aces and moderators .. need help on the attached. will give brainliest!!! find the derivative of e^x

Answers

To find the derivative, you must use the chain rule.

If u=x^3+2x:
dy/dx=(dy/du)(du/dx)
dy/du=d/du(e^u)=e^u=e^(x^3 + 2x)
du/dx =d/dx (x^3+2x) = 3x^2 + 2

So dy/dx=
e^(x^3+2x) * (3x^2+ 2)

The graph shows how the length of time a boat is rented is related to the
rental cost. What is the rate of change shown in the graph?
Boat Rental
AY
440
400
380
320
Cost (dollars)
240
200
100
120
80
40
0
Time (hours)
A. $40/hour
B. $80/hour
C. 80 hours/dollar
D. 40 hours/dollar

Answers

It’s actuallly A i hope it helped you

A slope is also known as the gradient of a line is a number. The correct option is B.

What is Slope?

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

slope = (y₂-y₁)/(x₂-x₁)


The rate of change shown in the graph is the slope of the given line.

Now, to know the slope of the line consider any two points on the line, such as (0,0) and (5,400).

Therefore, the slope of the line can be written as,

Slope, m = ($400 - $0)/(5-0) hour

               = $400/5 hour

               = $80/hour

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The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A one-sample t test will be carried out to see whether this is the case. What conclusion is appropriate in each of the following situations?
(a) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(b) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(c) n = 26, t = 2.55, a = 0.01
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(d) n = 26, t = 3.95
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answers

Answer:

Option C - Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in

Step-by-step explanation:

We are given;

n = 15

t-value = 1.66

Significance level;α = 0.05

So, DF = n - 1 = 15 - 1 = 14

From the one-sample t - table attached, we can see that the p - value of 0.06 at a t-value of 1.66 and a DF of 14

Now, since the P-value is 0.06,it is greater than the significance level of 0.05. Thus we do not reject the null hypothesis. We conclude that there is not sufficient evidence that the true diameter differs from 0.5 in.

Please amswere my school is due tommorow and i meed some help​

Answers

Answer:

88

Step-by-step explanation:

M : R

3 : 7

R : E

1 : 2

So make Ryan equal

1×7=7

2×7=14

tfo R : E

7 : 14

then add all 3forM+7forR+14forE = 24

192/24=8

so for Ethan, 8×14=112and for Marc, 8×3=24

therefore Ethan has 112-24=88 more stickers than Marc

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 17 subjects had a mean wake time of 104.0 min. After​ treatment, the 17 subjects had a mean wake time of 97.5 min and a standard deviation of 21.9 min. Assume that the 17 sample values appear to be from a normally distributed population and construct a 95​% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 104.0 min before the​ treatment? Does the drug appear to be​ effective?

Answers

Answer:

The 95% confidence interval of mean wake time for a population with treatment is between 86.2401 and  108.7599 minutes.

This interval contains the mean wake time before treatment and which does not prove to be effective

Step-by-step explanation:

GIven that :

sample size n = 17

sample mean [tex]\overline x[/tex] = 97.5

standard deviation [tex]\sigma[/tex] = 21.9

At 95% Confidence interval

the level of significance ∝ = 1 - 0.95

the level of significance ∝ =  0.05

[tex]t_{\alpha/2} = 0.025[/tex]

Degree of freedom df = n - 1

Degree of freedom df = 17 - 1

Degree of freedom df = 16

At ∝ =  0.05 and df = 16 , the two tailed critical value from the t-table [tex]t_{\alpha/2 , 16}[/tex] is :2.1199

Therefore; at 95% confidence interval; the mean wake time is:

= [tex]\overline x \pm t_{\alpha/2,df} \dfrac{s}{\sqrt{n}}[/tex]

= [tex]97.5 \pm 2.1199 \times \dfrac{21.9}{\sqrt{17}}[/tex]

= 97.5 ± 11.2599

= (86.2401 , 108.7599)

Therefore; the mean wake time before the treatment was 104.0 min

The 95% confidence interval of mean wake time for a population with treatment is between 86.2401 and  108.7599 minutes.

This interval contains the mean wake time before treatment and which does not prove to be effective

A satellite dish is being designed so that it can pick up radio waves coming from space. The satellite dish will be in the shape of a parabola and will be positioned above the ground such that its focus is 50 ft above the ground. Using the ground as the x-axis, where should the base of the satellite be positioned? Which equation best describes the equation of the satellite?

Answers

Answer:

[tex]y=\frac{x^2}{100}+2500[/tex]

Step-by-step explanation:

Given that the satellite is in the shape of parabola and will be positioned above the ground such that its focus is 50 ft, above ground.

let the point at the ground be (0,0) and focus (0,50). Thus, The base is at equal distance from the ground and focus that the vertex is at

(h,k) =(0,25).

Obtain the equation that describes the equation of the satellite as,

[tex](x-h)^2 =4a(y-k)\\

\Rightarrow (x-0)^2=4(25)(y-25)\\

\Rightarrow x^2=100(y-25)\\

\Rightarrow x^2 =100y-2500\\

\Rightarrow y=\frac{x^2}{100}+2500[/tex]

Thus, the equation of satellite is  [tex]y=\frac{x^2}{100}+2500[/tex]

Answer:

(0, 25); y = one over one hundred x2 + 25

Step-by-step explanation:

If your on question 7 of (04.04 MC)

It should be the third option. (C)

Different hotels in a certain area are randomly​ selected, and their ratings and prices were obtained online. Using​ technology, with x representing the ratings and y representing​ price, we find that the regression equation has a slope of 120 and a​ y-intercept of negative 353.
What is the equation of the regression​ line?
Select the correct choice below and fill in the answer boxes to complete your choice.
A) y=..+(..)^x
B) y=..+(..)^x
C) y=..+(..)^x
D) y=..+(..)^x

Answers

Answer:

y = -353 + 120x

Step-by-step explanation:

First step is using a linear regression equation:

In a linear regression model y = b0 + b1x

where y be the response variable

and x be the predictor variable.

let b1  = slope

b0 = intercept of the line.

Let the variable ratings be by denoted by x and the variable price be denoted by y.

From the given information it is known that, price (y) is response variable and ratings (x) predictor variable.

Therefore, price can be predicted using ratings.

Second step is to obtain the regression equation of the variables price (y) and ratings (x):

so the slope of the regression equation is 120 and the y-intercept is -353.

then b0 = -353

therefore,

(price)y = b0 + b1x (ratings)

y = -353 + 120x

The equation of the regression line is y = -353 + 120x.

Given that,

The regression equation has a slope of 120 and a​ y-intercept of negative 353.

Based on the above information, the equation is as follows:

y = -353 + 120x

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Which of the following is the minor arc for the circle shown below?



A. AWR


B. AW


C. RAW


D. RA

Answers

Answer:

RA

Step-by-step explanation:

Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1). • Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.) Xi 2 –1 P(xi) • What is Miguel’s expected value from playing the game? • Based on the expected value in the previous step, how much money should Miguel expect to win or lose each time he plays? • What value should be assigned to choosing two chips with the number 1 to make the game fair? Explain your answer using a complete sentence and/or an equation.

Answers

Answer:

See explanation

Step-by-step explanation:

Step 1

Miguel wins $2 is if he pulls two chips with the number 1.  

Probability of winning is:

2/4 * 1/3 = 1/6  as there are 4 chips in total

Probability of loosing is:

1- 1/6 = 5/6Step 2

Missing values we found in the step 1, can be populated in the table:

Xi === 2 === -1P(Xi) === 1/6 === 5/6

Expected Value as per table data:

1/6*2 + 5/6*(-1) = -1/2

Expected value is $1/2 loss each time he plays

Step 3

To make the game fair, the expected value should be zero.

Then as per the calculation above, let's replace 2, with x, and find its value.

1/6x + 5/6*(-1) = 0      1/6x = 5/6                   x= 5  

So the amount should be $5 to make the game fair.

The sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed. Find the Algebraic equation by replacing the tens digit with x.

Answers

Let a be the number in the 10s place and b in the 1s place. Then the original two-digit number is 10a + b.

The sum of the digits is 5:

a + b = 5

Subtract 9 from the original number, and we get the same number with its digits reversed:

(10a + b) - 9 = 10b + a

Simplifying this equation gives

9a - 9b = 9

or

a - b = 1

Add this to the first equation above:

(a + b) + (a - b) = 5 + 1

2a = 6

a = 3

Then

3 - b = 1

b = 2

So the original number is 32. Just to check, we have 3 + 2 = 5, and 32 - 9 = 23.

What is the initial value of the equation shown? y = −7x − 6 −13 −7 −6 −1

Answers

Answer:

-6.

Step-by-step explanation:

The equation is y = -7x - 6.

The initial value is found when x = 0.

y = -7(0) - 6

y = 0 - 6

y = -6

Hope this helps!

Rewriting the Equation:

Answer:

7x+y=-33

Step-by-step explanation:

1.) Combine Like Terms: y=-7x-33

2.) Move the variable to the left side and use the inverse operation:

y+7x=-33

3.) Reorder terms using commutative property since x comes before y:

7x+y=-33

If you want to find the function then tell me.

A business tenant has a percentage lease stating rent payment is greater of 2% of the business’s total gross sales volume or a minimum base rental of $1,000.00 per month. In the past year, sales totaled $435,000. How much rent did the business pay?

Answers

Answer:

$12,000

Step-by-step explanation:

By paying the minimum rent, the tenant would pay $1000 * 12 = $12,000.

Rent cannot be less than $12,000.

If the 2% of sales is greater than $12,000, then 2% of sales becomes the rent.

Now we calculate 2% of annual sales.

2% * $435,000 = $8,700

Since the minimum rent, $12,000, is greater than 2% of sales, then rent is $12,000.

Find the maximum and minimum values by evaluating the equation

Answers

Answer:

min = -9

max =3

Step-by-step explanation:

C = x-3y

x ≥0

x≤3

y≥0

y≤3

The minimum will be be when x is smallest and y is at its max

x =0 and y = 3

C = 0 - 3(3)

C = 0-9 = -9

The minimum is -9

The maximum occurs when x is largest and y is smallest

x =3 and y = 0

C = 3 - 3(0)

C = 3-0 = 3

The max is 3

Use differentials to estimate the amount of material in a closed cylindrical can that is 20 cm high and 8 cm in diameter if the metal in the top and bottom is 0.1 cm thick, and the metal in the sides is 0.1 cm thick. Note, you are approximating the volume of metal which makes up the can (i.e. melt the can into a blob and measure its volume), not the volume it encloses

Answers

Answer:

The volume is  [tex]dV = 19.2 \pi \ cm^3[/tex]

Step-by-step explanation:

From the question we are told that

    The height is  h =  20 cm

    The diameter is  d = 8 cm

    The thickness of both top and bottom is  dh  =  2 * 0.1  =  0.2 m

     The  thickness of one the side is dr =  0.1 cm

The  radius is mathematically represented as

            [tex]r = \frac{d}{2}[/tex]

substituting values

            [tex]r = \frac{8}{2}[/tex]

           [tex]r = 4 \ cm[/tex]

Generally the volume of a cylinder is mathematically represented as      

       [tex]V_c = \pi r^2 h[/tex]

Now the partial differentiation with respect to h is  

       [tex]\frac{\delta V_v}{\delta h} = \pi r^2[/tex]

Now the partial differentiation with respect to r is  

      [tex]\frac{\delta V_v}{\delta r} = 2 \pi r h[/tex]

Now the Total differential of [tex]V_c[/tex] is mathematically represented as

       [tex]dV = \frac{\delta V_c }{\delta h} * dh + \frac{\delta V_c }{\delta r} * dr[/tex]

       [tex]dV = \pi *r^2 * dh + 2\pi r h * dr[/tex]

substituting values

      [tex]dV = \pi (4)^2 * (0.2) + (2 * \pi (4) * 20) * 0.1[/tex]

     [tex]dV = 19.2 \pi \ cm^3[/tex]

(I deleted my answer because it was incorrect)

A circle has a radius of 8ft. Find the length s of the arc intercepted by a central angle of π3 radians. Do not round any intermediate computations, and round your answer to the nearest tenth.

Answers

Answer:

8.4ft

Step-by-step explanation:

Formula for calculating the length of an arc is expressed as [tex]L = \frac{\theta}{360} * 2\pi r\\[/tex]

[tex]\theta[/tex] is the central angle = π/3 rad

r is the radius of the circle = 8ft

Substituting the values into the formula above we have;

[tex]L =[/tex] [tex]\frac{(\frac{\pi}{3} )}{2 \pi} * 2\pi (8)\\\\[/tex]

[tex]L = \frac{\pi}{6 \pi} * 2\pi(8) \\\\L = 1/6 * 16\pi\\\\L = 8\pi/3\\\\L = \frac{8(22/7)}{3} \\\\L = \frac{8*22}{7*3}\\ \\L = 176/21\\\\L = 8.4 ft (to\ the\ nearest\ tenth)[/tex]

Hence, the length of the arc s is approximately 8.4 ft.

Help please someone I have solved this multiple times factoring out the quadratic equations and I keep getting m as -1. But the correct answer says m is -5.

Answers

Answer:  m = -5

Step-by-step explanation:

[tex]\dfrac{m+3}{m^2+4m+3}-\dfrac{3}{m^2+6m+9}=\dfrac{m-3}{m^2+4m+3}\\\\\\\dfrac{m+3}{(m+3)(m+1)}-\dfrac{3}{(m+3)(m+3)}=\dfrac{m-3}{(m+3)(m+1)}\quad \rightarrow m\neq-3, m\neq-1[/tex]

Multiply by the LCD (m+3)(m+3)(m+1) to eliminate the denominator. The result is:

(m + 3)(m + 3) - 3(m + 1) = (m - 3)(m - 3)

Multiply binomials, add like terms, and solve for m:

(m² + 6m + 9) - (3m + 3) = m² - 9

    m² + 6m + 9 - 3m - 3 = m² - 9

                  m² + 3m + 6 = m² - 9

                           3m + 6 =  -9

                                  3m = -15

                                    m = -5  

 

       

Find a solution to the linear equation y=−x+7 by filling in the boxes with a valid value of x and y.

Answers

Answer:

(0,7) and (7,0)

Step-by-step explanation:

When x = 0, y = 7

When y = 0, x = 7

The solution to this equation is: (0,7) and (7,0) and can be graphed on a cartesian plane like the attached graph.

Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.

Answers

Answer

240cm^2 (i think)

Step-by-step explanation:

find the area of each side then add

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