Given the graph of the circle find the equation

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)

Answer:

182

Step-by-step explanation:

The sequence has a common difference of +3.

Answer:

It's none of those. It's supposed to be 171.

Step-by-step explanation:

That's because in an arithmetic sequence it's a list of numbers with a definite pattern, and all you're doing is adding 3 to each number.

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.

Answer: 45.5

Step-by-step explanation:

Im in 6th grade and all you had to do was add 18.3 and 27.2 and you’ll get 45.5

Answer:

The garbage dump is 58.3 miles west of the hotel, and the hotel is 57.1 miles west of the hardware store. The hardware store is 44.8 miles west of the library. The hardware store is 57.9 miles north of the office supply store, and the office supply store is 55.5 miles north of the science lab.

Step-by-step explanation:

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)

Answer:

  16x^3 +64x^2 -40x

Step-by-step explanation:

Use the distributive property. The factor outside parentheses multiplies each term inside parentheses:

  8x(2x^2 +8x -5) = (8x)(2x^2) +(8x)(8x) +(8x)(-5)

  = 16x^3 +64x^2 -40x

Answer

240cm^2 (i think)

Step-by-step explanation:

find the area of each side then add

Answer:

y = -x + 0

Step-by-step explanation:

well the equation of a line is y = mx + b

m = the slope , b = the y-intercept

m = y2 - y1 / x2 - x1

m = -1

and b is the y-intercept of the line.

finally:

y = -1x + 0

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

Answer:

Factor 9 out of 18x.

9(2x)−9

Factor 9 out of −9

9(2x)+9(−1)

Factor 9 out of 9(2x)+9(−1)

9(2x−1)

Answer:

9 ( 2x - 1 )

Step-by-step explanation:

→ Look for the HCF of the whole numbers

HCF of 18 and 9 is 9

→ Put 9 outside the brackets

9 ( ? - ? )

→ Perform the calculation 18x ÷ 9 to determine the first question mark

18x ÷ 9 = 2x ⇔ 9 ( 2x - ? )

→ Perform the calculation 9 ÷ 9 to determine the second question mark

9 ÷ 9 = 1 ⇔ 9 ( 2x - 1 )

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.

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.

Answer:

direct variation

Step-by-step explanation:

For direct variation k = [tex]\frac{y}{x}[/tex] ← k is the constant of variation

For inverse variation k = yx

Expressing the data as ordered pairs

(6, 9), (8, 12), (12, 18), (20, 30)

k = [tex]\frac{9}{6}[/tex] = [tex]\frac{12}{8}[/tex] = [tex]\frac{18}{12}[/tex] = [tex]\frac{30}{20}[/tex] = [tex]\frac{3}{2}[/tex] = 1.5 ← indicating direct variation

Equation is

y = kx = 1.5x

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.

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  

Hey there! I'm happy to help!

PART A

There are 3 $1 bills, 1 $5 bill, and 1 $10 bill. This gives us 5 total bills.

First, we want to find the probability of winning $12. Well, to win, you have to draw the $10 bill. You only have room for two dollars beforehand to equal $12 dollars after pulling out the ten. So, this is the probability of drawing two one dollar bills and the the ten. Let's calculate this below.

[tex]\frac{3}{5} *\frac{1}{2} *\frac{1}{3} =\frac{1}{10}[/tex]

Where did I get these numbers from? Well 3 of the 5 bills are $1, so the first probability is 3/5. Then, if we draw one of the $1 bills, there are only 2 of those left and 4 total bills, so the probability is then one half. Finally, there would be only 3 left and you need to pick the $10 bill, which is a probability of 1/3.

The probability of winning $12 is 1/10 or 10%.

PART B

Now, we want to find the probability of picking every single bill before the ten. This means that we pick the three one dollar bills and the five dollar bill before the ten.

To pick the first $1 bill, our probability is 3/5, and then for the second it is 1/2. For the third, there are three total cards and 1 $1 bill, so the probability is 1/3. Then we have a 1/2 chance of picking the $5 bill over the $10 bill, giving us this solution.

[tex]\frac{3}{5} * \frac{1}{2} * \frac {1}{3} * \frac{1}{2}= \frac{1}{20}[/tex]

The probability of winning all bills in the urn is 1/20 or 5%.

PART C

For this event, we want to get any bill that isn't the $10 and then we want the $10 on the second one.

Since there are 4 bills that aren't the $10, our first probability is 4/5. Then, we only have 4 left, with 1 being the $10, so our second probability is 1/4.

[tex]\frac{4}{5}*\frac{1}{4}=\frac{1}{5}[/tex]

The probability of the game stopping at the second draw is 1/5 or 20%.

Have a wonderful day! :D

The probability of winning $12 will be 0.15.

The game stops after drawing$10 bill. There can also be 2 draws of $2 and $10 to make $12.

Therefore, the probability of winning $12 will be calculated thus:

= Probability of getting $2 × probability of getting $10

= 3/5 × 1/4

= 0.15

The probability of winning all balls in the urn will be:

= 4/5 × 3/4 × 2/3 × 1/2

= 0.2

Lastly, the probability of the game stopping at the second draw will be:

= First draw × Second draw

= 4/5 × 1/4

= 0.2

Learn more about probability on:

https://brainly.com/question/24756209

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

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

Learn more about Slope of Line:

https://brainly.com/question/14511992

#SPJ2

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.

Answer:

[tex] x = 2 [/tex]

Step-by-step explanation:

Given a right-angled triangle as shown above,

Included angle = 60°

Opposite side length = 3

Adjacent side length = x

To find x, we would use the following trigonometric ratio as shown below:

[tex] tan(60) = \frac{3}{x} [/tex]

multiply both sides by x

[tex] x*tan(60) = \frac{3}{x}*x [/tex]

[tex] x*tan(60) = 3 [/tex]

Divide both sides by tan(60)

[tex] \frac{x*tan(60)}{tan(60} = \frac{3}{tan(60} [/tex]

[tex] x = \frac{3}{tan(60} [/tex]

[tex] x = 1.73 [/tex]

[tex] x = 2 [/tex] (approximated to whole number)

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.

Answer:

The probability of winning the bet is 1/336

Step-by-step explanation:

We should understand that there is only one possible arrangement of the winning selection

Now, the horse that comes first can be selected in 8 ways given that all the horses have equal chances

The horse that comes second can be selected in 7 ways given that all the horses have equal chances

The horse that comes third can be selected in 6 ways given that all the horses have equal chances

Now the total number of ways of selection would be;

8 * 7 * 6 = 336

Since there is only one of the selections that is correct, the probability of making the correct choice is thus 1/336

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!

Answer:

A) 1  2/3 yards

Step-by-step explanation:

Hope this helped

Answer:

The answer is A

Let me finish the quiz then upload a picture to this answer showing you the correct answer is A

Step-by-step explanation:

Answer:

13, 21

Step-by-step explanation:

Add 8 to the next number from the left to the right.

Answer:

The next three numbers in the sequence are: 13, 21, 29.

Step-by-step explanation:

Common Pattern: +8

-27 +8 = -19

-19 + 8 = -11

-3 + 8 = 5

5 + 8 = 13

13 + 8 = 21

21 + 8 = 29

Answer:

Cada cuota tendrá un valor de $14,850.

Step-by-step explanation:

Dado que Tomás canceló la mitad del valor de la bicicleta, la cual costaba $199.900, el valor pagado al inicio fue de $99,950 (199,900 / 2).

Luego, para el valor restante, Tomás suscribió a una financiación con un interés de $4,000, elevando el monto a pagar a $103,950, pagaderos en 7 cuotas. Por lo tanto, dichas cuotas tendrán cada una un valor de $14,850 (103,950 / 7).

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)

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 range for the values of x:

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

Happy to help! You can certainly extend this range

Answer:

1:3

Step-by-step explanation:

3/3=1

9/3=6

Answer:

Option A is the correct option.

Step-by-step explanation:

Given,

Number of pears = 3

Number of apples = 9

Find : Ratio of the number of pears to the number of apples on the fruit salad

Now,

[tex] \frac{pear}{apples} [/tex]

Plug the values

[tex] = \frac{3}{9} [/tex]

Divide the numerator and denominator by 3

[tex] = \frac{3 \div 3}{9 \div 3} [/tex]

Divide the numbers

[tex] = \frac{1}{3} [/tex]

It can be written as :

1 : 3

Hope this helps..

Best regards!!!