find the sum of the values of a and b such that f(x)=2ax^2+bx+3 has a relative extremum at the point (-1,2)

The  work required to pump the water out of the spout is 70.9 * 10⁶ joules which is 71 M Joules approx.

Let the spherical tank be divided into a series of horizontal disks.

Let x be the height of each disk, g = gravity and p = density

Volume of each disk = πr2dx

Where r is the radius of each disk and dx is the thickness

By Pythagoras r² = 6² - x²= 36 -x²

Therefore Volume = π*(36-x²)*dx cubic metres

The distance each disk has to be lifted to escape the top of the spout = 2 + 6-x meters = (8-x)

Work needed to lift each disk to outlet = distance * mass where

mass = volume * density * gravity

        = pi(36-x²)*p*g = 9800pi(36-x²)dx

dW =  (8-x)* 9800pi(36-x²)dx

Since we have already accounted for the height of the spout, the work required is obtained by integrating the above expression from the bottom of the tank to the top. In other words, - 6 to + 6.

W = ⌠(8-x)*9800pi(36-x2)dx = 9800pi⌠[288 - 36x - 8x² +x³]dx

The odd terms evaluate to zero and we can rewrite the above as 2* I from 0 to 6.

W = 9800pi*2 [288x - 8x³/3] at x = 6 = 1152*19600π Joules = 22579200π joules = 70963200j

Total work required = 70.9 * 10⁶ joules

Visit here to learn more about spherical tank: https://brainly.com/question/11279278

#SPJ4

The probability statements after continuity correction are given as follows:

Continuity correction is used as a "correction" when a continuous distribution is used to approximate a discrete distribution. One example of this is the approximation of the binomial distribution to the normal distribution.

Hence, using continuity correction, the range of values that corresponds to a number of exactly x is given as follows:

x - 0.5 < x < x + 0.5.

Thus the range of values of 118 is given as follows:

117.5 < x < 118.5.

More can be learned about continuity correction at https://brainly.com/question/28984189

#SPJ1

Answer:

The answer is \(-9a^{7}b^{4}\).

Step-by-step explanation:

To simplify this problem, start by multiplying \(a^3\) by \(a^4\) by adding the exponents, which will look like \((-3a^7b)*(3b^3)\). Next, multiply \(b\) by \(b^3\) by adding the exponents, which will look like \((-3a^7b^4)*(3)\). Then, multiply 3 by -3, which will look like \(-9a^7b^4\). The final answer is \(-9a^7b^4\).  

Answer:

-9a^7b^4

Step-by-step explanation:

This function written in vertex form include the following: A. f(x) = (x –1)² – 7.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = x² – 2x – 6, we have:

a = 1, b = -2, and c = -6

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-2)/2(1)

Axis of symmetry, Xmax = 2/2

Axis of symmetry, Xmax = 1.

Next, we would determine vertex as follows;

f(x) = x² – 2x – 6

f(x) = 1² – 2(1) – 6

f(x) = -7.

Now, we can write quadratic function in vertex form;

f(x) = a(x - h)² + k

f(x) = (x - 1)² - 7

Read more on quadratic functions here: brainly.com/question/14201243

#SPJ1

Complete Question:

The image shows a geometric representation of the function f(x) = x² – 2x – 6 written in standard form.

What is this function written in vertex form?

f(x) = (x –1)² – 7

f(x) = (x +1)² – 7

f(x) = (x –1)² – 5

f(x) = (x +1)² – 5

Answer:

Samedy's statement is false. in total the class has 56 brothers and sisters

Step-by-step explanation:

Answer:

A. Samedy's statement is incorrect.

B. In total, the class has 71 brothers and sisters.

To arrive at this answer, we can use the information given in the problem to calculate the total number of brothers and sisters:

7 students have 2 siblings each, so there are 14 siblings in total.

4 students have 1 sibling each, so there are 4 siblings in total.

6 students have 3 siblings each, so there are 18 siblings in total.

The remaining students have 4 siblings each, so there are 4 x (24 - 7 - 4 - 3 - 6) = 4 x 4 = 16 siblings in total.

Adding all of these up, we get a total of 14 + 4 + 18 + 16 = 52 siblings. Therefore, Samedy's statement is incorrect, as the class has 52 siblings and not 24.

(Please could you kindly mark my answer as brainliest you could also follow me so that you could easily reach out to me for any other questions)

Step-by-step explanation:

1. w=4 v=-3

2. y=6 x=-2

4. m=6 p=3

5. b=-2 a=4

7. c=8 d=-7

8. g=-3 f=5

10. j=2.5 k=4

11. x=4 y=1.5

13. x=2 y=1

14. y=6 x=5

According to the Empirical Rule, a percentage of 99.74% of the returns are expected to be within these following values:

-55% to 95%.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

The mean and the standard deviation of the returns are given as follows:

The interval containing 99.74% of the values is within 3 standard deviations of the mean, hence the bounds are calculated as follows:

More can be learned about the Empirical Rule at https://brainly.com/question/10093236

#SPJ1

Step-by-step explanation:

directly proportional means

y = kx

with k being a constant factor for all values of x.

we get k by using the given data point (10, 15).

15 = k×10

k = 15/10 = 1.5

so, now for the other tree we know k and x and calculate y

y = 1.5×14.4 = 21.6 m

it is 21.6 m tall (its height is 21.6 m).

Answer:

see explanation

Step-by-step explanation:

(1)

4(m + 7) = 4 ( divide both sides by 4 )

m + 7 = 1 ( subtract 7 from both sides )

m = - 6

(2)

let the number be n , then

\(\frac{3}{5}\) n - 2 = 40 ( multiply through by 5 to clear the fraction )

3n - 10 = 200 ( add 10 to both sides )

3n = 210 ( divide both sides by 3 )

n = 70

The required number is 70

(3)

The 4 sides of a square are congruent , then

length of side = 36 cm ÷ 4 = 9 cm

A mathematical phrase, rule, or law describing the relationship between an independent variable and a dependent variable (the dependent variable).

Given,

\(g^{-1}(5)=\)

1/g × 5

therefore, 1 × 5/g

we get. 5/g

\(h^{-1}(x)=\) 1/h × x

= 1 × x/h

= x/h

\(\left(h^{-1} \circ h\right)(-2)=\)

\(\left(h^{-1} \circ h\right)(-2)\)

\(& h^{-1} h=h^{-1+1} \\\)

Simplifying,

\(& =\circ h^{-1+1}(-2)\)

\(={ }^{\circ} h^0(-2)\)

To learn more about Function, refer to:

https://brainly.com/question/11624077

#SPJ1

Answer:

Step-by-step explanation:

The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000,  3,983 rounded to the nearest thousand is 4,000,  13,560 rounded is 14,000.

7,000 + 4,000+ 14,000 = 25,000

Answer: Read the solution

Step-by-step explanation:

A. For diagram A, triangles ANC and BDE are similar. Thus, we can use similarity ratios to find the length of AC. (x+1)/12 = (x+5)/15. 15x+15=12x+60. Thus 3x=45, and x=15. Since we need to find AC, AC = 15+1 = 16.

B. For diagram B, triangles SRT and VUT are similar. Again, using similarity ratios, (4x-1)/14=(x+2)/6 or 14x+28=24x-6. 10x=34, x=3.4.

Answer:

A)    A(t) = 500e^(0.07)(t)

B)    575.137

Step-by-step explanation:

To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

The function g( x ) is translated to the left by 9 units and down by 5 units.

Given data ,

Let the first function be represented as f ( x )

where the value of f ( x ) = | x |

Let the translated function be g ( x )

where the value of g ( x ) = | x + 9 | - 5

A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.

On translating to the left , f ( x + a )

So , the function f ( x ) is translated 9 units to the left by f ( x + 9 ) = | x + 9 |

Now , when the function is translated 5 units down , f ( x ) - 5

So , the translated function is g ( x ) = | x + 9 | - 5

Hence , the function is translated to the left by 9 and up by 5 units.

To learn more about translations click :

https://brainly.com/question/19007400

#SPJ1

Answer: z = -4

Step-by-step explanation: I thinks

Answer:

z=-4

Step-by-step explanation:

48=50+5z+18

48=68+5z

-20/5=5z/5

-4=z

Answer:

The proportion of cars can get through the toll booth in less than 3 minutes is 67%.

Step-by-step explanation:

Let the random variable X be defined as the service times at a tool booth.

The random variable X follows an Exponential distribution with parameter μ = 2.7 minutes.

The probability density function of X is:

\(f_{X}(x)=\frac{1}{\mu}e^{-x/\mu };\ x\geq 0,\ \mu>0\)

Compute the probability that a car can get through the toll booth in less than 3 minutes as follows:

\(P(X<3)=\int\limits^{3}_{0} {\frac{1}{2.7}\cdot e^{-2.7x}} \, dx\)

                \(=\frac{1}{2.7}\cdot \int\limits^{3}_{0} {e^{-x/2.7}} \, dx \\\\=\frac{1}{2.7}\cdot [-\frac{e^{-x/2.7}}{1/2.7}]^{3}_{0}\\\\=1-e^{-3/2.7}\\\\=0.6708\)

Thus, the proportion of cars can get through the toll booth in less than 3 minutes is 67%.

The central angle measure, x, for the Baseball slice in the circle graph is 50.4 degrees.

Given that, a survey was conducted in which 2400 people were asked to name their favorite sport to watch and the table below shows their answers: Sport percentage of people are:

Football 29%

Soccer 9%

Baseball 14%

Basketball 8%

Hockey 8%

Other 32%

We need to find the central angle measure, x, for the Baseball slice in the circle graph.

For this, we need to use the formula that gives the central angle measure in degrees for a sector of a circle:

Central angle measure = (Percentage/100) × 360°

Now, using the above formula, we can calculate the central angle measure for each sport as shown below:

Football: (29/100) × 360° = 104.4°

Soccer: (9/100) × 360° = 32.4°

Baseball: (14/100) × 360° = 50.4°

Basketball: (8/100) × 360° = 28.8°

Hockey: (8/100) × 360° = 28.8°

Other: (32/100) × 360° = 115.2°

The sum of all central angle measures should be 360°, which is the measure of a full circle.

So we can check if the calculations are correct: 104.4° + 32.4° + 50.4° + 28.8° + 28.8° + 115.2° = 360°

We see that the sum is indeed 360°, so the calculations are correct. The central angle measure for the Baseball slice is 50.4°.

Therefore, the central angle measure, x, for the Baseball slice in the circle graph is 50.4 degrees.

For more such questions on central angle, click on:

https://brainly.com/question/10945528

#SPJ8

The mean amount of money the insurance company can expect to lose on each policy is $142.00 with a standard deviation of $1,243.67.

What is an insurance?

Let X be the random variable representing the amount of money the insurance company will lose on a policy. Then we can calculate the expected value (mean) of X and the standard deviation of X as follows:

Expected value:

E(X) = 30,000(1/1,000) + 10,000(1/250) + 0(1 - 1/1,000 - 1/250) = $142.00

The first term in the sum corresponds to the probability of a client dying (1/1,000) multiplied by the payout ($30,000), the second term corresponds to the probability of a client becoming disabled (1/250) multiplied by the payout ($10,000), and the third term corresponds to the probability of neither event occurring (1 - 1/1,000 - 1/250).

Standard deviation:

To calculate the standard deviation, we need to find the variance of X first:

Var(X) = [30,000 - E(X)]²(1/1,000) + [10,000 - E(X)]²(1/250) + [0 - E(X)]²(1 - 1/1,000 - 1/250)

= $1,547,797.56

The first term in the sum corresponds to the squared difference between the payout for a client dying and the expected payout, multiplied by the probability of a client dying, and so on for the second and third terms.

Then, we can take the square root of the variance to find the standard deviation:

SD(X) = √[Var(X)] = $1,243.67

Therefore, the mean amount of money the insurance company can expect to lose on each policy is $142.00 with a standard deviation of $1,243.67.

To know more about insurance, visit:

https://brainly.com/question/28015669

#SPJ1

The average rate of change in the elevation of the cyclist from 5 minutes to 10 minutes is: 400 ft/min

The formula for the average rate of change is:

Average rate of change = (y₂ - y₁)/(x₂ - x₁)

Now, we want to find the average rate of change  in the elevation of the cyclist from 5 minutes to 10 minutes.

Elevation at 10 minutes = 1140 ft

Elevation at 5 minutes = 940 ft

Thus:

Average rate of change = (1140 - 940)/(10 - 5)

Average rate of change = 200/5

Average rate of change = 400 ft/min

Read more about Average rate of change at: https://brainly.com/question/8728504

#SPJ1

Answer:

y = 7x + 25

Step-by-step explanation:

\(y - 11 = 7(x - ( - 2)) \\ y - 11 = 7(x + 2) \\ y - 11 = 7x + 14 \\ y = 7x + 14 + 11 \\ y = 7x + 25\)

Answer:

5.4

Step-by-step explanation:

square of 29 = 5.385164807

5.385164807 estimated is 5.4

Answer:

12 units

Step-by-step explanation:

V = (area of base) × height

height = V/(area of base)

height = 960 units³ / 80 units²

height = 12 units

Answer:1.6

Step-by-step explanation:

Answer:

2nd answer option : 6^(13/4)

Step-by-step explanation:

what are we doing, when 2 equal base terms with exponents are multiplied ? we add the exponents !

this is like 3⁴×3³ = 3⁷

because

3×3×3×3 × 3×3×3 = 3×3×3×3×3×3×3 = 3⁷

it is that simple.

and that concept is also valid for any kind of number as exponent. even for fractions and so on.

so,

6^3 × 6^(1/4) = 6^(3 + 1/4) = 6^(12/4 + 1/4) = 6^(13/4)

Answer:

36in

Step-by-step explanation:

12x3

Answer:

D

Step-by-step explanation:

Since a fraction is a division problem, you can do every answer and compare them until you get them in order, which D is the most reliable.

The "M" in M-value stands for "Maximum." For a given ambient pressure, an M-value is defined as the maximum value of inert gas pressure (absolute) that a hypothetical "tissue" compartment can "tolerate" without presenting overt symptoms of decompression sickness (DCS).

Hope this helps you if it does pls mark me brainiest

Answer:

circumference bc area is what is inside the circle

Step-by-step explanation:

There is no change in its slope as initial and final slope is 1.

What is slope?

In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.

Main body:

formula for slope with two points form is =

y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)

according to question ,

points are (0,0) and (3,3)

y - 0 = (3-0/3-0)(x -0)

y = 3/3 *x

y = x

hence slope of line is 1.

Now points are (0,0) and (-3,-3).

y - 0 = (-3-0/-3-0)(x -0)

y =- 3/-3 *x

y = x

hence slope of line is 1.

So there is no change in its slope.

To know more about slope , visit:

https://brainly.com/question/3493733

#SPJ1