help huryyyyyyyyyyyyy

Answer:

x = -6 and x = 4

Step-by-step explanation:

In math, the critical points of a function are the points where the derivative equals zero.

So, first we will find the derivative of the function. The derivative is:

[tex]f'(x)=3x^2 +6x-72[/tex]

Now, we are going to make the derivative equal zero and find the answers of the equation.

[tex]3x^2 +6x-72=0\\3(x^2 +2x-24)=0\\3(x+6)(x-4)=0\\[/tex]

So we have that the critical points are the answers to this equation:

[tex]x+6= 0 \\x= - 6[/tex]

and

[tex]x-4=0\\x=4[/tex]

Thus, the critical points are x=-6 and x=4

Using it's concept, it is found that the critical numbers of the function are:

x = -6 and x = 4.

The critical numbers of a function f(x) are the values of x for which it's derivative is zero, that is:

[tex]f^{\prime}(x) = 0[/tex]

In this problem, the function is:

[tex]f(x) = x^3 + 3x^2 - 72x[/tex]

The derivative is:

[tex]f^{\prime}(x) = 3x^2 + 6x - 72[/tex]

[tex]f^{\prime}(x) = 3(x^2 + 2x - 24)[/tex]

Then:

[tex]f^{\prime}(x) = 0[/tex]

[tex]3(x^2 + 2x - 24) = 0[/tex]

[tex]x^2 + 2x - 24 = 0[/tex]

Which is a quadratic equation with coefficients [tex]a = 1, b = 2, c = -24[/tex], which we have to solve.

[tex]\Delta = 2^2 - 4(1)(-24) = 100[/tex]

[tex]x_{1} = \frac{-2 + \sqrt{100}}{2} = 4[/tex]

[tex]x_{2} = \frac{-2 - \sqrt{100}}{2} = -6[/tex]

The critical numbers of the function are x = 4 and x = -6.

A similar problem is given at https://brainly.com/question/16944025

Answer:

[tex]\boxed{V = 339.12 ft^3}[/tex]

Step-by-step explanation:

V = [tex]\pi r^2 h[/tex]

Where r = 3, h = 12

V = (3.14)(3)²(12)

V = (3.14)(9)(12)

V = 339.12 ft³

Step-by-step explanation:

The amount left is:

A = A₀ (½)^(t/T)

where A₀ is the initial amount,

t is the amount of time,

and T is the half life.

a) A = 100 g (½)^(250 yr / 68.9 yr)

A = 8.09 g

b) 12.5 g = 100 g (½)^(t / 68.9 yr)

0.125 = (½)^(t / 68.9 yr)

3 = t / 68.9 yr

t = 206.7 yr

Answer:

1

Step-by-step explanation:

=> [tex]\sqrt[3]{3375} - \sqrt[4]{38416}[/tex]

Factorizing 3375 gives 15 * 15 * 15 which equals 15^3 and factorizing 38416 gives 14 * 14 * 14 * 14 which equals 14^4

=> [tex]\sqrt[3]{15^3} - \sqrt[4]{14^4}[/tex]

=> 15 - 14

=> 1

Answer:

Step-by-step explanation:

[tex] \sqrt[3]{3375} - \sqrt[4]{38416} [/tex]

Calculate the cube root

[tex] \sqrt[3]{ {15}^{3} } - \sqrt[4]{38416} [/tex]

Calculate the root

[tex] \sqrt[3]{ {15}^{3} } - \sqrt[4]{ {14}^{4} } [/tex]

[tex] {15}^{ \frac{3}{3} } - {14}^{ \frac{4}{4} } [/tex]

[tex]15 - 14[/tex]

Subtract the numbers

[tex]1[/tex]

Hope this helps...

Answer:

A) Null Hypothesis;H0: μ = 5

Alternative Hypothesis;Ha: μ ≠ 5

B) test statistic = -2.1226

C) p-value = 0.0598

D) Option A is correct

Step-by-step explanation:

We are given;

x = 4.52 minutes

s = 0.75 minutes

μ = 5 minutes

n = 11

degree of freedom = n - 1 = 11 - 1 = 10

A) The hypotheses are;

Null Hypothesis;H0: μ = 5

Alternative Hypothesis;Ha: μ ≠ 5

B) t-statistic = (x - μ)/(s/√n)

(4.52 - 5)/(0.75/√11) = -2.1226

C) From the t-score calculator results attached, the p-value is approximately 0.0598.

D) The P-value of 0.0598 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we say that the result is statistically nonsignificant. So option A is correct.

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

Perimeter = 128 feet

The width is 24 feet less than the length is written as

w = l - 24

128 = 2l + 2( l - 24)

128 = 2l + 2l - 48

Group like terms

4l = 176

Divide both sides by 4

l = 44

The length is 44 feet

Substitute l = 44 into w = l - 24

w = 44 - 24

w = 20

The width is 20 feet

Hope this helps you

Answer:

To make 16 pancakes, we would multiply each of the initial measurement of the ingredients by 16.

To make 4 pancakes, we would multiply each of the initial measurement of the ingredients by 4.

To make 12 pancakes, we would multiply each of the initial measurement of the ingredients by 12.

see explanation below

Step-by-step explanation:

If the ingredients to make 1 pancake is as follows:

1 1/2  cups all-purpose flour; 31/2 teaspoons baking powder; 1 teaspoon salt.

1 tablespoon white sugar.; 1 1/4 cups milk; 1 egg; and 3 tablespoons butter.

Then to make 16 pancakes, we would multiply each of the initial measurement of the ingredients by 16.

cups all-purpose flour =16× 1 1/2

=  16×3/2 = 24

teaspoons baking powder = 16 ×7/2 = 56

teaspoon salt = 1×16 = 16

tablespoon white sugar= 1×16 = 16

cups milk= 16×5/4 = 20

egg= 1×16 = 16

tablespoons butter= 3×16 = 48

Then to make 4 pancakes, we would multiply each of the initial measurement of the ingredients by 4.

cups all-purpose flour =4× 1 1/2

=  4×3/2 = 6

teaspoons baking powder = 4 ×7/2 =14

teaspoon salt = 1×4 = 4

tablespoon white sugar= 1×4 = 4

cups milk= 4×5/4 = 5

egg= 1×4 = 4

tablespoons butter= 3×4 = 12

Then to make 12 pancakes, we would multiply each of the initial measurement of the ingredients by 12.

cups all-purpose flour =12× 1 1/2

=  12×3/2 = 18

teaspoons baking powder = 12 ×7/2 =42

teaspoon salt = 1×12 = 12

tablespoon white sugar= 1×12 = 12

cups milk= 12×5/4 = 15

egg= 1×12 = 12

tablespoons butter= 3×12 = 36

The operation applied is multiplication with each fraction.

Answer:

The first one is correct

The second one is also correct

The third is also correct

Congrats!

Answer:

1) [tex]\boxed{Option \ B}[/tex]

2) [tex]\boxed{Option \ B}[/tex]

3) [tex]\boxed{Option \ B}[/tex]

You're totally correct, Man! :)

Step-by-step explanation:

Question 1:

[tex](6b^2-4b+3)-(9b^2-3b+6)\\Resolving \ the\ brackets\\6b^2-4b+3-9b^2+3b-6\\Combining \ like \ terms\\6b^2-9b^2-4b+3b+3-6\\-3b^3-b-3[/tex]

Question 2:

[tex](b+6)(b-3)\\Using \ FOIL\\b^2-3b+6b-18\\b^2+3b-18[/tex]

Question 3:

[tex](4x-3)(6x-1)\\Using \ FOIL\\24x^2-4x-18x+3\\24x^2-22x+3[/tex]

25/250 = 1/10

I do not know that much english. I an spanish so I might have done it wrong.

the probability that the horse is at least 25 feet away from all boundary lines is 0.5

To calculate the probability that the horse is at least 25 feet away from all boundary lines in an enclosed pasture that is 150 feet by 200 feet, we need to consider the available space for the horse to roam.

The area of the pasture is given by:

Area = Length * Width = 150 feet * 200 feet = 30,000 square feet

Now, let's consider the area where the horse must stay within at least 25 feet away from all boundary lines. We can imagine this as a rectangular strip along the inner boundary of the pasture, with dimensions reduced by 50 feet on each side.

The dimensions of this rectangular strip would be:

Length = 150 feet - 2 * 25 feet = 100 feet

Width = 200 feet - 2 * 25 feet = 150 feet

The area of this rectangular strip is given by:

Area_strip = Length * Width = 100 feet * 150 feet = 15,000 square feet

Therefore, the probability that the horse is at least 25 feet away from all boundary lines is:

Probability = Area_strip / Area = 15,000 square feet / 30,000 square feet = 0.5

The probability is 0.5 or 50%.

Learn more about probability here

https://brainly.com/question/32117953

#SPJ2

Answer:

The line that is perpendicular to B has a slope of -1/2

Step-by-step explanation:

First find the slope of line B

m = ( y2-y1)/(x2-x1)

    = (10-0)/(5-0)

    = 10/5

    = 2

Lines that are perpendicular have slopes that multiply to -1

m * 2 = -1

m = -1/2

The line that is perpendicular to B has a slope of -1/2

Answer:

-1/2x

Step-by-step explanation:

Hey there! :)

Well to find the slope of line B we'll use the following formula.

[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

We'll use the points (0,0) and (5,10),

10 - 0 = 10

5 - 0 = 5

Slope = 2x

The slopes of 2 perpendicular lines are reciprocals of each other,

meaning if the slope of line B is 2x then its perpendicular lines slope is -1/2x.

Hope this helps :)

Answer:

I think it is

Step-by-step explanation:

Answer:

5n√2m^ - 3mn

Step-by-step explanation:

Answer:

G 10

Step-by-step explanation:

2*3x+3*2x+15=135 inches

6x+6x=120 inches

12x=120 inches

x= 10 inches

Answer:

DEA

Step-by-step explanation:

Answer:

A. [tex]x^5+C[/tex]

Step-by-step explanation:

This is a great question! The first thing we want to do here is to take the constant out of the expression, in this case 5. Doing so we would receive the following expression -

[tex]5\cdot \int \:x^4dx[/tex]

We can then apply the power rule " [tex]\int x^adx=\frac{x^{a+1}}{a+1}[/tex] ", where a = exponent ( in this case 4 ),

[tex]5\cdot \frac{x^{4+1}}{4+1}[/tex]

From now onward just simplify the expression as one would normally, and afterward add a constant ( C ) to the solution -

[tex]5\cdot \frac{x^{4+1}}{4+1}\\[/tex] - Add the exponents,

[tex]5\cdot \frac{x^{5}}{5}[/tex] - 5 & 5 cancel each other out,

[tex]x^5[/tex] - And now adding the constant we see that our solution is option a!

Answer:

Answer A

Step-by-step explanation:

Use the property of integrals. You now have [tex]5 x\int\limits\,x^{4}dx[/tex] where the first x next to the 5 stands for multiplication. Let's evaluate it. We get [tex]5 (\frac{x^{5} }{5})[/tex]. From here, we can simplify this into [tex]x^{5}[/tex]. Add the constant of integration, which will give you the answer of [tex]x^{5} + C[/tex].

Answer:

132 people bought balcony tickets and 450 bout ground tickets

Step-by-step explanation:

let x be balcony and y for ground

x+y=582

15x+10y=6480  solve by adding(subtracting)/eliminating process

multiply first equation by 15 to eliminate x:

15x+15y=8730

15x+10y=6480      subtract

15x+15y-15x-10y=8730-6480

5y=2250

y=2250/5=450

x+y=582

x=582-450=132

Answer:se

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Answer:

The possible arrangement= 18 ways

Step-by-step explanation:

Six identical coin are tossed.

Coin has only a tail and a head.

In how many possible ways can the arrangement be 3 head and 3 tail.

The possible arrangement= (3! * 3!)/2

The reason for dividing by two because coin has two face.

The possible arrangement= (3! * 3!)/2

The possible arrangement=( 6*6)/2

The possible arrangement= 36/2

The possible arrangement= 18 ways

Answer:

The answer is "A'' -2 because anything next to the letter x is the slope

Step-by-step explanation:

The equation to slops is y=mx+b

m= slope

b= y intercept

Slope = -2

Y intercept = ( 0 , -1)

Step-by-step explanation:

Hope this helps. Your answer would be A

Hey there! I'm happy to help!

First, we need to rotate our points 180° about the origin. To find the coordinates after such a rotation, we simply find the negative version of each number in the ordered pair, which can be written as (x,y)⇒(-x,-y).

Let's convert this below

A: (1,1)⇒(-1,-1)

B: (5,4)⇒(-5,-4)

C: (7,1)⇒(-7,-1)

D: (3,-2)⇒(-3,2)

Now, we need to translate these new points five units to the right and one unit down. This means we will add 5 to our x-value and subtract 1 from our y-value. This will look like (x,y)⇒(x+5,y-1). Let's do this below.

A: (-1,-1)⇒(4,-2)

B: (-5,-4)⇒(0,-5)

C: (-7,-1)⇒(-2,-2)

D: (-3,2)⇒(2,1)

Therefore, this new parallelogram has coordinates of A'(4,-2), B'(0,-5), C'(-2,-2), and D'(2,1)

Now you know how to find the coordinates of translated figures! Have a wonderful day! :D

Answer:

8n6

step by step explanation.

Answer:

[tex]\displaystyle b = 5[/tex]

General Formulas and Concepts:

Calculus

Integration

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int\limits^b_1 {5x + 7} \, dx = 88[/tex]

Step 2: Solve

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:5

Step-by-step explanation:

got it right

Answer:

ΔV = 865.51 mm^3

Step-by-step explanation:

In order to calculate the difference in volume between both baseballs you use the following formula for the volume of a sphere:

[tex]V=\frac{4}{3}\pi r^3[/tex]       (1)

where r is the radius of he sphere.

You calculate the volume of each sphere:

First baseball:

radius = 23.2mm/2 = 11.61mm

[tex]V_1=\frac{4}{3}\pi (11.61mm)^3=6555.18\ mm^3[/tex]

Second baseball:

radius = 24.2mm/2 = 12.1mm

[tex]V_2=\frac{4}{3}\pi (12.10)^3=7420.70\ mm^3[/tex]

Then, the difference in the volumen of both spheres is:

[tex]\Delta V=V_2-V_1=7420\ mm^3-6555.18\ mm^3=865.51\ mm^3[/tex]

Answer:

Second Answer

Step-by-step explanation:

Answer:

The histogram for the data is attached below.

Step-by-step explanation:

Arrange the data in ascending order as follows:

S = {291 , 301 , 306 , 307 , 310 , 321 , 326 , 336 , 352 , 357 , 373 , 380 , 385 , 386 , 386 , 386 , 412 , 413 , 418 , 424 , 429 , 429 , 430 , 442 , 443 , 450 , 454 , 467 , 508 , 514}

Compute the range:

[tex]Range=Max.-Min.\\=514-291\\=223[/tex]

Compute the class width:

[tex]Class\ Width =\frac{Range}{No.\ of\ classes}=\frac{223}{8}=27.875\approx 28[/tex]

The classes are as follows:

290 - 318

319 - 347

348 - 376

377 - 405

406 - 434

435 - 463

464 - 492

493 - 521

Compute the frequency distribution as follows:

Class Interval         Frequency

 290 - 318                     5

 319 - 347                      3

 348 - 376                     3                  

 377 - 405                     5

 406 - 434                     7

 435 - 463                     4

 464 - 492                     1

 493 - 521                      2

The histogram for the data is attached below.

Answer:

cosΘ = - [tex]\frac{12}{13}[/tex]

Step-by-step explanation:

Given that Θ is in the third quadrant then cosΘ < 0

Given

tanΘ = [tex]\frac{5}{12}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]

Then 5 and 12 are the legs of a right triangle (5- 12- 13 ) with hypotenuse = 13

Thus

cosΘ = - [tex]\frac{adjacent}{hypotenuse}[/tex] = - [tex]\frac{12}{13}[/tex]

Answer:

We have the measure of both angles as  55 degrees and 35 degrees

Step-by-step explanation:

We know that there are three angles in a right-angled triangle. One of which is 90. FOr now, the other two are unknown, so we would designate them to be x and y.

We now set up an equation using the information we are given about the problem.

From this statement "The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle." we can set up the following equation:

x =2y -15 -------- equation 1

similarly, we know that the sum of angles in a triangle = 180 degrees. Hence, we can use this to set up another equation as follows:

x + y + 90 = 180

x+ y = 90 ------------- equation 2

we can now solve the two equations simultaneously as

x -2y =-15

x+ y = 90

from this, we have that

x = 55 and y = 35

We have the measure of both angles as  55 degrees and 35 degrees

Answer:

36.1683

Step-by-step explanation:

45*80.374/100=

The question is not written properly! Complete question along with answer and step by step explanation is provided below.

Question:

The charge to rent a trailer is ​$25 for up to 2 hours plus ​$9 per additional hour or portion of an hour.

Find the cost to rent a trailer for 2.8 ​hours, 3 ​hours, and 8.7 hours.

Then graph all ordered​ pairs, (hours,​ cost), for the function.

Answer:

ordered pair = (2.8, 34)

ordered pair = (3, 34)

ordered pair = (8.7, 88)

Step-by-step explanation:

Charge for 2.8 ​hours:

$25 for 2 hours

$9 for 0.8 hour

Total = $25 + $9

Total = $34

ordered pair = (2.8, 34)

Charge for 3 ​hours:

$25 for 2 hours

$9 for 1 hour

Total = $25 + $9

Total = $34

ordered pair = (3, 34)

Charge for 8.7 ​hours:

$25 for 2 hours

$9 for 1 hour

$9 for 1 hour

$9 for 1 hour

$9 for 1 hour

$9 for 1 hour

$9 for 1 hour

$9 for 0.7 hour

Total = $25 + $9 + $9 + $9 + $9 + $9 + $9 + $9

Total = $88

ordered pair = (8.7, 88)

The obtained ordered pairs are graphed, please refer to the attached graph.

====================================================

Explanation:

Triangle CDA is congruent to triangle CDB. We can use the HL (hypotenuse leg) congruence theorem to prove this. This only works because we have two right triangles.

Since CDA and CDB are congruent, this means their corresponding pieces are the same length. Specifically AD = DB, so

AD+DB = AB

AD+AD = 3

2*AD = 3

AD = 3/2 = 1.5

For triangle CDA, we have AD = 3/2 = 1.5 and CD = sqrt(3). We can use the pythagorean theorem to find the missing side AC

a^2 + b^2 = c^2

(AD)^2 + (CD)^2 = (AC)^2

(3/2)^2 + (sqrt(3))^2 = (AC)^2

9/4 + 3 = (AC)^2

(AC)^2 = 9/4 + 3

(AC)^2 = 9/4 + 12/4

(AC)^2 = 21/4

AC = sqrt(21/4)

AC = sqrt(21)/sqrt(4)

AC = sqrt(21)/2

This is the same as writing (1/2)*sqrt(21) or 0.5*sqrt(21)