Please find the derivative h(x)= sinh(x^5)

Step-by-step explanation:

The amount of anything a container can hold is it's volume or its capacity

The domain and range for the function shown in the graph above include the following:

D. D: [-∞, ∞]

    R: [-10, ∞]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [-10, ∞] or y ≥ -10

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Answer:

(15,8)

Step-by-step explanation:

steps are in the picture above.

Answer: Answer below

Step-by-step explanation: So you would simply have to divide 8 into 72 which would be 9.

we can verify our answer by doing 9x8 which equals 72.

Answer: 9

Step-by-step explanation:

bears divided by shelves = number of bears per shelf

72 bears divided by 8 shelves= 9 bears per shelf

Answer:

Step-by-step explanation:

You have omitted relevant parts of the question. What is the question? Are you looking for the area of the yard? The amount of fencing needed?

What units are used? (Feet, yards, meters, etc.)

area of yard = 75×55 = 4125 units²

amount of fencing needed = perimeter of rectangle = 2(75+55) = 260 units.

The total length of the fencing is the perimeter of the rectangular yard which is P = 260 feet

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

The width of the rectangular yard W = 55 feet

The length of the rectangular yard L = 75 feet

Let the perimeter of the rectangular yard be = P

And , the required fencing = Perimeter of rectangular yard

Perimeter of rectangular yard P = 2 ( L + W )

Substituting the values in the equation , we get;

Perimeter of rectangular yard P = 2 ( 55 + 75 )

Perimeter of rectangular yard P = 2 ( 130 )

Perimeter of rectangular yard P = 260 feet

Therefore , the value of P is 260 feet

Hence , the perimeter of yard is 260 feet

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Mr. Fuller wants to put fencing around his rectangular-shaped yard. the width of the yard is 55 feet and the length is 75 feet. how many feet of fencing does Mr. Fuller

if 1 2 3 = 2

then 3 5 4 = 5

hope it helps:)

In the event that cells B1, C1, and D1 were highlighted and then used to fill E1, F1, and G1, the values we would see are A. Seat1Row2, Seat2Row2, Seat3Row2.

When using a spreadsheet, you can autofill succeeding cells if you highlight the preceding ones and then drag the cursor.

If Seat1Row1, Seat2Row1, and Seat3Row1 are in the cells B1, C1, and D1, then the spreadsheet would take note of the "1s" at the end of the values.

When it is then used to autofill the next cells, it would make this a 2 such that we see Seat1Row2, Seat2Row2, Seat3Row2.

If cells H1, I1, and J1 are filled, we would then see Seat1Row3, Seat2Row3, Seat3Row3.

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Answer:

The rate of change of f(x) is greater than that of g(x)

They have the same y intercept of 14

Step-by-step explanation:

Given

\(g(x) = -\frac{1}{2}x + 14\)

Table for function f(x)

Required

Compare their rate of change and intercept

For g(x), we have:

\(g(x) = -\frac{1}{2}x + 14\)

The form of an equation is:

\(y = mx + b\)

Where

\(m = slope\)

\(b =y\ intercept\)

So:

\(m = -\frac{1}{4}\)

\(b = 14\)

For f(x): Start by calculating the slope (m)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m = \frac{17-16}{6-4}\)

\(m = \frac{1}{2}\)

The intercept is calculated using:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Where

\((x_1,y_1) = (-2,13)\)

\((x_2,y_2) = (0,y)\) --- we want to solve for y

So:

\(\frac{1}{2} = \frac{y - 13}{0 --2}\)

\(\frac{1}{2} = \frac{y - 13}{2}\)

Multiply both sides by 2

\(1 =y - 13\)

Make y the subject

\(y =1 + 13\)

\(y = 14\)

So, we have:

\(m = -\frac{1}{4}\) and \(b = 14\) -- for g(x)

\(m = \frac{1}{2}\) and \(y = 14\) --- for f(x)

By comparison:

The rate of change (i.e. slope) of f(x) is greater than that of g(x) because \(1/2 > -1/2\)

They have the same y intercept of 14

The volume of the spherical segment above the plane is\((1/3) *\pi * (r^2 - (r-h)^2) * h\) and the volume of the ring resulting from drilling a hole through the center of a sphere is \(\pi * (R^2 - r^2) * R.\).

A sphere of radius "r" is cut by a plane "h" units above the equator. To find the volume of the solid (spherical segment) above the plane, we first need to find the height of the segment, which is (r - h). Then, we can use the formula for the volume of a spherical segment: \((1/3) * \pi * (r^2 - (r-h)^2) * h.\)

A manufacturer drills a hole through the center of a metal sphere of radius R. The hole has a radius r. To find the volume of the resulting ring, we can use the formula for the volume of a cylindrical ring: \(\pi * (R^2 - r^2) * h\), where h is the height of the ring. Since the hole goes all the way through the sphere, the height of the ring is equal to the radius of the sphere, R. So the volume of the ring is \(\pi * (R^2 - r^2) * R\).

In the first problem, the volume of the solid (spherical segment) above the plane is \((1/3) * \pi * (r^2 - (r-h)^2) * h\). In the second problem, the volume of the resulting ring is \(\pi * (R^2 - r^2) * R.\)

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Answer: It's, 80+6>150

Step-by-step explanation:

Answer:

80+6x>150

The least amount of sales are 12

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

We use definitions to help us in this problem. The definition of an integer is a whole number that is not a fraction or has any fractional value. This definition includes all whole numbers, so we know that all whole numbers can be classified as integers. That's one condition done. The definition of a rational number is a number that can be written as a fraction. All whole numbers can be written as a fraction (i.e. 12/1, -3/1, 10000/1). This means that all whole numbers are also rational numbers, giving us our final answer of True.

FINAL ANSWER: True

Answer:

Step-by-step explanation:

This is the combination of 2 out of 20:

We have to find,

The number of ways in which he can choose two students.

Now the 2 out of 20 combination is,

→ 20C2

→ 20!/18!2!

→ 20 × 19/2

→ 10 × 19

→ 190 ways

Hence, there are 190 ways.

1 times 2 is equal to 2.

Multiplication is a mathematical operation that combines two numbers (known as "factors") to produce a third number (known as the "product"). It is represented using the symbol "x" or the asterisk (*).

For example, consider the multiplication of the numbers 2 and 3:

2 x 3 = 6

Here, 2 and 3 are the factors, and 6 is the product. Multiplication is a type of arithmetic operation that can be used to find the total number of items in a set, the area of a rectangle, the volume of a rectangular prism, and many other quantities.

In summary, multiplication is a mathematical operation that combines two numbers to produce a third number, and it is represented using the symbol "x" or the asterisk (*). It is an important operation in mathematics, used to find the total number of items in a set, the area of a rectangle, the volume of a rectangular prism, and many other quantities.

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Answer:

there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.

Step-by-step explanation:

The counting principle states that if there are n ways to do one thing and m ways to do another, then there are n x m ways to do both.

In this case, we want to determine how many ways we can select 3 batteries out of 6. Using the counting principle, we can break down the selection process into three steps:

Select the first battery. There are 6 choices for the first battery.

Select the second battery. There are 5 choices left for the second battery, since we've already selected one.

Select the third battery. There are 4 choices left for the third battery.

Using the counting principle, we can multiply the number of choices for each step to get the total number of ways to select 3 batteries:

6 x 5 x 4 = 120

Therefore, there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.

Answer:

a

Step-by-step explanation:

27-17= 10$ 2.5 goes into 10 4 times

The solution to the inequality expression is n < -9

The inequality expression is given as

4n - 6(n + 1) > 12

Open the bracket in the above inequality expression

4n - 6n - 6 > 12

Evaluate the like terms

-2n > 18

Divide both sides by -2

n < -9

Hence, the solution to the inequality expression is n < -9

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Answer:

If the transversal cuts across parallel lines (the usual case) then alternate exterior angles have the same measure. So in the figure above, as you move points A or B, the two alternate angles shown always have the same measure.

Step-by-step explanation:

Hope this helps

Answer:

A= 30 sq. cm

Step-by-step explanation:

We want to find the area of both triangles seprately than add them together. For the area of a traingle, we use the equation 1/2 base times height. For triangle ABE we do this:

\(A = \frac{1}{2} (12)(4)\)

\(A = (6) (4)\)

\(A = 24\)

For triangle BDC, we do this:

\(A = \frac{1}{2} (6) (2)\)

\(A = (3) (2)\)

\(A=6\)

Now we have to add both areas ot get A=30 sq cm

The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be the vehicle's speed befοre tο using the brakes was rοughly 352.7256 mph.

The speed (cοmmοnly referred tο as v) οf an οbject is the magnitude οf the change οf its pοsitiοn οver time οr the magnitude οf the change οf its pοsitiοn per unit οf time; it is thus a scalar quantity.

The average speed οf an οbject in an interval οf time is the distance travelled by the οbject divided by the duratiοn οf the interval the instantaneοus speed is the limit οf the average speed as the duratiοn οf the time interval apprοaches zerο. Speed is nοt the same as velοcity.

Here,

The 216-fοοt length οf the car's skid marks is all that is presented tο us. The speed οf the car befοre the brakes were applied can be calculated using the fοrmula s = 24d(1/2), where s is the speed οf the car in miles per hοur (mph) and d is the length οf the skid marks in feet.

When we replace the specified value οf d, we οbtain:

=> s = 24√(216)

=> s = 24(14.6969)

=> s = 352.7256

Thus, the vehicle's speed befοre tο using the brakes was rοughly 352.7256 mph.

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Answer:

\( z = \frac{500-520}{\frac{90}{\sqrt{100}}}= -2.22\)

And we can find this probability using the normal standard distribution and we got:

\( P(z<-2.22) =0.0132\)

Step-by-step explanation:

For this case we have the foolowing parameters given:

\( \mu = 520\) represent the mean

\( \sigma =90\) represent the standard deviation

\( n = 100\) the sample size selected

And for this case since the sample size is large enough (n>30) we can apply the central limit theorem and the distribution for the sample mean would be given by:

\( \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}}) \)

And we want to find this probability:

\( P(\bar X <500)\)

We can use the z score formula given by:

\( z = \frac{500-520}{\frac{90}{\sqrt{100}}}= -2.22\)

And we can find this probability using the normal standard distribution and we got:

\( P(z<-2.22) =0.0132\)

Answer:

  y = {-1/2x +7 for x < 6; 1/2x +1 for x ≥ 6}

Step-by-step explanation:

You want y = 1/2|x -6| +4 written as a piecewise function.

The absolute value function changes its definition when its argument is negative:

  y = |x|   ⇒   y = -x for x < 0, and y = x for x ≥ 0

This means our piecewise function will have one definition for (x-6) < 0 and another for (x -6) ≥ 0.

The argument is negated in this domain, so we have ...

  y = -1/2(x -6) +4

  y = -1/2x +3 +4

  y = -1/2x +7

The absolute value function is an identity function in this domain:

  y = 1/2(x -6) +4

  y = 1/2x -3 +4

  y = 1/2x +1

Combining these descriptions into one, we have ...

  \(\boxed{y=\begin{cases}-\dfrac{1}{2}x+7&\text{for }x < 6\\\\\dfrac{1}{2}x+1&\text{for }x\ge6\end{cases}}\)

<95141404393>

The polar coordinates of (1, -9) are (9.06, -1.47 radians).

To convert from rectangular coordinates to polar coordinates, we can use the following formulas:

r = √(x² + y²)

θ = tan⁻¹(y/x)

where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.

In this case, x = 1 and y = -9. Plugging these values into the formulas, we get:

r = √(1² + (-9)²) = √82 ≈ 9.06

θ = tan⁻¹((-9)/1) ≈ -1.47 radians

Therefore, the polar coordinates of (1, -9) are (9.06, -1.47 radians). The distance from the origin to the point is approximately 9.06 units, and the angle between the positive x-axis and the line connecting the origin to the point is approximately -1.47 radians (or approximately -84.26 degrees).

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Answer:

If p - q = 10, then p = 10 + q.  Replace the other p with this:

q(2(10 + q) - 10) = 3600

q(20 + 2q - 10) = 3600

q(10 + 2q) = 360

The equilibrium point of a demand and supply function is the point where both functions are equal.

The equilibrium price is 40, and the corresponding demand is 30 supplies

Given

\(p- q = 10\) --- the supply function

\(q(2p - 10) = 2100\) --- the demand function

Make q the subject in \(p- q = 10\)

\(q = p - 10\)

Substitute \(q = p - 10\) in \(q(2p - 10) = 2100\)

\((p - 10)(2p - 10) = 2100\)

Factor out 2

\(2(p - 10)(p - 5) = 2100\)

Divide both sides by 2

\((p - 10)(p - 5) = 1050\)

Open brackets

\(p^2 -10p - 5p + 50 = 1050\)

\(p^2 -10p - 5p + 50 - 1050 =0\)

\(p^2 -15p - 1000 =0\)

Expand

\(p^2 -40p + 25p- 1000 =0\)

Factorize

\(p(p -40) + 25(p- 40) =0\)

Factor out p - 40

\((p+ 25) (p- 40) =0\)

Solve for p

\(p = -25\) or \(p = 40\)

The price cannot be negative.

So: \(p =40\)

Recall that:

\(q = p - 10\)

\(q = 40 - 10\)

\(q = 30\)

Hence, the equilibrium price is 40, and the corresponding number of supplies is 30

See attachment for the graphs of both functions

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The instantaneous velocity must be v= 265 at t=2

The height in feet after t second is given by y(t)=95t−16t^2.

Average velocity is defined by:

\(v_{ave} = \frac{x_{f} -x_{i} }{t_{f} -t_{i} }\)

i)

\(t_{i}\) = 2

\(x_{i}\)=y(2)=174

\(t_{f}\)=2+0.1

\(x_{f}\) = y(2+0.1) = 365.4

\(v_{ave}\) = 280.54

ii)

\(t_{i}\) = 2

\(x_{i}\)=y(2)=174

\(t_{f}\)=2+0.01

\(x_{f}\) = y(2+0.01) = 349.74

\(v_{ave}\) = 264.88

iii)

\(t_{i}\) = 2

\(x_{i}\)=y(2)=174

\(t_{f}\)=2+0.001

\(x_{f}\) = y(2+0.001) = 348.174

\(v_{ave}\) = 263.316

Instantaneous velocity is defined by: \(v= lim_{t-0} \frac{delta x}{delta t}\)

When, delta t = 0, v = 265

So instantaneous velocity must be v= 265 at t=2

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The Domain: (-∞, -3) ∪ (-3, 6) ∪ (6, ∞) and Range: (-∞, 0) ∪ (0, ∞).

What is domain?

The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.

According to question:

In this case, the denominator of the function is a quadratic expression, and we know that dividing by zero is undefined. Therefore, we need to find the values of x that make the denominator equal to zero, and exclude those values from the domain.

To find the values that make the denominator equal to zero, we can factor it as follows:

x² - 3x - 18 = 0

(x - 6)(x + 3) = 0

So, the denominator is equal to zero when x = 6 or x = -3. Therefore, the domain of the function is all real numbers except x = 6 and x = -3.

Domain: (-∞, -3) ∪ (-3, 6) ∪ (6, ∞)

The range of a function consists of all possible output values of the function, given the domain of the function.

To find the range of this function, we need to analyze the behavior of the function as x approaches positive or negative infinity.

As x approaches positive infinity, both the numerator and denominator of the function approach positive infinity. Therefore, the function approaches zero.

As x approaches negative infinity, both the numerator and denominator of the function approach negative infinity. Therefore, the function approaches zero.

Since the function approaches zero as x approaches positive or negative infinity, we can say that the range of the function is all real numbers except zero.

Range: (-∞, 0) ∪ (0, ∞).

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The minimum production rate of bushels per acre of corn needed this year is 97 for two year's production to reach the goal of 49,100.

To calculate the minimum production rate for this year, we must subtract the production rate of the previous year, with what is expected to be obtained this year.

Then we must divide the minimum that must be obtained by the total area, by the 300 acres that we have, to know how much corresponds to each acre.

According to the above, each acre must produce 97 bushels of corn to reach the goal of 49,100 for both years.

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Answer:

x = 21

Step-by-step explanation:

ABF is a right angle and m∠EBA + m∠EBF = m∠ABF

3x - 1 + x + 7 = 90 add like terms

4x + 6 = 90 subtract 6 from both sides

4x = 84 divide both sides by 4

x = 21

The run is 9x miles long, while the bike race is 22y miles long.

The distance between two points in mathematics is referred to as the distance. The distance formula, which is simply a derivation of the Pythagorean theorem, which is used to find the length of any one side of a right triangle when you know the lengths of the other two sides, can be used to calculate this distance.

Therefore,

d = vt

where:

d = distance (miles)

v = speed (mph)

t = time (hours)

Let  x = run time

Let  y = bike time

Total time:      x + y = 4

We can create an equation that represents the formula using these variables.

d total = d bike + d run

49 = 9x + 22y

The equation is then only expressed in terms of x or y. We're going to get it in terms of x.

49 = 9x +22(4 - x)

49 = 9x + 88 - 22x

-39 = -13x

3 = x

To determine the distance between each part, enter this value of x into the variables.

run distance = 9x

bike distance = 22(4 - x)

Let x be run time, y be the bicycle race time.

Total time

x+y = 4

Run distance R = 9x

Bicycle race distance  B = 22y

Total distance

9x + 22y = 49

Replace y in the second equation with 4 - x to solve this system.

You'll obtain

y = 1

x = 3

so

R = 9x = 27

B = 22y = 22

Hence, The run is 9x miles long, while the bike race is 22y miles long.

The complete question is:

Suppose you have entered a 49?-mile biathlon that consists of a run and a bicycle race. During your? run, your average velocity is 9 miles per? hour, and during

Suppose you have entered a 49?-mile biathlon that consists of a run and a bicycle race. During your? run, your average velocity is 9 miles per? hour, and during your bicycle? race, your average velocity is 22 miles per hour. You finish the race in 4 hours. What is the distance of the? run? What is the distance of the bicycle? race?

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The cost of students ticket is $37.5and the cost of general admission is $187.5.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.

Assume s be the students tickets cost and g be the general admission cost.

From the given information,

⇒  s + g = 225             ..(1)

 5s + 7g = 1500         ..(2)

From equation (1),

s = 225 - g

Plug the value of s in equation (2)

5(225 - g) + 7g = 1500

1125 - 5g + 7g = 1500

                  2g = 1500 - 1125

                  2g = 375

                    g = 187.5

Plug g = 125 in equation (1),

s + 187.5= 225

        s = 225 - 187.5

        s = 37.5

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