A soccer ball is kicked from the ground by the goalie and lands 40 meters from where it waskicked. The ball's path is that of a parabola, and the ball reaches a maximum height of 3 meters,How far from where the ball was kicked will it have a height of 2 meters? (Round your answer tothe nearest tenth.)

The correct  differential equation for [tex]x(e^{y}+1)^{2} e^{-y}dx+ e^{x^{2} }dy =0[/tex]

is [tex](e^{y}+1)^{2}e^{-y}/ -e^{x^{2}}= dy/dx\\[/tex].

to extract the differential equation we need to express it in the form of dy/dx.

[tex]x(e^{y}+1)^{2}e^{-y}dx=-e^{x^{2}}dy\\x(e^{y}+1)^{2}e^{-y} = -e^{x^{2}}dy/dx\\x(e^{y}+1)^{2}e^{-y}/ -e^{x^{2}}= dy/dx\\[/tex]

What are differential equations?

An equation involving one or more functions and their derivatives is referred to as a differential equation in mathematics. The rate of change of a function at a place is determined by the derivatives of the function. Physicists, engineers, biologists, and other professionals primarily use it in these domains.

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The functions are solved below

What is a function?

A function from either a given Set X to a set Y allocates exactly one item of Y to each member of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

The functions are solved as follows

(a) f(4) = 6x4 = 24

(b) g(2) = 9x2² + 5 = 36 + 5 = 41

(c) f(1) = 6x1 = 6

(d) g(0) = 9x0² + 5 = 0 + 5 = 5

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Slope

[tex]\frac{-10-(-2)}{1-(-3)}=-2[/tex]

Equation

[tex]y+10=-2(x-1)[/tex]

After evaluating the limit we have came to find that the limit of        [tex]\lim_{h\rightarrow 0 }\frac{(4/3 +h)^3-(4/3)^3}{h}[/tex] as h approaches 0 is Undefined

A limit is the value that a function, sequence, or index approaches as an input or as an index approaches a particular value in mathematics. The definitions of continuity, derivatives, and integrals depend on limits, which are essential to calculus and mathematical analysis.

The concept of a limit of a sequence is further generalized to include the concept of a limit of a topological network, in addition to having a connection to the category theory concepts of limit and direct limit.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit

⇒ [tex]\lim_{h\rightarrow 0 }\frac{(4/3 +h)^3-(4/3)^3}{h}[/tex]

Evalúe 0 as h

⇒ [tex]\frac{(4/3 +0)^3-(4/3)^3}{0}[/tex]

⇒ Undefined

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The number of ways that the landscaper can plant the trees in a row, assuming that the trees are evenly spaced is 630 ways.

According to the data, the golf course architect needs to plant 2 bald cypress trees, 5 white birch trees, and 4 linden trees in a row along a fairway. It should be noted that the number of feasible arrangements will be shown as follows based on the information provided:

Based on the information given, it should be noted that n1 =4, n2 = 5 and n3 = 2.

Therefore, the number of ways that the lineup can be possible will be:

n! / (n − r)!

where n is the number of things to choose from and we choose r of them

This will be illustrated as:

= 10! /4!5!2!

= 630

There are 630 ways.

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The probability that exactly 11 of them use their smartphones in meetings or classes is 3.89%

Probability is the likelihood of something occurring. This branch of mathematics studies the nature of chance. It is expressed as a number between 0 and 1. Probability has been brought to mathematics in order to foresee the potential of events. Probability can be defined as the degree of likely that something will occur. The probability that the outcomes of a random experiment will be as expected can be calculated using this fundamental theory of probability, which is also applied to the probability distribution. To establish the probability that a particular event will occur, we must first determine the total number of choices.

x = 11

n= 15

P =48%

=0.48

P(x=11)=[tex]15C_{11} (0.48)^{11} (1-0.48)^{4}[/tex]

=1365(0.0003116403)(0.09150625)

=0.0389

=3.89%

The probability that exactly 11 of them use their smartphones in meetings or classes is 3.89%

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I hope this is clear enough , although I did not arrive at the same answer using x in both equation .

The length of one side of the base is 7 inches.

The height of the box is 3.5 inches.

The minimum surface area of the box is 147 inch².

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Answer:

I believe it's 160. Hope this helps.

Step-by-step explanation:

170 - 66 = 104

104 / 0.65 = 160

The value of cos(A - B) in the simplest form​ will be 0.547.

It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.

It is given that,

tan A = 11/60

tan A = p/b

From Pythagoras therorm

h=√(p²+b²)

h=√(11²+60²)

h=61

Sin A = p/h = 11/60

Cos A = b/h = 60/61

If cos B = 5/13

Sin B = 12/13

cos (A - B) = cos A cos B + sin A sin B

cos (A - B) = (60/61)×(5/13)  + (11/60)×(12/13)

cos (A - B) =0.547

Thus, the value of cos(A - B) in the simplest form​ will be 0.547.

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Solution

Option D

Hence the correct answer is Option D

The height of the air ballon at 'm' minutes is expressed in the function and the value of h(3)=1600, h(9)=2800,h(11)=3200

We have given a function h in terms of m. Now we have to explain the contextual meaning of each and every expression it contains

1.) h = It is height at which ballon is cruising above from the ground level.

2.) m = It denotes the instance of minute at which we are talking about

3.) h(m) = The height as the function of minute, means the height of the ballon in changing with respect to the minute

4.) 1000 = It is the height at which ballon was cruising earlier and then started ascending

5.)200 = 200 feet the distance covered in a minute while ascending above

6.) 200m = distance ascended for 'm ' minutes

7.) 1000+200m = The total height that balloon covered after ascending for m minutes.

Now,

height at 3 minute = h(3) = 1000+200(3)=1000+600=1600

height at 9 minute = h(9) = 1000+200(9)=1000+1800=2800

height at x minute = h(x) = 1000+200(x)= 3200

1000 + 200x = 3200

200x = 2200

x = 11

Therefore, h(3) = 1600 , h(9)= 2800,h(11)=3200 are the different values of height 'h' at different 'm' minutes.

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The value of [tex]x^{2}[/tex] is 25 when we have (cube of x = 125) [tex]x^{3}[/tex] = 125.

According to the question,

We have the following expression:

[tex]x^{3} = 125[/tex]

Now, we will do the cube roots on both the sides:

[tex]\sqrt[3]{x^{3} } = \sqrt[3]{125}[/tex]

(We can find the cube roots of 125 by finding the Least Common Multiple or LCM.)

So, we will have the following expression:

x = 5

Now, to find the value of [tex]x^{2}[/tex], square on both the sides:

[tex]x^{2} = 5^{2}[/tex]

[tex]x^{2}[/tex] = 25

(More to know: when we square a number we multiply a number two times and when we find cube of a number then we multiply a number three times.)

Hence, the value of [tex]x^{2}[/tex] is 25.

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The possible measures using this scale are 742.5 grams and 300.0 grams.

The link between a measurement on a model and the corresponding measurement on the real item is represented by scale.

Note that a tenth of a gram is 0.1 grams, therefore, the precision of the scale is 0.1 grams.

Note that 370 milligrams are equivalent to 0.370 grams.

Since the measures on the scale increase by 0.1 units, 0.25 and 0.370 are not possible on this scale.

Hence, the possible measures using this scale are 742.5 grams and 300.0 grams.

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The expression that represents the combined function of f(x) and g(x) is h(x) = 2x/(5 - x)

From the question, we have the following parameters:

Function f(x) = 2x

Function g(x) = 2 - x + 3

Evaluate the like terms in the equation of the function g(x)

So, we have

g(x) = 5 - x

From the question, we understand that:

The function h(x) is a combination of the functions f(x) and g(x) by division

This can be represented as

h(x) = f(x)/g(x)

The above also implies that the function h(x) is a composite function

Substitute the known values in the above equation

So, we have the equation of the composite function h(x) to be

h(x) = 2x/(5 - x)

Hence, the equation of the composite function h(x) is h(x) = 2x/(5 - x)

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Answer:

Sine is negative in III and IV quadrants. Now sin 30 1/2. Taking = 30, Sin (180+0) = sin (360-0): =- sin 0. So x = 210 degrees or 330 degrees

Step-by-step explanation:

Answer: what

Step-by-step explanation:bye

A two-variable linear equation is one with the formula ax + by + c = 0.

The solution of the system exists  (1, 1) and (2, 4).

Let the system of Equations be

y = 3x - 2 and y = x²

From these Equations:

x² = 3x - 2,

simplifying the above equation, we get

⇒ x² - 3x + 2 = 0

⇒ x = 1, 2.

Therefore, the value of x exists x = 1, 2.

Therefore, the solution of the system exists  (1, 1) and (2, 4).

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∠4 ≅ ∠5 Alternate internal angles

Applying the description we have the table is completed as follows

Statement                                          Reasons

x is parallel to y                                    Given

w is a transversal                                  Given  

angle 4 is congruent to angle 1           Vertical opposite angle

angle 1 is congruent to angle 5            Corresponding angle

angle 4 is congruent to angle 5           Alternate internal angles

The prove ∠4 ≅ ∠5 is done by the Alternate angle theorem

∠4 ≅ ∠ 1 vertical opposite angles

∠ 1 ≅ ∠5  Corresponding angle

then we can say that

∠ 1 ≅ ∠4 ≅ ∠5

hence: ∠4 ≅ ∠5 Alternate internal angles

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Answer:

A ✔ vertical angles

B ✔ corresponding angles theorem

C ✔ transitive property

Step-by-step explanation: i hope this helps :)

Step 1: Write out the formula for logistic growth model

Step 2: Write out the given values and substitute them into the formula

Hence,

Hence, the number of plants after 5 months is approximately 112

The linear combination of the given vector is computed to be:

[tex]-4u+v=\left[\begin{array}{ccc}23\\-28\\\end{array}\right][/tex]

given data

[tex]u=\left[\begin{array}{ccc}-6\\6\\\end{array}\right][/tex]

[tex]v=\left[\begin{array}{ccc}-1\\-4\\\end{array}\right][/tex]

Required to compute the linear combination in the form -4u + v

solving for -4u

[tex]-4u=\left[\begin{array}{ccc}-6*-4\\6*-4\\\end{array}\right][/tex]

[tex]-4u=\left[\begin{array}{ccc}24\\-24\\\end{array}\right][/tex]

solving for -4u + v

[tex]-4u+v=\left[\begin{array}{ccc}24+-1\\-24+-4\\\end{array}\right][/tex]

[tex]-4u+v=\left[\begin{array}{ccc}24-1\\-24-4\\\end{array}\right][/tex]

[tex]-4u+v=\left[\begin{array}{ccc}23\\-28\\\end{array}\right][/tex]

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⇒I will use the laws of exponents. When you multiply powers of the same base you keep one base and add the exponents.

Below are all the steps in details

[tex]=9^{-8+(-2)} \\=9^{-8-2} \\=9^{-10} \\=\frac{1}{9^{10} } \\=\frac{1}{3486784401}[/tex]

Depth= 45 feet

The force applied perpendicular to the surface of an object per unit area over which that force is distributed is defined as Pressure.

Pressure causes serious problems for people as you travel deeper in water because pressure increases. This is called hydrostatic pressure.  Water doesn’t only push down from above. It pushes from all sides and also from below. The upward force is called buoyancy. It helps you keep afloat in water.

Given Pressure, p of under water is 312,

Given equation is:

P=12+4d/11

312=12+4d/11

312=12*11+4d

312-(12*11)= 4d

312-132= 4d

180=4d

d=180/4

=45 feet

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Given:

The objective is to translate the statement and solve the inequality.

Explanation:

Consider the unknown number as x. The quotient of a number and 7 can be written as,

By subtracting 10 from the quotient, the value is less than -6.

On substituting the equation (2) in (1),

To find x :

On solving the equation (3), the value of x can be calculated as,

Hence, the value of x is less than 28.

The step function and its graph that represents the relationship between the number x of days and the total cost y of renting the chipper are present in the first option.

Given:

Charge for 1 day = $100

Charge for each additional day = $50

Let's assume

The cost of rent is y.

The number of days is x.

The total cost, y according to the data provided can be calculated by the equation,

y = 100 + 50x

Using y = mx+c, when graphing a step function that represents the relationship between the number of days and the total cost,

The gradient or slope will be always 50 for the graph.

So, when x = 0, y = 100 + 0 = 100

When x = 1, y = 100 + 50 = 150

When x = 2, y = 100 + 50 × 2 = 200

When x = 3, y = 100 + 50 × 3 = 250

Thus the step function is,

f(x) = 100 , if 0 < x ≤ 1

f(x) = 150 , if 1 < x ≤ 2

f(x) = 200 , if 2 < x ≤ 3

f(x) = 250 , if 3 < x ≤ 4

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Answer:

each side would be 9m long

The length of each side of the square garden is 9 meters long.

The perimeter of any 2D figure is the sum of the lengths of all the sides except the circle which has a perimeter or circumference which is 2πr.

We know the area of a square is a product of any two sides of the square and all four sides of a square are of the same length.

Given a square has an area of  81m².

∴ We have to determine such a number which when multiplied by itself results in 81.

Such a unique number is 9.

So, the area of the square can be written as (9×9) m².

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INFORMATION:

Using the graph of f(x) = x^2, we must describe transformations for the function g(x)=-8x^2

STEP BY STEP EXPLANATION:

First, we need to use the graph of f(x) = x^2 which is

Then, if analyze difference between f(x) and g(x), we can see that g(x) = -1*8*f(x)

So, to graph g(x) we have two transformations:

- Multiply f(x) by -1: When we multiply by -1 we obtain the parabola opening down

- Multiply f(x) by 8: When we multiply by 8 we obtain a more closed parabola

Finally, the final graph would be

ANSWER:

The fraction of juice that is orange juice is 40/73

From the question, we have the following parameters that can be used in our computation:

Juice containers = 292

Orange juice = 160

The fraction of juice that is orange juice is then calculated as

Fraction = Orange juice/Juice containers

Substitute the known values in the above equation

So, we have the following equation

Fraction = 160/292

Simplify the fraction

Fraction = 40/73

Hence, the fraction is 40/73

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Using proportions, it is found that Victor has a higher ratio of of sand dollars to starfish.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using multiplications such as division or multiplication.

One example of proportions is for ratio problems, as:

Hence the ratios of sand dollars to starfish for Victor and Cheyenne are given as follows:

0.6 > 0.5, hence Victor has the higher ratio.

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