PLEASE HELP ASAP 50 POINTS PLSSSSSSSSS

Answer:

(a+4)(b-2)=t

a+4=0

-4+4=0

and

b-2=0

2-2=0

Step-by-step explanation:

A is opposite of what is in the equation = -4

b is opposite of what is in the equation = 2

As you said, the equation is separable:

dy/dt = 2t / exp(y)

exp(y) dy = 2t dt

Integrate both sides:

∫ exp(y) dy = ∫ 2t dt

exp(y) + C₁ = t ² + C₂

Move the constant terms to one side. When you add them together, you get another constant, so you can ignore the subscript altogether:

exp(y) = t ² + C

Solve for y explicitly by taking the logarithm of both sides:

ln(exp(y)) = ln(t ² + C )

y = ln(t ² + C )

C can be any number; if it happens to be 0, then you have

y = ln(t ²) = 2 ln(t )

so B is the correct choice.

You can also approach this from the opposite angle: Assume y is one of the given solutions, then substitute it into the ODE. (Bit more trial-and-error involved, so not a good idea if you're short on time.)

For example, if y = 2 exp(t ) as in choice A, you have dy/dt = 2 exp(t ), so the ODE would become

2 exp(t ) = 2t / exp(2 exp(t ))

which is clearly (I hope) not true.

Answer:

1. Ella can scale it up by 3 or by using the ratio 3:1, the smaller bed is exactly 1/3 of the bigger bed.

2A. No I am way taller than the 75".

2B. Ella can scale the bed up by 7:1 so that it can fit me.

Step-by-step explanation:

Answer:

A triangle can have one obtuse and two acute angles. A triangle can have three acute angles.

Answer:

12

Step-by-step explanation:

Use the Pythagorean Theorem to solve.

10 squared minus 8 squared=36

Square rt = 6

6 + 6=12

The length, in centimeters, of AC should be considered as the 12

Since

In ABC, BD is perpendicular to AC. The dimensions are shown in centimeters.

So here the length should be like

= 10^2 - 8^2

= 100 - 64

= 36

= 6

So for AC it should be

=  6+ 6

= 12

Hence, The length, in centimeters, of AC should be considered as the 12

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Answer:

Step-by-step explanation:

[tex]2(n+7)=\frac{n}{3}-4\\ \\ 2n+14=\frac{n-12}{3}\\ \\ 6n+42=n-12\\ \\ 5n+42=-12\\ \\ 5n=30\\ \\ n=6[/tex]

Answer:

1/5

Step-by-step explanation:

Answer:

it's the third one

Step-by-step explanation:

Model A represent the given situation. Therefore, option A is the correct answer.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given that, Ben and his friends ordered 3 hoagies and they cut each hoagie into thirds.

Here, model A represent 3 hoagie and each cut into three pieces.

Therefore, option A is the correct answer.

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Answer:

130 miles

Step-by-step explanation:

Answer:

by adding. positive, you move towards right.

Answer:

Right

Step-by-step explanation:

when looking at a number line, you will see 0, and you will notice all numbers go from 0 to the right in an increasing manner, so it would be 0, then 1, then 2, then 3....

its the other way for negative numbers tho, so (from a line of negative numbers) -3, then -2, then -1, then 0

a good way to remember is to imagine a race, you want to gain progress and go further away from the start (0) so the RIGHT way to go would be UP the number line and INCREASE your progress

Answer:

The dimensions of the field to maximise the area are 100 metres (width) and  200 metres (height).

Step-by-step explanation:

The formulas for the area ([tex]A[/tex]), measured in square metres, and the perimeter ([tex]p[/tex]), measured in metres, of the rectangle are, respectively:

[tex]A = x\cdot y[/tex] (1)

[tex]p = 2\cdot x +y[/tex] (2)

Where:

[tex]x[/tex] - Width, measured in metres.

[tex]y[/tex] - Height, measured in metres.

Note: We assume that height of the rectangle is parallel to the wall of the house.

By (2):

[tex]y = p - 2\cdot x[/tex]

In (1):

[tex]A = x\cdot (p-2\cdot x)[/tex]

[tex]A = p\cdot x - 2\cdot x^{2}[/tex] (3)

Then, we obtain its first and second derivatives by Differential Calculus:

[tex]A' = p - 4\cdot x[/tex] (4)

[tex]A'' = -4[/tex] (5)

By equalising (4) to zero, we find the following critical value for [tex]x[/tex]:

[tex]x = \frac{p}{4}[/tex]

And besides the Second Derivative Test, this solution is associated to an absolute maximum. Given that [tex]p = 400\,m[/tex], then the maximum area enclosed by fencing is:

[tex]x = 100\,m[/tex]

[tex]A = 20000\,m^{2}[/tex]

And the height of the triangle is:

[tex]y = 200\,m[/tex]

The dimensions of the field to maximise the area are 100 metres (width) and  200 metres (height).

Answer:

The answer is b

Step-by-step explanation:

Answer: Did it in ways that are different.

Step-by-step explanation:

35.25 hours

2115 minutes

5 3 minutes + 5 7 hours

Answer:

D = 18 miles

Step-by-step explanation:

The coordinate of a library = (4,3)

The coordinate of the school = (-5,3)

We need to find the distance between the library and the school. We can use the distance formula i.e.

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\=\sqrt{(-5-4)^2+(3-3)^2}\\\\=\sqrt{81}\\\\=9\ miles[/tex]

As the distance between each unit represents 2 miles. It means the distance is 2(9) = 18 miles

So, the correct option is (c).

Answer:

26.96 inches of fabrics per person

Step-by-step explanation:

Headband

Number of players = 32

Number of coaches = 2

Total people = 32 + 2 = 34

Total fabrics used for headband = 623.22 inches

Fabrics per person = Total fabrics used for headband / Total people

= 623.22/34

= 18.33 inches per person

Wristband

Number of players = 32

Total fabrics used for wristband = 276.16 inches

Fabrics per person = Total fabrics used for wristband / Number of players

= 276.16 / 32

= 8.63 inches per person

Total fabrics used for headband and wristband for each player = 18.33 inches + 8.63 inches

= 26.96 inches of fabrics per person

Answer: 5.4

Step-by-step explanation:

Use cosine to find the adjacent side.

cosine = adjacent/hypotenuse

Substitute these values in the cosine equation:

cos(39) = x/7

7*cos(39) = x

Use a calculator to find the value of x:

x = 5.4

The proof that wxyz is a parallelogram has been done below

We can prove that WXYZ is a parallelogram by using the properties of congruent angles and congruent sides.

Given: WX ≅ YZ; ∠WXZ ≅ ∠YZX

From the given information, we know that WX is congruent to YZ and that the angle WXZ is congruent to angle YZX.

Since WX is congruent to YZ, we can conclude that WY is congruent to XZ.

From the given information, we know that angle WXZ is congruent to angle YZX.

Since the angles are congruent, we can conclude that the lines WX and YZ are parallel.

By using the properties of congruent sides and congruent angles, we can now conclude that WXYZ is a parallelogram.

In a parallelogram opposite sides are parallel and congruent. The opposite angles are also congruent. In this case, WX and YZ are parallel and congruent and ∠WXZ and ∠YZX are congruent. So, WXYZ is a parallelogram.

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See diagram below.

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

Explanation:

The highest point on f(x) is the vertex point since the leading coefficient is negative. The vertex is located at (h,k)

For the general parabola y = ax^2 + bx + c, we can define h to be

h = -b/(2a)

In this case, we plug in a = -2 and b = 8 to find h to be...

h = -b/(2a)

h = -8/(2*(-2))

h = -8/(-4)

h = 2

Then the value of k is equal to f(h). So we plug x = 2 into the f(x) function to get

f(x) = -2x^2 + 8x - 1

f(2) = -2(2)^2 + 8(2) - 1

f(2) = -2(4) + 8(2) - 1

f(2) = -8 + 16 - 1

f(2) = 8 - 1

f(2) = 7

This means k = 7

So the vertex for f(x) is at (h,k) = (2,7)

The max value of f(x) is f(x) = 7 which is the same as y = 7.

The graph shows the highest point is at (0,10). The highest point of g(x) is when y = 10. So this is the largest g(x) can get. We only are concerned with output values when we want to maximize whatever the function is.

Therefore, g(x) produces the larger maximum value compared to f(x).

We can see that if we were to graph both f(x) and g(x) together. The g(x) curve peaks higher compared to f(x).

The diagram is shown below. I used GeoGebra to make the graph, though you could use Desmos or a TI calculator (or similar) if you want.

Answer:

Step-by-step explanation:

ℎ

[tex] \frac{5}{12} [/tex]

ℎ ℎ

[tex] \\ \frac{1}{12} + \frac{1}{3} = \frac{5}{12} [/tex]

Answer:

-6 -4 3 7

Step-by-step explanation:

This is right because if it goes- it goes lower and if it goes up on + it goes higher.

Answer:

-6, -4, 3, 7

Step-by-step explanation:

First you need to know that negative numbers are smaller than positive numbers, the larger the number beside the negative sign is, the smaller the number.

Answer:

12

Step-by-step explanation:

∛1728 = ∛2*2*2*2*2*2*3*3*3*3 = 2*2*3 = 12

Answer:12

Step-by-step explanation: Using Prime Factorization Method

1728=2*2*2*2*2*2*3*3*3

1728=(2*2*2)(2*2*2)(3*3*3)

1728=2^3 *2^3*2

Cube root the number above you would get 2*2*3=12.

Answer: that the solution is true

Step-by-step explanation: if you get something like 10=10 it’s true but if you get like 4= 7 it’s false

Answer:

d

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

AC² + BC² = AB² , that is

x² + x² = (12[tex]\sqrt{2}[/tex] )²

2x² = 288 ( divide both sides by 2 )

x² = 144 ( take the square root of both sides )

x = [tex]\sqrt{144}[/tex] = 12

Answer:

=540

Step-by-step explanation:

To get the answer all we have to do is convert the scientific notation into a regular one. We can do this by moving the decimal place depending on what the power is.

In this case, the power/exponent/the number raised, whatever you would call it is 2, so we are going to move it to two places.

Hope this helps!!

Answer:

The reciprocal of 7 is 1/7.

Step-by-step explanation:

7 = 7/1

Reciprocal of 7/1 = 1/7

Answer: See explanation

Step-by-step explanation:

Aisha gets on the elevator at sixth floor and then rides up three floors to meet shaimaa before riding down seven floors to meet abeer. This means Shel be at the (6+3-7) = 2nd floor.

The number of floors that aisha is from where she start will be:

= 6 - 2

= 4 floor downwards. Or -4.