Find the particular solution of the differential equation?
/=5^3+9^2, when =1, =8

Answer:

20 square feet

Step-by-step explanation:

area of a triangle = (1/2) base x height

The "base" for this one gigantic triangle is the 'top' of the diagram - - - - it's the entire 3+7 = 10 side. (We can calculate the area of the whole thing at once. We don't have to do the left and the right halves separately!!!)

The height is 4.

So area = (1/2) base x height

= (1/2) * 10 * 4

= 20 square feet

The cost of packaging per weight unit is given by (1/4) (x / (x + 2)) x.

We have,

To find the cost of packaging per weight unit, we need to calculate the cost of packaging (C) and divide it by the weight of the chocolates (W).

Given:

Cost of packaging (C) = 1/4 x²

Weight of chocolates (W) = x + 2

To find the cost of packaging per weight unit, we can express it as C/W.

Substituting the given expressions:

C/W = (1/4 x²) / (x + 2)

To simplify the expression, we can first simplify the numerator:

C/W = (1/4 x²) / (x + 2)

= (1/4) x (x² / (x + 2))

= (1/4) x (x(x) / (x + 2))

= (1/4) x (x / (x + 2)) * x

Now, we can rewrite the expression as:

C/W = (1/4) x (x / (x + 2)) x

Therefore,

The cost of packaging per weight unit is given by (1/4) (x / (x + 2)) x.

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Function graph that has y- intercept of 3 is g(x) = 3[tex](\frac{1}{4}) ^{x}[/tex].

y- intercept will be 3 when we will put value of x = 0 and y will be 3 that graph will have y intercept 3

A) h(x) = 5[tex](2)^{x}[/tex]

when x = 0

Any number with zero power is always 1

h(x) = 5

B) h(x) = 5[tex](0.5)^{x}[/tex] + 0.5

when x = 0

h(x) = 5 + 0.5

h(x) = 5.5

C) g(x) = 3[tex](\frac{1}{4}) ^{x}[/tex]

when x = 0

g(x) = 3

Here we get y intercept as 3.

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The angle between A and B is 90 degrees.

The angle between two vectors A and B, you can use the dot product formula:

A · B = [tex]|A| |B| cos(\theta)[/tex]

where A · B is the dot product of A and B, |A| is the magnitude of A, |B| is the magnitude of B, and theta is the angle between the two vectors.

First, let's calculate the dot product of A and B:

A · B = (3)(4) + (2)(-3) + (-6)(1)

= 12 - 6 - 6

= 0

Next, let's calculate the magnitudes of vectors A and B:

|A| = √((3)² + (2)² + (-6)²)

= √(9 + 4 + 36)

= √(49)

= 7

|B| = √((4)² + (-3)² + (1)²)

= √(16 + 9 + 1)

= √(26)

Now, we can substitute these values into the formula to find the angle theta:

0 = [tex](7)(\sqrt(26)) cos(\theta)[/tex]

Since the dot product is 0, we know that the angle between A and B is either 90 degrees or 270 degrees.

To determine which one it is, we can look at the sign of the dot product. If it's positive, the angle is acute (less than 90 degrees) and if it's negative, the angle is obtuse (greater than 90 degrees).

The dot product is 0, so the angle is orthogonal (perpendicular) and is exactly 90 degrees.

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Based on the information, tere are 16224000 possible passwords.

There are 52 possible letters for the first two characters (26 uppercase and 26 lowercase).

There are 6 possible special characters for the third character.

There are 10 possible numbers for the last three characters.

We can use the Fundamental Counting Principle to calculate the number of possible passwords. The Fundamental Counting Principle states that if there are n ways to do one thing and m ways to do another thing, then there are n×m ways to do both things.

In this case, there are 52×52=2704 ways to choose the first two characters, 6 ways to choose the third character, and 10×10×10=1000 ways to choose the last three characters.

Therefore, there are 2704×6×1000

=16224000 possible passwords.

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Answer:12,890 centimeters

Step-by-step explanation: 1 meter equals 100 centimeters.

The required, 128.9 meters is equal to 12,890 centimeters, as following the unit system.

To convert meters to centimeters, we can use the conversion factor that states there are 100 centimeters in one meter.

Therefore, to find out how many centimeters are equal to 128.9 meters, we multiply the number of meters by 100:

128.9 meters * 100 centimeters/meter = 12,890 centimeters

In summary, when converting meters to centimeters, we multiply the number of meters by 100 to obtain the equivalent length in centimeters. In this case, 128.9 meters is equal to 12,890 centimeters.

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The statement that justifies that ΔBAE ≅ Δ DAE is Side-Side-Angle Postulate. The best option from the statements given is "Classify A triangle". That is definition of a triangle.

The Side Side Angle Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Between both triangles, here are the congruent sides and angles:

AB ≅ AD  - Given

AE  = EA - Reflexive Property. Note that AE is shared by both triangles so we have Two congruent sides.

AC ⊥ BD - that means ∠AEB = ∠AED = ∠BEC = ∠CED = 90°

(perpendicular bisector theorem)

A perpendicular bisector is a line segment that cuts another line segment at 90 degrees. A perpendicular bisector, in other terms, meets another line segment at 90° and splits it into two equal halves.

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Answer:

Jurek is 8. His brother is 14

Step-by-step explanation:

let's call Jurek J, and let's call his brother B.

his brother is 6 years older than Jurek.

So, B = J + 6.

B + J = 22

(J + 6) + J = 22

2J + 6 = 22

2J = 16

J = 8

so Jurek is 8

B + J = 22, B = 22 - J = 22 - 8 = 14.

Brother is 14

Answer:

66.6 miles/hour

Step-by-step explanation

50/7.5 = 66.6

Fifty-four and eight tenths" can be expressed in expanded form as the sum of 54 (representing 50 + 4) and 0.8, which represents the decimal part.

To write the number "fifty-four and eight tenths" in expanded form, we can break it down into its individual place values and numerical components.

The number "fifty-four" can be broken down as follows:

The digit 5 represents the value of 50, which is 5 tens.

The digit 4 represents the value of 4, which is 4 ones.

So, "fifty-four" can be expressed as 50 + 4.

Next, we have "eight tenths". This can be expressed as 8/10 or simply 0.8 since each tenth is equal to 0.1.

Putting it all together, the number "fifty-four and eight tenths" can be written in expanded form as:

50 + 4 + 0.8

Simplifying further, we can combine the integer and decimal parts:

54 + 0.8

Therefore, the expanded form of "fifty-four and eight tenths" is 54 + 0.8.

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Answer:

Three Hundred.

Answer:

75 points ( more than?? you didn't add the drop-down list ) today's score.

Hope this helps!

Step-by-step explanation:

y = mx + b

y = 5x + b

(50) = 5(6) + b  -> b = 20

y = 5x + 20

If Carlos plays the game today for 0 min, he will get a score of 20 ( odd...  how is that possible )

But tomorrow, he plans to play for an extra 15 min, so he will get a score of 95 ( ( 5 × 15 ) + 20 ). The question asks for how much his score will change so his score will change by 75 points ( 95 - 20 ).

You could also just do 15 × 5 to get 75 :)

Answer:

Step-by-step explanation:

The cylinder contains three areas, the top circle, the bottom circle, and the middle. The surface area of it is the sum of the three;

[tex]As = \pi r^{2} + \pi r^{2} + 2\pi r (h) \\[/tex]

or

[tex]As = 2\pi r^{2} + 2\pi r (h)[/tex]

where h is the height,

104[tex]\pi[/tex] = [tex]2 \pi (4)^{2} + 2\pi (4)(h)[/tex]

h = 9m

The only relation that is a function is the one in option C.

A relation maps elements from a set called the domain into elements of another set, called the range.

Particularly, if each of the elements in the domain is mapped to a single value in the range, then we have a function.

When we have a graph, we can do the vertical line thest, if a vertical line touches the graph more than once, then it is not a function, with that we can discard the two graphs in the left.

And for option D, we can see that the input 22 is mapped into two different values.

The remaining option, C, is the correct one.

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Answer:

96 cubic inches

Step-by-step explanation:

To calculate the empty space that will be left in the box once the book is inside, we need to find the difference between the volume of the box and the volume of the book.

Volume of the box:

20" x 12" x 2 1/2" = 600 cubic inches

Volume of the book:

18" x 3 1/2" x 8" = 504 cubic inches

Empty space in the box:

600 cubic inches - 504 cubic inches = 96 cubic inches

Therefore, there will be 96 cubic inches of empty space left in the box once Kylie puts the book inside.

Note that the substance(s) that Jacob and Natalie should use to make a cold pack that will do the BEST job of keeping food cool is " Sample 1, because it absorbs the most energy" (option A)

In physics, energy is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light.

Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed

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Full Question:

Although part of your question is missing, you might be referring to this full question:

People use self-warming and self-cooling devices for many purposes such as keeping drinks cold or food warm. Medical professionals also use these types of devices to store medicines and other substances that need to stay colder than room temperature. These cooling and warming devices use a chemical reaction to produce their chilling and warming effects. Compounds combine in endothermic (heat absorbing) or exothermic (heat releasing) reactions within these devices to help them keep items cool or warm.

Jacob and Natalie are asked by their science teacher to design a warming or cooling device. They decide to design a cold pack that can be used to help keep food cool. Jacob

and Natalie read about different substances that can be used inside cold packs and learn that most cold packs use endothermic reactions to cool objects. They find the table below while researching.

Which sample uses the substance(s) that Jacob and Natalie should use to make a cold pack that will do the BEST job of keeping food cool?

answer choices

Sample 1, because it absorbs the most energy

Sample 2, because it absorbs the most energy

Sample 3, because it absorbs the least energy

Sample 4, because it absorbs the least energy

The function is a quadratic function, and none of the given options is a factor of the graph of the function.

Here,, we have,

to determine the factor:

The zeros of the function are given as:

-3 and 5

This means that:

x = -3 and x = 5

Rewrite as:

x + 3 = 0 and x - 5 = 0

Multiply both equations

(x + 3)(x -5) = 0 * 0

This gives

(x + 3)(x -5) = 0

Express as a function

f(x) = (x + 3)(x -5)

The above means that the factors of the function are (x + 3) and (x -5)

Hence, none of the given options is a factor of the graph of the function

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complete question:

Graph of a function, f(x), has zeros at - 3, and 5. Which of

following is a factor of f(x)?

(2x - 3)

(2x + 3)

(3x + 2)

(x + 5)

The value of the given angle which is N and that is rounded to the nearest hundredth would be =45.58°

To calculate the missing angle N, the sine formula should be used and it is given below;

= a/sin A = b/sin B

Where;

a= 7

A= 90°

b= 5

B= N

That is;

7/sin90°= 5/sinN

sinN= 5×1/7

= 5/7

= 0.714285714

N = Sin-1(0.714285714)

= 45.58°

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The area of the larger square is 900% of the area of the smaller square.

Let's assume that the side of the smaller square is "s". Therefore, the area of the smaller square will be:

Area of smaller square = s²

Now, the sides of the square are increased by a scale factor of 3, which means that the new side length of the larger square will be 3s. The area of the larger square will be:

Area of larger square = (3s)² = 9s²

To find the percentage of the larger square with respect to the smaller square, we need to divide the area of the larger square by the area of the smaller square, and then multiply by 100:

(9s²/s²) x 100 = 900%

This means that the larger square is 9 times the area of the smaller square.

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Answer:

[tex]\dfrac{-1}{2}[/tex]

Step-by-step explanation:

          (-2 , 3) ⇒ x₁ = -2 & y₁ = 3

          (0 , 2) ⇒  x₂ = 0 & y₂ = 2

[tex]\boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

            [tex]\sf = \dfrac{2-3}{0-[-2]}\\\\\\=\dfrac{-1}{0+2}\\\\=\dfrac{-1}{2}[/tex]

The dot product of vectors a and b is option D. 30.

To find the dot product of two vectors, you need to multiply their corresponding components and then sum the results.

Let's calculate the dot product of vectors a = <5, 2> and b = <4, 5>:

a • b = (5 x 4) + (2 x 5)

= 20 + 10

= 30

Therefore, the dot product of vectors a and b is 30.

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Answer:

------------------

There are 15 black pens out of total 80.

The probability of a black pen is:

The equation that could be used to represent the whole pizza is 4/8 + 2/8 = 6/8 = 3/4.

We are given that;

Pizza ate by children= 4/8

Pizza ate by Jonus= 2/8

Now,

4/8 + 2/8 + x = 1

where x is the fraction of the pizza that was saved for later. This equation shows that the sum of the fractions of the pizza that were eaten and saved is equal to 1, which represents the whole pizza. To solve for x, we can simplify the fractions and subtract them from both sides:

4/8 + 2/8 = 6/8 = 3/4

3/4 + x = 1

x = 1 - 3/4

x = 1/4

Therefore, the equation will be 4/8 + 2/8 = 6/8 = 3/4

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1260° is the sum of all interior angles of the given polygon.

Generally speaking, the measure of the angle at the center of a regular polygon is equal to 360 degrees.

The sum of the interior angles in a polygon can be calculated using the formula:

Sum of interior angles = (n - 2) * 180 degrees

In this formula, "n" represents the number of sides or vertices of the polygon.

In the given problem the number of sides is 9.

Thus,

Sum of all interior angle = (9-2)*180

The sum of all interior angles = 1260°

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Answer:

5. 94 square units.

6. 159 square units.

Step-by-step explanation:

By using Heron's Formula: [tex]\bold{\sqrt{s(s-a)(s-b)(s-c)}}[/tex]

5.

Using the values c = 17, b = 13, and a = 15,

Calculate the semi-perimeter of the triangle as:

s =[tex]\frac{a+b+c}{2}[/tex]

s =[tex]\frac{15 + 13 + 17}{2}=22.5[/tex]

Using Heron's formula, the area of the triangle is:

A = [tex]\bold{\sqrt{s(s-a)(s-b)(s-c)}}[/tex]

A = [tex]\sqrt{22.5(22.5-15)(22.5-13)(22.5-17)}=93.90[/tex] ≈94 approximately

Therefore, the area of triangle ABC is approximately 94 square units.

6.

Using the values, a = 23, b = 25, and c = 14,

we can calculate the semi-perimeter of the triangle as:

s =[tex]\frac{a+b+c}{2}[/tex]

s =[tex]\frac{ 23 + 25 + 14}{2}[/tex]

s = 31

Using Heron's formula, the area of the triangle is:

A = [tex]\bold{\sqrt{s(s-a)(s-b)(s-c)}}[/tex]

A = [tex]\sqrt{31(31-23)(31-25)(31-14)}=159.05[/tex]≈159 approximately

Therefore, the area of triangle ABC is approximately 159 square units.

Answer:

5)  93.90 square units (2 d.p.)

6)  159.05 square units (2 d.p.)

Step-by-step explanation:

To find the area of a triangle given its side lengths, use Heron's formula.

[tex]\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}[/tex]

[tex]\hrulefill[/tex]

Given side lengths of triangle ABC:

To find the half perimeter, s, half the sum of the 3 side lengths:

[tex]\implies s=\dfrac{a+b+c}{2}=\dfrac{15+13+17}{2}=22.5[/tex]

Substitute the values of a, b, c and s into Heron's formula and solve for area, A:

[tex]\begin{aligned}A&=\sqrt{s(s-a)(s-b)(s-c)}\\&=\sqrt{22.5(22.5-15)(22.5-13)(22.5-17)}\\&=\sqrt{22.5(7.5)(9.5)(5.5)}\\&=\sqrt{8817.1875}\\&=93.89988019...\\&=93.90\; \sf units^2\;(2\;d.p.)\end{aligned}[/tex]

Therefore, the area of triangle ABC is 93.90 square units, to two decimal places.

[tex]\hrulefill[/tex]

Given side lengths of triangle ABC:

To find the half perimeter, s, half the sum of the 3 side lengths:

[tex]\implies s=\dfrac{a+b+c}{2}=\dfrac{23+25+14}{2}=31[/tex]

Substitute the values of a, b, c and s into Heron's formula and solve for area, A:

[tex]\begin{aligned}A&=\sqrt{s(s-a)(s-b)(s-c)}\\&=\sqrt{31(31-23)(31-25)(31-14)}\\&=\sqrt{31(8)(6)(17)}\\&=\sqrt{25296}\\&=159.0471628...\\&=159.05\; \sf units^2\;(2\;d.p.)\end{aligned}[/tex]

Therefore, the area of triangle ABC is 159.05 square units, to two decimal places.

The ratio t : u : v in its simplest form is 0.4 : 1 : v/0.4.

To find the ratio t : u : v, we'll need to express each variable in terms of one another. Given the information provided, we know that:

T = 0.4u   (T is 40% of u)

Y = 0.5t   (Y is half of t)

We can substitute the value of t from the second equation into the first equation:

T = 0.4u

Y = 0.5(0.4u) = 0.2u

Now, we have the values of T and Y in terms of u. To find v, we need additional information since it is not provided.

Without that information, we cannot determine the specific value of v or its relationship to the other variables. Therefore, we cannot simplify the ratio t : u : v any further.

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Using a rule for exponents, we can simplify the expression and see that the correct option is B, 8.

Remember that when we have the quotient of two powers with the same base (like in this case, where the base is 2) the outcome will be a power of the same base, such that the exponent is equal to the difference between the other two exponents.

The rule is:

[tex]\frac{x^m}{x^n} = x^{m - n}[/tex]

Then we can use that to simplify the expression, we will get:

[tex]\frac{2^6}{2^3} = 2^{6 - 3} = 2^3 = 2*2*2 = 8[/tex]

We can see that the correct option is B.

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Jorge's gross earnings for the week assembling 317 game boards would be $633.

To calculate Jorge's gross earnings for the week, we need to determine how many game boards fall into each pay rate category and then multiply the quantity by the corresponding pay rate. Let's break down the calculation step by step:

Determine the number of game boards that fall into each pay rate category:

First 100 boards: 100 boards (as the rate applies to the first 100 boards).

Next 200 boards: Since Jorge assembled 317 boards in total and the first 100 boards are already accounted for, we subtract 100 from 317 to get 217 boards that fall into this category.

Over 300 boards: We check if the total number of boards exceeds 300. In this case, since Jorge assembled 317 boards, we have

317 - 300 = 17

boards that fall into this category.

Calculate the earnings for each category by multiplying the number of boards by the corresponding pay rate:

Earnings for the first 100 boards:

100 boards * $1.82 per board = $182.

Earnings for the next 200 boards:

217 boards * $1.92 per board = $416.64.

Earnings for the over 300 boards:

17 boards * $2.08 per board = $35.36.

Sum up the earnings from each category to find the gross pay for the week:

Gross pay = Earnings for the first 100 boards + Earnings for the next 200 boards + Earnings for the over 300 boards

Gross pay = $182 + $416.64 + $35.36

Gross pay = $633.

Therefore, Jorge's gross earnings for the week assembling 317 game boards would be $633.

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The given supply curve is: Qs = 6700 + 75P

To find how many AirPods Apple would produce at a price of $185, we can substitute P = $185 in the equation and find the corresponding quantity (Qs).

Qs = 6700 + 75P Qs = 6700 + 75($185) Qs = 6700 + 13875 Qs = 20575

Therefore, at a price of $185, Apple would produce 20,575 AirPods according to the given supply curve.

Answer:

84°

Step-by-step explanation:

opposite angles in a cyclic quadrilateral (4-sided shape) add up to 180.

c + 96 = 180

c = 180 - 96 = 84°