Cameron spent 32 minutes on Instagram on Friday. The next day
he spent 30% of that on Instagram. In total, how much time did
Cameron spend on Instagram?

Answer:

The solution of the problem is \(y(t) = e^{2 t} cos(2 t)\)

Step-by-step explanation:

First we will write the characteristic equation which is

\(x^{2} -4x + 8 = 0\)

Now, we will solve this quadratic equation using the general formula.

Given a quadratic equation of the form, \(ax^{2} +bx +c = 0\), then

From the general formula,

\(x = \frac{-b+\sqrt{b^{2}-4ac } }{2a}\) or \(x = \frac{-b-\sqrt{b^{2}-4ac } }{2a}\)

From the characteristic equation, \(a = 1, b = -4,\) and \(c = 8\)

Hence,

\(x = \frac{-(-4)+\sqrt{(-4)^{2}-4(1)(8) } }{2(1)}\) or \(x = \frac{-(-4)-\sqrt{(-4)^{2}-4(1)(8) } }{2(1)}\)

\(x = \frac{4+\sqrt{-16} }{2}\) or \(x = \frac{4-\sqrt{-16} }{2}\)

\(x = \frac{2+4i }{2}\) or \(x = \frac{2-4i }{2}\)

\(x = 2 + 2i\) or \(x = 2 - 2i\)

That is, \(x\) =  \(2\) ± \(2i\)

Then, \(x_{1} = 2 + 2i\) and \(x_{2} = 2 - 2i\)

These are the roots of the characteristic equation

The roots of the characteristic equation are complex, that is, in the form

(\(\alpha\) ± \(\beta i\)).

For the general solution,

If the roots of a characteristic equation are in the form  (\(\alpha\) ± \(\beta i\)), the general solution is given by

\(y(t) = C_{1}e^{\alpha t} cos(\beta t) + C_{2}e^{\alpha t} sin(\beta t)\)

From the characteristic equation,

\(\alpha = 2\) and \(\beta = 2\)

Then, the general solution becomes

\(y(t) = C_{1}e^{2 t} cos(2 t) + C_{2}e^{2 t} sin(2t)\)

Now, we will determine \(y'(t)\)

\(y'(t) = 2C_{1}e^{2 t} cos(2 t) - 2C_{1}e^{2t}sin(2t) + 2C_{2} e^{2t}sin(2t) +2C_{2}e^{2t}cos(2t)\)

From the question,

y(0) = 1

and

y'(0) = 2

Then,

\(1 = y(0) = C_{1}e^{2 (0)} cos(2 (0)) + C_{2}e^{2 (0)} sin(2(0))\)

\(1 = C_{1}e^{ 0} cos(0) + C_{2}e^{0} sin(0)\)

(NOTE: \(e^{0} = 1, cos(0) = 1\) and \(sin(0) = 0\) )

Then,

\(1 = C_{1}\)

∴\(C_{1} = 1\)

Also,

\(2 = y'(0) = 2C_{1}e^{2 (0)} cos(2 (0)) - 2C_{1}e^{2(0)}sin(2(0)) + 2C_{2} e^{2(0)}sin(2(0)) +2C_{2}e^{2(0)}cos(2(0))\)\(2 = 2C_{1}e^{0} cos(0) - 2C_{1}e^{0}sin(0) + 2C_{2} e^{0}sin(0) +2C_{2}e^{0}cos(0)\)

\(2 = 2C_{1} +2C_{2}\)

Then,

\(1 = C_{1} +C_{2}\)

\(C_{2} = 1 - C_{1}\)

Recall, \(C_{1} = 1\)

∴ \(C_{2} = 1 - 1 = 0\)

\(C_{2} = 0\)

Hence, the solution becomes

\(y(t) = e^{2 t} cos(2 t)\)

something is wrong with your question bc 690 plus 575 equals to 1265

Answer:

C

Step-by-step explanation:

By trial and error.

A: 50*12-100=500, 50*15-100=650. (A is not correct)

B: 500(12-11)=500, 500(15-11)=2000. (B is not correct)

C: 300(12-12)+500=500, 300(15-12)+500=1400. (if you continue try the numbers, you will see that this is the correct answer)

D: 200(12-5)+400=1800. (D is not correct)

Solution :

Along the edge \($C_1$\)

The parametric equation for \($C_1$\) is given :

\($x_1(t) = 9t , y_2(t) = 0 \ \ for \ \ 0 \leq t \leq 1$\)

Along edge \($C_2$\)

The curve here is a quarter circle with the radius 9. Therefore, the parametric equation with the domain \($0 \leq t \leq 1 $\) is then given by :

\($x_2(t) = 9 \cos \left(\frac{\pi }{2}t\right)$\)

\($y_2(t) = 9 \sin \left(\frac{\pi }{2}t\right)$\)

Along edge \($C_3$\)

The parametric equation for \($C_3$\) is :

\($x_1(t) = 0, \ \ \ y_2(t) = 9t \ \ \ for \ 0 \leq t \leq 1$\)

Now,

x = 9t, ⇒ dx = 9 dt

y = 0, ⇒ dy = 0

\($\int_{C_{1}}y^2 x dx + x^2 y dy = \int_0^1 (0)(0)+(0)(0) = 0$\)

And

\($x(t) = 9 \cos \left(\frac{\pi}{2}t\right) \Rightarrow dx = -\frac{7 \pi}{2} \sin \left(\frac{\pi}{2}t\right)$\)

\($y(t) = 9 \sin \left(\frac{\pi}{2}t\right) \Rightarrow dy = -\frac{7 \pi}{2} \cos \left(\frac{\pi}{2}t\right)$\)

Then :

\($\int_{C_1} y^2 x dx + x^2 y dy$\)

\($=\int_0^1 \left[\left( 9 \sin \frac{\pi}{2}t\right)^2\left(9 \cos \frac{\pi}{2}t\right)\left(-\frac{7 \pi}{2} \sin \frac{\pi}{2}t dt\right) + \left( 9 \cos \frac{\pi}{2}t\right)^2\left(9 \sin \frac{\pi}{2}t\right)\left(\frac{7 \pi}{2} \cos \frac{\pi}{2}t dt\right) \right]$\)

\($=\left[-9^4\ \frac{\cos^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} -9^4\ \frac{\sin^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} \right]_0^1$\)

= 0

And

x = 0,  ⇒ dx = 0

y = 9 t,  ⇒ dy = 9 dt

\($\int_{C_3} y^2 x dx + x^2 y dy = \int_0^1 (0)(0)+(0)(0) = 0$\)

Therefore,

\($ \oint y^2xdx +x^2ydy = \int_{C_1} y^2 x dx + x^2 x dx+ \int_{C_2} y^2 x dx + x^2 x dx+ \int_{C_3} y^2 x dx + x^2 x dx $\)

                        = 0 + 0 + 0

Applying the Green's theorem

\($x^2 +y^2 = 81 \Rightarrow x \pm \sqrt{81-y^2}$\)

\($\int_C P dx + Q dy = \int \int_R\left(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\right) dx dy $\)

Here,

\($P(x,y) = y^2x \Rightarrow \frac{\partial P}{\partial y} = 2xy$\)

\($Q(x,y) = x^2y \Rightarrow \frac{\partial Q}{\partial x} = 2xy$\)

\($\left(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y} \right) = 2xy - 2xy = 0$\)

Therefore,

\($\oint_Cy^2xdx+x^2ydy = \int_0^9 \int_0^{\sqrt{81-y^2}}0 \ dx dy$\)

                            \($= \int_0^9 0\ dy = 0$\)

The vector field F is = \($y^2 x \hat i+x^2 y \hat j$\)  is conservative.

Answer: 50000 feet

Step-by-step explanation:

The function values are f(10) = 198 and g(-6) = 24/7; the range of h(x) is 3/5 < h(x) < 31/25 and the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

Given that

f(x) = 2x^2 - 2

g(x) = 4x/(x - 1)

So, we have

f(10) = 2(10)^2 - 2 = 198

g(-6) = 4(-6)/(-6 - 1) = 24/7

Here, we have

h(x) = (7x - 4)/5x

Where

1 < x < 5

So, we have

h(1) = (7(1) - 4)/5(1) = 3/5

h(5) = (7(5) - 4)/5(5) = 31/25

So the range is 3/5 < h(x) < 31/25

Here, we have

P(x) = (5x - 1)/(3 - x)

So, we have

x = (5y - 1)/(3 - y)

This gives

3x - xy = 5y - 1

So, we have

y(5 + x) = -1 - 3x

This gives

y = -(1 + 3x)/(5 + x)

So, the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

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1.The temperature will be, T2= 169.8 K

2. The volume if the temperature is 318 K is 0.170 L

Charles's law, a statement that the volume occupied by a fixed amount of gas is directly proportional to its absolute temperature, if the pressure remains constant.

Given: V1= 250 ml=0.25L

V2=150 ml= 0.15 L

T1= 10 °C=283 K, T2=?

Now using Charles law

V1/T1=V2/T2

0.25/283=0.15/T2

T2= 169.8 K

2. T1= 20 °C= 293 K

    V1= 160 cm³

     T2= 318 K

     V2=?

Using Charles Law,

V1/T1=V2/T2

0.16/293=V2/313

0.170 L=V2

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Answer:

Answer: 2

Step-by-step explanation:

\( \frac{2}{3} (4 \frac{1}{6} - \frac{7}{6} ) \\ \)

express the mixed fraction into proper fraction:

\( { \boxed{4 \frac{1}{6} = \frac{(6 \times 4) + 1}{6} = \frac{25}{6} }}\)

then solve simplify:

\( = \frac{2}{3} ( \frac{25}{6} - \frac{7}{6} ) \\ \)

solve the bracket:

\( = \frac{2}{3} ( \frac{25 - 7}{6} ) \\ \\ = \frac{2}{3} ( 3)\)

then simplify:

\( = \frac{2 \times 3}{3} \\ \\ = 2\)

An equation of the new graph is: A. y = ∣x - 4∣ - 9.

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The height of the wall would be 54 inches if the bricklayer works for 9 hours.

Hence, the answer is option B) 54 inches.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

We can use the information given in the table to create a linear equation relating the time worked and the wall height.

First, we can find the slope of the line that passes through the two points (2, 12) and (5, 30):

slope = (change in y) / (change in x)

= (30 - 12) / (5 - 2)

= 18 / 3

= 6

Now we can use the slope-intercept form of a linear equation to find the equation of the line:

y = mx + b

where m is the slope and b is the y-intercept.

Using the point (2, 12), we can find b:

12 = 6(2) + b

b = 0

So the equation of the line is:

y = 6x

This equation tells us that the wall height is directly proportional to the time worked.

Now we can use the equation to find the height of the wall when the bricklayer works for 9 hours:

height = 6(time worked)

= 6(9)

= 54 inches

Therefore, the height of the wall would be 54 inches if the bricklayer works for 9 hours.

Hence, the answer is option B) 54 inches.

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The road trip will take approximately 5 hours.

Two one-step equations:

a) 2x + 5 = 13

In this equation, the variable 'x' represents an unknown number. By performing one step of subtraction, we can find the value of 'x' that makes the equation true.

The solution is x = 4.  

b) 3y - 7 = 16

Similar to the first equation, 'y' represents an unknown number.

By adding 7 to both sides of the equation, we can isolate the variable and solve for 'y.'  

The solution is y = 7.

Two equations with fractions:

a) (1/3)x + 2 = 5

Here, the variable 'x' is multiplied by a fraction.

To isolate 'x,' we can subtract 2 from both sides and then multiply both sides by the reciprocal of 1/3, which is 3/1.

The solution is x = 9.

b) (2/5)y - 3 = 1

In this equation, 'y' is multiplied by a fraction.

We can isolate 'y' by adding 3 to both sides and then multiplying both sides by the reciprocal of 2/5, which is 5/2.

The solution is y = 4.

One equation with the distributive property:

a) 2(x + 3) = 10

This equation demonstrates the distributive property.

By applying it, we multiply 2 by both x and 3, resulting in 2x + 6 = 10.

We can then solve for 'x' by subtracting 6 from both sides.

The solution is x = 2.

One equation with decimals:

a) 0.4x + 0.8 = 1.6

In this equation, 'x' is multiplied by a decimal.

To isolate 'x,' we subtract 0.8 from both sides and then divide both sides by 0.4.

The solution is x = 2.

Real-world problem:

Imagine you're planning a road trip.

The distance you'll be traveling is 250 miles, and your car's average speed is 50 miles per hour.

You want to determine how long the trip will take.

Let 't' represent the time in hours it will take to complete the trip.

The equation that represents this situation is:

50t = 250

By dividing both sides of the equation by 50, we find that t = 5.

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The dot plot that displays the data distribution is the dot plot on the lower left corner of the options with

Two dots at 0

One dot at 2

Two dots at 3

Four dots each at 4, 5, and 6

One dot at 7

A dot plot is a graphical presentation of data, on a number line, with the number of points of dot representing the frequency of data at each value on the number line.

The data can be presented as follows;

2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6

The above data can be arranged in increasing order as follows; 0, 0, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
Therefore, the frequencies of 0s is two, the frequencies of 4s, 5s and 6s are four each, and the frequency of 7 is one, which corresponds to the third graph or the graph in the bottom left corner of the figure.

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Answer:

y = 7

Step-by-step explanation:

3y + 1 = 4y - 6

-3y        -3y

1 = y - 6

+6     +6

7 = y

Answer:

7 = y

3y + 1 = 4y - 6

-3y. -3y

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

1 = 1y - 6

+6 +6

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

7 = y

Answer:

24.6 cm

Step-by-step explanation:

27-2.4 = 24.6         24.6 + 2.4 = 27

The coordinates of the vertex of the following parabola is (0,6).

The given equation of the parabola is \(& y=-3 x^2+6 \\\)

The point where the parabola and its axis of symmetry intersect is called the vertex of a parabola. It is used to determine the coordinates of the point on the parabola's axis of symmetry where it crosses it.

The standard form of a parabola is \(y=ax^{2} +bx+c.\)

The vertex form of a parabola is \(y = a(x-h)^{2} + k\).

\($$\begin{aligned}& y=-3 x^2+6 \\& y-6=-3 x^2 \\& y-6=-3(x-0)^2\end{aligned}$$\)

The vertex formula is used to find the vertex of a parabola. The formula to find the vertex is (h, k) = (-b/2a, -D/4a), where D = \(b^{2} -4ac\).

Now comparing the above equation by the equation of parabola

⇒\($$y-b=4(x-a)^2 \cdots$$\)

With vertex (a, b)

So a=0 and b=6.

So vertex of above parabola is\($(\mathbf{0}, \mathbf{6})$\).

Therefore, the vertex of the given parabola \($\mathbf{y}=-\mathbf{3} \mathbf{x}^{\mathbf{2}}+\mathbf{6}$ is $(\mathbf{0}, \mathbf{6})$\).

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Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) point. \(& y=-3 x^2+6 \\\)

When 1,493,600 is divided by 8 the quotient is 186,700.

To divide 1,493,600 by 8, you can follow these steps:

We have to write down the dividend (1,493,600) and the divisor (8).

Now start with the largest place value in the dividend (the leftmost digit) and perform the division.

Divide 1 by 8. Since 1 is smaller than 8, you move to the next digit.

Bring down the next digit (4) and combine it with the previous quotient (0). This gives you 04.

Divide 4 by 8. Since 4 is smaller than 8, you move to the next digit.

Bring down the next digit (9) and combine it with the previous quotient (0). This gives you 09.

Divide 9 by 8. The quotient is 1, and the remainder is 1.

Bring down the next digit (3) and combine it with the remainder (1). This gives you 13.

Divide 13 by 8. The quotient is 1, and the remainder is 5.

Bring down the next digit (6) and combine it with the remainder (5). This gives you 56.

Divide 56 by 8. The quotient is 7, and there is no remainder.

Bring down the next digit (0) and combine it with the quotient (7). This gives you 70.

Divide 70 by 8. The quotient is 8, and there is no remainder.

There are no more digits to bring down, and the division is complete.

The quotient is the result of the division. In this case, 1,493,600 divided by 8 is equal to 186,700.

Therefore, the result of 1,493,600 ÷ 8 is 186,700.

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Answer:

9

Step-by-step explanation:

Using the triangle midsegment theorem,

\(2x=18 \implies x=9\)

It seems that the sequence you provided is the sequence of triangular numbers. The function that generates this sequence could be defined as:

f(n) = n*(n+1)/2

Where n is the position of the number in the sequence.

So, for example:

f(1) = 1*(1+1)/2 = 1

f(2) = 2*(2+1)/2 = 3

f(3) = 3*(3+1)/2 = 6

and so on.

The point at (-3, 4) is at a distance of 5 units from the point (0, 0).

For two points (x₁, y₁) and (x₂, y₂), the distance between them is given by the formula:

distance = √( (x₁ - x₂)² + (y₁ - y₂)²)

In this case, we want to get the distance between (-3, 4) and (0, 0), using the above formula we will see that the distance is:

distance = √( (-3 - 0)² + (4 - 0)²) = √25 = 5

The distance is 5 units.

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Answer:

Step-by-step explanation:

Here you go mate

Step 1

9(x + 3)< 6x - 12  equation

Step 2

9(x + 3)< 6x - 12  simplify

3x+27<-12

Step 3

3x+27<-12  Simplify by adding and dividing

x<-13

Answer^

The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).

In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:

3(2a^2 - 5a + 2)

Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.

The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:

3(2a - 1)(a - 2)

Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

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Answer:

Jadon is 18yrs

Cousin 6 yrs

Step-by-step explanation:

Answer:

Jason is 18 years old and his cousin is 6 years old.

Step-by-step explanation:

Just took the test

Answer:

I think the answer is six i just searched it  or it could be 12

Step-by-step explanation:

The greatest common factor (GCF) of 48 and 6 is 6, so:

48 - 6 = 42.

this isn't college level *laugh*

Answer:

The upper bound for the total mass of the 50 parcels is 850 kilograms.

Step-by-step explanation:

From statement we infer that upper bound is represented by the 50 identical parcels completely full. Then, the upper bound is the product of number parcels and maximum capacity of each parcel:

\(m_{UP} = (50\,parcel)\cdot \left(17\,\frac{kg}{parcel} \right)\)

\(m_{UP} = 850\,kg\)

The upper bound for the total mass of the 50 parcels is 850 kilograms.

Answer:

The first type of solid shapes to be discovered are known as Platonic solids, which include the cube, the tetrahedron, the octahedron, the dodecahedron, and the icosahedron

Answer:

Mean = 0.45

Standard deviation = 0.04035

Step-by-step explanation:

This is actually a very simple problem.

The question gives us the report that 45% of the teenagers in the age bracket own smartphones.

P = mean = 45%

Therefore the mean is 0.45.

I will go ahead to help you calculate the standard deviation.

√p(1-p)/n

n = 152

P = 0.45

√0.45(1-0.45)/152

= √0.45(0.55)/152

= √0.2475/152

= √ 0.001628

= 0.04035

Answer: 0.14 is the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'm assuming that the barrel is in the shape of a cylinder..

Givens

r = 7

pi = 3.14

V = 2041.11

Formula

V = pi * r^2 * h

h = V / (pi * r^2)

Solution

h = 2041.11/(3.14 * 7^2)

H = 2014.11 / 153.86

H = 13.09

Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units