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Brooke has $7 in an account that earns 10% interest compounded annually.
To the nearest cent, how much will she have in 2 years?

Answer: [tex]y=Ce^(^3^t^{^9}^)[/tex]

Step-by-step explanation:

Beginning with the first differential equation:

[tex]\frac{dy}{dt} =27t^8y[/tex]

This differential equation is denoted as a separable differential equation due to us having the ability to separate the variables. Divide both sides by 'y' to get:

[tex]\frac{1}{y} \frac{dy}{dt} =27t^8[/tex]

Multiply both sides by 'dt' to get:

[tex]\frac{1}{y}dy =27t^8dt[/tex]

Integrate both sides. Both sides will produce an integration constant, but I will merge them together into a single integration constant on the right side:

[tex]\int\limits {\frac{1}{y} } \, dy=\int\limits {27t^8} \, dt[/tex]

[tex]ln(y)=27(\frac{1}{9} t^9)+C[/tex]

[tex]ln(y)=3t^9+C[/tex]

We want to cancel the natural log in order to isolate our function 'y'. We can do this by using 'e' since it is the inverse of the natural log:

[tex]e^l^n^(^y^)=e^(^3^t^{^9} ^+^C^)[/tex]

[tex]y=e^(^3^t^{^9} ^+^C^)[/tex]

We can take out the 'C' of the exponential using a rule of exponents. Addition in an exponent can be broken up into a product of their bases:

[tex]y=e^(^3^t^{^9}^)e^C[/tex]

The term e^C is just another constant, so with impunity, I can absorb everything into a single constant:

[tex]y=Ce^(^3^t^{^9}^)[/tex]

To check the answer by differentiation, you require the chain rule. Differentiating an exponential gives back the exponential, but you must multiply by the derivative of the inside. We get:

[tex]\frac{d}{dx} (y)=\frac{d}{dx}(Ce^(^3^t^{^9}^))[/tex]

[tex]\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*\frac{d}{dx}(3t^9)[/tex]

[tex]\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*27t^8[/tex]

Now check if the derivative equals the right side of the original differential equation:

[tex](Ce^(^3^t^{^9}^))*27t^8=27t^8*y(t)[/tex]

[tex]Ce^(^3^t^{^9}^)*27t^8=27t^8*Ce^(^3^t^{^9}^)[/tex]

QED

I unfortunately do not have enough room for your second question. It is the exact same type of differential equation as the one solved above. The only difference is the fractional exponent, which would make the problem slightly more involved. If you ask your second question again on a different problem, I'd be glad to help you solve it.

Answer:

2 hours

Step-by-step explanation:

1/7 + 1/3 = 10/21

21/10= 2.1

Answer:

∠ 1 = 155° , ∠ 2 = 25°

Step-by-step explanation:

the 2 angles are adjacent angles and sum to 180° , that is

5x + x - 6 = 180

6x - 6 = 180 ( add 6 to both sides )

6x = 186 ( divide both sides by 6 )

x = 31

then

∠ 1 = 5x = 5(31) = 155°

∠ 2 = x - 6 = 31 - 6 = 25°

Step-by-step explanation:

If 76° gives 7.5 meters, we must find out how many meters it is for 360°.

Find how much for 1°: [tex]\frac{7.5}{76}[/tex]

For 360°: [tex]\frac{7.5}{76} \times 360[/tex] = 35.53 meters

Answer:

if not 24.5, it should be 31 yds

Step-by-step explanation:

ok so, I don't know how you want me to solve this but, if you're asking the distance diagonally, then it will be 24.5 yds. If you want the distance in straight lines, it will be 31 yds

lol there wasn't much information, sorry

Answer:

D. 638 in

Step-by-step explanation:

W+X+U+2Y+Z+V+T = 638

Answer:

-940.5

Step-by-step explanation:

Answer:

-940.5

Step-by-step explanation:

use pemdas

1.parenthesis

2.exponets

3.multiply

4.divide

5.add

6.subtract

Answer:

Step-by-step explanation:

We need to multiply each dimension by 3.

The base was 3*15 = 45

and the height = 3*9 = 27.

Answer:

18t >= 78

Step-by-step explanation:

Not sure if there's an equals sign in the problem that you were given, but there should be. The 18 in the inequality stands for the hourly wage. The t stands for hours worked. 18(wage) x t(hours) has to be greater than or equal to 78 in order for Martin to at LEAST $78 per day. :)

Answer:

50

Step-by-step explanation:

It is on edge

Answer:

it is counting 48 than going down

Step-by-step explanation:1,48

Answer:

IT will lie in the quardant 1

because  want you to plot a point for "July 1963 was 63 degrees Fahrenheit" so that's in the positive temp region

so the correct option will be 1 and it is

D

Step-by-step explanation:

hope this helps

Answer:

  C. N=300; I%=6.7; PV=-175000; PMT=; FV=0; P/Y=12; C/Y=12; PMT:END

Step-by-step explanation:

To find the payment on a loan, a TVM solver needs the Present Value (PV) to be the loan amount, the Future Value (FV) to be zero, and N to be the actual number of payments (25×12 = 300).

Most solvers will take I% to be the annual interest rate. (An HP-12C financial calculator uses the monthly interest rate.)

The set of values needed for finding the monthly payment on this $175,000 loan at 6.7% are listed in choice C.

__

Additional comment

The sign of the cash flow is usually negative for amounts paid, and positive for amounts received. Here, the answer choices show the loan amount to be negative and the payment amount to be positive. We ordinarily expect to receive the loan amount and pay the payments. By the above criteria, the signs are reversed in this problem from what we usually expect.

Answer:

  278°

Step-by-step explanation:

You want the measure of arc RSQ given inscribed angle RSQ has a measure of 41°.

An inscribed angle has half the measure of the arc it subtends. This means short arc RQ will have double the measure of angle RSQ:

  arc RQ = 2 × 41° = 82°

The measure of long arc RSQ will complete the 360° circle:

  arc RSQ = 360° -arc RQ

  arc RSQ = 360° -82°

  arc RSQ = 278°

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According to the given figures of triangle.. The value of x is 2.

Answer:

x = 3

Step-by-step explanation:

assuming the triangle is right.

using Pythagoras' identity

(x + 2)² = x² + 4²

x² + 4x + 4 = x² + 16 ( subtract x² from both sides )

4x + 4 = 16 ( subtract 4 from both sides )

4x = 12 ( divide both sides by 4 )

x = 3

Answer:

21

Step-by-step explanation:

10*7 = 70

3*7 = 21

Answer:

6 Cups of Flower

Step-by-step explanation:

First form a ratio
Cookies:Flour
60:4
Simplify
15:1
Since we now need to find the amount of cups for 90 cookies we must finds the amount of flower.
90:X
Using our old ratio of 15:1 we must divide 90/15 in order to get a factor to multiply 1 to make 15:1 equivalent to 90:X.
90/15 = 6 | 6 is the factor
15(6):1(6)

90:6

Answer:

Its going to be 79 degrees still because it doesnt change.

Step-by-step explanation:

.

Answer:

$272

Step-by-step explanation:

9x7x12.5=787.5 120x7=840  38.95x7= 272.65 and she said to round to the nearest dollar so $272 dollars

The scenario that could be modelled with an exponential function is when Tim adds $10 to his savings account each week.

A function assigns the value of each element of one set to the other specific element of another set.

As we know that a continuous compounding function is an exponential function. Therefore, we need to find the situation where the principal amount is invested for an infinitely long time.

A.) Since the amount is invested and a certificate of deposit is taken the amount will be invested for a fixed period of time. Thus, this is not a continuous compound function.

B.) The amount put into the account and taken out of the account varies for each term. Thus, this is not a continuous function.

C.) As in Jaylon's account the money is reduced by $125 every month, therefore, at a certain point, it will become zero. Thus, this is not a continuous compound function.

D.) As Tim adds $10 to his saving account every month, and there is no time specified, also the account will be always positive. Thus, this is a continuous compound function.

Hence, the scenario that could be modelled with an exponential function is when Tim adds $10 to his savings account each week.

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The total number of gallons of diesel Truck B used to travel 132 miles is 11.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

A dairy farmer uses two trucks to deliver milk. The two trucks use different kinds of fuel. Truck A uses gasoline and Truck B uses diesel.

From the given table we can see that

The total number of gallons of diesel Truck B used to travel 12 miles = 1

Number of gallons of diesel Truck B used to travel 1 mile = 1 /12

The total number of gallons of diesel Truck B used to travel 132 miles

= 1 /12 x 132

= 132 / 12

= 11

Thus, The total number of gallons of diesel Truck B used to travel 132 miles is 11.

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To find the volume of a rectangular prism:

  ⇒ must know the formula

        [tex]Volume = length * width * tall[/tex]

Let's convert all the known lengths into improper fractions if needed

Thus: [tex]Volume = \frac{14}{5} *2*\frac{3}{5} =\frac{84}{25}=3.36yd^3[/tex]

When rounded to the nearest tenth, the volume of the pool is 3.4 [tex]yd^3[/tex]

Hope that helps!

Answer:

An Isosceles trapezoid

Step-by-step explanation:

The shape is triangle.

In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides. If the remaining two sides are parallel, they are referred to as the legs (or lateral sides); if not, the trapezoid is a parallelogram, and there are two pairs of bases.

Given a trapezoid,

number of vertex trapezoid have = 4

one less vertex than trapezoid = 4 - 1 = 3

number of sides trapezoid has = 4

one less side than trapezoid = 4 - 1 = 3

the shape which has 3 sides and 3 vertex is triangle.

Hence the new shape is triangle.

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{1, 3, 5, 7, 9, 11, ... , 47}

To Write The Following in Set-builder notation

[tex] \text{A} = [/tex] {x : x ∈ N;x is an odd number, x ≤ 47}

Answer:

convert the mixed fractions into decimals. do this by converting them into improper fractions and dividing the numerator by the denominator

Answer:

 A. see below for a graph

 B. f(x, y) = f(0, 15) = 90 is the maximum point

Step-by-step explanation:

A. See below for a graph. The vertices are those defined by the second inequality, since it is completely enclosed by the first inequality: (0, 0), (0, 15), (10, 0)

__

B. For f(x, y) = 4x +6y, we have ...

 f(0, 0) = 0

 f(0, 15) = 6·15 = 90 . . . . . the maximum point

 f(10, 0) = 4·10 = 40

_____

Comment on evaluating the objective function

I find it convenient to draw the line f(x, y) = 0 on the graph and then visually choose the vertex point that will put that line as far as possible from the origin. Here, the objective function is less steep than the feasible region boundary, so vertices toward the top of the graph will maximize the objective function.

The vertex points of this system are (0, 0), (0, 15) and (10, 0). And the maximum point of the system is 90.

At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

The given system:

2x+y ≤20

3x+2y ≤30

x, y ≥0

To find the vertex points,

first, we take inequalities in slope-intercept form.

y = 20 - 2x

And y = -3x/2 + 15

x, y ≥0

From that we interpreted the graph.

And the graph is given in the attached image.

A:

Check out the graph below. Given that the first inequality entirely encloses it, the vertices are those defined by the second inequality: (0, 0), (0, 15), (10, 0).

B:

We have objective function f(z) = 4x + 6y

To find the maximum point:

Substituting (0,0) to the function,

4x + 6y

= 4(0) + 6(0)

= 0

Substituting (0,15) to the function,

4x + 6y

= 4(0) + 6(15)

= 0 + 90

= 90

Substituting (10,0) to the function,

4x + 6y

= 4(10) + 6(0)

= 40 + 0

The maximum point is 90.

Therefore, (0, 0), (0, 15) and (10, 0) are the vertex of the system. And the maximum point is 90.

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Answer:

B. Cube and E. hexahedron

Step-by-step explanation:

Icosahedron are made of triangles, cubes are made of squares, tetrahedron are made of triangles, octahedron are made of triangles, hexahedron are made of squares, dodecahedron are made of pentagons.

i hope it helps! Have a great day!

Sandra~