1. If you have a 100A as a grade and you get 8 bonus points, what is your grade now?

2. If you have a 90B as a grade and you get 8 bonus points, what is your grade now?

**ANSWER QUICK**

The surface area of the cylinder is 150.72cm²

A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis.

The surface area of a cylinder is the addition of the area of the faces on the cylinder.

The surface area of a cylinder = 2πr(r+h)

= 2×3.14 × 3( 3+5)

= 18.84 × 8

= 150.72cm²

therefore the surface area of the cylinder is 150.72cm²

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Luckily, the integral is basically set up for you:

\(\displaystyle \int_{\theta=0}^{2\pi} \int_{\phi=\frac\pi4}^{\frac\pi2} \int_{\rho=2}^6 \cos(\phi) \, d\rho \, d\phi \, d\theta\)

Since the limits on every variable are constant, and we can factorize \(f(\rho,\theta,\phi) = f_1(\rho) f_2(\theta) f_3(\phi)\), we can similarly factorize the integrals. (This is a special case of Fubini's theorem, if I'm not mistaken.)

So the triple integral is equivalent to

\(\displaystyle \left(\int_0^{2\pi} d\theta\right) \left(\int_{\frac\pi4}^{\frac\pi2} \cos(\phi) \, d\phi\right) \left(\int_2^6 d\rho\right)\)

and each of these subsequent integrals are easy to compute:

\(\displaystyle \int_0^{2\pi} d\theta = \theta \bigg|_0^{2\pi} = 2\pi - 0 = 2\pi\)

\(\displaystyle \int_{\frac\pi4}^{\frac\pi2} \cos(\phi) \, d\phi = \sin(\phi) \bigg|_{\frac\pi4}^{\frac\pi2} = \sin\left(\frac\pi2\right) - \sin\left(\frac\pi4\right) = 1 - \frac1{\sqrt2} = \frac{2 - \sqrt2}2\)

\(\displaystyle \int_2^6 d\rho = \rho\bigg|_2^6 = 6 - 2 = 4\)

Taken together, the triple integral evaluates to

\(\displaystyle \int_{\theta=0}^{2\pi} \int_{\phi=\frac\pi4}^{\frac\pi2} \int_{\rho=2}^6 \cos(\phi) \, d\rho \, d\phi \, d\theta = 2\pi \times \frac{2-\sqrt2}2 \times 4 = \boxed{4\pi(2-\sqrt2)}\)

Answer: (1,-4)

Step-by-step explanation:

Answer:

She will see that the pressure went up, not down!

Step-by-step explanation:

1. In a closed system, The volume inside the tire shouldn't change much (the losses will be small)

2. For a closed system, the Pressure inside a bicycle tire will increase with the increase of its Temperature

3. In a long bicycle ride, the constant friction of the tire to the ground will heat up the air inside the tire, thus increasing the pressure inside the tire

12,480 es par y la suma de sus digitos da un multiplo de 3, por ello concluimos que es divisible por 6.

Para que un número sea divisible por 6 debe cumplir dos condiciones.

En este caso tenemos 12,480, que sabemos que es par.

La suma de sus digitos da:

1 + 2 + 4 + 8 + 0 = 15

15 es multiplo de 3.

Entonces este número cumple ambas condiciones, por lo que concluimos que 12,480 es divisible por 6.

Sí quieres aprender más sobre divisiones.

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The Interpretatiom of the equation is that;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

The algebra word problem can be solved by using variables to denote certain parameters I'm the question.

The general form of equation of a line in slope intercept form is;

y = mx + c

Where;

m is slope

c is y-intercept

We are given the equation:

$25w + $65

This equation represents the amount of money Kelly will have saved after some amount of weeks.

Thus;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

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The cost of each sandwich, given the number that was sold and the profit made was  $15.

Let S be the price of a sandwich and A be the price of a salad.

From the lunch sale, we know:

14 S + 14 A = $280

From the evening sale, we know:

42S + 154 A = $ 1400

Simplify the first equation by dividing through by 14:

S + A = $20

Solving this equation for S gives:

S = $20 - A

Substitute this equation into the second equation:

42 ( $20 - A ) + 154 A = $1400

$ 840 - 42 A + 154 A = $1400

112A = $560

A = $5

Substitute A = $5 into the first equation:

S + $5 = $20

S = $15

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Answer:

y= -x²-4x+2

Step-by-step explanation:

write in vertex form

a(x-h)²+k

in our case h = -2 and k= 6

y=a(x+2)²+6

now we just need to solve for a. we know that when x= 1 y = -3. plug these values in and solve for a

-3= a(1+2)²+6

-9=9a

a= -1

thus the formula is -(x+2)²+6

generally, teachers want things in standard form, so expand the exponent and simplify.

-(x²+4x+4)+6

y= -x²-4x+2

Answer:

\(y = -x^2 - 4x + 2\)

Step-by-step explanation:

The equation of a parabola in vertex form is:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex of the parabola.

In this case, the vertex is (-2, 6), so h = -2 and k = 6.

We also know that the parabola passes through the point (1, -3).

Plugging these values into the equation, we get:

\(-3 = a(1 - (-2))^2 + 6\)

\(-3 = a(3)^2 + 6\)

-9 = 9a

a = -1

Substituting a = -1 into the equation for a parabola in vertex form, we get the equation of the parabola:

\(y = -1(x + 2)^2 + 6\)

This equation can also be written as:

\(y = -x^2 - 4x -4+6\\y=x^2-4x+2\)

Answer:

Cardiorespiratory capacity, muscular strength and motor capacity have an impact on school performance. Better breathing encourages communication between cells and motor skills help improve concentration.

Answer:

u spend half an hour on your blog

Step-by-step explanation:

(1/5)*(5/2) = 1/2

Step-by-step explanation:

Log(x²+8)=log 10+ log x

Log(x²+8)=log(10×x)

x²+8=10x

x² - 10x + 8=0

x is approximately to - 1 and - 8✅

The solutions to the given equation are x = -1 and x = 8.

Option A is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

Using logarithmic properties, we can simplify the given equation:

logs(x² + 8) = 1 + log g(x)

logs(x² + 8) - log g(x) = 1

log[(x² + 8)/g(x)] = 1

(x² + 8)/g(x) = 10

x² + 8 = 10g(x)

Now we can solve for x by substituting the given answer options and solving for g(x):

For x = -2 and x = -4:

x = -2:

(-2)² + 8 = 12, which is not equal to 10 g(x) for any value of g(x).

So x = -2 is not a solution.

x = -4:

(-4)² + 8 = 24, which is also not equal to 10g(x) for any value of g(x).

So x = -4 is not a solution.

For x = -1 and x = 8:

x = -1:

(-1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.

So x = -1 is a solution.

x = 8:

(8)² + 8 = 72, which is equal to 10g(x) when g(x) = 7.2.

So x = 8 is a solution.

For x = 1 and x = -8:

x = 1:

(1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.

So x = 1 is a solution.

x = -8:

(-8)² + 8 = 56, which is not equal to 10g(x) for any value of g(x).

So x = -8 is not a solution.

Therefore,

The solutions to the given equation are x = -1 and x = 8.

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The true statement about the axis of rotation is the option;

It is parallel to a side of the equilateral triangle, but is separate from the equilateral triangle.

The axis of rotation is a straight line around which all points on a rotating body rotates.

The diagram shows a figure with a hollow cylindrical cross section and triangular cross section on the left and right, which indicates that the figure is created by the rotation of the equilateral triangle about height of the cylinder, such that the axis of rotation is a vertical line through the center of the hollow cylinder. Therefore, the axis of rotation is parallel to the height of the cylinder, and therefore, it is parallel to the base of the equilateral triangle, but it it seperate from walls of the cylinder, and therefore, separate from the equilateral triangle

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The growth constant is 1.0986 and the trout population will increase to 14600 after 2.1 years. The result is obtained by using the logistic equation.

The increase of population can be found by using the logistic equation. It is

\(P(t) = \frac{K}{1 + Ae^{-kt} }\)

Where

Sunset Lake is stocked with the rainbow trout. We have

Find the growth constant k and time t when P(t) = 14600!

A = (K - P₀)/P₀

A = (28000 - 2800)/2800

A = 25200/2800

A = 9

After 1 year, we have 7000 rainbow trout. The growth constant is

\(7000 = \frac{28000}{1 + 9e^{-k(1)} }\)

\(1 + 9e^{-k} = 4\)

\(9e^{-k} = 3\)

\(e^{-k} = \frac{1}{3}\)

k = - ln (1/3)

k = 1.0986

Use k value to find the time when the population will increase to 14600!

\(14600 = \frac{28000}{1 + 9e^{-1.0986t} }\)

\(1.9178 = 1 + 9e^{-1.0986t}\)

\(0.9178 = 9e^{-1.0986t}\)

\(\frac{0.9178 }{9} = e^{-1.0986t}\)

\(t = \frac{ln \: 0.10198}{-1.0986}\)

t = 2.078

t ≈ 2.1 years

It is in another 1.1 years after t = 1.

Hence, the growth constant k is 1.0986 the population will increase to 14600 when t is 2.1 years.

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Answer:

The answer is 4 batches I tried it and it was right

Step-by-step explanation:

Answer:

its A i got it right

Step-by-step explanation:

Answer:

1). Mass of water present= 18000 kg

2).4/3 meters deep

Step-by-step explanation:

Area of the rectangle= 6*3= 18m²

Volume of water in the pool

= Deepness of water*area of rectangle

= 1*18

= 18 m³

density of water is about 1 gram per cubic centimeter

In kg per m³= 1000 kg/me

Mass of water present= density*volume

Mass of water present= 1000*18

Mass of water present= 18000 kg

2)6000 kilograms of water is added to 18000 of

Total mass present= 6000+18000

Total mass present=24000 kg

If density= 1000kg/m³

Volume present= mass/density

Volume present= 24000/1000

Volume present= 24 m³

Area of the rectangle= 18 m²

deepness of the pool= volume/area

deepness of the pool= 24/18

deepness of the pool= 4/3 meters deep

The correct equivalent expression to the square root containing a variable is 2a³/5 and the correct option is E.

We shall simplify the expression of the square root containing a variable by carrying out basic mathematics operations to derive its equivalent as follows:

squre root of (36a⁸/255a²) = square root of (36a⁶ × a²/255 × a²)

a² is common and can be cancel out

square root of (36a⁸/255a²) = square root of (36a⁶/255)

square root of (36a⁸/255a²) = square of 36 multiplied by the square root of a⁶ all divided by the square root of 255 {take square root of each}

square root of (36a⁸/255a²) = 6a³/15

square root of (36a⁸/255a²) = 2a³ × 3/5 × 3

we divide through by the common factor 3

square root of (36a⁸/255a²) = 2a³/5

Therefore, the equivalent expression to square root of (36a⁸/255a²) is derived as 2a³/5 which is option E.

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Positive number is a square root

Answer:

\((0,-\frac{11}{3} ),(1,-\frac{4}{3} ),(2,1)\)

Step-by-step explanation:

Given Equation:

Required:

Steps:

Subtract 7x from both sides of the equation.

-3y = 11 - 7x

Divide each term in -3y = 11 - 7x by -3 and simplify.

-3y/-3 = 11/-3 + -7x/-3

Simplify the left side.

Cancel the common factor of -3.

-3y/-3 (canceled) = 11/-3 + -7x/-3

Divide y by 1.

y = 11/-3 + -7x/-3

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

y = -11/3 + -7x/-3

Dividing two negative values results in a positive value.

y = -11/3 + 7x/3

Choose any value for x that is in the domain to plug in to the equation.

Choose 0 to substitute in for x to find the ordered pair.

Remove parentheses.

y = -11/3 + 7(0)/3

Simplify  -11/3 + 7(0)/3.

⇒ Combine the numerators over the common denominator.

y = -11/3 + 7(0) / 3

Simplify the expression.

y = -11 + 0/3

y = -11/3

y = -11/3

Use the x and y values to form the ordered pair.

(0, -11/3)

Choose 1 to substitute in for x to find the ordered pair.

Remove parentheses.

y = -11/3 + 7(1)/3

Simplify -11/3 + 7(1)/3.

Combine the numerators over the common denominator.

y =  -11/3 + 7(1)/3

Simplify the expression.

Multiply 7 by 1.

y = -11 + 7/3

Add -11 and 7.

y = -4/3

Move the negative in front of the fraction.

y = -4/3

Use the x and y values to form the ordered pair.

(1, -4/3)

Choose 2 to substitute in for the x in the ordered pair.

Remove parentheses.

y = -11/3 + 7(2)/3

Simplify -11/3 + 7(2)/3.

Combine the numerators over the common denominator.

y =  -11/3 + 7(2)/3

Simplify the expression.

Multiply 7 by 2.

y = -11 + 14/3

Add -11 and 14.

y = 3/3

Divide 3 by 3,

y = 1

Use the x and y values to form the ordered pair.

(2, 1)

These are three possible solutions to the equation.

(0, -11/3), (1, -4/3), and (2,1)

Thanks,
Eddie

The function represented by the series is \($\quad f(x)=\frac{4}{1-x^2}$\)

The interval of convergence of the series is ( - 1, 1 )

As per the question the given function is:

\($$\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k$$\)

\($$\sum_{n=0}^{\infty} a r^n=\frac{1}{1-r}$$\)

\($$\sum_{n=0}^{\infty} x^n=\frac{1}{1-x}$$\)

\($$\begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\frac{1}{1-\frac{x^2+3}{4}} \\& =\frac{1}{\frac{4-x^2-3}{4}} \\& =\frac{4}{1-x^2}\end{aligned}$$\)

Thus, \($\quad f(x)=\frac{4}{1-x^2}$\)

\($$\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k=\sum_{k=0}^{\infty} \frac{\left(x^2+3\right)^k}{4^k}$$\)

\($$\begin{aligned}L & =\lim _{k \rightarrow \infty}\left|\frac{\left(x^2+3\right)^{k+1}}{4^{k+1}} \frac{4^k}{\left(x^2+3\right)^k}\right| \\& =\lim _{k \rightarrow \infty}\left|\frac{\left(x^2+3\right)}{4}\right| \\& =\left|\frac{\left(x^2+3\right)}{4}\right|\end{aligned}$$\)

The series will converge, if L<1

\($$\begin{array}{ll} & \left|\frac{\left(x^2+3\right)}{4}\right| < 1 \\ & \frac{\left(x^2+3\right)}{4} < 1 \\ & x^2+3 < 4 \\\end{array}\)

\(& x^2 < 1 \\\)

 |x| < 1

 -1 < x < 1

Substitute the values of 'x' in the given function

At, x = - 1

\(\begin{aligned} \\\qquad \begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\sum_{k=0}^{\infty}\left(\frac{(-1)^2+3}{4}\right)^k \\& =\sum_{k=0}^{\infty}\left(\frac{4}{4}\right)^k \\& =\sum_{k=0}^{\infty} 1^k\end{aligned}\end{aligned}$$\)

Also, at x = 1

\($$\begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\sum_{k=0}^{\infty}\left(\frac{(1)^2+3}{4}\right)^k \\& =\sum_{k=0}^{\infty}\left(\frac{4}{4}\right)^k \\& =\sum_{k=0}^{\infty} 1^k\end{aligned}$$\)

Thus, the interval of convergence is ( - 1, 1 )

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Answer:

Step-by-step explanation:

1) c

x² = 1

x² - 1 = 0

Degree of quadratic equation should be 2.

2) 'a'- coefficient of x² cannot be 0

option a

3) option c

Standard form: ax² + bx +c = 0

4) c = 5

3x² + 8x = -5

3x² + 8x + 5 = 0

option c

5) b= 0

option a

1. The exact value of sin²θ given cosθ = 5/13 and 3π/2 <θ<2π is 2√(1 - (25/169))(5/13).

2. The correct answer is -240/289.

Pythagorean identity states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.

1. The first step is to use the Pythagorean identity to find the value of sinθ. The identity states that sin²θ + cos²θ = 1, so in this case, sin²θ = 1 - (5/13)². We then square root both sides to find that sinθ = √(1 - (25/169)).

Next, we use the double angle formula for sine, sin²θ = 2sinθcosθ, to find the value of sin²θ. Substituting in the values of sinθ and cosθ, we get sin²θ = 2√(1 - (25/169))(5/13).

Therefore, the exact value of sin²θ given cosθ = 5/13 and 3π/2 <θ<2π is 2√(1 - (25/169))(5/13).

2. To find the value of sin(2θ), we can use the identity sin(2θ) = 2sinθcosθ. Since we know the value of tanθ (15/8), we can calculate the value of sinθ (8/17) and cosθ (15/17). Plugging these values into the identity and simplifying yields -240/289.

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Answer:

177

Step-by-step explanation:

Step-by-step explanation:

CFB reads as twenty five degrees

complementary angle  will add to it to sum 90 degrees  = sixty five degrees

   angle CFD is sixty five degrees

Hello !

Answer :

Explanation :

\( \to \boxed{ ({x}^{a}) {}^{b} = {x}^{ab} } \)

\( \to \boxed{ {x}^{ \frac{1}{n} } {}^{} = \sqrt[n]{x} } \)

\( ({x}^{4} ) {}^{ - \frac{2}{3} } = {x}^{- \frac{2}{3} \times 4} \\ \boxed{= {x}^{ - \frac{8}{3} } } \\ \boxed{= \sqrt[3]{ {x}^{ - 8} }} \\ \boxed{ = \sqrt[3]{ ({x}^{ 4}) {}^{ - 2} }}\)

Have a nice day ;)

Answer:

  5.2 square units

Step-by-step explanation:

You want the area of a triangle with sides 4 and 3, and the angle between them measuring 60°.

The formula for the area of a triangle is ...

  A = 1/2ab·sin(C)

Here, we have a=4, b=3, C=60°, so the area is ...

  A = 1/2·4·3·sin(60°) = 3√3 ≈ 5.2 . . . . square units

The area of the triangle is about 5.2 square units.

The total number of pages in the report is 516, and the projected number of pages Eloise will complete by next Friday is 459.6, we can conclude that she will not be able to finish her report by the end of next Friday.

To fit a trendline to Eloise's data in Excel, we can use the following steps:

Enter the data points for the "Day" and "Pages" into two columns in Excel.

Select the data points.

Go to the "Insert" tab in Excel and click on the "Scatter" chart type.

Choose the scatter plot with smooth lines and markers option.

Right-click on any data point on the chart and select "Add Trendline."

In the "Format Trendline" pane, choose the "Linear" trendline type.

Now, let's determine the slope and intercept for the trendline:

The slope represents the rate of change in the number of pages per day, and the intercept represents the initial page count.

According to the provided data:

Pages: [423, 466, 473, 432]

Day: [Monday, Tuesday, Wednesday, Thursday]

Using Excel's trendline, we obtain the following results:

A: The slope of the trendline is 5.4 (rounded to one decimal place).

B: The intercept of the trendline is 432.6 (rounded to one decimal place).

Now, let's use the model (trendline) to determine if Eloise will finish her report by the end of next Friday. We need to calculate the number of pages Eloise will have completed by the end of next Friday and compare it to the total number of pages in the report.

Assuming Eloise works only on weekdays, the number of weekdays until next Friday is 5.

Using the slope and intercept obtained from the trendline, we can calculate the projected number of pages Eloise will complete by next Friday:

Projected pages = (slope * number of days) + intercept

= (5.4 * 5) + 432.6

= 27 + 432.6

= 459.6

Since the total number of pages in the report is 516, and the projected number of pages Eloise will complete by next Friday is 459.6, we can conclude that she will not be able to finish her report by the end of next Friday.

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From the given box plot, it is found that:

The minimum height is of 156 cm, the first quartile Q1 is 168.1 cm, the second quartile Q2(or the median) is of 173.7 cm, the third quartile Q3 is of 181.4 cm, and the maximum height is of 192 cm.

A box and whisker plot shows five things:

The measures are shown in order, from left to right, hence:

The minimum height is of 156 cm, the first quartile Q1 is 168.1 cm, the second quartile Q2(or the median) is of 173.7 cm, the third quartile Q3 is of 181.4 cm, and the maximum height is of 192 cm.

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Answer:

the slope should be -4

Step-by-step explanation:

to find the slope we use the equation y2 - y1/ x2 - x1

-15 - (-7) / 5 - 3

-15 + 7 / 2

-8 / 2

-4