Find the total surface area of the following


cone. Leave your answer in terms of a.


4 cm


3 cm


SA = [ ? ]7 cm


Hint: Surface Area of a Cone = tre + B


Where e = slant height, and B = area of the base

Answer:

123456789101112131415

Answer:

-10.08

Step-by-step explanation:

Using order of operations:

\( - 17 + (\frac{ - 2.3 + 8.12}{6} ) \times {4}^{2} - 8.6\)

\( - 17 + \frac{5.82}{6} \times 16 - 8.6\)

\( - 17 + .97 \times 16 - 8.6\)

\( - 17 + 15.52 - 8.6\)

\( - 10.08\)

Answer:

29°

Step-by-step explanation:

:)

Answer: The measure of angle 1 is 39 degrees,the measure of angle 2 is 78 degrees and the measure of angle 3 is 63 degrees.

Step-by-step explanation:

We will represent the measure of angle 1 by x because it is unknown.

It says that the measure of angle 2 is twice angle 1   so we could represent that as  2x  and the measure of angle 2  is 15 less than angle 3 and we could also represent that by  2x - 15.

Now we know they all add up to 180 so add them up and set them equal to 180 and solve for x.

x + 2x + 2x -15 = 180  

5x - 15 = 180

      +15   +15

5x = 195

x = 39  

If x is equal to 39 then the measure of angle 1 is 39 degrees and the measure of angle 2 is twice that so 2(39) = 78   which also gives us the measure of angle 2 as 78.

For angle 3 it says that it has to be 15 less than the measure of angle so  subtract 15 from  78 to find the measure of angle 3.

78 - 15 = 63   The measure angle 3 is 63 degrees. Now add the measures all together to see if they equal 180 degrees .

Check:

39 + 78 + 63 = 180

  180 = 180

Answer:

3(4x-4)-7x

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Given a quadratic equation in standard form ax² + bx + c = 0 (a ≠ 0 )

Then the discriminant b² - 4ac determines the nature of the roots.

• If b² - 4ac > 0 then 2 real and distinct roots

• If b² - 4ac = 0 then 2 real and equal roots

• If b² - 4ac < 0 then no real roots

Given

2x² + 8x + 3 = 0 ← in standard form

with a = 2, b = 8, c = 3 , then

b² - 4ac = 8² - (4 × 2 × 3) = 64 - 24 = 40

Since b² - 4ac > 0 then 2 real and distinct roots → a

Answer:

a

Step-by-step explanation:

Answer:

3:1

Step-by-step explanation:

Out of 4/4 tulips...

Davon has 3/4 white tulips.

Davon therefore has 1/4 red tulips.

3/4:1/4 is basically 3:1 (After dividing 1/4 by 3/4)

Answer: It’s A

Step-by-step explanation:

x4 + 2x2y + y2

The values of b and a for the logarithmic function in this problem are given as follows:

The logarithmic function in the context of this problem has the format given as follows:

\(y = b\log_3{x + a}\)

The vertical asymptote is at x = -4, hence:

\(y = b\log_3{x - 4}\)

When x = 5, y = -1, hence the parameter b is obtained as follows:

\(-1 = b\log_3{5 - 4}\)

0.477b = -1

b = -1/0.477

b = -2.1.

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Answer: C) y=-2+2

Step-by-step explanation: Rise over run says that the slope is -2 and the line hits the y axis at +2 so the equation would be y = -2 + 2.

Answer:

No

Step-by-step explanation:

No, it is not because the 3 dollars is a steady price. A expression will look like 7n+3. Since the 3 dollars is a steady price you can never have a unit rate.

Answer:

It's proportional

Step-by-step explanation:

10-3=7  7/1 = 7

17 - 3= 14 1 4/2 = 7

31 - 3 = 28 28/4 = 7

38 -3 = 35 35/5 = 7

73 - 3 = 70 70/10 = 7

Answer:

7 + 5 = 12

Step-by-step explanation:

7 steps plus 5 steps equals 12 steps

Answer:

  (x, y) = (4, 3)

Step-by-step explanation:

The first step in solving any math problem is to read and understand what is given and what is asked.

Two linear equations are given, each in standard form. The coefficients of y are the same in the two equations, and both coefficients are 1 in the first equation.

You are asked to "solve" this system of equations. That means you want an (x, y) ordered pair that will satisfy both equations. On a graph, these are the coordinates of the point where the lines cross.

There are many ways to solve a system of linear equations. In this case, the y-coefficients being the same suggests that "elimination" or "linear combination" would be a good choice of solution method.

We note that the coefficients in the second equation are generally larger than those in the first equation. Subtracting the first equation from the second equation will generally leave positive coefficients, making the arithmetic less error-prone.

  (3x +y) -(x +y) = (15) -(7) . . . . . . subtract the first equation from the second

  2x = 8 . . . . . . simplify

  x = 4 . . . . . . divide by 2

Using this value in the first equation, we can find y:

  4 +y = 7

  y = 3 . . . . . . subtract 4

The solution to this pair of equations is (x, y) = (4, 3).

__

Additional comment

A graphical solution is attached.

Either equation can be solved for y, and that expression substituted into the other. Solving the first equation for y gives ...

  y = 7 -x

Substituting that into the second equation, we have ...

  3x +(7 -x) = 15

  2x = 8 . . . . . . . subtract 7

  x = 4 . . . . . . divide by 2

  y = 7-4 = 3

(x, y) = (4, 3) is the solution.

We have shown 3 methods of solving the given system of equations. There are other methods that can be used, too, including matrix methods and methods that make use of arrays of the coefficients.

Yes, the vectors v1 = (0,0,-4), v2 = (0,-4,12), and v3 = (6,-5,-8) do span ℝ3.  This is because any 3 vectors in ℝ3 will span the entire space, meaning that any vector in ℝ3 can be written as a linear combination of these 3 vectors.

To determine if a set of vectors spans a space, we can create a matrix with the vectors as columns and row reduce it to see if there are any free variables. If there are no free variables, the vectors span the space.

The matrix with v1, v2, and v3 as columns is:

| 0 0 6 |
| 0 -4 -5 |
| -4 12 -8 |

Row reducing this matrix gives us:

| 1 0 0 |
| 0 1 0 |
| 0 0 1 |

Since there are no free variables, the vectors v1, v2, and v3 do span ℝ3.

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Answer:

The size of the garden is 75 by 1! The perimeter is 75 + 1 + 75 + 1, or 152.

Step-by-step explanation:

Alright, so what I'm seeing is that the measure of the sides will never change. It's always 2. That makes your life easier because you just take the remaining 2 sides!

So, to figure that out, first, you've gotta subtract 2 from 152. That's 150. Then, for the remaining 2 sides, you have to divide 150 by 2, which is 75.

Therefore, the size of the garden is 75 by 1! The perimeter is 75 + 1 + 75 + 1, or 152.

*mike dropeth*

Answer:

d)    \(\frac{13 - 5x}{2x -8}\)    

Step-by-step explanation:

Explanation:-

Given expression

                               \(\frac{\frac{3}{x-2}-5 }{2-\frac{4}{x-2} }\)

we will do L.C.M  both numerator term and denominator term

                     ⇒    \(\frac{\frac{3-5(x-2)}{x-2} }{\frac{2(x-2)-4}{x-2} }\)

on simplification , we get

                ⇒    \(\frac{\frac{13-5x}{x-2} }{\frac{2x-8}{x-2} }\)

cancellation 'x-2'

we will get

          \(\frac{13 - 5x}{2x -8}\)    

The lower bound of the confidence interval is $672,743

Given data are: 41 college graduates who took a statistics course in college have a mean of $88,513 and a standard deviation of $1,508.

We are required to construct an 84.7% confidence interval for estimating the population variance.

To find the lower bound of the confidence interval, we use the following formula: Lower bound of confidence interval:  χ2 = ((n - 1)s²) / χ2(α/2, n-1)

Where n = sample size, s = sample standard deviation, χ2 = chi-square critical value, and α = level of significance.

Here, n = 41, s = $1,508, α = 1 - 0.847 = 0.153 (using the complement of the given confidence level), and degree of freedom (df) = n - 1 = 41 - 1 = 40.

To find the chi-square critical value, we use the chi-square distribution table:

χ2(α/2, n-1) = χ2(0.0765, 40) = 26.509.

So, Lower bound of confidence interval:  χ2 = ((n - 1)s²) / χ2(α/2, n-1) = ((41 - 1) x $1,508²) / 26.509≈ $672,743.

Hence, the lower bound of the confidence interval is $672,743 (rounded to the nearest whole number).

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If the probability of observing at least one car on a highway during any 20-minute time interval is 609/625, then the probability of observing at least one car during any 5-minute time interval is 609/2500

Given The probability of observing at least one car on a highway during any 20 minute time interval is 609/625.

We have to find the probability of observing at least one car during any 5 minute time interval.

Probability is the likeliness of happening an event among all the events possible. It is calculated as number/ total number. Its value lies between 0 and 1.

Probability during 20 minutes interval=609/625

Probability during 1 minute interval=609/625*20

=609/12500

Probability during 5 minute interval=(609/12500)*5

=609/2500

Hence the probability of observing at least one car during any 5 minute time interval is 609/2500.

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Answer:

"Which number has a 2 with a value ten times less than the 2 in the number 725,983?"

First, the value of the 2 in the number 725,983 can be find by separatig each digit as:

725,983 = 700,000 + 20,000 + 5,000 + 900 + 80 + 3.

Then the value of the 2 is: 20,000.

Now we want a number that has a 2 with a value then times less than 20,000.

this is:

20,000/10 = 2,000.

Then we want a number that has a 2 in the thousands place.

For example, 132,000 is a number that can be an answer, the only thing you need is that the 2 is in the thousands place (the fourth digit counting from the right)

Answer:

\(\frac{y^{2}}{25}-\frac{x^{2}}{3}=1\)

Step-by-step explanation:

Para resolver este problema debemos tomar en cuenta los datos que nos dan y la ecuación de una hipérbola. Comencemos con los datos:

centro: (0,0)

focos: \((0,-\sqrt{28}),(0,\sqrt{28})\)

eje conjugado = \(2\sqrt{3}\)

por los focos podemos ver que la hipérbola se dirige hacia el eje y, por lo que debemos tomar la siguiente forma de la ecuación de la parábola:

\(\frac{y^{2}}{a^{2}}+\frac{x^{2}}{b^{2}}=1\)

de los focos podemos obtener que:

\(c=\sqrt{28}\)

y del eje conjugado podemos saber que al dividir la longitud del eje conjugado dentro de 2 obtenemos b, así que:

\(b=\sqrt{3}\)

podemos utilizar la siguiente fórmula para obtener a:

\(c^{2}-a^{2}=b^{2}\)

si despejamos a en la ecuación obtenemos lo siguiente:

\(a=\sqrt{c^{2}-b^{2}}\)

ahora podemos sustituir los valores:

\(a=\sqrt{(\sqrt{28})^{2}-(\sqrt{3})^{2}}\)

\(a=\sqrt{28-3}\)

\(a=\sqrt{25}\)

a=5

así que media vez conozcamos a, podemos sustituir los datos en la ecuación de la hipérbola así que obtenemos lo siguiente:

\(\frac{y^{2}}{a^{2}}+\frac{x^{2}}{b^{2}}=1\)

\(\frac{y^{2}}{(5)^{2}}+\frac{x^{2}}{(\sqrt{3})^{2}}=1\)

\(\frac{y^{2}}{25}+\frac{x^{2}}{3}=1\)

si graficamos la hipérbola, queda como en el documento adjunto.

Answer:

a and d

or

c and b

Step-by-step explanation:

supplementary angles are angles that add up to 180 degrees

when looking at the rectangle you see two possible answers

Answer:

d

Step-by-step explanation:

The direction angles of vector v are approximately α ≈ 38.7°, β ≈ 142.1°, and γ ≈ 57.3°.

To find the direction angles of the vector v = 3i - 2j + 2k, we can use the direction cosines. The direction cosines are given by the ratios of the vector's components to its magnitude.

The magnitude of vector v is:

|v| = √(3² + (-2)² + 2²) = √17

The direction cosines are:

cosα = vₓ / |v| = 3 / √17

cosβ = vᵧ / |v| = -2 / √17

cosγ = vᵢ / |v| = 2 / √17

To find the direction angles α, β, and γ, we can take the inverse cosine of the direction cosines:

α = cos⁻¹(3 / √17)

β = cos⁻¹(-2 / √17)

γ = cos⁻¹(2 / √17)

Calculating the direction angles using a calculator, we get:

α ≈ 38.7° (rounded to the nearest tenth)

β ≈ 142.1° (rounded to the nearest tenth)

γ ≈ 57.3° (rounded to the nearest tenth)

Therefore, the direction angles of vector v are approximately α ≈ 38.7°, β ≈ 142.1°, and γ ≈ 57.3°.

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Answer:

80+100=supplementary, right? A sup. angle is 2 angles making 180 digres.

The integral representing the length of the parametric curve is ∫[0, 4] √(17 - 8 cos(t)) dt.

To find the length of the parametric curve represented by the equations x = t − 4 sin(t) and y = 1 − 4 cos(t) over the interval 0 ≤ t ≤ 4, we can use the arc length formula for parametric curves. The arc length formula is given by:

L = ∫[a, b] √(dx/dt)^2 + (dy/dt)^2 dt

where [a, b] represents the interval of the parameter, dx/dt and dy/dt are the derivatives of x and y with respect to t, and √ denotes the square root.

Let's calculate the integral for the given parametric curve:

dx/dt = 1 - 4 cos(t)

dy/dt = 4 sin(t)

Now we can set up the integral for the arc length:

L = ∫[0, 4] √((1 - 4 cos(t))^2 + (4 sin(t))^2) dt

Simplifying the integrand:

L = ∫[0, 4] √(1 - 8 cos(t) + 16 cos^2(t) + 16 sin^2(t)) dt

= ∫[0, 4] √(1 - 8 cos(t) + 16) dt

= ∫[0, 4] √(17 - 8 cos(t)) dt

Therefore, the integral that represents the length of the given parametric curve is:

L = ∫[0, 4] √(17 - 8 cos(t)) dt

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Answer:

x > 2/3

Step-by-step explanation:

2x -x - 2 > 0  

add 2x and x (It becomes 3x)

3x -2 >0

subtract 0 from both sides

3x> 2

divide 3 on both sides

And the answer is

X> 2/3