The figure below shows a sphere with its center at O. The points A, B, C, and D are on the
surface of the sphere.
How many tangents to the sphere have been shown in the figure?
A. 0
B. 1
C. 2
(D. 3

The calculated measure of angle y is 60 degrees

from the question, we have the following parameters that can be used in our computation:

The figure

From the figure, we can see that

The shape can be divided into two triangles such that

Each triangle is an equilateral triangle

The measure of an angle in an equilateral triangle is 60 degrees

using the above as a guide, we have the following:

y = 60

Hence, the value of y is 60 degrees

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The cost price of an article is Rs.600 and the profit of dealer is Rs.200

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given;

An article marked at Rs.800 sold at a discount of 10%.

That means,

selling price = 800 - 10% 0f 800

                 =  800 - (10 x 800 / 100)

                 = 800 - 80

                 = 720

The dealer makes a profit of 20% means is selling the article at 120%.

120%=720

1%=6

Hence, 100% = 600

Thus, the cost price of article = 600

Profit= SP-CP = 800-600 = 200

Therefore, Rs.600 is the cost price and the profit is Rs.200

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Answer: 224

Step-by-step explanation:

Answer:

224

Step-by-step explanation:

i did it myself

Chase can create apprοximately 105 villagers tο live in his 17th tοwn.

We can use the expοnential grοwth fοrmula tο create an equatiοn tο predict the number οf villagers in any specific tοwn. The general fοrmula fοr expοnential grοwth is:

\(y = a * r^x\)

where:

y is the value we want tο predict (in this case, the number οf villagers)

a is the initial value (in this case, the starting number οf villagers)

r is the grοwth rate (in this case, 1.13, since each tοwn creates 1.13 times as many villagers as the οne befοre)

x is the number οf times the grοwth rate is applied (in this case, the number οf tοwns)

We can use this fοrmula tο predict the number οf villagers in any specific tοwn fοr Chase's situatiοn. Since Chase started with 4 villagers, we can plug in a = 4, and since the grοwth rate is 1.13 (οr 113% increase), we can plug in r = 1.13. Tο predict the number οf villagers in the 17th tοwn, we can plug in x = 17. Sο the equatiοn tο predict the number οf villagers in any specific tοwn is:

\(y = 4 * 1.13^x\)

Tο find the number οf villagers in the 17th tοwn, we can plug x = 17 intο this equatiοn and sοlve fοr y:

\(y = 4 * 1.13^{17\)

y ≈ 105.3

Therefοre, Chase can create apprοximately 105 villagers tο live in his 17th tοwn.

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Answer:

y = 11

Step-by-step explanation:

It is just an equation with one variable ( 'y') which you can solve

-7y + 2 = - 75     subtract 2 from both sides of the equation

-7y = -77             divide both sides by -7

y = 11  

Answer:

-7y+2=-75

-7y=-75-2

-7y=-77

y=11

The limit of sums method can be used to determine the area of the region enclosed by the x-axis, the lines x = -3 and x = 0, and the function y = f(x) = (x+3)2.

We create narrow subintervals of width x within the range [-3, 0] on the x-axis. Suppose there are n subintervals, in which case x = (0 - (-3))/n = 3/n.

We can approximate the area under the curve using rectangles within each subinterval. Each rectangle has a width of x and a height determined by the function f(x).

Each rectangle has an area of f(x) * x = (x+3)2 * (3/n).

As n approaches infinity, we take the limit and add the areas of all the rectangles to determine the total area:

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False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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The very low likelihood that there will be 45 or more people in the sample who have consumed alcoholic beverages.

a) The number of people in the sample expected to have consumed alcoholic beverages can be calculated as follows:First, we multiply the number of individuals in the sample by the proportion of people in that age group who drink alcohol.50 x 0.697 = 34.85Thus, we anticipate that about 34.85 people in the sample will have consumed alcoholic beverages.b) No, 45 or more accounts for six different events -- this wouldn't be surprising, you would not be surprised if the sample contained 45 or more people who have consumed alcoholic beverages. This is because it falls within the margin of error.c) To calculate the probability that 45 or more people in this sample have consumed alcoholic beverages, we will need to compute the z-score first.We use the following formula to calculate the z-score:$$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$$Where, x = 45μ = 0.697 x 50 = 34.85σ = √[(50 x 0.697 x 0.303)] = 3.77n = 50After plugging the values into the formula, we have:$$z=\frac{45-34.85}{\frac{3.77}{\sqrt{50}}}$$ = 3.89Since we are trying to determine the probability of having 45 or more people who have consumed alcoholic beverages, we will calculate the probability of having a z-score greater than or equal to 3.89.Instead of looking up the z-score in the z-table, we can use a calculator to determine the probability. From a standard normal distribution, the calculator provides the following output:P(Z ≥ 3.89) = 0.0000317Rounded to four decimal places, the probability is approximately 0.0000. Therefore, there is a very low likelihood that there will be 45 or more people in the sample who have consumed alcoholic beverages.

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The slope of the table is 2

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

to determine the slope:

From the table, we have the following points:

(x,y) = (0, 4) and (1,7)

The slope is then calculated as:

m = (y2 - y1)/(x2 - x1)

Substitute known values

m = (7 - 4)/(1 - 0)

Evaluate the differences

m = 3/1

Divide

m = 2

Hence, the slope of the table is 2

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Answer:

D.

Step-by-step explanation:

Answer: 1 1/3

Step-by-step explanation: slope is the difference in y values over the difference in the c values

Answer:

\( m = \frac{14 - 2}{19 - 10} \\ \frac{12}{9} \\ m = \frac{4}{3} \)

the slop is equal to 4/3

The minimal point does not have x = 0.

(a) Kuhn-Tucker conditions for the minimal value of fThe Kuhn-Tucker conditions are a set of necessary conditions for a point x* to be a minimum of a constrained optimization problem subject to inequality constraints. These conditions provide a way to find the optimal values of x1, x2, ..., xn that maximize or minimize a function f subject to a set of constraints. Let's first write down the Lagrangian: L(x, y, λ1, λ2, λ3) = f(x, y) - λ1(x+y-1) - λ2(xy-3) - λ3x - λ4y Where λ1, λ2, λ3, and λ4 are the Kuhn-Tucker multipliers associated with the constraints. Taking partial derivatives of L with respect to x, y, λ1, λ2, λ3, and λ4 and setting them equal to 0, we get the following set of equations: 4x - 2y - λ1 - λ2y - λ3 = 0 2y - 2x - λ1 - λ2x - λ4 = 0 x + y - 1 ≤ 0 xy - 3 ≤ 0 λ1 ≥ 0 λ2 ≥ 0 λ3 ≥ 0 λ4 ≥ 0 λ1(x + y - 1) = 0 λ2(xy - 3) = 0 From the complementary slackness condition, λ1(x + y - 1) = 0 and λ2(xy - 3) = 0. This implies that either λ1 = 0 or x + y - 1 = 0, and either λ2 = 0 or xy - 3 = 0. If λ1 > 0 and λ2 > 0, then x + y - 1 = 0 and xy - 3 = 0. If λ1 > 0 and λ2 = 0, then x + y - 1 = 0. If λ1 = 0 and λ2 > 0, then xy - 3 = 0. We now consider each case separately. Case 1: λ1 > 0 and λ2 > 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have the following possibilities: x + y - 1 = 0, xy - 3 ≤ 0 (i.e., xy = 3), λ1 > 0, λ2 > 0 x + y - 1 ≤ 0, xy - 3 = 0 (i.e., x = 3/y), λ1 > 0, λ2 > 0 x + y - 1 = 0, xy - 3 = 0 (i.e., x = y = √3), λ1 > 0, λ2 > 0 We can exclude the second case because it violates the constraint x, y ≥ 0. The first and third cases satisfy all the Kuhn-Tucker conditions, and we can check that they correspond to local minima of f subject to the constraints. For the first case, we have x = y = √3/2 and f(x, y) = -1/2. For the third case, we have x = y = √3 and f(x, y) = -2. Case 2: λ1 > 0 and λ2 = 0From λ1(x + y - 1) = 0, we have x + y - 1 = 0 (because λ1 > 0). From the first Kuhn-Tucker condition, we have 4x - 2y - λ1 = λ1y. Since λ1 > 0, we can solve for y to get y = (4x - λ1)/(2 + λ1). Substituting this into the constraint x + y - 1 = 0, we get x + (4x - λ1)/(2 + λ1) - 1 = 0. Solving for x, we get x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4. We can check that this satisfies all the Kuhn-Tucker conditions for λ1 > 0, and we can also check that it corresponds to a local minimum of f subject to the constraints. For this value of x, we have y = (4x - λ1)/(2 + λ1), and we can compute f(x, y) = -3/4 + (5λ1^2 + 4λ1 + 1)/(2(2 + λ1)^2). Case 3: λ1 = 0 and λ2 > 0From λ2(xy - 3) = 0, we have xy - 3 = 0 (because λ2 > 0). Substituting this into the constraint x + y - 1 ≥ 0, we get x + (3/x) - 1 ≥ 0. This implies that x^2 + (3 - x) - x ≥ 0, or equivalently, x^2 - x + 3 ≥ 0. The discriminant of this quadratic is negative, so it has no real roots. Therefore, there are no feasible solutions in this case. Case 4: λ1 = 0 and λ2 = 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have x + y - 1 ≤ 0 and xy - 3 ≤ 0. This implies that x, y > 0, and we can use the first and second Kuhn-Tucker conditions to get 4x - 2y = 0 2y - 2x = 0 x + y - 1 = 0 xy - 3 = 0 Solving these equations, we get x = y = √3 and f(x, y) = -2. (b) Show that the minimal point does not have x=0.To show that the minimal point does not have x=0, we need to find the optimal value of x that minimizes f subject to the constraints and show that x > 0. From the Kuhn-Tucker conditions, we know that the optimal value of x satisfies one of the following conditions: x = y = √3/2 (λ1 > 0, λ2 > 0) x = √3 (λ1 > 0, λ2 > 0) x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4 (λ1 > 0, λ2 = 0) If x = y = √3/2, then x > 0. If x = √3, then x > 0. If x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4, then x > 0 because λ1 ≥ 0.

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r = 2

Area = πr^2

= π2^2

= π4

= 12.566370

The area of the circle is 12.57 units squared.

Answer:

The radius is 8

Step-by-step explanation:

Square the radius of the circle and multiply the result by "pi" (the symbol π), or approximately 3.14. Multiply this result by the cylinder's height to get its volume. So if the base of your cylinder has a radius of 3 cm, its area is 32 × 3.14, or 28.26 square centimetres..

The exchange rate of the euro/pound expressed to four decimal places is 1.0100 euro/pound.

To find the exchange rate of the euro/pound, we can use the given exchange rates of dollar/pound and dollar/euro.

Let's denote the exchange rate of euro/pound as E.

Given:

Exchange rate of dollar/pound = 1.21 dollar/pound

Exchange rate of dollar/euro = 1.22 dollar/euro

To find the exchange rate of euro/pound, we can divide the exchange rate of dollar/euro by the exchange rate of dollar/pound:

E = (Exchange rate of dollar/euro) / (Exchange rate of dollar/pound)

E = 1.22 dollar/euro / 1.21 dollar/pound

Simplifying this expression, we get:

E = 1.01 euro/pound

Therefore, the exchange rate of the euro/pound, is 1.0100 euro/pound.

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Answer:

complementary angles

Step-by-step explanation:

The sum of the angles is 67+23 = 90

When angles sum together to 90, the are called complementary

Answer:

Option A

Step-by-step explanation:

The measures of the two angles have a sum of 90°.

\(67+23=90\)

Therefore, they are complementary angles, since complementary angles have a total measure of 90°.

Option A is the best answer.

Brainilest Appreciated.

Answer: 2

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

Step-by-step on how to solve it is in the image below.

Hope this helps! :)

The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
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The closed-form solution for the given recurrence relation t(n) = t(n-1) * 3 with the base case t(0) = 1 is:

t(n) = 3^n


1. Start with the given recurrence relation: t(n) = t(n-1) * 3
2. Notice that the base case is t(0) = 1
3. We can rewrite the relation for a few terms to recognize the pattern:

  t(1) = t(0) * 3 = 3^1
  t(2) = t(1) * 3 = (3^1) * 3 = 3^2
  t(3) = t(2) * 3 = (3^2) * 3 = 3^3

4. Based on this pattern, we can generalize the closed-form solution as t(n) = 3^n


The closed-form solution for the given recurrence relation t(n) = t(n-1) * 3 with the base case t(0) = 1 is t(n) = 3^n.

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Answer:

n = number of nickels = 7

d = number of dimes = 10

p = number of pennies = 20

Step-by-step explanation:

Let

n = number of nickels

d = number of dimes

p = number of pennies.

n + d + p = 37

0.05n + 0.10d + 0.01p = 1.55

p = 2d

Substitute p = 2d into the equation

n + d + 2d = 37

0.05n + 0.10d + 0.01(2d) = 1.55

n + 3d = 37

0.05n + 0.10d + 0.02d = 1.55

n + 3d = 37 (1)

0.05n + 0.12d = 1.55 (2)

Multiply (1) by 0.05

0.05n + 0.15d = 1.85

0.05n + 0.12p = 1.55

Subtract

0.15d - 0.12d = 1.85 - 1.55

0.03d = 0.3

d = 0.3/0.03

= 10

d = 10

p = 2d

= 2(10)

p = 20

n + d + p = 37

n + 10 + 20 = 37

n + 30 = 37

n = 37 - 30

n = 7

n = number of nickels = 7

d = number of dimes = 10

p = number of pennies = 20

Given:

The area of a semicircle is 0.7693 square centimeters.

Explanation:

To find the radius:

Using the area of a semicircle formula,

Thus, the radius of the semicircle is 0.7 cm.

Answer:

3x - 6

Step-by-step explanation:

5x -(6+2x)

= 5x -6 -2x

= 5x - 2x - 6

=3x -6

Answer:

B , C and d are true because thsimilarey are

Answer:

Simplify the expression.

58

Step-by-step explanation:

Answer: 1/2 f(to the exponent of 2)

Step-by-step explanation: 4f8/8f10=1/2f2

Answer:

64

Step-by-step explanation:

(x-8)^2

derived from the middle term divided by 2

Answer:

64

Step-by-step explanation:

x^2 − 16x + ___

Complete the square

Take the coefficient of the x term

-16

Divide by 2

-16/2 = -8

Then square it

(-8)^2 = 64

Answer:

0.5 or 1/2

Step-by-step explanation:

so we make 6/8 have the same denominator as 1/4 (but if you want to make it harder sure make 1/4 have the same denominator loll)

6/8 = 3/4

3/4 - 1/4 = 2/4 = 1/2

Answer:

0.5 or 1/2

Step-by-step explanation:

hope this he's you

The lengths of the diagonals are:

GE = 8√5 units

DE = 4√5 Units

Area = 80 sq. units

We have been given an image of a kite on coordinate plane.

To find the length of GE we will use distance formula:

Distance = √[x₂ - x₁)² + (y₂ - y₁)²]

Substituting coordinates of point G and E in above formula we will get,  

GE = √[16 - 0)² + (8 - 0)²]

GE = √(256 + 64)

GE = √320

GE = 8√5 units

Similarly we will find the length of diagonal DF using distance formula.

DF = √[14 - 10)² + (2 - 10)²]

DE = √(16 + 64)

DE = √80

DE = 4√5 Units

Area of kite is given by the formula:

Area = (p * q)/2

where p and q are diagonals of kite.

Thus:

Area = ( 8√5 *  4√5)/2

Area = 80 sq. units

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1. \(Given that c(0) = (1, 1, 2) and c'(t) = (3t², 2t, 4).\)Find c(1)\(We are given that c'(t) = (3t², 2t, 4)\)Integrating both sides w.r.t t, \(we getc(t) = (t³ + C1, t² + C2, 4t + C3)Where C1, C2, and C3 are constants of integration.\)

\(To find these constants, we use the initial condition c(0) = (1, 1, 2)\)

\(Here's how:Given that c(0) = (1, 1, 2)Therefore,C1 = 1, C2 = 1, and C3 = 2\)

\(Therefore,c(t) = (t³ + 1, t² + 1, 4t + 2)\)

\(Hence, c(1) = (1³ + 1, 1² + 1, 4×1 + 2)= (2, 2, 6)Ans: c(1) = (2, 2, 6)2.\)

\(We are given that c(1) = (1,5, 3) and c'(1) = (3, 0, 0). Compute (c(t) || ²)|t-1. dt\)

We are to find the length of the curve in the neighborhood of t = 1. i.e., we need to find the length of a curve from a point just to the left of t = 1 to a point just to the right of t = 1.

\(We know that the length of a curve, c(t), from t = a to t = b is given by:L = ∫a^b ( ||c'(t)|| ) dt\)

\(Given that c(1) = (1,5, 3) and c'(1) = (3, 0, 0).\)

Therefore, the curve passes through the point (1,5, 3) at t = 1 and the tangent vector at this point is (3, 0, 0).

Now we need to find the length of the curve near this point.

\(We can write c(t) as follows: c(t) = (x(t), y(t), z(t)).\)

\(Using the derivative c'(t) = (3, 0, 0) and integrating w.r.t t, we get: x(t) = 3(t - 1) + 1, y(t) = 5 and z(t) = 3\)

\(Therefore,c(t) = (3t - 2, 5, 3)Now, ||c'(t)|| = √(3² + 0² + 0²) = 3\)

Therefore,L = ∫(c(t) || ²)|t-1. dt= ∫0¹ (3²)dt= 9[1 - 0]= 9

\(Hence, the length of the curve near the point (1,5, 3) is 9.\)

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Here are the solutions to the given problems.1. Given:

The position vector c(t) is c(t) = (1, 1, 2) + ∫(0 to t) c'(t) dt = (1, 1, 2) + ∫(0 to t) (3t², 2t, 4) dt

To find: c(1).Solution:

we will integrate each component of c'(t) with respect to t.∫3t² dt = t³∫2t dt = t²∫4 dt = 4t

Now, we have∫(0 to t) c'(t) dt = (t³, t², 4t)

Putting the limits of integration,

we getc(t) = (1, 1, 2) + (1³, 1², 4(1)) - (0³, 0², 4(0)) = (2, 2, 6)Therefore, c(1) = (2, 2, 6)

Answer: The required position vector is c(1) = (2, 2, 6).

2. Given: c(1) = (1,5, 3) and c'(1) = (3, 0, 0).

To Find: (c(t)||²)|t-1. dt

Solution: We can use the formula: ||c'(t)||² = c' .

c'.Differentiating c(t) and using the given data, we have:c(t) = ∫ c'(t) dt + C

Where C is the constant of integration.

Now, c(1) = (1,5, 3). So, we can write∫ c'(t) dt + C = (1,5, 3)or, ∫ c'(t) dt = (1,5, 3) - C

Also, we have c'(1) = (3, 0, 0).

sing this, we can write:c'(t) = c'(1) + ∫(1 to t) c''(t) dt

Differentiating c'(t), we getc''(t) = (3, 0, 0).

Hence,c'(t) = (3, 0, 0) + ∫(1 to t) (3, 0, 0) dt = (3t, 0, 0)

Putting t = 1, we havec'(1) = (3, 0, 0) = c'(t).

Therefore, we can write:||c'(t)||² = c' . c' = 3² + 0² + 0² = 9

Now, using the given formula, we have:(c(t)||²)|t-1. dt = ∫||c'(t)||² dt = ∫9 dt = 9t + K

where K is the constant of integration.

Putting the limits of integration, we get:(c(t)||²)|t-1. dt = [9t]1 to t = t - 9

Answer: (c(t)||²)|t-1. dt = t - 9.

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