If y is 6 when x is 3 and y varies directly with x, find y when x is 8.
04
16
11

We have to inscribe a  n-sided polygon inside a circle of radius 1 and compute the area of the polygon for the given values of n. We need to find out the area of square which is inscribed in a circle of radius 1.

Let's begin with part (a).When we inscribe a square of side 2r in a circle of radius r, the diagonal of the square is equal to the diameter of the circle. Therefore, the diagonal of the square is 2. Let's use the Pythagorean Theorem to find the length of one side of the square. We get:\(\[a^2+a^2=2^2\]\[2a^2=4\]\[a^2=2\]\[a=\sqrt2\]\)Now that we have found the length of one side of the square, we can find the area of the square:\(\[A=a^2\]\[A=(\sqrt2)^2\]\[A=2\]\)herefore, the area of the square inscribed in the circle of radius 1 is 2 square units. Answer: \[2\] square units.

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y(t) = 3u(t) is a constant function that is equal to 3 for t >= 0 and equal to 0 for t < 0.

The function x(t) = 3tu(t) is a product of a scalar 3 and a unit step function u(t). Here, u(t) is defined as:

u(t) = 0 for t < 0

u(t) = 1 for t >= 0

So, x(t) is equal to 3t for t >= 0 and equal to 0 for t < 0.

The function y(t) is the derivative of x(t) with respect to t. To find the derivative of x(t), we use the power rule for differentiation, which states that the derivative of tx(t) is x(t) + t × dx(t)/dt.

So, we have:

y(t) = dx(t)/dt = d(3tu(t))/dt = 3u(t) + 3tu'(t) = 3u(t)

Here, u'(t) is the derivative of u(t) with respect to t, which is equal to the Dirac delta function δ(t).

So, we have:

y(t) = 3u(t) = 3 for t >= 0

y(t) = 0 for t < 0

Hence, y(t) = 3u(t) is a constant function that is equal to 3 for t >= 0 and equal to 0 for t < 0.

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Answer:

12

Step-by-step explanation:

Area of a triangle = (1/2) * base * height

base width = 4 squares

height = 6 squares

area = (1/2) * 4 * 6 = 12

Answer:

The volume of the solid bounded by the given equations is approximately 170.67 cubic units.

Step-by-step explanation:

To find the volume of the solid, we need to set up the double integral as follows:

V = ∫∫R (x + y) dA

where R is the region in the first octant bounded by the graph of x^2 + y^2 = 64.

Converting the equation of the boundary to polar coordinates, we have:

\(r^2 = x^2 + y^2 = 64\)

so r = 8.

The limits of integration for r are 0 to 8, and for θ are 0 to π/2, since we are only interested in the first octant.

Thus, the double integral is:

V = ∫0^(π/2) ∫0^8 (r cosθ + r sinθ) r dr dθ

\(= ∫0^(π/2) ∫0^8 r^2 cosθ dr dθ + ∫0^(π/2) ∫0^8 r^2 sinθ dr dθ\)

Evaluating each integral separately, we get:

\(V = (1/3)[r^3 cosθ]0^π/2 [0^8] + (1/3)[r^3 sinθ]0^π/2 [0^8]\)

\(= (1/3)[(8^3)(1) - (0^3)(1)] + (1/3)[(8^3)(0) - (0^3)(0)]\)

= (1/3)(512) + 0

= 170.67

Therefore, the volume of the solid bounded by the given equations is approximately 170.67 cubic units.

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Since industry, land use, transportation, technology, natural resources, and other similar criteria influence economic activity, the scope of cooperation in matters of trade must be limited to national infrastructures

What group the listed items in the question belong?

The listed items, industry, land use, transportation, technology and natural resources can be regarded as national infrastructures, which are facilities that ensure smooth running of trade in a country, the more of them a nation has and can deploy efficiently, the more wealth it generate from trade.

The above analysis indicates that such factors restrict or aid the level of success a country can achieve which means it is limited  to national infrastructures

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Answer:

answer is (1) 6yd 68 meter (2) 8dy 190 meter (3) 6yd 127 meter (4) 10 yd s

The correct option is the third one; (14, 4); The vertex represents the maximum profit.

For a general quadratic equation

y = ax² + bx + c

The vertex is at the x-value:

x = -b/2a

Here the quadratic function is:

f(x)=  -x² + 28x - 192

The vertex is at:

x = -28/2*-1 = 14

Evaluating in x= 14 we get:

f(14) = -14² + 28*14 - 192 = 4

So the vertex is at (14, 4), and because the leading coefficient is negative, this is the maximum profit.

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In summary: Sequence 1 has no term out of increasing order. Sequence 2 has the first term out of increasing order at position 2. Sequence 3 has the first term out of increasing order at position 7. Sequence 4 has the first term out of increasing order at position 4. Sequence 5 has the first term out of increasing order at position 3.

1 5 78 99 101 202 400: This sequence is in increasing order throughout, so there is no term that breaks the increasing pattern.

5 2 7 90 85 80 72: The sequence starts with 5, then decreases to 2 (out of increasing order) at position 2.

5 6 9 10 14 21 20: The sequence is increasing until position 6, where it reaches 21. However, the next term, 20, is lower than the previous term, 21 (out of increasing order) at position 7.

3 7 10 9 8 14 17: The sequence starts with 3 and increases until position 3 (10). However, at position 4, the next term, 9, is lower than the previous term, 10 (out of increasing order).

5 77 25 45 22 94 58 99: The sequence is increasing until position 2, where it reaches 77. However, at position 3, the next term, 25, is lower than the previous term, 77 (out of increasing order).

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Answer:

B

Step-by-step explanation:

The mathematical constant e is approximately equal to 2.71828.

Let's evaluate each expression and see which one is closest to e.

A. (1+1/12)^12 = 1.12682503013

B. (1+1/11)^11 = 1.13314845307

C. (1+1/13)^13 = 1.11916664569

D. (1+1/14)^14 = 1.11594725281

Out of these options, option B is the closest to e, with a value of 1.13314845307

Answer:

4.5

Step-by-step explanation:

first you divide 36 from 8

then to check if its right then do 4.5 times 8

Answer:

375

425

.......................

Answer:

The correct answer is 375 and 425.

Step-by-step explanation:

Hope this helps:) Goodluck!

Step-by-step explanation:

Not sure ...it probably means  'measure'   ( like in geometry or trig)

   but in a different context like physics it means 'mass/

Confidence interval = (y ± t∗s/√n)g1 = y - t*s/√ng2 = y + t*s/√n Substituting the values, g1 = 26.22 - 1.860*(0.11)/√9 = 25.84g2 = 26.22 + 1.860*(0.11)/√9 = 26.59Therefore, the statistics g1 and g2 that will satisfy the required inequality are 25.84 and 26.59 respectively.

The formula for finding the confidence interval is as follows: n − 1, where t is the value of the t-distribution corresponding to the specified confidence level and the sample size minus one.

As per the given exercise 7.11, suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample.

If a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that p(g1 ≤ (y - u) ≤ g2) = 90

To find the statistics g1 and g2 that will satisfy the required inequality

the following formula can be used: Confidence interval = \((y ± t∗s/√n)\)

From the formula, we can see that the confidence interval depends on the values of y, s, t and n.

The value of y is the sample mean

the value of s is the sample standard deviation

And the value of n is the sample size.

The value of t depends on the confidence level desired and the degrees of freedom for the t-distribution. In this case, the confidence level is 90%, which means that we want to find the value of t that will give us a total area of 0.90 under the t-distribution curve with 8 degrees of freedom .Using the t-table, the value of t can be found to be 1.860, where the value for 90% and 8 degrees of freedom is 1.860.t = 1.860Now, we need to calculate the value of s, which is the sample standard deviation.

Since we do not have any information about the population standard deviation, we will use the sample standard deviation as an estimate of the population standard deviations = σ/√nσ = s*√nσ = 0.11*√9σ = 0.33Substituting the values in the confidence interval formula

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The required answers are:

1) The center of the circle = (4, 8)

2) The radius of the circle = 2.5 units

3) The equation of the circle = (x - 4)² + (y - 8)² = 6.25

The equation of the circle which has a center at (h, k) and a radius of 'r' units is (x - h)² + (y - k)² = r²

To calculate radius 'r', we have r = sqrt( (x1 - h)² + (y1 - k)²)

Where (x1, y1) is the point that lies on the circle.

Given that,

The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5)

We know that the longest chord on a circle is nothing but the diameter of the circle.

So, the center is the midpoint of the diameter. I.e.,

(h, k) = (\(\frac{4+4}{2}\), \(\frac{5.5+10.5}{2}\))

⇒ (h, k) = (4, 8)

Therefore, the center of the circle is (4, 8)

Then, the radius is calculated by

r = sqrt( (x1 - h)² + (y1 - k)²)

⇒ r = \(\sqrt{(4-4)^2+(5.5-8)^2}\)

⇒ r = 2.5 units

Thus, the radius of the circle is 2.5 units.

So, the equation of the circle with center (4, 8) and radius of 2.5 units is,

(x - h)² + (y - k)² = r²

⇒ (x - 4)² + (y - 8)² = 2.5²

⇒ (x - 4)² + (y - 8)² = 6.25

Thus, the equation of the circle is x - 4)² + (y - 8)² = 6.25.

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Answer:

it would b 2 in half cups of powder

Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

\(x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6\)

Answer:

3210

Step-by-step explanation:

3.21 x 10000 = 3210

Answer:

a) 1/10

b) 1/2

c) 1/2

d) 2/5

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = Total event/Total sample space

Since there are ten ball in the bag numbered 1 to 10

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

n(S) = 10

Total sample space = 10

a) If we are to get the probability of picking the number 7.

(E) = {7}

n(E) = 1

Event = 1

Pr(picking 7) = 1/10

b) a) If we are to get the probability of picking an odd number

(E) = {1, 3, 5, 7 , 9}

n(E) = 5

Event = 5

Pr(an odd number) = 5/10 = 1/2

c) a) If we are to get the probability of picking an even number

(E) = {2, 4, 6, 8,10}

n(E) = 5

Event = 5

Pr(an even number) = 5/10 = 1/2

d) a) If we are to get the probability of picking prime

(E) = {2, 3, 5, 7}

n(E) = 4

Event = 4

Pr(prime) = 4/10 = 2/5

Answer:

\(y=\frac{1}{2} x-\frac{5}{2}\)

Step-by-step explanation:

Hi there!

Note that:

1) Determine the slope (m)

When we look at the given line, \(y=-2x-1\), we can identify that -2 is in the place of m, the slope of the line. Because perpendicular lines are negative reciprocals of each other, we know that a line perpendicular to this would have a slope of \(\frac{1}{2}\). Plug this into \(y=mx+b\):

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

2) Determine the y-intercept (b)

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

Plug in the given point (1,-2)

\(-2=\frac{1}{2}(1)+b\\-2=\frac{1}{2}+b\)

Subtract 1/2 from both sides

\(-2-\frac{1}{2}=\frac{1}{2}+b-\frac{1}{2}\\-\frac{5}{2} = b\)

Therefore, the y-intercept of the line is \(-\frac{5}{2}\). Plug this back into \(y=\frac{1}{2} x+b\)

\(y=\frac{1}{2} x-\frac{5}{2}\)

I hope this helps!

Answer:

$13286.02

Step-by-step explanation:

100 + 8 = 108

108 / 100 = 1.08

6154 x \(1.08^{10}\) = $13286.02

Answer:

Step-by-step explanation:

Since it doesn't specify the interest type, we'll consider both simple and compound interests.

Given:

Simple interest:

Compound interest (compounded annually):

Answer:

Angle a=92, angle c=88, angle b=100, angle d=80

Step-by-step explanation:

The domain and the range of an exponential parent function, that is, y = eˣ are equal to all real numbers and non-negative numbers, respectively. (Correct choice: C)

In this problem we should determine what an exponential parent function is. The most common exponential functions have the following form:

\(y = A\cdot e^{B\cdot x} + C\)     (1)

(1) is an exponential parent function for A = 1, B = 1 and C = 0.

All functions are relations with a domain and range, the domain is an input set related to the range, that is, an output set. In the case of an exponential parent function, the domain and the range of the expression are \(\mathbb{R}\) and y ≥ 0, respectively. (Correct choice: C)

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According to the Question we have the objective function in terms of y is q=484/y.

If the objective function is q=x^2 y and we know that xy=22, we can write the objective function in terms of x by solving for y in the equation xy=22. We can do this by dividing both sides by x:

y = 22/x

Now we can substitute this expression for y into the objective function:

q = x^2(22/x)

Simplifying this, we get:

q = 22x

So the objective function in terms of x is q=22x.

To write the objective function in terms of y, we can again use the equation xy=22, but solve for x this time. We can do this by dividing both sides by y:

x = 22/y

Now we can substitute this expression for x into the objective function:

q = (22/y)^2 y

Simplifying this, we get:

q = 484/y

So the objective function in terms of y is q=484/y.

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Answer:

x=2, y=1. (2, 1).

Step-by-step explanation:

x+3y=5

-x+6y=4

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

9y=9

y=9/9=1

x+3(1)=5

x+3=5

x=5-3=2

Answer:

x=2

y=1

Step-by-step explanation:

Using Laplace transform to solve for x(t) in

\(x(t) = cos(t) + \int_0^t e^{\lambda-t} x(\lambda) d\lambda\) gives \(X_{int(s)} = X(s) \times (1 / (s - 1)).\)

To solve the given integral equation using the Laplace transform, we first take the Laplace transform of both sides of the equation.

Let X(s) be the Laplace transform of x(t), where s is the complex frequency variable. The Laplace transform of x(t) is defined as X(s) = L{x(t)}.

Taking the Laplace transform of the given equation, we have:

\(L{x(t)} = L{cos(t)} + L{\int_0^t e^{\lambda-t} x(\lambda) d\lambda}\)

Using the linearity property of the Laplace transform, we can split the equation into two parts:

\(X(s) = X_{cos(s)} + X_{int(s)},\)

where \(X_{cos(s)}\) is the Laplace transform of cos(t) and \(X_{int(s)}\) is the Laplace transform of the integral term.

The Laplace transform of cos(t) is given by:

Lcos(t) = s / (s² + 1).

For the integral term, we can use the convolution property of the Laplace transform. Let's denote X(s) = L{x(t)} and \(X_{int(s)} = L{\int_0^t e^{\lambda-t} x(\lambda) d\lambda}\) . Then, the convolution property states that:

\(L{\int_0^t e^{\lambda-t} x(\lambda) d\lambda} = X(s) * L{e^{\lambda - t}},\)

where * denotes convolution.

The Laplace transform of \(e^{\lambda - t}\) is given by:

\(L{e^{\lambda - t}} = 1 / (s - 1).\)

Therefore, we have: \(X_{int(s)} = X(s) \times (1 / (s - 1)).\)

To solve for X(s), we can substitute these results back into the equation \(X(s) = X_{cos(s)} + X_{int(s)}\)and solve for X(s). Finally, we can take the inverse Laplace transform of X(s) to obtain the solution x(t) to the integral equation.

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Complete Question:

Use Laplace transform to solve for x(t) in

\(x(t) = cos(t) + \int_0^t e^{\lambda-t} x(\lambda) d\lambda\)

The trapezoidal rule is a numerical integration method that frequently overestimates the real value of a function's definite integral.

The trapezoidal rule is a strategy for approximating the definite integral in calculus. The trapezoidal rule works by computing the area of the region under the graph of the function f(x) that is approximated as a trapezoid. The trapezoidal rule is commonly used to calculate the area under curves. This is achievable if the overall area is divided into smaller trapezoids rather than rectangles. The Trapezoidal Rule integration determines the area by approximating the area under a function's graph as a trapezoid. The midway rule uses rectangular areas to approximate the definite integral, whereas the trapezoidal rule uses trapezoidal approximations to approximate the definite integral. Simpson's approach works by first approximating the original function with piecewise quadratic functions.

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Complete question:

The trapezoidal rule is a numerical integration method that frequently overestimates the real value of a function's definite integral. True/False

Answer: yes

Step-by-step explanation: i just did 450 / 5, 9, and 10

Answer:

2√6

Step-by-step explanation:

find the hypotenuse of the triangle thats 3 and 7

pythagorean

3 squared + 7 squared

16 + 49 = 57

√57 is the hypotenuse

√57 is also the base of the triangle that has side thats 9

pythagorean theorem

x squared + √57 squared = 9 squared

x^2 + 57 = 81

x^2 = 81 - 57

x^2 = 24

x = √24

x = √4 * √6

x = 2√6

Answer:

The weight : 9 pound

Lamar would pay for his dinner : $71

Step-by-step explanation:

Let x represent the weight of the lobster

the cost of the dinner at restaurant 1 is 4x + 35  

the cost of the dinner at restaurant 2 is 3x + 44

Now ,we have to solve the equation :  

4x + 35 = 3x + 44

-3x - 35   -3x  - 35    -> trying to get all x terms on one side. other just #

4x - 3x = 44 - 35

⇔ 1x = 9

⇔ x = 9

In this case Lamar would pay the same amount for his dinner at any restaurant:

the price = 4×(9)+35 = 71

               = 3×(9)+44 = 71.

Hope this helps, Let me know if you have any question/concerns !

Have a nice rest of your day :)