find an equation for each sphere that passes through the point (5, 1, 4) and is tangent to all three coordinate planes

Answer:

Step-by-step explanation:

slope= y2-y1/x2-x1 ---->  3-2/1-3 ----> 1/-2 ----> slope=-1/2

slope intercept form is y=mx+b. (b is the y-intercept, and m is the slope.)

y=-1/2x+b

we need to find b so you plug in one of the points and isolate b.

3=-1/2(1)+b

+1/2 on both sides to move it over.

3.5=b

FULL EQN: y=-1.2x+3.5

The terminal point determined by t on the unit circle is given by (cos(t), sin(t)).

The terminal point determined by -t:

The point determined by -t is given by (cos(-t), sin(-t)). By the identity sin(-t) = -sin(t), and cos(-t) = cos(t), the terminal point determined by -t is (cos(t), -sin(t)).

The terminal point determined by t + 4π:

The point determined by t + 4π is given by (cos(t + 4π), sin(t + 4π)). By the identity sin(t + 2π) = sin(t) and cos(t + 2π) = cos(t), the terminal point determined by t + 4π is (cos(t), sin(t)).

The terminal point determined by t - π:

The point determined by t - π is given by (cos(t - π), sin(t - π)). By the identity sin(t - π) = -sin(t) and cos(t - π) = -cos(t), the terminal point determined by t - π is (-cos(t), -sin(t)).

The terminal point determined by t + π:

The point determined by t + π is given by (cos(t + π), sin(t + π)). By the identity sin(t + π) = -sin(t) and cos(t + π) = -cos(t), the terminal point determined by t + π is (-cos(t), sin(t)).

The terminal point determined by π - t:

The point determined by π - t is given by (cos(π - t), sin(π - t)). By the identity sin(π - t) = sin(t) and cos(π - t) = -cos(t), the terminal point determined by π - t is (-cos(t), sin(t)).

If the terminal point determined by t is (-3/5, 4/5), then:

The terminal point determined by -t is (3/5, -4/5).

The terminal point determined by t + 4π is (-3/5, 4/5).

The terminal point determined by t - π is (3/5, -4/5).

The terminal point determined by t + π is (3/5, -4/5).

The terminal point determined by π - t is (3/5, -4/5).

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The circuit starts at the final AND gate. It has two inputs, one from an OR gate and one from a NOT gate.

The OR gate has two inputs, p and q. If either p or q is high (1), the OR gate will output a high signal. If both p and q are low (0), the OR gate will output a low signal. In this case, we only have the value of p, which is high, so the output from the OR gate is also high.

The NOT gate has one input, q. It inverts the signal, so if q is high (1), the NOT gate will output a low signal (0), and if q is low (0), the NOT gate will output a high signal (1). We don't know the value of q, so we don't know the output from the NOT gate.

Finally, the AND gate takes the outputs from the OR gate and the NOT gate as its inputs. If both inputs are high (1), the AND gate will output a high signal (1). If either input is low (0), the AND gate will output a low signal (0). Since we don't know the output from the NOT gate, we can't determine the output from the AND gate.

So, to summarize, without knowing the value of q, we can't determine the output from the final AND gate.

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The object traveled 300 ft in 15 seconds.

The problem can be solved using precalculus. The distance traveled in 15 seconds can be calculated using the formula d = rt, where d is the distance traveled, r is the rate of speed, and t is the time. In this case, d = 20 ft/sec * 15 sec = 300 ft. Therefore, the object traveled 300 ft in 15 seconds. To calculate this using a graphical approach, we can plot the points (0,0) and (15,300) on a graph. The slope of the line connecting the two points is 20 ft/sec, which is the rate of speed of the object. This confirms that the object traveled 300 ft in 15 seconds.

The object traveled 300 ft in 15 seconds.

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Answer: 19-20 people

Step-by-step explanation:

I turned 26% into a decimal which is .26 then multiplied it by 76.

Answer:

The probability of a family having 0 teenagers with an Apple device can be calculated as (0.26)^0 * (0.74)^2 = 0.5356.

The probability of a family having 1 teenager with an Apple device can be calculated as 2 * (0.26) * (0.74)^1 * (0.74)^1 = 0.4428.

The probability of a family having 2 teenagers with an Apple device can be calculated as (0.26)^2 * (0.74)^0 = 0.0676.

Therefore, the probability of a family having 0, 1, or 2 teenagers with an Apple device can be calculated as 0.5356 + 0.4428 + 0.0676 = 1.0.

Answer:

x² -  4 = 0

4x² = 16

Step-by-step explanation:

x² -  4 = 0 can be rewritten as
x² = 4

x = ± √4

x = ± 2

So this gives two solutions for x => x = 2 and x = -2

4x² = 16

Divide by 4 both sides

x² = 16/4

x² = 4

which is the same as above

x = ± 2

The value of the cash flows four years from today is $22,609.26.

The value of a set of cash flows can be calculated using the present value of an annuity formula. This formula takes into account the time value of money, which states that money has a different value at different points in time due to the opportunity cost of the money. In other words, the money you have today is more valuable than the money you will have in the future.

The present value of an annuity formula is PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of periods. In this example, the cash flows are $3,000, $4,040, $5,885, and $7,975, the interest rate is 5.4%, and the number of periods is 4. Plugging these numbers into the formula, the present value is $22,609.26. This is the value of the cash flows four years from today.

The value of the cash flows four years from today is $22,609.26.

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The distance between the points (−3, −5) and (9, −5) is the difference in the absolute value of the x-coordinates.

What are coordinates?

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

Given points are (−3, −5) and (9, −5).

The separation between two points, if the coordinate points are in the same quadrant, is equal to the difference between the larger absolute value and the smaller absolute value of the coordinates.

The distance between the two points is

|9| + |-3|

= 12

Since the x-coordinate of (−3, −5) is negative.

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Answer:

The 1. is sufficiently tangent

The 2. is not tangent

Step-by-step explanation:

The solution that each system of equations have would be = 2 solutions of the value of X and y.

The substitution method of solving an equation is defined as the way of solving an equation whereby one variable is solved and is substituted into the second unknown variable.

For the above sets of equations, the solutions would be the value of both X and y which can be solved as follows:

4x-y = 2 ---->. equation 1

16x-4y = 8 -----> equation 2

Make y the subject of formula in equation 1

y = 2-4x

substitute y = 2-4x into y in equation 2

16x - 4( 2-4x) =8

16x - 8 + 16x = 8

32x = 16

X = 16/32

X= 0.5

Substitute 0.5 = X in equation 1;

4(0.5) - y = 2

y = 2-2

y = 0

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FALSE: Finding non-linear correlations between two variables cannot be done using regression.

To determine the association between two quantitative variables, simple linear regression is performed. Simple linear regression can be used to determine:

Regression analysis is a mathematical technique for creating predictive models in which one or more existing independent or explanatory factors influence an unknown target variable.

The determination coefficient value serves as a measure of a regression model's fitness.

Thus, finding non-linear correlations between two variables cannot be done using regression is a incorrect statement.

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The complete question is-

Determine if the following statement is true or false:

Regression cannot be used to identify non-linear relationships between two variables.

The sum of the measures of the angles in a triangle is 180 degrees, so we have the equation:

m angle Q + m angle R + m angle T = 180

94 + 42 + 71 = 207

The sum of the measures of the angles in the triangle is greater than 180 degrees, so this is not a valid triangle.

Without further information, it is not possible to determine the scale factor from PQRS to TUVW. A scale factor refers to the ratio of corresponding side lengths between two similar figures. In order to find the scale factor, you would need to know the lengths of corresponding sides in the two figures.

can't find x rn

Answer:

  B. Angles 26°, 64°, 90°, hypotenuse 74

Step-by-step explanation:

You want to know which combinations of dimensions form a scalene right triangle.

A right triangle has one angle that is 90°. (Eliminates choices C and D.)

All side lengths and angles are different from each other in a scalene triangle. (Eliminates choice A.)

Sides 32, 67, and 74 cm, and angles 26°, 64°, 90° will form a scalene right triangle.

__

Additional comment

If more than one side is specified along with two or more angles, the triangle is "overspecified." That is, in all likelihood, the specifications are inconsistent with each other. In general, if the angles in a scalene triangle are integer numbers of degrees, the side lengths cannot be integer numbers of units. That is the case for the so-called right triangle here.

The given side lengths make the largest angle about 89.5°, not 90°. The given angles make the side lengths have irrational values.

Answer:

B

Step-by-step explanation:

The difference quotient for the given function is given by f(x) - f(x)/x - a, which simplifies to -(x-a)/x.

The difference quotient for the given function is given by f(x) - f(x)/x - a, which simplifies to -(x-a)/x. This expression is obtained by subtracting f(x)/x - a from f(x). The numerator is the difference between x and a, while the denominator is x.

The difference quotient for the given function f(x) = 1/x can be expressed as:

f(x) - f(x)/x - a = -(x-a)/x

This expression can be further expanded as follows:

f(x) - f(x)/x - a = [1/x - 1/x] - (x - a)/x

                   = 0 - (x - a)/x

                   = -(x - a)/x

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The solution is: (x,y)= (-1, -6), the graph is given below.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

y> -x-5

y< 2x-8

Solve graphically

See attachment for graph;

Next, determine the intersection points between the two lines

From the attached graph, we have:

(x,y)= (-1, -6)

Hence, the solution is: (x,y)= (-1, -6).

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Answer:

y=-1/3x+1/2

Step-by-step explanation:

2x+6y=3

bring 2x to the other side by subtracting : 6y=-2x+3

divide by 6 : y=-1/3x+1/2

Answer:

y = -1/3x + .5

Step-by-step explanation:

First we are  going to get y on a side by itself

6y = 3 - 2x

Then we divide by six to get our equation

y= .5 - 1/3x

In slope intercept form

y = -1/3x + .5

Based on the provide data, the predicted drag on the full-sized pole is 52.53 lb.

We have a graph between model velocity and model drag. Also we have two set of dimensions and we have to predict drag on the full-sized pole. Write the details as shown : Since, the working temperature is not given, assume T= 60°F. For model :

Length Lₘ = 2 ft

Diameter, dₘ = 1 in = 1/12 ft.

Velocity = Vₘ

Density in water, ρₘ =1.94 slugs/ft³

Dynamic Viscosity, μₘ= 2.373×10⁻⁵ lb-s/ft² ( water)

For prototype :

Length, Lₚ = 30 ft

Diameter, dₚ = 1.25 ft.

Velocity, Vₚ = 30 mph = 30 × 1.467 ft/s

= 44 ft/s

Density in air, ρₐ = 2.34×10⁻⁵ slugs/ft³

Dynamic Viscosity, μₐ= 3.75×10⁻⁶ lb-s/ft²

Determine the velocity of air using Reynolds number similarity as below :

ρₘ Vₘdₘ/μₘ = ρₐ Vₚ dₚ/ μₐ

=> Vₘ = (ρₐ/ρₘ)(dₚ/dₘ)(μₘ/μₐ)Vₚ

=> Vₘ = ( 2.34×10⁻⁵ /1.94)(1.25 /1/12 )(2.373×10⁻⁵/3.75×10⁻⁷ )44

Vₘ = 50.37 ft/s

From the graph, the value of drag corresponding to Vₘ = 50.37 ft/s is 253.7 lb. Determine the drag on the full-sized pole: Fₚ/dₚ² Vp²ρₐ = Fₘ(Vₘ²dₘ²ρₘ)

=> Fₚ = Fₘ( dₚ/dₘ)²(Vₚ/Vₘ)²(ρₐ/ρₘ)

=> Fₚ = 253.7 lb ( 1.25 ft/1/12ft )²( 44 ft/s/50.37 ft/s)²( 2.34×10⁻⁵slugs/ft³/1.94 slugs/ft³)

=> Fₚ = 52.53 lb

Hence, required full-sized pole is 52.53 lb.

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Complete question:

The drag on a 30-ft long, vertical, 1.25-ft diameter pole subjected to a 30 mph air wind is to be determined with a model study. It is expected that the drag is a function of the pole length and diameter, the fluid density and viscosity. Laboratory model tests were performed in a high-speed water tunnel using a model pole having a length of 2 ft and a diameter of 1 in. Some model drag data are shown in the figure. Based on these data, predict the drag on the full-sized pole. 350 300 250 200 150 100 50 10 30 40 50 60 Model velocity, f's.

Answer:

f(-7) = 60

Step-by-step explanation:

In this problem, we are asked to find the output of the function f(x) when x = -7.

First, substitute -7 in for x.

f(x) = -9x - 3

f(-7) = -9(-7) - 3

Then, simplify the right side of the equation. Remember that a negative times a negative becomes positive.

f(-7) = 63 - 3

f(-7) = 60

After three steps, the average value of the displacement and the average value of the squared displacement are given by zero and two, respectively.

The average value of the displacement is calculated by summing up all the displacement values and dividing by the total number of steps. In this case, the average value will be zero because each step has an equal probability of moving forward or backward, resulting in an average net displacement of zero.

The average value of the squared displacement is calculated by summing up the squares of all the displacement values and dividing by the total number of steps. In this case, the average value will be two because each step has an equal probability of moving two units forward or two units backward, resulting in an average squared displacement of two.

These values can be used to calculate various statistical measures such as the mean squared displacement, which can provide insight into the diffusion of particles or the behavior of random walks.

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The equation of the line that passes through the points (1,9) and (−4,8) is y= 1/5 x+45.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given coordinate points are (1, 9) and (-4, 8).

Here, slope (m)= (8-9)/(-4-1)

m= 1/5

Substitute m=1/5 and (x, y)=(1, 9) in y=mx+c, we get

9=1/5 (1)+c

c=45

Substitute m=1/5 and c=45 in y=mx+c, we get

y= 1/5 x+45

Therefore, the equation of the line that passes through the points (1,9) and (−4,8) is y= 1/5 x+45.

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Answer:

[tex]y=\dfrac{1}{5}x+\dfrac{44}{5}[/tex]

Step-by-step explanation:

To write the equation of the line that passes through the points (1, 9) and (-4, 8), first find its slope.

To do this, substitute the given points into the slope formula:

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{8-9}{-4-1}=\dfrac{-1}{-5}=\dfrac{1}{5}[/tex]

To write the equation of the line, we can use the point-slope form of a linear equation.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope m = 1/5 and point (1, 9) into the formula:

[tex]y-9=\dfrac{1}{5}(x-1)[/tex]

Simplify:

     [tex]y-9=\dfrac{1}{5}x-\dfrac{1}{5}[/tex]

[tex]y-9+9=\dfrac{1}{5}x-\dfrac{1}{5}+9[/tex]

           [tex]y=\dfrac{1}{5}x+\dfrac{44}{5}[/tex]

Therefore, the equation of the line that passes through the points (1, 9) and (-4, 8) is:

[tex]\boxed{y=\dfrac{1}{5}x+\dfrac{44}{5}}[/tex]

Answer:

the mean is 3/4

Step-by-step explanation:

to find mean, add all terms and then divide by the number of terms

0.5 + 0.33 + 0.67 + 1.5 = 3

divide by 4

mean: 3/4

Answer:

0.75

Step-by-step explanation:

0.5+0.33+0.67+1.5 = 3

3/4 = 0.75

The solution to the initial value problem is:

y(x) = √{16}/{8x-1}} + 3e^{-2x} + 2√{2} + 1

The solution to the initial value problem is given by:

y(x) = √{16}/{8x-1}} + 3e^{-2x} + C

Where C is the constant of integration. To find C, we can use the initial condition y(0) = 2√{2}:

y(0) = √{16}/{8(0)-1}} + 3e^{-2(0)} + C = 2√{2}

Solving for C:

C = 2√{2} - √{16}/{-1}} - 3 = 2√{2} + √{16} - 3 = 2√{2} + 4 - 3 = 2√{2} + 1

So the solution to the initial value problem is:

y(x) = √{16}/{8x-1}} + 3e^{-2x} + 2√{2} + 1

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The equivalent formula that does not involve integrals is A(x) = 2x - 2x^2 + 4x - 4.

The First Fundamental Theorem of Calculus states that if f(x) is a continuous function on the interval [a, b], then the function F(x) = integral^x_a f(t) dt is an antiderivative of f(x), meaning that its derivative is equal to f(x). Therefore, if we have the antiderivative of a function, we can use the derivative to find an equivalent formula without an integral.

In this case, the derivative of the antiderivative of f(t) = 4 - 2t is f(t) = 4 - 2t, which is the original function. So, the equivalent formula for A(x) is A(x) = 2x - 2x^2 + 4x - 4, which does not involve integrals.

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Therefore , the solution of the given problem of probability comes out to be probability that Both Rise - 0.06.

The possibilities of a given outcome in an event of sequence of events are referred to as probability.Consider the prices of two stocks as A & B based on the information provided. The following formula will be used to determine the likelihood that both stocks' prices will fall:

Here,

Decline Probability in A and B = PA(D) x PB (D)

Probability of Decline for A and B is -0.2 x 0.3.

Decline probabilities in A and B are 0.06

Now there will be a 100% chance of a price increase.

The likelihood of one rising is given by PA(U) x [PB(R) + PB(D)] + PB(U) x [PA(R) + PA(D)].

Chance of one rising is equal to 0.2 x (0.4 + 0). .3] +0.3 x (0.6+0.2

Chance that one increases is -0.38

For just one price remaining the same, now

One Unchanged Probability = PA (U) x [PB(R) + PB(D)]

[PA(R)+ P1 (D)] +PB(U)

Probability for a Single Unchanged Value is equal to 0.6 x [0.3 +0.3] +0.4 x [0.2+0 .2]

Probability for a Single Unchanged Value: 0.52

the likelihood that both prices will increase,

Both Rising Probability = PA(R)APB (R)

Chance that Both Will Rise 0.2 x 0.3

Chance that both will rise: 0.06

Therefore , the solution of the given problem of probability comes out to be probability that Both Rise - 0.06.

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The value of f(-2) is 1.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given is a table of x values and f(x) values corresponding to those x.

When x = -6, f(x) = f(-6) = 3

When x = -2, f(x) = f(-2) = 1

When x = 0, f(x) = f(0) = 4

When x = 3, f(x) = f(3) = -2

So the value of f(-2) = 1.

Hence f(-2) = 1 from the table.

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Answer:

y-10

Step-by-step explanation:

Jaelyn is training for the upcoming new york marathon, jaelyn started running 3 to 4 miles daily during the week with an 8-mile distance run on the weekend. after 6 months is- progression

The six fundamental principles in the training are the principle of- distance individual difference, overload, progression, use/disuse, adaptation, specificity.

The principle of progression tells us that to improve performance and fitness there should be a systematic and gradual increase in the intensity with respect to time. This helps in increasing the performance of any athlete without the chances of injury.

So here Barbara has increased running distance up to 25 miles after 6 months of starting training which shows she is following progression principle.

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None of the values given in this problem make the equation 2(3 - p) = 4p + 10 true.

To obtain the value that makes the equation true, we must solve the equation.

The equation for this problem is defined as follows:

2(3 - p) = 4p + 10.

Applying the distributive property on the left side of the equality, we have that:

6 - 2p = 4p + 10

Isolating the variable p, the result is given as follows:

-2p - 4p = 10 - 6

-6p = 4

6p = -4

p = -4/6

p = -2/3.

Which isn’t any of the presented options in the context of this problem.

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The high-temperature yesterday was -5° C.

Temperature is a degree of hotness or coldness the can be measured using a thermometer. It's also a measure of how fast the atoms and molecules of a substance are moving. Temperature is measured in degrees on the Fahrenheit, Celsius, and Kelvin scales.

Given that, the high temperature today is 7°C higher than twice the high-temperature yesterday.

Let the high-temperature yesterday be x.

The high-temperature today is -3° C.

Now, 2x+7=-3

2x=-10

x=-5

Therefore, yesterday's temperature was -5° C.

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