Use this equation to find dy/dx for the following.

y^3+ x^4y^6 = 5+ ye^x

If square based pyramid's perimeter is 18.5 ft and it's height is 7.6 ft, then volume of that pyramid is 54.4 cubic foot.

The "Volume" of a square pyramid is known as the space which is occupied by pyramid, and it is represented as : V = (1/3) × B × h, where V is volume, B is area of base, and h is height of pyramid,

The shape of "base-of-pyramid" is a square,

So, we find "base-area" by dividing perimeter by 4 and squaring it;

⇒ Perimeter of base of pyramid = 18.5 ft,

⇒ Length of "one-side" of base = 18.5/4 = 4.625 ft,

So, ⇒ Base area = (4.625 ft)² = 21.390625 sq ft,

Now, using the formula to find volume;

⇒ Volume = (1/3) × 21.390625 × 7.6 ,

⇒ Volume = 54.384375 cubic feet,

Rounding volume to "nearest-tenth" of a cubic foot,

We get,

⇒  Volume ≈ 54.4 ft³.

Therefore, Volume of pyramid is 54.4 ft³.

Learn more about Volume here

brainly.com/question/29084051

#SPJ1

The given question is incomplete, the complete question is

Find the volume of a pyramid with a square base, where the perimeter of the base is 18.5 ft and the height of the pyramid is 7.6 ft. Round your answer to the nearest tenth of a cubic foot.

The recurrence relation for the number of ways to arrange cars in a row with n parking spaces if we can use Cadillacs, Hummers, or Fords can be written as: A(n) = 3A(n-1) .

Let A(n) be the number of ways to arrange cars in a row with n parking spaces. We can place either a Cadillac, Hummer, or Ford in the first parking space. If we place a Cadillac, then we have A(n-1) ways to arrange the remaining (n-1) parking spaces.

Similarly, if we place a Hummer or a Ford in the first parking space, we have A(n-1) ways to arrange the remaining parking spaces. Therefore, the recurrence relation can be written as: A(n) = 3A(n-1)

with initial condition A(1) = 3. This recurrence relation tells us that the number of ways to arrange cars in a row with n parking spaces is three times the number of ways to arrange cars in a row with (n-1) parking spaces.

To know more about relation , refer here:

https://brainly.com/question/30640806#

#SPJ11

The points where constraints intersect on the boundary of the feasible region are termed as the "c. extreme points." In the context of linear programming problems, the feasible region represents the area where all constraints are satisfied.

Constraints are typically linear inequalities that define the limitations or conditions of a problem. When these constraints intersect, they form the boundaries of the feasible region.
Extreme points are critical because they often represent potential optimal solutions to the linear programming problem. The objective function contour refers to the graphical representation of the objective function, which is a linear function that represents the goal of the problem (e.g., minimizing cost or maximizing profit). Feasible points are any points within the feasible region that satisfy all constraints, while feasible edges are the lines or segments along the boundary of the feasible region that connect extreme points.

In summary, extreme points are the specific locations where constraints intersect on the boundary of the feasible region and play a significant role in determining the optimal solution to a linear programming problem.

To learn more about feasible region : brainly.com/question/29314086

#SPJ11

The maximum error of the estimated mean amount spent by customers for a 99% level of confidence is $2.803. This means that the company can estimate the mean amount spent by customers with a 99% level of confidence and an error of no more than $2.803.

The maximum error of the estimated mean amount spent by customers for a 99% level of confidence can be determined using the formula:

Maximum Error = Z-value * (Estimated Standard Deviation / √Sample Size)

Where the Z-value for a 99% level of confidence is 2.576 (found using a standard normal distribution table or calculator).

Given that the local retail company's budget limits the number of surveys to 250 and the estimated standard deviation is $17.00, the maximum error can be calculated as:

Maximum Error = 2.576 * (17 / √250) = 2.576 * (17 / 15.8114) = 2.803

Therefore, the maximum error of the estimated mean amount spent by customers for a 99% level of confidence is $2.803. This means that the company can estimate the mean amount spent by customers with a 99% level of confidence and an error of no more than $2.803.

It's important to note that the maximum error decreases as the sample size increases. However, since the budget limits the number of surveys to 250, the company must work within this constraint to obtain the most accurate estimate of the mean amount spent by customers.

learn more about the mean amount here: brainly.com/question/15799398

#SPJ11

To find the probability that both events occur (the kids eat their vegetables and the dog plays in the mud), we need to multiply their individual probabilities:  0.43 (probability of kids eating vegetables) x 0.38 (probability of dog playing in mud) = 0.1634

To find the probability of two independent events happening at the same time, you can multiply the probabilities of each event. In this case, the events are your brother's kids eating vegetables and your dog playing in the mud.
Probability of kids eating vegetables = 43% (0.43 as a decimal)
Probability of dog playing in the mud = 38% (0.38 as a decimal)
Now, we multiply these probabilities:
0.43 * 0.38 ≈ 0.1634
So, the probability of both events happening when your brother's family visits for dinner after a huge rainstorm is approximately 0.163 or 16.3%.

Learn more about probability here: brainly.com/question/30034780

#SPJ11

a) The approximate value of cos(1/2) using the linear approximation is 0.877.

b) The length of the person's shadow is decreasing at a rate of 1.8 m/s when the person is 3 m from the post.

a) To find the linear approximation to f(x) = cos(2x) at x = π/6, we need to use the formula:

L(x) = f(a) + f'(a) * (x - a)

where a is the point of approximation, in this case a = π/6, and f'(x) is the derivative of f(x).

So, first we calculate the derivative of f(x):

f'(x) = -2sin(2x)

Then, we plug in the values for a, f(a), and f'(a):

L(x) = cos(π/3) + (-2sin(π/3))*(x - π/6)

Simplifying:

L(x) = 1/2 - √3/2 * (x - π/6)

Now, to approximate cos(1/2) using this linear approximation, we plug in x = 1/4 (since π/6 is approximately 0.524, and 1/4 is approximately 0.785, which is closer to 1/2):

L(1/4) = 1/2 - √3/2 * (1/4 - π/6) ≈ 0.877

So, the approximate value of cos(1/2) using the linear approximation is 0.877, to three significant digits.

b) We can use similar triangles to find the relationship between the length of the person's shadow and the distance from the post. Let L be the length of the person's shadow, and let x be the distance from the person to the post. Then, we have:

L/x = 6/2

Simplifying:

L = 3x

Now, we take the derivative of both sides with respect to time t:

dL/dt = 3(dx/dt)

We are given that dx/dt = -0.6 m/s (since the person is walking towards the post), and we want to find dL/dt when x = 3. Plugging in these values:

dL/dt = 3(-0.6) = -1.8 m/s

So, the length of the person's shadow is decreasing at a rate of 1.8 m/s when the person is 3 m from the post.

To know more about linear approximation, refer to the link below:

https://brainly.com/question/31617205#

#SPJ11

The correct equation to find the number of miles Alberto is running after training for w weeks is B. M= 2w + 5.

We know that Alberto starts with running 5 miles, and increases his distance by 2 miles each week. So after w weeks, he would have run 5 + (2 x w) miles.

Therefore, the equation that represents the number of miles, M, run by Alberto after training for w weeks would be:

M = 2w + 5

To verify this, we can substitute different values of w in the equation to calculate the corresponding value of M. For example, if w=3, then:

M = 2(3) + 5

M = 11

So after training for 3 weeks, Alberto will be running 11 miles. Similarly, we can check for other values of w to see that the equation holds true.

Learn more about equations

https://brainly.com/question/2972832

#SPJ4

Let's represent the speed of the plane in still air as "p" and the speed of the wind as "w".

When the plane is traveling with the wind, its speed is (p + w) and against the wind, its speed is (p - w).

Given that it travels d1 miles with the wind in t hours and d2 miles against the wind in the same time, we can form the following equations:

d1 = t(p + w)
d2 = t(p - w)

Now, we need to solve for "p" and "w". Divide the first equation by t, and the second equation by t as well:

d1/t = p + w
d2/t = p - w

Add the two equations together to eliminate "w":

(d1/t) + (d2/t) = 2p

Solve for "p":

p = (d1 + d2) / (2t)

Now, substitute the value of "p" in either equation to solve for "w":

w = (d1/t) - p

Once you have the specific values for d1, d2, and t, plug them into the equations to find the speed of the plane in still air (p) and the speed of the wind (w).

learn more about speed here:brainly.com/question/28224010

#SPJ11

(1) T: If f'(c) = 0, then f has a local maximum or minimum at c, according to Fermat's theorem. (2) False 3) True 4) True 5) True 6) False 7) False

1) True. This is because when the derivative of a function is equal to zero at a certain point, it indicates that the slope of the function at that point is zero. This can only happen at a local maximum or minimum point.
2) False. Although having an absolute minimum value may suggest that the function has a critical point, it does not necessarily mean that the derivative of the function is equal to zero at that point.
3) True. This is because the Extreme Value Theorem states that a continuous function on a closed interval will have both an absolute maximum and minimum value.

4) True. This is because of the Mean Value Theorem, which states that if a function is differentiable on an interval, then there exists at least one point in that interval where the derivative equals the slope of the secant line connecting the endpoints of the interval.
5) True. This is because a negative derivative indicates a decreasing function.
6) False. Although having a zero second derivative may suggest a possible inflection point, it does not guarantee it. Further analysis is needed to determine if the point is indeed an inflection point.
7) False. While having equal derivatives may suggest that two functions are the same, it is not a sufficient condition. The two functions may differ by a constant.

For more about local maximum:

https://brainly.com/question/10878127

#SPJ11

The derivative is y' = cos(x). However, based on our calculations, we found that y' = sec^2(x). Therefore, the given function and derivative do not match, and we cannot verify that the function satisfies the differential equation.

Let's use the given function and its derivative:

Function: y = 2 tan(x) - x
Derivative: y' = cos(x)

Now, let's rewrite the function in terms of sin(x) and cos(x), since tan(x) = sin(x) / cos(x):

y = 2 (sin(x) / cos(x)) - x

To find the derivative y', we will need to apply the Quotient Rule, which states:

(d/dx)[u(x) / v(x)] = (v(x) * (du/dx) - u(x) * (dv/dx)) / [v(x)]^2

Here, u(x) = sin(x) and v(x) = cos(x). Thus, we have:

(du/dx) = cos(x) and (dv/dx) = -sin(x)

Applying the Quotient Rule:

y' = (cos(x) * cos(x) - sin(x) * -sin(x)) / cos^2(x)

y' = (cos^2(x) + sin^2(x)) / cos^2(x)

Using the Pythagorean identity, cos^2(x) + sin^2(x) = 1:

y' = 1 / cos^2(x)

Now, recall that 1 / cos^2(x) is equal to the secant squared function, sec^2(x). Therefore, we can rewrite y' as:

y' = sec^2(x)

For more about derivative:

https://brainly.com/question/25752367

#SPJ11

The final hash table with collisions resolved by chaining looks like this:

0: 36
1: 10 -> 1
2: (empty)
3: 12 -> 21
4: 22
5: (empty)
6: 6 -> 15 -> 33
7: (empty)
8: 35

To insert the keys into a hash table with 9 slots using the hash function h(k) = k mod 9 and resolving collisions by chaining, follow these steps:

1. Initialize an empty hash table with 9 slots.

2. Calculate the hash values for each key using the hash function h(k) = k mod 9:

- 10 mod 9 = 1
- 22 mod 9 = 4
- 35 mod 9 = 8
- 12 mod 9 = 3
- 1 mod 9 = 1
- 21 mod 9 = 3
- 6 mod 9 = 6
- 15 mod 9 = 6
- 36 mod 9 = 0
- 33 mod 9 = 6

3. Insert the keys into the hash table according to their hash values, using chaining to resolve collisions:

- Slot 0: 36
- Slot 1: 10 -> 1
- Slot 2: (empty)
- Slot 3: 12 -> 21
- Slot 4: 22
- Slot 5: (empty)
- Slot 6: 6 -> 15 -> 33
- Slot 7: (empty)
- Slot 8: 35

For more about hash table:

https://brainly.com/question/29970427

#SPJ11

The derivative dy/dx for the given functions [tex]y = 6u^-5[/tex] and [tex]u = 2(14x)[/tex]is:

[tex]dy/dx = (-30(28x)^-6) * 28[/tex]

GIven the functions y = f(u) and u = g(x), and we need to find the derivative dy/dx using the chain rule. The given functions are [tex]y = 6u^-5[/tex]and [tex]u = 2(14x).[/tex] Let's begin.

First, let's find the derivative of y with respect to u, which is f'(u). We have:

[tex]y = 6u^-5\\f'(u) = -30u^-6[/tex]

Next, let's find the derivative of u with respect to x, which is g'(x). We have:

u = 2(14x)
g'(x) = 28

Now we can apply the chain rule to find dy/dx:

dy/dx = f'(g(x)) * g'(x)

Substitute the derivatives we found earlier and the function u = g(x):

dy/dx = (-30(2(14x))^-6) * 28

Simplify the expression:

dy/dx = (-30(28x)^-6) * 28

Learn more about derivative here :-

https://brainly.com/question/18722002

#SPJ11

a. It makes sense to test the same cats in both treatments (Still and Fountain) rather than using two independent samples because this approach eliminates any potential individual differences among cats. By using the same cats, the study can better isolate the effect of the water source on water consumption, making the comparison more accurate and meaningful.

b. To determine if there is convincing evidence at a = 0.05 that cats tend to drink more water from fountains than from a bowl, follow these 7 steps:

1. State the null hypothesis (H0): There is no difference in water consumption between still and fountain sources (µ_still = µ_fountain).
2. State the alternative hypothesis (Ha): Cats drink more water from fountains than from a bowl (µ_still < µ_fountain).
3. Choose the significance level (α): 0.05.
4. Identify the appropriate test: Paired t-test (since each cat is tested under both conditions).
5. Calculate the test statistic using the provided data (you may use statistical software like JMP or Excel for this calculation).
6. Determine the p-value by comparing the test statistic to the t-distribution with degrees of freedom equal to the number of cats minus 1 (n-1).
7. Make a decision: If the p-value is less than α, reject the null hypothesis in favor of the alternative hypothesis, concluding that there is convincing evidence that cats drink more water from fountains than from a bowl. If the p-value is greater than α, fail to reject the null hypothesis.

c. The characteristic feature of a pilot study present in this dataset is its small sample size, with only nine cats participating. Pilot studies are often conducted as a preliminary test to evaluate the feasibility of a research design and gather preliminary data before conducting a full-scale study. These results can be used to improve future research by identifying any potential issues in the experimental design, determining appropriate sample sizes for a larger study, or providing initial data to support funding applications for more extensive research.

Learn more about hypothesis:

https://brainly.com/question/29519577

#SPJ11

The correct answer is a. single-factor, independent groups design. In this design, there is one independent variable with two or more levels, and participants are randomly assigned to these levels, making the groups independent.

A t test for independent groups is specifically used to compare the means of two independent groups in an experimental design, where participants are randomly assigned to either a control or treatment group. This design is also known as a between-subjects design, as participants are only exposed to one level of the independent variable (the treatment or control condition). The other options listed - matched groups design and nonequivalent groups design - both involve some form of matching or pairing of participants, which would require a different type of statistical test (e.g. a paired t test or ANOVA). This t-test compares the means of the experimental conditions to determine if there is a significant difference between them.

learn more about ANOVA here: brainly.com/question/23638404

#SPJ11

Answer:

E' is (4, 6)

F' is (5, 4)

Step-by-step explanation:

To translate an object is to move it exactly as it is to another place on the graph.  Therefore, E' is (4, 6) and F' is (5, 4).

Answer:20

Step-by-step explanation:20+20=40+20=60-40=20

The statistical strategy that would allow the professor to determine if the average score on the final exam has gone higher is a hypothesis test. The professor can formulate a null hypothesis (H0) that the average score is still 83 and an alternative hypothesis (Ha) that the average score is greater than 83. Then the professor can collect a sample of final exam scores and calculate the sample mean.

The professor can use the sample mean and standard deviation to calculate a test statistic, which can be compared to a critical value or p-value to determine if the null hypothesis should be rejected or not.

Hypothesis testing is a commonly used statistical method to make decisions about a population based on a sample. In this case, the professor wants to determine if the average score on the final exam has increased or not. By setting up a hypothesis test, the professor can use the sample data to make an inference about the population. The null hypothesis assumes that there is no difference between the population mean and the previous average score of 83.

The alternative hypothesis assumes that the population mean has increased. By calculating a test statistic and comparing it to a critical value or p-value, the professor can make a decision to either reject or fail to reject the null hypothesis. If the null hypothesis is rejected, the professor can conclude that there is evidence to support the claim that the average score on the final exam has increased.

In the past, students have scored an average of 83 points on the final exam in a statistics course. The professor thinks that this average has now gone higher. What statistical strategy would allow the professor to determine if he is correct? Confidence interval Regression analysis Empirical rule Hypothesis test

To learn more about null hypothesis : brainly.com/question/28920252

#SPJ11

The statistical strategy that would allow the professor to determine if the average score on the final exam has gone higher is a hypothesis test. The professor can formulate a null hypothesis (H0) that the average score is still 83 and an alternative hypothesis (Ha) that the average score is greater than 83. Then the professor can collect a sample of final exam scores and calculate the sample mean.

The professor can use the sample mean and standard deviation to calculate a test statistic, which can be compared to a critical value or p-value to determine if the null hypothesis should be rejected or not.

Hypothesis testing is a commonly used statistical method to make decisions about a population based on a sample. In this case, the professor wants to determine if the average score on the final exam has increased or not. By setting up a hypothesis test, the professor can use the sample data to make an inference about the population. The null hypothesis assumes that there is no difference between the population mean and the previous average score of 83.

The alternative hypothesis assumes that the population mean has increased. By calculating a test statistic and comparing it to a critical value or p-value, the professor can make a decision to either reject or fail to reject the null hypothesis. If the null hypothesis is rejected, the professor can conclude that there is evidence to support the claim that the average score on the final exam has increased.

In the past, students have scored an average of 83 points on the final exam in a statistics course. The professor thinks that this average has now gone higher. What statistical strategy would allow the professor to determine if he is correct? Confidence interval Regression analysis Empirical rule Hypothesis test

To learn more about null hypothesis : brainly.com/question/28920252

#SPJ11

The graph that represents the inequality y > x + 2 is given as follows:

Graph A.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The function for this problem is given as follows:

y = x + 2.

Meaning that it has an intercept of b = 2, passing through the point (0, 2).

The inequality is:

y > x + 2.

Meaning that the shaded region is composed by the values that are above the line. The line is dashed and not solid, as it is not part of the solution of the inequality. Hence Graph A is the solution.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Using an infinite series approximation, we estimate the number 1/3 e to be approximately 0.239.

To approximate the number 1/3 e, we can use the Maclaurin series expansion of the function f(x) = [tex]e^x[/tex], which is:

[tex]e^x = 1 + x + x^2/2! + x^3/3! + ...[/tex]

Substituting x = -1/3, we have:

[tex]e^{(-1/3)} = 1 - 1/3 + 1/2(1/3)^2 - 1/3!(1/3)^3 + ...[/tex]

Truncating the series after the third term, we get:

[tex]e^{(-1/3)[/tex] ≈ 1 - 1/3 + 1/2(1/3)^2 = 0.716

Multiplying by 1/3, we have the approximate value:

1/3 e ≈ 0.239

To know more about infinite series approximation, refer to the link below:

https://brainly.com/question/30557123#

#SPJ11

To factor the denominator, we need to find the roots of the quadratic equation 2x^2 + x - 1 = 0.

The quadratic equation can be factored as follows:

2x^2 + x - 1 = (2x - 1)(x + 1)

So, the denominator can be written as:

2x^2 + x - 1 = (2x - 1)(x + 1)

Now we can express the fraction as partial fractions:

(2+x)/(2x^2+x-1) = A/(2x - 1) + B/(x + 1)

To find the values of A and B, we need to find a common denominator:

(2+x)/(2x^2+x-1) = (A(x + 1) + B(2x - 1))/(2x^2 + x - 1)

Now we equate the numerators:

2 + x = A(x + 1) + B(2x - 1)

Expanding the right side:

2 + x = Ax + A + 2Bx - B

Grouping like terms:

2 + x = (A + 2B)x + (A - B)

By comparing the coefficients of x and the constant term on both sides, we get the following system of equations:

A + 2B = 1

A - B = 2

Solving this system of equations, we find A = 3/5 and B = -7/5.

Therefore, we can write the partial fraction decomposition as:

(2+x)/(2x^2+x-1) = 3/5/(2x - 1) - 7/5/(x + 1)

The coefficient of x^r is determined by the constant term in the expansion of the numerator in the series form. Since the numerator is 2 + x, the coefficient of x^r is 0 when r is not equal to 0. When r is equal to 0, the coefficient is 2.

So, the coefficient of x^r in the series representation of the given generating function is 2 when r = 0.

To know more about denominator refer here

https://brainly.com/question/15007690#

#SPJ11

(a) The average value of f(x) = 3x - 2 over the interval [2,4] is 1.

(b) The average value of f(x) = 2x^2 - 2x + 2 over the interval [1,2] is 5/3.

To find the average value of a function f(x) over an interval [a,b], we use the formula:

Average value of f(x) over [a,b] = (1/(b-a)) * Integral(a to b) of f(x) dx

(a) For f(x) = 3x - 2 over the interval [2, 4], we have:

Average value of f(x) over [2,4] = (1/(4-2)) * Integral(2 to 4) of (3x-2) dx

= (1/2) * [(3/2)x^2 - 2x] from 2 to 4

= (1/2) * [(3/2)*(4^2) - 2(4) - (3/2)*(2^2) + 2(2)]

= (1/2) * [12 - 8 - 6 + 4]

= 1

Therefore, the average value of f(x) = 3x - 2 over the interval [2,4] is 1.

(b) For f(x) = 2x^2 - 2x + 2 over the interval [1,2], we have:

Average value of f(x) over [1,2] = (1/(2-1)) * Integral(1 to 2) of (2x^2 - 2x + 2) dx

= (1) * [(2/3)x^3 - x^2 + 2x] from 1 to 2

= (2/3)*(2^3 - 1^3) - (2^2 - 1^2) + 2(2-1)

= (2/3)*7 - 3 + 2

= 5/3

Therefore, the average value of f(x) = 2x^2 - 2x + 2 over the interval [1,2] is 5/3.

Learn more about "average value of a function ":

https://brainly.com/question/22847740

#SPJ11

Answer:

8.5

Step-by-step explanation:

To solve the equation 32 = 5h + 15 − 3h, we can combine like terms on the right side of the equation to get:

32 = 2h + 15

Then we can subtract 15 from both sides of the equation:

17 = 2h

Finally, we can divide both sides of the equation by 2 to solve for h:

h = 8.5

Therefore, h = 8.5 is the solution to the equation.

Answer:

h=8.5

I'm not sure why this isn't one of the options though....

Step-by-step explanation:

32=5h+15-3h

combine like terms

32=2h+15

subtract 15 from both sides

17=2h

divide both sides by 2

8.5=h

The reduced normal form of the expression is (x y z) (x y z).

To reduce the expression to normal form, we need to apply beta-reductions until we cannot apply any more.

The first step is to apply the function (ax.Ay.xy z) to the argument (Ac.c):

(ax.Ay.xy z) (Ac.c)

=> A(Ac.c)y.(xy z)[x:=Ax.Ay.xy z]

=> A(Ac.c)y.(Ay.xy z)c

=> A(Ac.c)(Az.yz)c

=> Ac

Next, we apply the function ((a.a) b) to the argument Ac:

((a.a) b) Ac

=> (a.a) (b Ac)

=> a[b:=b Ac].a[b:=b Ac]

=> b Ac b Ac

Finally, we apply the function b to the argument (x y) z:

b ((x y) z)

=> ((x y) z) ((x y) z)

=> (x y z) (x y z)

Therefore, the reduced normal form of the expression is (x y z) (x y z).

To know more about apply beta-reductions refer here:

https://brainly.com/question/15869181

#SPJ11

The domain of the revenue function is the set of all possible values of p. In this case, the price-demand equation tells us that the highest possible price for the table saws is $400, so the domain of the revenue function is 0 ≤ p ≤ 400.

Revenue is equal to the number of units sold times the price per unit. To obtain the revenue function, multiply the output level by the price function.

To find the revenue function, we need to multiply the price-demand equation by the quantity produced (x).

Revenue function = p * x = p * (8,000 - 20p)

Simplifying the expression, we get:

Revenue function = 8,000p - 20p^2

Know more about revenue function here:

https://brainly.com/question/31367893

#SPJ11

The inequality that represents the normal temperature range of a dog, where t represents body temperature is given as follows:

|t - 101.8| ≤ 0.7.

The absolute value of a number gives the distance of a number from the origin, hence it basically can be interpreted as the number without the signal, as for example, |-2| = |2| = 2.

The average temperature for a dog is 101.8° F, but it can vary by as much as 0.7° F, hence the absolute value of the difference between t and 101.8 is of at most 0.7, hence the inequality is:

|t - 101.8| ≤ 0.7.

More can be learned about the absolute value function at brainly.com/question/3381225

#SPJ1

Answer:

Step-by-step explanation:

x-y/2

The number 8007 is congruent to 7 modulo 8, so it cannot be written as the sum of three perfect squares, the equation: x^2 + y^2 + z^2 = 8007 has no solutions.

We can prove this by working modulo 8. Any perfect square is congruent to either 0, 1, or 4 modulo 8. Therefore, the sum of three perfect squares is congruent to either 0, 1, 2, 3, 4, or 5 modulo 8. However, 8007 is congruent to 7 modulo 8, so it cannot be written as the sum of three perfect squares.

Therefore, the equation x^2 + y^2 + z^2 = 8007 has no solutions.

To demonstrate that there are infinitely many positive integers which cannot be expressed as the sum of three squares, we can use a similar argument. If n is a positive integer such that n is congruent to 7 modulo 8, then n cannot be written as the sum of three perfect squares, as shown above.

Since there are infinitely many positive integers congruent to 7 modulo 8, there must be infinitely many positive integers which cannot be expressed as the sum of three squares. This is a consequence of the fact that the sum of three squares is a quadratic form, and the theory of quadratic forms tells us that there are only finitely many positive integers which cannot be expressed as the sum of three squares.

To know more about modulo, refer here:

https://brainly.com/question/30893547#

#SPJ11

Complete question:

8. Prove that the equation x2 + y2 + z2 = 8007 has no solutions.

(HINT: Work Modulo 8.) Demonstrate that there are infinitely many positive integers which cannot be expressed as the sum of three squares.

The value of x that makes the equation 3(x − 6) − 8x = − 2 + 5(2x+1) true is - 7 / 5.

An equation is an expression with an 'equal to' symbol between two expressions that have equal values.

Therefore, let's find the variable x in the equation to know what make the value of x that makes the equation true.

A variable is a number represented with letters in an equation.

3(x − 6) − 8x = − 2 + 5(2x+1)

3x - 18 - 8x  = -2 + 10x + 5

3x - 8x - 18 = 3 + 10x

-5x - 18 = 3 + 10x

-5x - 10x = 3 + 18

-15x = 21

x = 21 / -15

Therefore,

x = -  7 / 5

learn more on equation here: https://brainly.com/question/24427465

#SPJ1

Answer:

6 3/5+ 3 2/5 =10

Step-by-step explanation:

EZ 6+3 3/5+2/5 10

When the slope of the tangent to a curve at every point is the reciprocal of the y-value of the curve, it signifies that the tangent lines' steepness at every point on the curve is inversely related to the curve's y-value at that same point.

When the slope of the tangent to a curve at every point is reciprocal to the y-value of the curve, it means that the function is of the form y = 1/x + C, where C is a constant. This is because the slope of the tangent at any point on the curve is given by the derivative of the function at that point. So, if the derivative is equal to 1/y, then the original function must be the reciprocal of y, plus a constant. This relationship is important in calculus and can be used to solve problems involving the slope of a curve at a specific point. When the slope of the tangent to a curve at every point is the reciprocal of the y-value of the curve, it means the following:
1. At any point on the curve, draw a tangent line. A tangent line is a straight line that touches the curve at that point without crossing it.
2. Calculate the slope of that tangent line. The slope represents the rate of change (steepness) of the line, and is defined as the change in the vertical direction (y-axis) divided by the change in the horizontal direction (x-axis).
3. Compare the slope of the tangent line to the y-value of the curve at that point. If the slope is the reciprocal of the y-value, it means that the slope is equal to 1 divided by the y-value (slope = 1/y).

learn more about slope of tangent here: brainly.com/question/31326507

#SPJ11