Pls help ASAP find the slope !!

a) The point on the curve where the tangent is horizontal is at t = 0.

b) The points where the tangent is vertical are at t₁ = -5 and t₂ = 5.

To find the points on the curve where the tangent is horizontal, we need to find the values of t that satisfy dy/dt = 0.

a.) Differentiating y = 3(t² - 75) with respect to t, we get:

dy/dt = 6t

Setting dy/dt = 0, we have:

6t = 0

t = 0

Therefore, when t = 0, the tangent is horizontal.

b.) To find the points where the tangent is vertical, we need to find the values of t that satisfy dx/dt = 0.

Differentiating x = t(t² - 75) with respect to t, we get:

dx/dt = 3t² - 75

Setting dx/dt = 0, we have:

3t² - 75 = 0

t² = 25

t = ±5

Therefore, the points where the tangent is vertical are when t = -5 and t = 5, with t₁ = -5 and t₂ = 5.

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The question is -

Consider the curve given by the parametric equations

x = t (t²-75) , y = 3 (t²-75)

a.) Determine the point on the curve where the tangent is horizontal.

t=

b.) Determine the points t_1,t_2 where the tangent is vertical and t_1 < t_2.

t_1=

t_2=

The interquartile range of the data set is 4.7 liters.

To find the interquartile range, we first need to sort the data from least to greatest. This gives us the following data set:

2.8, 7.5, 8.5, 11.6, 12, 12.1

The first quartile (Q1) is the median of the lower half of the data set. In this case, the lower half of the data set is {2.8, 7.5, 8.5}. The median of this data set is 7.5. Therefore, Q1 = 7.5.

The third quartile (Q3) is the median of the upper half of the data set. In this case, the upper half of the data set is {11.6, 12, 12.1}. The median of this data set is 12. Therefore, Q3 = 12.

The interquartile range (IQR) is calculated by subtracting Q1 from Q3. In this case, IQR = 12 - 7.5 = 4.7 liters.

The interquartile range is a measure of the variability of the middle 50% of the data. In this case, the interquartile range tells us that the middle 50% of the race car drivers have between 7.5 and 12 liters of gas in their tanks.

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Answer:

The car was traveling for 1.5 hours.

Step-by-step explanation:

Given that distance d, in kilometers, that a car travels at a speed of 80 km per hour , for t hours, is given by the equation d=80t.

Here wee need to find the time if the car has gone 120 kilometers.

That is

            d = 120 km

we need to find t.

            d=80t

           120 = 80 x t

The car was traveling for 1.5 hours.

Answer: D

Step-by-step explanation: As we can see, D is the only one that has matching inputs, but those inputs have separate outputs. If they don't have the same output, it is not a function

Hope this helps :)

*see attachment for the diagram given

Answer:

Volume of the toy = 68 in.³

Step-by-step explanation:

The equation to find the volume of the toy = volume of the wooden rectangular prism - volume of the triangular prism removed form the center

Volume of the toy = (L*W*H) - (½*bhl)

Where,

L = 8 inches

W = 3 inches

H = 3 inches

b = 1 inch

h = 1 inch

l = 8 inches

Plug in the values into the equation

Volume of the toy = (8*3*3) - (½*1*1*8)

Volume = 72 - 4

Volume of the toy = 68 in.³

Answer:

16 + 5 =21 21 is your answer

Step-by-step explanation:

Answer:

The answer your looking for is, C.

Answer:

4 yards saved

Step-by-step explanation:

two adjacent sides: 6 + 8 = 14

diagonal: √(6² + 8²) = √100 = 10

14 - 10 = 4

In a normal distribution, approximately 68% of scores fall between the z-scores of -1.00 and +1.00.

In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, the Empirical Rule (also known as the 68-95-99.7 Rule) applies. According to this rule, approximately 68% of the data falls within one standard deviation from the mean.

Since the z-scores represent the number of standard deviations a particular value is away from the mean, a z-score of -1.00 represents one standard deviation below the mean, and a z-score of +1.00 represents one standard deviation above the mean. Therefore, using the Empirical Rule, we can conclude that approximately 68% of scores fall between these two z-scores (-1.00 and +1.00).

This percentage represents the central portion of the distribution that is within one standard deviation from the mean, providing a useful measure of the spread and concentration of data in a normal distribution.

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Answer:

x = 18

Step-by-step explanation:

The "Angle Bisector" Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.

So, 20/8 = (4x + 3)/30

8(4x + 3) = 20(30)

32x + 24 = 600

32x = 576

x = 18

Answer:

Seven cups of canned apples are required to make apple pie recipe

Step-by-step explanation:

The weight of one canned apple is 0.45 pounds

Weight of total canned apple required to make the apple pie recipe is 3 pounds.

Total number of cups of canned apples required

[tex]= \frac{3}{0.45} \\= \frac{300}{45} \\= \frac{20}{3} \\[/tex]

So approximately seven cups of canned apples are required to make apple pie recipe

Answer:

bestie thats hard

Step-by-step explanation:

Answer:

D. x=-4.5

Step-by-step explanation:

Since they are both vertical angles, m∠BOD must also be equal to 30 degrees, and if you input -4.5 as x, (2 x -4.5x) + 39, that is rewritten as -9 and 39. 39 - 9 is 30 degrees.

The point (-10, 1) in Cartesian-Coordinates can be represented in polar coordinates as approximately (10.05, 3.0416 radians).

To convert the point (-10, 1) from Cartesian-Coordinates to polar coordinates, we can use the formulas:

r = √(x² + y²)

θ = arctan(y / x)

We know that, the point is (-10, 1), we substitute the values into the formulas:

We get,

r = √((-10)² + 1²) = √(100 + 1) = √101 ≈ 10.05, and

The point lies in second-quadrant, so, the angle is measured counterclockwise from the positive x-axis, which means it is between π/2 and π radians.

Therefore, The adjusted θ is : θ = π + arctan(1/-10) ≈ 3.0416 radians.

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a. Matrix A is invertible when |A| = -m ≠ 0 then statement true.

b. The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.

c. The system AX = B has an infinite number of solutions when m = n = 0 then statement true.

d. Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.

e. The system AX = 0 has a unique solution when m ≠ 0 then statement true.

f. At least one eigenvalue of the matrix A is zero when m = 0 then statement true.

g. Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.

Given that,

The augmented matrix of a system of linear equations AX = B was reduced to upper-triangular form so that

[A|B] = [tex]\left[\begin{array}{ccc}2&1&0 \ | \ 2\\0&-1&3 \ | \ 1 \\0&0&m \ | \ n\end{array}\right][/tex]

Where m and n are real numbers.

We know that,

a. We have to prove matrix A is invertible.

For A to be invertible.

|A| ≠ 0

|A| is the determinant of the matrix A.

|A| = 2(-m) -1(0) + 0(0) = -m

Here, m is the real number.

So, |A| = -m ≠ 0

Therefore, Matrix A is invertible when |A| = -m ≠ 0 then statement true.

b. We have to prove the system AX = B has no solution.

When Rank[A|B] > Rank[A]

m = 0 and n ≠ 0 has a real number

Therefore, The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.

c. We have to prove the system AX = B has an infinite number of solutions.

When m = n = 0, and Rank[A] < 3

Therefore, The system AX = B has an infinite number of solutions when m = n = 0 then statement true.

d. We have to prove columns of the augmented matrix (AB) are linearly independent.

When m ≠ 0 and m∈R and n= 0

Therefore, Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.

e. We have to prove the system AX = 0 has a unique solution.

When [tex]\left[\begin{array}{ccc}2&1&0 \\0&-1&3 \\0&0&m \end{array}\right]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}0\\0\\0\end{array}\right][/tex]

The equation are 2x + y = 0, -y + 3z = 0 and mz = 0

m ≠ 0 should be any real number except zero.

Therefore, The system AX = 0 has a unique solution when m ≠ 0 then statement true.

f. We have to prove at least one eigenvalue of the matrix A is zero.

When λ = 2, 1, m

m = 0 then eigen value is zero

Therefore, At least one eigenvalue of the matrix A is zero when m = 0 then statement true.

g. We have to prove columns of the matrix A form a basis in R³.

When m ≠ 0

Therefore, Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.

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Answer:

9 square units

Step-by-step explanation:

Area of a square = base * height

= 3*3

= 9

Answer:

The class in the second and longest bar graph (the one labeled 3) has the most students.

Step-by-step explanation:

When looking for the largest amount of something in bar graphs, the largest bar graph is correct. In this case the second bar graph is the longest, and we can see it indicates the class contains 28 students.

Answer:

Below :)

Step-by-step explanation:

Least/Minimum: 0

Greatest/Maximum: 6

Median: 2

Lower Quartile Range: 1

Upper Quartile Range: 3

Find median:

0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 6

Find Lower Quartile:

0, 1, 1, 1, 1, 1, 1, 2, 2, 2

Find Upper Quartile:

2, 2, 3, 3, 3, 3, 4, 4, 4, 6

Answer:

y=-2+8

Step-by-step explanation:

The answer is y=-2+8 because of course the slope has to be -2 as you stated in your Question. So all you have to do is change the Y-Intercept until you reach the point. Since the Slope is negative, the Y-Intercept will rise until you reach your point. You may double check my answer to see if it is right, it is up to you. If you find any fault in my answer please let me know. Have a good day!

The  diameter of the rod required to limit the total elongation to 0.10 inches is approximately 1-1/2 inches (or 1.441 inches to be more precise). Hence, the correct answer is option (A) with an elongation of 0.2358 inches and using a 1-1/2" diameter rod.

(a) To compute the total elongation, we can use the formula:

Elongation = (P * L) / (A * E)

where P is the axial tensile load, L is the length of the rod, A is the cross-sectional area of the rod, and E is the modulus of elasticity for the material.

Given:
P = 30,000 lb
L = 20 ft = 240 in
Diameter of the rod = 1-1/2 in

First, we need to calculate the cross-sectional area:

Area = π * (diameter/2)^2
Area = π * (1.5/2)^2
Area ≈ 1.767 in^2

Next, we need to determine the modulus of elasticity for the material. Assuming it's a standard structural steel, we can use a typical value of 29,000,000 psi.

Now we can plug the values into the formula:

Elongation = (30,000 * 240) / (1.767 * 29,000,000)
Elongation ≈ 0.2358 in

Therefore, the total elongation is approximately 0.2358 inches.

(b) If the total elongation must not exceed 0.10 inches, we need to determine the diameter of the rod that satisfies this requirement.

We can rearrange the formula for elongation to solve for the cross-sectional area:

A = (P * L) / (E * Elongation)

Using the given values:

A = (30,000 * 240) / (29,000,000 * 0.10)
A ≈ 2.069 in^2

To find the corresponding diameter, we use the formula:

Diameter = √(4 * A / π)

Diameter = √(4 * 2.069 / π)
Diameter ≈ 1.441 in

Therefore, the diameter of the rod required to limit the total elongation to 0.10 inches is approximately 1-1/2 inches (or 1.441 inches to be more precise). Hence, the correct answer is option (A) with an elongation of 0.2358 inches and using a 1-1/2" diameter rod.

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Answer: The mood of the third-person account is less emotional and more matter-of-fact. The mood of Claudette's account is less emotional and more matter-of-fact.

Step-by-step explanation:

Answer:

3n + 2

Step-by-step explanation:

−n+(−4)−(−4n)+6

-n - 4 + 4n + 6

3n + 2

Answer:

c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

There is a 40% probability of Jonah grabbing  a powdered doughnut from  Bag 1.

Step-by-step explanation:

Total number of doughnuts in the bag 1 =20

Total powdered doughnuts in each bag = 8

Probability of selecting powdered doughnut from  Bag 1 by Jonah =

[tex]\frac{8}{20} * 100\\40[/tex]%

The sum of the squared deviation for the given sample data (23, 27, 35, 44) is 212.00.

In statistics, the squared deviation is calculated by subtracting each data point from the mean and then squaring the result. The sum of these squared differences gives us a measure of how much the individual data points vary from the mean.  

Find the sum of squared deviations, we first calculate the mean of the data set. In this case, the mean is found by adding up all the values (23 + 27 + 35 + 44) and dividing the sum by the number of data points (4).

The mean turns out to be 32.25.Next, we subtract the mean from each data point:

(23 - 32.25) = -9.25

(27 - 32.25) = -5.25

(35 - 32.25) = 2.75

(44 - 32.25) = 11.75

Then, we square each of these differences:

(-9.25)² = 85.56

(-5.25)² = 27.56

(2.75)² = 7.56

(11.75)² = 138.06

Finally, we sum up these squared deviations:

85.56 + 27.56 + 7.56 + 138.06

= 212.00

Therefore, the sum of the squared deviations is 212.00 (rounded to two decimal places).

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Answer:

[tex]y = 0.25x + 4[/tex]

[tex](x,y) = (2,4.5)[/tex]

Step-by-step explanation:

Given

[tex]x = 2[/tex]

[tex]y = 4.5[/tex]

Required

Make up a linear function

A linear function is represented as:

[tex]y = mx + b[/tex]

Assume [tex]b = 4[/tex]

The equation becomes

[tex]y = mx + 4[/tex]

Substitute [tex]x = 2[/tex] and [tex]y = 4.5[/tex] to solve for m

[tex]4.5 = m*2 + 4[/tex]

[tex]4.5 = 2m + 4\\[/tex]

Solve for m

[tex]2m = 4.5 - 4[/tex]

[tex]2m = 0.5[/tex]

[tex]m = 0.5/2[/tex]

[tex]m = 0.25[/tex]

So, we have:

[tex]m = 0.25[/tex], [tex]b = 4[/tex], [tex]x = 2[/tex] and [tex]y = 4.5[/tex]

[tex]y = mx + b[/tex] becomes

[tex]y = 0.25x + 4[/tex]

[tex](x,y) = (2,4.5)[/tex]

Answer:

13 ft

Step-by-step explanation:

The formula to find the length of the diagonal of a rectangle =

Diagonal² = Length² + Width²

Diagonal = √Length² + Width²

Length = 12 ft

Width = 5ft

Diagonal = √12² + 5²

Diagonal = √144 + 25

Diagonal = √169

Diagonal = 13 ft

The length of the diagonal of the rectangle = 13 ft

Answer:

32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

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