In problem 4, we found the center of the circle to be (2,3) and in problem 5, we found the center of the ellipse to be (2,4). To determine where the slopes of the tangent lines at x-values near x=a are changing slowly, we need to look at the derivatives of the functions at those points. In problem 4, the function was f(x) = sqrt(4 - (x-2)^2), which has a derivative of - (x-2)/sqrt(4-(x-2)^2). At x=2, the derivative is undefined, so we cannot determine where the slope is changing slowly. In problem 5, the function was f(x) = sqrt(16-(x-2)^2)/2, which has a derivative of - (x-2)/2sqrt(16-(x-2)^2). At x=2, the derivative is 0, which means that the slope of the tangent line is not changing, and therefore, the center of the ellipse is where the slopes of the tangent lines at x-values near x=a are changing slowly.
To compare the slopes of the tangent lines near x=a for the circle and ellipse, we need to look at the derivatives of the functions at those points. In problem 4, we found the center of the circle to be (2,3), and the function was f(x) = sqrt(4 - (x-2)^2). The derivative of this function is - (x-2)/sqrt(4-(x-2)^2). At x=2, the derivative is undefined because the denominator becomes 0, so we cannot determine where the slope is changing slowly.
In problem 5, we found the center of the ellipse to be (2,4), and the function was f(x) = sqrt(16-(x-2)^2)/2. The derivative of this function is - (x-2)/2sqrt(16-(x-2)^2). At x=2, the derivative is 0, which means that the slope of the tangent line is not changing. Therefore, the center of the ellipse is where the slopes of the tangent lines at x-values near x=a are changing slowly.
In summary, we compared the slopes of the tangent lines near x=a for the circle and ellipse, and found that the center of the ellipse is where the slopes of the tangent lines at x-values near x=a are changing slowly. This is because at x=2 for the ellipse, the derivative is 0, indicating that the slope of the tangent line is not changing. However, for the circle, the derivative is undefined at x=2, so we cannot determine where the slope is changing slowly.
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i need help with this page
what is x and y? i’m having trouble finding what x and y are
Answer:
y is 7, x is 14
Step-by-step explanation:
This is a 30-60-90 triangle,
The hypotenuse, the side opposite of the 90 degree angle, is twice the length of the side opposite of the 30° angle,
The side opposite of the 60° degree angle, is root 3 times the side opposite of the 30° degree angle
So y is
[tex] \frac{7 \sqrt{3} }{ \sqrt{3} } = 7 = y[/tex]
Then, that means x is
[tex]7 \times 2 = 14[/tex]
Angle 0 intersects the unit circle at point (-0.9483, -0.3173). What is the value of tan(0)
The tangent in the unit circle is equal to 0.334.
How to calculate the value of the function tangent with the help of a unit circle
In trigonometry, unit circles are representations of a circle with radius 1 and centered at the origin of a Cartesian plane commonly use to estimate and understand angles and trigonometric functions related to them.
Angles are generated by line segments whose coordinates are of the form (x, y), where x is the position of the terminal point along the x-axis and y is the position of the terminal point along the y-axis.
In addition, the tangent of the angle generated in a unit angle is defined by the following equation:
tan θ = y / x (1)
If we know that x = - 0.9483 and y = - 0.3173, then the tangent of the angle generated in the unit circle is:
tan θ = (- 0.3173)/(- 0.9483)
tan θ = 0.334
The tangent in the unit circle is equal to 0.334.
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20 PIONTSSS TO WHOEVER ANDWER THIS QUESTION !!! NEED HELP
The surface area of prism 1 is 36 cm²
Calculating surface areaFrom the question, we are to calculate the surface area of prism 1
From the given information, we have that the two hexagon-based prism are similar
Since the shapes are similar, we can write that
(Length of a side in prism 1)² / (Length of the similar side in prism 2)² =
Area of prism 1 / Area of prism 2
From the given information,
Length of a side in prism 1 = 3 cm
Length of the similar side in prism 2 = 8 cm
Area of prism 2 = 256 cm²
Thus,
3² / 8² = Area of prism 1 / 256
Area of prism 1 = (256 × 3²)/ 8²
Area of prism 1 = (256 × 9)/ 64
Area of prism 1 = (2304)/ 64
Area of prism 1 = 36 cm²
Hence, the surface area of prism 1 is 36 cm²
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Question 6 of 25
A high school teacher grades a math test. She wants to see the numerical
grade of each student. Which item should she use so she can quickly see
how many students got each score?
A. None of these
B. Frequency table
OC. Line plot
OD. Pie chart
Suppose you start at the origin, move along the x-axis a distance of 6 units in the positive direction, and then move downward parallel to the z-axis a distance of 4 units. What are the coordinates of your position
The coordinates of your position are (6, 0, -4).
place 3 numbers between 12 and 60 to make a sequence of 5 numbers with a common difference
Answer:
12-24-36-48-60
if I'm wrong I will try to get back to you and right my wrong
The ratio of color paper to white is 3:8, if there is 48 white paper how many is colour
There might be 18 colored papers.
colored papers to white papers:
3:8
48 white papers
8x6 = 48
Then 3x6= 18
There might be 18 colored papers.
Ratios evaluate numbers, normally through dividing them. in case you are evaluating one facts factor (A) to another statistics factor (B), your formulation might be A/B. this indicates you are dividing data A by using information B. for example, if A is 5 and B is 10, your ratio will be 5/10.
In mathematics, a ratio indicates how many times one quantity incorporates some other. for instance, if there are 8 oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is 8 to 6. further, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the full amount of fruit is 8:14.
Ratios can be absolutely simplified just like fractions. To simplify a ratio, divide all the numbers in the ratio through the same wide variety until they can not be divided anymore.
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Common significance levels are 0.01 and 0.05. why would it be unwise to use a significance level with a number like 0.0483?
Common significance levels are 0.01 and 0.05. Because the observations in the sample do not come from a random pool, it is impossible to conduct a test based on a population percentage by utilizing the normal approximation approach. This is further explained below.
What is probability?Generally, The possibility of an occurrence may be quantified using the concept of probability. There are many occurrences that cannot be foreseen with complete accuracy.
In conclusion, Both 0.01 and 0.05 are considered to be significant values. It is not feasible to perform a test based on a population percentage using the normal approximation technique because the observations in the sample do not originate from a random pool. This makes it impossible to utilize the normal approximation approach.
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Use the graph to find the solution.
Given the graph of w(x), w(2) = ?
(the graph is below)
THE FIRST ANSWER WILL GET BRAINLIEST OR 5 STARS! PLEASE ANSWER QUICK :)
Answer:
W(2) = 5
Step-by-step explanation:
Because when you look at the graph, the y value is 5 when the x value is 2.
Answer:
w(2) = 5
Step-by-step explanation:
by using rise over run to find the slope easily, you get a slope of 4 and an equation of w(x) = 4x - 3, -3 being the y-intercept
to calculate w(2):
w(2) = 4(2) - 3
w(2) = 8 - 3
w(2) = 5
or you could just look at when y is 2 and see that the corresponding x value is 5 but i wanted to provide a longer explanation in case :)
After working 80 hours at his job, Tyshawn earned a total of $1080. How much does Tyshawn earn
per hour?
The amount Tyshawn earn per hour is $13.5
Ratio and proportionFractions are written as a ratio of two integers
If after working 80 hours at his job, Tyshawn earned a total of $1080, then;
80 hrs = $1080
In order to calculate the amount earned per hour
Amount per hour = 1080/80
Amount per hour = $13.5
Hence the amount Tyshawn earn per hour is $13.5
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You start driving west for 20 miles, turn left, and drive south for another 14 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile
Answer:
24.4
Step-by-step explanation:
The polygon circumscribes the circle. Which of the following is the perimeter of the polygon?
A. 39 cm
B. 56 cm
C. 61 cm
D. 78 cm
The perimeter of the polygon that circumscribes the circle is 78 cm
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The circle tangent theorem states that tangents which meet at the same point are equal in length. Hence:
The missing lengths are 8, 6, 9 and 16.
Perimeter of the polygon = 2(8) + 2(6) + 2(9) + 2(16) = 78 cm
The perimeter of the polygon that circumscribes the circle is 78 cm
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How many triangles are there?
Answer:
15 triangles.
Step-by-step explanation:
just count them eventually you will reach there.
13. If 3x = xy - 5 and y = 6, what is the value of x? (A) (C) / (B) 3) - 5 (D) slas1 5 اقعا our win
Answer:
x = 5/3
Step-by-step explanation:
3x = xy - 55
3x = x*6 - 5
3x = 6x - 5
3x = 5
x = 5/3
What is the result of taking the difference between sample means, minus the null hypothesized difference, divided by the standard error of the difference between means?
The result of taking the difference between sample means, minus the null hypothesized difference, divided by the standard error of the difference between means is the t-statistic.
What is a t-statistic?When deciding whether to accept or reject the null hypothesis in a T test, the t-statistic is used. It functions similarly to a Z-score in that you choose a cutoff point, calculate your t score, and then compare the two. When you have a limited sample size or don't know the population standard deviation, you utilize the t-statistic.
On its own, the t-statistic doesn't actually reveal much. Similar to how the word "average" is meaningless on its own without any context.
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Which expressions represent rational numbers? Check all that apply
The expressions that represent rational numbers are; √64 + 6/11, √16 + √169 and 17.43 + √49.
What are the rational expressions?A rational number is simply any integer, terminating decimal/repeating decimal or fraction.
1) √6 + √9 = √6 + 3 → Not rational
2) √64 + 6/11 = 94/11 → Rational number
3) √36 + √21 = 6 + √21 → Not rational
4) √16 + √169 = 17 → Rational number
5) 17.4343434343434343 + √49 = 24.43434343 → Rational number
6) √44 + √25 = 2√11 + 5 → Not rational
Therefore, the expressions that represent rational numbers are; √64 + 6/11, √16 + √169 and 17.43 + √49.
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Find the missing side length in the image below.
Answer:
6 is the ?
Step-by-step explanation:
Select the correct answer. A linear function graph of the x-axis and y-axis has a diagonal line that passes the x-axis at (minus 0.5, 0), and the y-axis at (0, 1) In the function above, the slope will be multiplied by , and the y-value of the y-intercept will be increased by 3 units. Which of the following graphs best represents the new function?
Answer: Graph Y
Step-by-step explanation:
Triangle RST has sides measuring 22 inches and 13 inches and a perimeter of 50 inches. What is the area of triangle RST? Round to the nearest square inch.
Heron’s formula: Area
19 square inches
37 square inches
60 square inches
95 square inches
Using the Heron's formula, the area of the triangle is: D. 95 square inches.
What is the Heron's Formula?Area = √[s(s - a)(s - b)(s - c)] where s is half the perimeter, or (a + b + c)/2.
Given the following:
s = semi-perimeter = 1/2(50) = 25 in.
a = length of side a = 22 in.
b = length of side b = 13 in.
c = length of side c = 50 - 22 - 13 = 15 in.
Plug in the values
Area = √[25(25 - 22)(25 - 13)(25 - 15)]
Area = √[25(3)(12)(10)]
Area ≈ 95 square inches.
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Answer:
d
Step-by-step explanation:
Which piece of additional information can be used to prove triangle cea triangle cdb
Answer:
well I don't get the question
An angle measures 8.8° more than the measure of its complementary angle. What is the measure of each angle?
Based on the definition of complementary angles, the two angles are: 49.4° and 40.6°.
What are Complementary Angles?Angles that are complementary angles have a sum of 90 degrees.
Let the angle be represented as x
Complement of the angle = (90 - x)
Therefore, we would have:
x = (90 - x) + 8.8
x = 90 - x + 8.8
x = 98.8 - x
x + x = 98.8
2x = 98.8
x = 98.8/2
x = 49.4°
The second angle would be: 90 - 49.4 = 40.6°
The angles are 49.4° and 40.6°.
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Mrs. Anderson had twice as many chickens as ducks. she sold 272 chickens and 16 ducks. She then had half as many chickens as ducks. How many chickens does she have?
The number of chickens she had was 352
Applications of equationsFrom the question, we are to determine the number of chicken she has
Let c represent chicken
and d represent ducks
From the given information,
Mrs. Anderson had twice as many chickens as ducks
c = 2d ---------- (1)
She sold 272 chickens and 16 ducks and then had half as many chickens as ducks
(c-272) = 1/2(d -16) ---------- (2)
Put equation (1) into (2)
2d - 272 = 1/2(d - 16)
2(2d - 272) = d- 16
4d - 544 = d - 16
4d - d = 544 - 16
3d = 528
d = 528/3
d = 176
Substitute the value of d into equation (1)
c = 2d
c = 2(176)
c = 352
Hence, the number of chickens she had was 352
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A rectangular rug is 12.5 feet long and 10 feet wide. The rug needs to be reduced by a factor of One-fifth. What is the area of the reduced rug?
The area of the reduced rug is 25 square feet
How to determine the area?The dimensions are given as:
Length = 12.5 feet
Width = 10 feet
The area is calculated as:
Area = Length * Width
So, we have:
Area = 12.5 * 10
Evaluate
Area = 125
When reduced by one-fifth, we have:
Area =1/5 * 125
Evaluate
Area = 25
Hence, the area of the reduced rug is 25 square feet
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After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly.
The relationship between the elapsed time ttt, in seconds, and the number of bacteria, B_{\text{second}}(t)B
second
(t)B, start subscript, start text, s, e, c, o, n, d, end text, end subscript, left parenthesis, t, right parenthesis, in the petri dish is modeled by the following function:
Bsecond(t)=6000⋅(1516)t
Complete the following sentence about the rate of change in the number of bacteria in minutes.
After a special medicine is introduced into a petri dish full of bacteria, Every second, the number of harmful bacteria remaining in the body decays by a factor of 0.97
What is bacteria?Generally, a kind of unicellular bacteria that has characteristics with many disease-causing organisms, such as having a cell wall but lacking organelles and an organized nucleus.
In conclusion, When a certain medication is put into a petri dish that is full of bacteria, the amount of pathogenic bacteria that are still present in the body decreases by a factor of 0.97 every single second.
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The ratio of butter:flour:sugar in a recipe is 1:9:6. When using 8 cups of sugar in this recipe, how many total cups of ingredients will be used
Answer:
21 and a third cups bxisjsbdn
Hurricane Andrew swept through southern Florida causing billions of dollars of damage. Because of the severity of the storm and the type of residential construction used in the semitropical area, there was some concern that the average claim size would be greater than the historical average hurricane claims of $24,000. Several insurance companies collaborated in a data gathering experiment. They randomly selected 84 homes and sent adjusters to settle the claims. In the sample of 84 homes, the average claim was $27,5000 with a population standard deviation of $2400. Is there sufficient evidence at a 0.02 significance level to support the claim that the home damage is greater than the historical average? Assume the population of insurance claims is approximately normally distributec. Compute the value of the test statistic.
The value of the t test is 13.36, we have to conclude that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.
The hypothesis formulationH0: u = 24000
H1: u > 24000
This test is a right tailed testwe have n = 84 homes
bar x = 27500
s = 2400
Next we have to find the test statistic
The formula for this is given as
[tex]t = \frac{x-u}{s/\sqrt{n} }[/tex]
When we out in the values we would have
[tex]t = \frac{27500-24000}{2400/\sqrt{84} }[/tex]
This would give us the answeer of the t test as
t test = 13. 3658
We have alpha = 0.02
the degree of freedom = 84 - 1 = 83
we have to find tα/2, df
= ±2.0865
Given that the value of the test statistic is greater than critical value we would have to then reject the null hypothesis.
Hence the conclusion that we can make is that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.
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Anna is reading a 300-page book. She can read a page in two minutes. If she has finished reading 75 percent of the pages, how many minutes of reading does she have left
Answer:
150 minutes
Step-by-step explanation:
If Anna read 75% of her 300-page book, then she has already read:
300 × 75%
= 300×0.75
= 225
225 pages.
If Anna has already read 225 pages, then she has:
300 - 225 = 75
75 pages left still to read.
If Anna reads 2 minutes per page, then she has
75 × 2 = 150 minutes.
She has 150 minutes of reading left to finish her book.
By the way, it's weird to say you have 150 minutes of something to do. In real life 150 minutes = 2 1/2 hours. jfyi. Have a great day!
ASAP PLEASEEEEE: The perimeter of a triangle is 44 inches.If one side is 5 inches longer than the smallest side and another side is 1 inch less than twice the smallest side, how many inches are there in the smallest side?
The measure of the smallest side of the triangle is 10 inches
Perimeter of a triangleA triangle is a shape that has 3 sides and angles. The perimeter of a shape is defined as the sum of the sides of the figure.
Let the length of the smallest side be x
If one side is 5 inches longer than the smallest side, then;
L1 = x + 5
If another side is 1 inch less than twice the smallest side, then;
L2 = 2x - 1
Take the sum to have:
x+x+5+2x-1 = 44
4x+4= 44
Subtract 4 from both sides
4x =44 - 4
4x = 40
Divide both sides by 4
x = 40/4
x = 10
Hence the measure of the smallest side of the triangle is 10 inches
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Which one of the following foods is the top source of protein chosen by Americans in the United States?
Answer:
The correct answer is beef
Step-by-step explanation:
I took the quiz and got it correct