"Need b and c anwsered please with work shown.
thank you.
(b) What is the limit definition of f'(x), the derivative of f(x)? (c) Give an example of a function that is continuous at z = 2, but that is not differentiable at z = 2.
b) The limit definition of f'(x), the derivative of f(x), is given by:
f'(x) = lim(h→0) [f(x + h) - f(x)] / h
This definition represents the slope of the tangent line to the function f(x) at a given point x. By taking the limit as h approaches 0, we calculate the instantaneous rate of change of f(x) with respect to x.
c) An example of a function that is continuous at z = 2 but not differentiable at z = 2 is the function f(z) = |z - 2|. This function represents the absolute value of the difference between z and 2. At z = 2, the function is continuous since the left and right limits are equal. However, the function is not differentiable at z = 2 because the left and right derivatives do not match. The left derivative is -1, while the right derivative is +1.
the limit definition of the derivative provides a way to calculate the instantaneous rate of change of a function. The function f(z) = |z - 2| serves as an example of a function that is continuous but not differentiable at z = 2. This demonstrates that continuity alone does not guarantee differentiability at a specific point.
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Compound Probability. What is the probability that either event will occur?
Now, find the probability of event A and event B.
A
B
6
6
20
20
P(A and B) = [?]
The probability of event A and event B occurring simultaneously is 0.09.
The probability that either event A or event B will occur, we need to use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
So,
P(A) = 6/20 = 0.3
P(B) = 6/20 = 0.3
P(A and B) = the probability of both events A and B occurring simultaneously, which is not given in the question.
Therefore, we cannot find the probability that either event A or event B will occur without knowing P(A and B).
To find the probability of event A and event B occurring simultaneously, we use the formula:
P(A and B) = P(A) x P(B)
So,
P(A and B) = (6/20) x (6/20) = 0.09
Therefore, the probability of event A and event B occurring simultaneously is 0.09.
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If Cos A = 9/41 and tan B = 28/45 angle A and B are in quadrant I find the value of Tan(A+B)
4. consider the matrix a = 1 0 1 0 1 1 1 1 0 . (a) solve the equation det(a − λi) = 0 to find the eigenvalues.
To find the eigenvalues of matrix A, we need to solve the equation det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix.
Given matrix A:
A = |1 0 1|
|0 1 1|
|1 1 0|
We subtract λI from A:
A - λI = |1-λ 0 1 |
|0 1-λ 1 |
|1 1 -λ |
Taking the determinant of A - λI:
det(A - λI) = (1-λ)[(1-λ)(-λ) - 1] - [(0)(-λ-1) - (1)(1)] + [1 - 0 + (1-λ)(1)]
= (1-λ)[-λ^2 + λ - 1] - 1 + [1 - λ + 1 - λ^2]
= -λ^3 + 2λ^2 - 2λ
To find the eigenvalues, we set the determinant equal to zero:
-λ^3 + 2λ^2 - 2λ = 0
This is a cubic equation, which can be factored or solved using numerical methods to find the eigenvalues.
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Please help me with this problem.
Answer:
60
Step-by-step explanation:
\(45^{2} +b^{2} =75^{2} \\2025+b^{2}=5625\\b^{2} =3600\\b=60\)
Answer:
60 m
Step-by-step explanation:
use Pythagorean Theorem:
a = missing side
a² + 45² = 75²
a² + 2025 = 5625
a² = 3600
a = \(\sqrt{3600}\)
a = 60
Pls help me. It due ASAP...
Answer:
b
Step-by-step explanation:
Please help!!!! I don’t understand show all your work please
The surface area of the prism is 426 square cm
How to solve the areas?The given parameters are:
Length = 9 cm
Width = 5 cm
Height = 12 cm
The areas are calculated as:
Area of the left side = 9 * 12 = 108 square cmArea of the top = 5 * 9 = 45 square cmArea of the front = 5 * 12 = 60 square cmArea of the bottom = 5 * 9 = 45 square cmArea of the right side = 9 * 12 = 108 square cmArea of the back = 5 * 12 = 60 square cmAdd the above areas to determine the surface area
Surface area = 108 + 45 + 60 + 108 + 45 + 60
Evaluate
Surface area = 426
Hence, the surface area of the prism is 426 square cm
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use a calculator to evaluate the function at the indicated value of x. round your result to three decimal places. function value f(x) = 3 ln(x) x = 0.36
The function value f(x) = 3 ln(x) at x = 0.36 is approximately equal to -3.065 when rounded to three decimal places.
To evaluate the function value f(x) = 3 ln(x) at x = 0.36 using a calculator and rounding the result to three decimal places, we can follow these steps:
1. Enter the value of x in the calculator: 0.36
2. Find the natural logarithm of x by pressing the "ln" or "log" button on the calculator: ln(0.36) = -1.02165124753
3. Multiply the result by 3: 3 * (-1.02165124753) = -3.06495374259
4. Round the final result to three decimal places: -3.065
The function value f(x) = 3 ln(x) at x = 0.36 is approximately equal to -3.065 when rounded to three decimal places.
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3. Find the area of the triangle T with sides u = (4,4,4), v = (16,0,16), and u-v. (The area of a triangle is half the area of the corresponding parallelogram.)
The area is_______________
(Type an exact answer, using radicals as needed.)
To find the area of a triangle with sides u, v, and u-v, we can use the formula: area = 1/2 ||u x v||, where ||u x v|| is the magnitude of the cross product of u and v.
Given the sides of the triangle as u = (4,4,4), v = (16,0,16), and u-v, we can calculate the area of the triangle.
First, we calculate the cross product of u and v: u x v = (4,4,4) x (16,0,16) = (4,4,4) x (0,16,0) = (64,0,-64).
Next, we calculate the magnitude of the cross product: ||u x v|| = sqrt(64^2 + 0^2 + (-64)^2) = sqrt(2 * 64^2) = 64 * sqrt(2).
Finally, we use the formula for the area of the triangle: area = 1/2 ||u x v|| = 1/2 * 64 * sqrt(2) = 32 * sqrt(2).
Therefore, the area of the triangle T with sides u, v, and u-v is 32 * sqrt(2).
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HELP IM MARKING BRAINLEIST
Answer:
x = 104
y = 74
Step-by-step explanation:
According to the figure, the quadrilateral has two pairs of parallel, opposite sides. That makes the quadrilateral a parallelogram.
In a parallelogram, opposite sides are congruent and opposite angles are congruent.
Because of congruent sides:
x - 7 = 97
x = 104
Because of congruent angles:
y = 74
Please help me. Solve for x.
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
\(\cfrac{x}{48}=\cfrac{48}{64}\implies \cfrac{x}{48}=\cfrac{3}{4}\implies 4x=144\implies x=\cfrac{144}{4}\implies \boxed{x=36}\)
what is 10000 in expanded form ?
Answer:
\({ \red{ \bold{ = 1 \times 10 {}^{4}}}}\)
Step-by-step explanation:
Step 1: Write the initial number as a product of its first digit and matching place value
\( {\red {\bold{10 \: 000 = 1 \times 10 \: 000}}}\)
Step 2: Write 10000 as 10 to the power of 4
\({ \boxed{ \red{ \bold{10 \: 000 = 1 \times 10 {}^{4}}}}}\)
Hence, This is the expanded form with exponents of the initial number !
What type of number is shown below?
Answer:
Irrational number
Step-by-step explanation:
It's an Irrational number
Help me with this pls
find the values of the basic trigonometric functions for an angle in standard position passing through (6,8)
The values οf the basic trigοnοmetric functiοns fοr an angle in standard pοsitiοn passing thrοugh (6,8) are:
\(\sin \theta &= 0.8\\\) \(\cos \theta &= 0.6\), etc.
What is trigοnοmetry?Trigοnοmetry is a branch οf mathematics that deals with the study οf triangles and the relatiοnships between their sides and angles.
We can begin by finding the length οf the hypοtenuse οf the right triangle fοrmed by the given pοint and the οrigin. This will give us the value οf the trigοnοmetric functiοns sine, cοsine, and tangent.
The hypotenuse can be found using the Pythagorean theorem:
\(c^2 &= a^2 + b^2\)
\(&= 6^2 + 8^2\)
\(&= 36 + 64\)
\(&= 100\)
\(c &= \sqrt{100}\)
\(c &= 10\)
Therefore, the point (6,8) is 10 units away from the origin.
The sine of the angle can be found by dividing the opposite side (8) by the hypotenuse (10):
\(\sin \theta &= \frac{8}{10}\)
\(&= 0.8\)
The cosine of the angle can be found by dividing the adjacent side (6) by the hypotenuse (10):
\(\cos \theta &= \frac{6}{10}\)
\(&= 0.6\)
The tangent of the angle can be found by dividing the opposite side (8) by the adjacent side (6):
\(\tan \theta &= \frac{8}{6}\)
\(&= \frac{4}{3}\)
Therefore, the values of the basic trigonometric functions for an angle in standard position passing through (6,8) are:
\(\sin \theta &= 0.8\)
\(\cos \theta &= 0.6\)
\(\tan \theta &= \frac{4}{3}\)
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Find the probability, expressed to the nearest percent, that a variable has a z-score less than 0.42. 65% 6690 6798 689
Explanation:
The probability that a variable has a z-score less than a number - let's call this number 'a'- is represented on a z-score table. Each number in the table represents the area under the curve on to the left of 'a':
In other words, the numbers in the table are the probability of the variable being less than a:
\(P(Z\(P(Z<0.42)=0.6628\)If we multiply by 100 we have the probability expressed as a percent: 66.28%.
Answer:
Rounded to the nearest percent, P( Z < 0.42) = 66%
select all the expressions that equal.. *see picture for problem*
Answer:
Step-by-step explanation:
oknjbgfkdfrgn jnfbfl
A cafeteria worker is cutting apple wedges for student lunches.Each student lunch requires two apple wedges
The number of apple wedges that the cateteria worker needs to prepare is a linear function of the number of student lunches. Which statement correctly describes the domain of this function?
A numbers
B all real numbers
C all whole numbers
D all even whole numbers
t + (-5) = 14
can someone solve the equation please?
Answer: 19
Add 5 to both sides
t - 5 = 14
t - 5 + 5 =14 + 5
Simplify
T=19
Hope this helped
What must be the value of c , if the following is to be a probability density function? Round your answer to two decimal places.
{c(5x − 4 − x2)0if 1 ≤ x ⩽ 4otherwise Numeric Response
The value of c that makes the given function a probability density function is 3/2.
A probability density function is a function that describes the likelihood of a random variable taking on a specific value within a given range.
In order for a function to be a probability density function, it must satisfy certain conditions, such as being non-negative and integrating to 1 over its domain.
In this problem, we are given a function:
c(5x - 4 - x²)if 1 ≤ x ≤ 4, and 0 otherwise.
We need to find the value of c that will make this function a probability density function. That means we need to check whether the function is non-negative and integrates to 1 over the interval [1, 4].
First, let's check whether the function is non-negative. Since c is a constant, we just need to look at the expression inside the parentheses.
For this expression to be non-negative, we need to find its roots:5x - 4 - x² = 0⇒ x² - 5x + 4 = 0⇒ (x - 1)(x - 4) = 0The roots are x = 1 and x = 4.
We can see that the expression inside the parentheses is negative between these two roots, and positive outside this interval.
Therefore, the function is only non-negative for values of x between 1 and 4.Next, let's check whether the function integrates to 1 over the interval [1, 4].
We can do this by evaluating the integral:
integral(1, 4, c(5x - 4 - x²)) = 1
We can simplify this expression by pulling the constant c outside the integral and then integrating the expression inside the parentheses:
integral(1, 4, 5x - 4 - x²) = 1
Using the power rule of integration, we get:
[(5/2)x² - 4x - (1/3)x³]1⁴ = 1
Simplifying this expression, we get:
(5/2)(4²) - 4(4) - (1/3)(4³) - (5/2)(1²) + 4(1) + (1/3)(1³) = 1
Solving for c, we get:
c = 3/2
So the value of c that makes the given function a probability density function is 3/2.
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In a two-way ANOVA with interaction, a significant interaction term indicates that A) The response variable is interactive. B) A blocking factor is present. C) Both factors are unrelated. D) Both factors have a combined effect on the response variable.
The correct option is D) Both factors have a combined effect on the response variable.
In a two-way ANOVA with interaction, the interaction term refers to the combined effect of two independent variables (factors) on the response variable. It assesses whether the relationship between one independent variable and the response variable changes based on the different levels of the other independent variable.
If the interaction term is found to be significant, it indicates that the effect of one independent variable on the response variable is not consistent across different levels of the other independent variable. In other words, the impact of one factor on the response variable depends on the specific level or condition of the other factor.
This suggests that the factors are not independent of each other and that they interact to influence the response variable.
Therefore, option D is the correct answer. A significant interaction term in a two-way ANOVA with interaction indicates that both factors have a combined effect on the response variable, with the relationship between one factor and the response variable being influenced by the levels of the other factor.
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What is another word that describes the zeros of a quadratic function.
A different term for a quadratic function's zeros is "roots." The zeros or roots of a quadratic function are the points on the x-axis where the function meets or crosses it.
They stand in for the x values at which the quadratic function equals zero. Depending on the discriminant of the quadratic equation, the zeros or roots of a quadratic function can either be real or complex integers. The quadratic has two unique real roots if the discriminant is positive. The quadratic has a single real root, also referred to as a double root or repeating root, if the discriminant is zero. The quadratic has two complex roots that can be represented as a + bi if the discriminant is negative.
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WHAT IS THE RADIUS OF A SPHERE IF THE
SURFACE AREA IS 256T?
Answer: \(\frac{8}{\sqrt{\pi} }\) , simplified to \(\frac{8\sqrt{\pi} }{\pi} }\)
Step-by-step explanation:
The formula for the surface area of a sphere is:
Surface area = \(4\pi r^2\)
256 = \(4\pi r^2\)
64 = \(\\\pi r^2\)
\(\sqrt{\frac{64}{\pi} } = r\)
Thats the radius!
Answer the following questions. (a) Find the determinant of matrix B by using the cofactor formula. B= 3 0 - 2 0
2 3 0 7
-2 0 1 0
5 0 0 1 (b) First, find the PA= LU factorization of matrix A. Then, det A.
A= 0 2 5
3 1 2 3 5 5
Therefore, the determinant of matrix B is 13. The determinant of A is the product of the pivots in the upper triangular matrix U is 6/5.
(a) Using the cofactor formula, we have:
|B| = 3 * |3 0 7|
- 2 * |2 0 1|
+ 0 * |-2 0 1|
= 3 * (3*1 - 0*5) - 2 * (2*1 - 0*(-2)) + 0 * (-2*0 - 0*1)
= 9 + 4 + 0
= 13
(b) To find the PA=LU factorization of matrix A, we perform Gaussian elimination with partial pivoting. The first step is to interchange the first and second rows to get a nonzero pivot in the (1,1) position:
| 3 1 2 | | 3 1 2 |
| 0 2 5 | -> | 0 -5 -1 |
| 3 5 5 | | 0 0 5 |
Next, we perform row operations to get zeros below the pivot in the second row:
| 3 1 2 | | 3 1 2 |
| 0 -5 -1 | -> | 0 -5 -1 |
| 0 4 3 | | 0 19 11 |
Finally, we divide the second row by -5 and subtract 3 times the second row from the third row to get zeros below the (3,2) position:
| 3 1 2 | | 3 1 2 |
| 0 1 1/5| -> | 0 1 1/5|
| 0 0 2/5| | 0 0 32/5|
Therefore, we have:
A = LU = | 3 1 2 | | 1 0 0 | | 3 1 2 |
| 0 1 1/5 | * | 0 1 0 | = | 0 1 1/5|
| 0 0 2/5 | | 0 0 32/5| | 0 0 2/5 |
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Two parallel lines are cut by a transversal as shown below.
Suppose m /_4 = 81. Find m /_ 5 and m /_ 7.
When the parallel lines are cut by a transversal, the values for the measurement of ∠5 and ∠7 is 99° each.
What are parallel lines?
Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible.
Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.
In the given diagram the parallel lines are cut by a transversal.
The measure of angle 4 is, m∠4 = 81°.
It is known that each pair of interior angles on the same side of a transversal that cuts two parallel lines are supplementary, or they add up to 180 degrees.
So, m∠4 + m∠5 = 180°
81° + m∠5 = 180°
m∠5 = 180° - 81°
m∠5 = 99°
Now, as it can be seen in the image ∠5 and ∠7 are vertically opposite angles.
So, they will be congruent or equal to each other.
So, it is obtained that -
m∠5 = m∠7
m∠7 = 99°
Therefore, the measures of angles are m∠5 = 99° and m∠7 = 99°.
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Find the critical value Za/2 corresponding to a 99.5% confidence level.
0.0025
2.575
2.81
1.96
Answer:
The correct option is;
2.81
Step-by-step explanation:
The critical value \(Z_{\alpha /2}\), is found from the z score table as follows, where the the confidence level is 99.5
Therefore, we have α = 1 - 99.5/100 = 1 - 0.995 = 0.005
α/2 = 0.0025
The critical value is thus found from the z-score table value of 1 - 0.0025 = 0.9975
From the z-table, we can find the 0.9975 score on the row with z = 2.8 where 0.9975 can be located under the 0.1 column giving the critical value as 2.81
help me please!!! will mark brainliest!!
Answer:
2
Step-by-step explanation:
(0,2) is the y-intercept
Change the word phrase to an algebraic expression. Use x to represent the number. The product of 9 and two more than a number
The algebraic expression for "The product of 9 and two more than a number" is 9(x + 2).
In the given word phrase, "a number" is represented by the variable x. The phrase "two more than a number" can be translated as x + 2 since we add 2 to the number x. The phrase "the product of 9 and two more than a number" indicates that we need to multiply 9 by the value obtained from x + 2. Therefore, the algebraic expression for this word phrase is 9(x + 2).
"A number": This is represented by the variable x, which can take any value.
"Two more than a number": This means adding 2 to the number represented by x. So, we have x + 2.
"The product of 9 and two more than a number": This indicates that we need to multiply 9 by the value obtained from step 2, which is x + 2. Therefore, the algebraic expression becomes 9(x + 2).
In summary, the phrase "The product of 9 and two more than a number" can be algebraically expressed as 9(x + 2), where x represents the number.
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imani got a notice from the bank saying that she had overspent, so her account balance was -$43. She wrote an additional check for $50 after she overdrew her account. What will be imanis bank account balance once the new check goes through?
Answer:
-93
..................................................................................................................................................
Answer:
i believe its 7 because -43+50 = 7
Step-by-step explanation:
(PLEASE ANSWER ASAP I JUST NEED TO CHECK MY ANSWER PLEASE EXPLAIN ALSO)
Answer:
1 hour and half an hour
Step-by-step explanation:
cause 3 hours minus 1 hour minus half an hour equal to 1 hour and half, hope this help u