You could use coordinate geometry to prove that ABCD is a rectangle by checking the side lengths, slope, and diagonal lengths using the distance and slope formulas.
What is a rectangle?
A rectangle is a quadrilateral with four right angles, meaning each of its angles measures 90 degrees. It is a type of parallelogram where opposite sides are parallel and equal in length. The opposite sides of a rectangle also have equal length, and its diagonals bisect each other. In addition to its geometrical properties, rectangles are commonly used in various fields for their symmetry, regularity, and practicality, such as in architecture, engineering, and graphic design.
To prove that quadrilateral ABCD is a rectangle using coordinate geometry, one possible method is to use the properties of a rectangle. Specifically, a rectangle is a quadrilateral with all four angles equal to 90 degrees and opposite sides equal in length.
So, to use coordinate geometry to prove that ABCD is a rectangle, you could:
Assign coordinates to the four vertices of ABCD, say A(x1,y1), B(x2,y2), C(x3,y3), and D(x4,y4).
Use the distance formula to calculate the lengths of each side of the quadrilateral, i.e., AB, BC, CD, and DA.
Use the slope formula to find the slopes of the four sides. Since opposite sides of a rectangle are parallel, their slopes will be equal.
Use the distance formula again to calculate the diagonal lengths, AC and BD.
Check that the opposite sides are equal in length and parallel, and that the diagonals are equal in length. If all these conditions are satisfied, then ABCD is a rectangle.
Therefore, you could use coordinate geometry to prove that ABCD is a rectangle by checking the side lengths, slope, and diagonal lengths using the distance and slope formulas.
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he buys a 5kg lwisa samp and repacks the samp into 125g packets. determine how many packets will be able to get from one pack of 5kg samp?
Answer:5
Step-by-step explanation:5555555
K
Factor the four-term polynomial by grouping.
x³ +9x² + 3x + 27
The factorization of the polynomial x³ + 9x² + 3x + 27 by grouping is:
x³ + 9x² + 3x + 27 = (x + 9)(x² + 3)
What is grouping?In algebra, "grouping" refers to a method of factoring polynomials that involves grouping together pairs of terms within the polynomial, in order to factor out a common factor.
What is polynomial?In mathematics, a polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
In the given question,
To factor the four-term polynomial by grouping, we can follow these steps:
Step 1: Group the first two terms and the last two terms together.
x³ + 9x² + 3x + 27
= (x³ + 9x²) + (3x + 27)
Step 2: Factor out the common factor from each group.
= x²(x + 9) + 3(x + 9)
Step 3: Notice that the expression (x + 9) is a common factor of both terms, and factor it out.
= (x + 9)(x² + 3)
Therefore, the factorization of the polynomial x³ + 9x² + 3x + 27 by grouping is:
x³ + 9x² + 3x + 27 = (x + 9)(x² + 3).
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Please help! Use the properties of exponents to simplify the expression.
Answer:
[tex] {y}^{6} {x}^{ - 2} [/tex]
Step-by-step explanation:
4 will get multiplied to the exponents of x and y inside the bracket.
What is the meaning of "field"?
This group is isomorphic to the group of invertible matrices GL(n) if the vector space has finite dimension n.
What is matrices?Matrices are rectangular arrays of numbers or other mathematical objects, such as complex numbers, polynomials, or functions. Matrices are an important tool in many branches of mathematics, including linear algebra, calculus, and statistics. A matrix is usually written with square brackets enclosing its elements, with rows and columns separated by commas or spaces.
by the question.
Yes, you are correct! The set of all n x n matrices with entries in a field (such as the real numbers) is a group under addition, known as the general linear group GL(n), where the operation is matrix addition. This group satisfies the four group axioms:
Closure: The sum of two matrices is also a matrix.
Associativity: Matrix addition is associative.
Identity: The zero matrix is the identity element of GL(n).
Inverse: For every matrix A in GL(n), there exists a matrix -A such that A + (-A) = 0.
However, the set of all n x n matrices with entries in a field is not a group under multiplication because matrix multiplication is not always commutative and not every matrix has an inverse with respect to matrix multiplication.
On the other hand, the set of invertible n x n matrices, denoted by GL(n) or GL (n, F) when the field is specified, does form a group under matrix multiplication. The group axioms are satisfied:
Closure: The product of two invertible matrices is invertible.
Associativity: Matrix multiplication is associative.
Identity: The identity matrix I_n is the identity element of GL(n).
Inverse: For every invertible matrix A in GL(n), there exists an inverse matrix A^-1 such that A * A^-1 = I_n.
Similarly, the set of invertible linear transformations of a vector space into itself forms a group under composition of functions, known as the general linear group GL(V) of the vector space V.
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Find the distance from Link to the Octorok so Link can attack
The distance from Link to the Octorok is 10.63 units.
How to find the distance?We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula below:
distance = √( (x₂ - x₁)² + (y₂ - y₁)²)
Here we want to find the distance from Link to the Octorok so Link can attack, so we need to get the distance between the points (-4, -5) and (3, 3).
The distance will be:
distance = √( (3 + 4)² + (3 + 5)²)
distance = √( (7)² + (8)²)
distance = √113
distance = 10.63
The distance is 10.63 units.
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find the coordinates of p so that p partitions segment ab in the part-to-whole ratio of 1 to 5 with a(-9, 3) and b(1, 8)
The coordinates of p so that p partitions segment ab in the part-to-whole ratio of 1 to 5 with a(-9, 3) and b(1, 8) is (-44/6, 23/6).
To find the coordinates of point P, we can use the following formula:
P = ( (5 x Ax + 1 x Bx) / 6 , (5 x Ay + 1 x By) / 6 )
Here, Ax and Ay are the x and y coordinates of point A, and Bx and By are the x and y coordinates of point B. By plugging in the values we have, we get:
P = ( (5 x (-9) + 1 x 1) / 6 , (5 x 3 + 1 x 8) / 6 )
P = ( (-45 + 1) / 6 , (15 + 8) / 6 )
P = ( -44/6 , 23/6 )
So the coordinates of point P are (-44/6, 23/6).
To check if we got the right answer, we can measure the distance between A and P and the distance between P and B, and make sure that the ratio is indeed 1 to 5. We can use the distance formula for this:
Distance between A and P:
√( (-9 - (-44/6))² + (3 - 23/6)² )
= √( (35/6)² + (5/6)² )
= √( 1225/36 + 25/36 )
= √( 1250/36 )
= 5/6 x √(50)
Distance between P and B:
√( (1 - (-44/6))² + (8 - 23/6)² )
= √( (55/6)² + (41/6)² )
= √( 3025/36 + 1681/36 )
= √( 4706/36 )
= 5/6 x √(94)
The ratio of the distance between A and P to the distance between P and B is:
(5/6 x √(50)) / (5/6 x √(94)) = √(50/94)
Simplifying this gives us:
√(50/94) = √(25/47)
The ratio of the distances is indeed 1 to 5, which confirms that our answer for the coordinates of P is correct.
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Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch.
I need help D: Please !!!!
The width of the top of the bookcase should be approximately 12.2 inches to give Bria's soap carving collection an area of 300 square inches.
How do you compute the area of a square inch?Simply multiply the length and width measurements to get the area of your square or rectangular area in square inches.
Assume the bookcase's top is rectangular, with length "L" and width "b". Because the area of a rectangle is the product of its length and width, we get:
L * b = 300
To find "b," we can rearrange the equation as follows:
b = 300 / L
We don't have enough information to directly solve for "L," but we can make an educated guess based on the figure provided. Based on the illustration, the bookcase appears to be roughly twice as long as it is wide. So let us suppose:
L ≈ 2b
When we plug this into the equation above, we get:
b = 300 / (2b) (2b)
To simplify, we have:
b^2 = 150
When we take the square root of both sides, we get:
b ≈ 12.2
We have, rounded to the nearest tenth of an inch:
b ≈ 12.2 inches
As a result, the width of the top of the bookcase should be approximately 12.2 inches in order to give Bria's soap carving collection a 300-square-inch area.
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can someone help please thank you. please
Answer:
1. Volume: 912 cm³
Surface Area: 672 cm²
2. Volume: 1239 1/3 cm³
Surface Area: 819 cm²
3. Volume: 216 2/3 cm³
Surface Area: 240 cm²
Step-by-step explanation:
Formula for Volume of a Pyramid: [tex]\frac{1}{3} * lwh[/tex]
(where l, w, and h are the length, width, and height, respectively)
Formula for Surface Area of a Square Pyramid: [tex]B + \frac{1}{2} ps[/tex]
(where B is the area of the base, p is the perimeter of the base, and s is the slant height)
1 (Volume) - V = (1/3)(12)(12)(19)
= (4)(12)(19)
= 912 cm³
1 (Surface Area) - SA = (12)(12) + (1/2)(4)(12)(22)
= 144 + 528
= 672 cm²
2 (Volume) - V = (1/3)(13)(13)(22)
= 1239 1/3 cm³
2 (Surface Area) - SA = (13)(13) + (1/2)(4)(13)(25)
= 169 + 650
= 819 cm²
3 (Volume) - V = (1/3)(10)(10)(6.5)
= 216 2/3 cm³
3 (Surface Area) - SA = (10)(10) + (1/2)(4)(10)(7)
= 100 + 140
= 240 cm²
Find the prime factorization of 792. What is the sum of the distinct prime factors?
The sum of the distinct prime factors is 16.
Solution:There are overall 24 factors of 792 among which 792 is the most significant factor and its prime factors are 2, 3, and 11.
Hence sum = 2 + 3 + 11 = 16
PLEASE I NEED HELP, what is the equivalent of 7/tan b+7tan b
In response to the stated question, we may state that The equivalent trigonometry expression of 7/tan b + 7tan b is (7 - 7tan b cot b)/sin b.
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
tan(A + B) = (tan A + tan B)/(1 - tan A tan B)
Set A = 90 degrees and B = b degrees:
tan(90 + b) = (tan 90 + tan b)/(1 - tan 90 tan b)
tan(90 + b) = (undefined + tan b)/(1 - undefined tan b)
tan(90 + b) = -cot b
7/tan b + 7tan b
= 7/(tan b) + 7(tan(90 + b) - 1)
= 7/(tan b) + 7(-cot b - 1)
= (7 - 7tan b cot b)/sin b
The equivalent expression of 7/tan b + 7tan b is (7 - 7tan b cot b)/sin b.
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-0.1x^2+10=0
find the x
Answer:
x = ±10
Step-by-step explanation:
1) Subtract 10 from both sides.
[tex]-0.1 \times x^2=-10[/tex]
2) Divide both sides by -0.1.
[tex]x^2=\frac{-10}{-0.1}[/tex]
3) Simplify [tex]\frac{-10}{-0.1}[/tex] to 100.
[tex]x^2=100[/tex]
4) Take the square root of both sides.
[tex]x=\pm \sqrt{100}[/tex]
5) Since 10 * 10 is 100, the square root of 100 is 10.
[tex]x=\pm10[/tex]
Eric and Erica collect phone cards, and their phone
cards are in a ratio of 3:4. If Erica has 14 more phone
cards than Eric, how many cards does Eric have?
Answer:
18.67
Step-by-step explanation:
my calculate ratio results
Simplify (number on picture) to an expression involving a single trig function with no fractions. If needed, enter squared trigonometric expressions using the following notation
Step-by-step explanation:
[tex] \frac{1 - \ { \sin(t) }^{2} } { { \sin(t) }^{2} } = \frac{1} { { \sin(t) }^{2} } - \frac{{ \sin(t) }^{2}}{{ \sin(t) }^{2}} \: = \frac{1} { { \sin(t) }^{2} } - 1[/tex]
[tex] = { \sin(t) }^{ - 2} - 1[/tex]
hope this helps
Write the slope-intercept form of the equation of the line.
Answer:
y = x + 2
Step-by-step explanation:
The slope intercept form is y = mx + b
m = the slope
b = y-intercept
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0,2) (-2, 0)
We see the y decrease by 2, and the x decrease by 2, so the slope is
m = -2 / -2 = 1
Y-intercept is located at (0,2)
So, the equation is y = x + 2
how do you find the simplest radical form for this please help me i got a (f) and i really need help that’s why i’m up this late trying to do all of my missing assignments.
Answer:
[tex]14 {y}^{2} \sqrt{ {x}^{3} {z}^{9} }[/tex]
Step-by-step explanation:
[tex] \sqrt{196 {x}^{3} {y}^{4}{z}^{9} }= \sqrt{196} \times \sqrt{ {x}^{3} } \times \sqrt{ {y}^{4} } \times \sqrt{ {z}^{9} } \\ \sqrt{196} = 14 \\ \sqrt{ {x}^{3} } = {x}^{ \frac{3}{2} } \\ \sqrt{ {y}^{4} } = {y}^{2} \\ \sqrt{ {z}^{9}} = {z}^{ \frac{9}{2} }[/tex]
A fractional exponent is not necessarily simpler so just take out the 1st and 3rd parts of the term which simplify nicely:
[tex] \sqrt{196 {x}^{3} {y}^{4}{z}^{9} } = 14 {y}^{2} \sqrt{ {x}^{3} {z}^{9} } [/tex]
Find the missing length indicated
The value of x is 5
Define the term Similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. To be more specific, two triangles are comparable if their respective sides are proportionate and their corresponding angles are congruent.
Two triangles are similar if corresponding angles are congruent and corresponding sides are proportional.
from the below figure, both the triangles are similar, ∆ABC ≈ ∆EFB
By using Thales's theorem, the ratio of the sides of triangles are;
BE/EA = BF/FC
15/30 = x/10
x = 5
Therefore the value of x is 5
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The ratio of triangle sides can be calculated using Thales' theory, and it is the value of x is 5
Define the term Similar triangles?Similar triangles are those with the same shape but varying sizes. To be more precise, two triangles are comparable if their matching angles and respective sides are congruent.
If matching sides are proportional and corresponding angles are congruent, two triangles are similar.
Both triangles in the following figure are comparable ∆ABC ≈ ∆EFB
The ratio of triangle sides can be calculated using Thales' theory, and it is;
BE/EA = BF/FC
15/30 = x/10
x = 5
Therefore the value of x is 5
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A bicycle wheel travels 30π inches for each revolution. What is the diameter of the wheel?
Answer:30 inches
Step-by-step explanation:
Question This figure is made up of two rectangular prisms. What is the volume of the figure? Enter your answer in the box. giveing brainelslist pls answer
The volume of figure made up of two rectangular prisms is found to be 1092 sq. in.
Explain about the volume of rectangular prisms?The amount of three-dimensional space that an object takes up is its volume. Cubic units are used to measure volume.For instance, the rectangular prism below, which is composed of 18 unit cubes, has a volume of 18 cubic units.volume of rectangular prisms = length * width * height
So,
Volume of A and C are same as their dimensions are same.
Volume of A and C = 2*(7*2*3)
Volume of A and C = 84 sq. in
Now, volume of B = 12*12*7
volume of B = 1008 sq. in.
Complete volume = Volume of A and C + volume of B
Complete volume = 84 sq. in + 1008 sq. in.
Complete volume = 1092 sq. in.
Thus, the volume of figure made up of two rectangular prisms is found to be 1092 sq. in.
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IF A SOUP RECIPE YIELDS 20 GALLONS, HOW MANY 5-FLUID OUNCE PORTIONS WILL THE RECIPE YIELD?
The number of 5 fluid ounce portions needed in 20 gallons is a total of 512 portions
Calculating the number of ounce portions neededTo solve this problem, we first need to convert the volume of the soup recipe from gallons to fluid ounces, and then divide by the size of each portion to find the total number of portions.
Given that
1 gallon = 128 fluid ounces
Therefore, the recipe yields:
20 gallons x 128 fluid ounces per gallon = 2560 fluid ounces
Now, we can find the number of 5-fluid ounce portions by dividing the total volume by the portion size:
2560 fluid ounces / 5 fluid ounces per portion = 512 portions
Therefore, the soup recipe yields 512 portions of 5 fluid ounces each.
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In December last year, Kelantan experienced a major flood. This flood is continuously distributed. It is found that 50% of the rainy days are non-stop rain. If there is non-stop rain, 80% will flood; otherwise 30% flooding will occur. If a flood occurs, what is the percentage that it rains non-stop in December of that year? [5 marks]
If a flood occurs, there is a 72.7% probability that it rains non-stop in December of that year
What is probability ?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur. Probabilities between 0 and 1 indicate the likelihood of an event occurring, with smaller values indicating lower likelihoods and larger values indicating higher likelihoods.
Probabilities can be determined using mathematical formulas, statistical analysis, and empirical data. They are used in a wide range of fields, including mathematics, science, economics, and social sciences, to make predictions and inform decision-making.
According to the question:
Let's use the following notation:
NR: Non-stop rain
F: Flood
We want to find the conditional probability of NR given that F occurred, or P(NR|F). We can use Bayes' theorem to find this probability:
P(NR|F) = P(F|NR) * P(NR) / P(F)
We know that 50% of the rainy days are non-stop rain, so P(NR) = 0.5. We also know that if there is non-stop rain, 80% will flood, so:
P(F|NR) = 0.8
If there is no non-stop rain, 30% flooding will occur, so:
P(F|~NR) = 0.3
We can use the law of total probability to find P(F), which is the probability of flooding occurring:
P(F) = P(F|NR) * P(NR) + P(F|~NR) * P(~NR)
P(~NR) = 1 - P(NR) = 0.5
P(F) = 0.8 * 0.5 + 0.3 * 0.5 = 0.55
Now we can plug in all the values to find P(NR|F):
P(NR|F) = P(F|NR) * P(NR) / P(F)
P(NR|F) = 0.8 * 0.5 / 0.55 = 0.727 or 72.7% (rounded to one decimal place)
Therefore, if a flood occurs, there is a 72.7% chance that it rains non-stop in December of that year.
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If A = [ 1 2 4 0 5 6 ] and B= [ 7 3 2 5 1 9] find C= A+B and D=A-B
Step 1: Arrange the arrays so that A and B are in the same order: A = [ 1 2 4 0 5 6 ], B = [ 7 3 2 5 1 9]
Step 2: To find C = A+B, add each element of A and B together.
C = [1+7, 2+3, 4+2, 0+5, 5+1, 6+9]
C = [8, 5, 6, 5, 6, 15]
Step 3: To find D = A-B, subtract each element of B from A.
D = [1-7, 2-3, 4-2, 0-5, 5-1, 6-9]
D = [-6, -1, 2, -5, 4, -3]
Determine the relationship between the two triangles and whether or
not they can be proven to be congruent.
The two triangles are related by_____, so the triangles______
The two triangles are related by SAS criteria, so the triangles are congruent.
What are congruent triangles?Congruent triangles are triangles that are precisely the same size and form. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent. Corresponding portions are those areas of the two triangles that share the same dimensions (are congruent). This indicates that corresponding triangle parts are congruent (CPCTC).
From the given figure we observe for that the two triangles two sides and the corresponding angle of 90 degree is similar.
Thus, using the SAS criteria we see that the two triangles are equal.
Hence, the two triangles are related by SAS criteria, so the triangles are congruent.
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Brandi has a deck of 12 cards labeled A through L. Brandi draws a card from the deck and returns it, then draws a card again. What is the theoretical probability that Brandi draws a card with a vowel both times?
A) 6.25%
B) 2.08%
C) 25%
D) 75%
Answer: The probability of drawing a vowel from a deck of 12 cards is 5/12, since there are 5 vowels (A, E, I, O, U) and 12 cards in total.
Since Brandi returns the first card drawn to the deck before drawing the second card, the outcome of the first draw does not affect the outcome of the second draw. Therefore, we can treat the two draws as independent events.
The probability of drawing a vowel on the first draw is 5/12, and the probability of drawing a vowel on the second draw is also 5/12. Since we want to find the probability of both events happening (drawing a vowel both times), we can multiply the probabilities:
P(vowel on both draws) = P(vowel on first draw) * P(vowel on second draw)
= (5/12) * (5/12)
= 25/144
Therefore, the theoretical probability that Brandi draws a card with a vowel both times is 25/144, which is approximately 0.1736 or 17.36%.
So the closest answer choice is B) 2.08%.
Step-by-step explanation:
✪ Explain why Jack should keep the policies you placed in the "Policies to Keep" column.
The policies listed in the "Policies to Keep" column are beneficial to Jack as they help to reduce the risk of fraud, financial loss, and mismanagement of resources. They also serve to ensure that the business is operating in a compliant and legal manner. Additionally, these policies can help to ensure that the organization is operating efficiently and in an ethical manner.
Determine the slope from the table given below.
Answer:
m = 6
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points on the table (4,6) (5,12)
We see the y increase by 6 and the x increase by 1, so the slope is
m = 6
So, the slope is 6
PLEASE HELP ASAP!! 25 POINTS AND BRAINLIEST
Answer: 62°
Step-by-step explanation:
All angles of a triangle add up to 180°.
So, add up all the other angles.
15 + 25 + 39 = 79
180 - 79 = 101
Then, to find x, subtract 39 from 101, to get 62!
Given: -4+16-64 +256..., Sn=3,276
Find the number of terms in the series.
There are 4 terms in the series.
what is an arithmetic sequence?
An arithmetic sequence is a sequence of numbers where each term is equal to the previous term plus a fixed constant difference, called the common difference.
The given series is an arithmetic sequence with a common difference of 16. We can find the first term by plugging in n=1 into the sequence:
a1 = -4 + 16(-1)^1 = -4 + 16 = 12
Using the formula for the sum of an arithmetic sequence, we have:
Sn = n/2(2a1 + (n-1)d)
where n is the number of terms, a1 is the first term, and d is the common difference. Plugging in the given values, we have:
3276 = n/2(2(12) + (n-1)(16))
Simplifying this equation, we get:
3276 = n/2(28 + 16n - 16)
3276 = n/2(12 + 16n)
Multiplying both sides by 2 and rearranging, we get:
6544 = n(6 + 8n)
Dividing both sides by 2, we get:
3272 = n(3 + 4n)
We can see that n must be an even number, since the left side is even. We can also see that n cannot be too large, since the right side increases much faster than the left side. Trying some even values of n, we find that:
n=8 -> 3272 = 8(3 + 4(8)) is false
n=6 -> 3272 = 6(3 + 4(6)) is false
n=4 -> 3272 = 4(3 + 4(4)) is true
Therefore, there are 4 terms in the series.
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Construct a 99% confidence interval of the population proportion using the given information.
x = 75, n = 250
The 99% confidence interval for the population proportion p is :lower bound= 0.225, upper bound 0.375
What does a confidence interval actually mean?
Your estimate's mean is added to and subtracted from by the estimate's range to create a confidence interval. If you repeat your test, within a specific level of confidence, this is the range of values you anticipate your estimate to fall within.
Given that,
n = 250
x = 75
Point estimate = sample proportion = p = x / n = 75/250=0.3
1 - p =1 - 0.3=0.7
At 99% confidence level the z is ,
α = 1 - 99% = 1 - 0.99 = 0.0
α / 2 = 0.01 / 2 = 0.005
Z /2 = Z0.005 = 2.576 ( Using z table )
Margin of error = E = Zα / 2 * √(( p * (1 - p)) / n)
= 2.576 (√((0.3*0.7) /250 )
E = 0.075
A 99% confidence interval for population proportion p is ,
p - E < p < p + E
0.3 -0.075 < p < 0.3 + 0.075
0.225< p < 0.375
The 99% confidence interval for the population proportion p is :lower bound= 0.225, upper bound 0.375.
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right triangle that i’m confused on please help
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Find the derivative of the function g(t), below. It may be to your advantage to simplify before differentiating. g(t)=tan(ln(t)) g'(t)=
The derivative of the function g(t) = -2tsint - sint + 2tcost.
In mathematics, the derivative of a function of a real variable measures the sensitivity of the function's value (the output value) to changes in its independent variable (the input value). Derivatives are a fundamental tool of calculus. The process of finding derivatives is called differentiation. The reverse process is called retro differentiation.
The fundamental theorem of calculus associates inverse differentiation with integration. Differentiation and integration form the two basic operations in univariate calculus.
Given that:
g(t) = tan(ln(t)) g'(t)
Now, Differentiating for the first time:
(t²+1) d/dt (sin t) + Sin t d/dt (t²+1)
= (t²+1) cos t + sint (2t)
Now,
h'(t) = t²cos t + cost + 2tsint
Differentiating again:
h''(t) = d/dt (t²cos t) + d/dt (cost) + d/dt (2tsint)
= -2tsint - sint + 2tcost
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