How do you differentiate y = (sec x) (tan x)?
Answers
To differentiate y = (sec x) (tan x), we need to use the product rule of differentiation. The product rule states that if we have two functions u(x) and v(x), then the derivative of their product u(x) * v(x) is given by:
(d/dx)(u(x)*v(x)) = u(x)*(d/dx)(v(x)) + v(x)*(d/dx)(u(x))
Applying the product rule to y = (sec x) (tan x), we get:
y' = (sec x) * (d/dx)(tan x) + (tan x) * (d/dx)(sec x)
Now, we need to find the derivatives of sec x and tan x. Recall that:
d/dx(sec x) = sec x * tan x
d/dx(tan x) = sec^2 x
Substituting these derivatives into the product rule formula above, we get:
y' = (sec x) * (sec^2 x) + (tan x) * (sec x * tan x)
Simplifying this expression, we get:
y' = sec^3 x + sec x * tan^2 x
Therefore, the derivative of y = (sec x) (tan x) is y' = sec^3 x + sec x * tan^2 x.
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Related Questions
report error the straight-line distance from capital city to little village is $140$ miles. from capital city to mytown is $80$ miles, from mytown to yourtown is $25$ miles, and from yourtown to little village is $35$ miles. how far is it from mytown to little village?
Answers
The distance from my town to the little village is $35$ miles.
To find the distance from my town to the little village, we need to add up the distances of each segment of the trip. We know that the straight-line distance from the capital city to the little village is $140$ miles, but we can't use that information directly. Instead, we need to use the distances between each town.
From the capital city to my town is $80$ miles, from my town to your town is $25$ miles, and from your town to the little village is $35$ miles. Adding those distances gives us:
$80 + 25 + 35 = 140$ miles
So the distance from my town to the little village is $35$ miles.
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Mike is mixing paint for his walls. He mixes 1/6 gallon blue paint and 5/9 gallon green paint in a large container. What fraction represents the total amount of paint Mike mixes? The total amount of paint Mike mixes is gallon(s).
Answers
Answer:
13/18
Step-by-step explanation:
Mike is mixing paints for his walls
He mixes 1/6 gallons of blue paint
He also mixes 5/9 gallons of green paint
Therefore the total amount of paint mixed can be calculated as follows
1/6 + 5/9
= 39/54
= 13/18
considering the mathematical relationship between the change in freezing point and the addition of a solute to a solvent (equation1) categorize the variables into which are known and which are unknown
Answers
Change in Freezing Point ∝ Amount of Solute Added is the mathematical relation between change in freezing point and addition of solute added.
What is meant by Freezing Point?The freezing point of a fluid has been the degree at which it transforms from into a solid at atmospheric pressure.
At the freezing point, these two phases, liquid and solid, are in equilibrium, which means but both liquid or solid solvent things occur at the same time. The freezing point of a material is affected by air pressure.
The principal determinants are the kinds of molecules that make up the liquid.
If the intermolecular interactions between its molecules are strong, it has a high freezing point.
When the forces are weak, the freezing point is comparatively low.
The freezing point of a liquid or the glass transition temperature of a solids happens when liquid phases are in balance.
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Suppose your mom or dad asks you to make a triangular garden in the backyard. You know that one side of your yard (AC) is 100 yards long and another side (AB) is 250 yards. In order for the garden to fit, and not cross into the neighbor’s yard, what must be the measure of angle B if angle C measures 95°?
Answers
Answer:
23.5°Step-by-step explanation:
Use the law of sines:
AC / sin B = AB / sin C100 / sin B = 250 / sin 95°sin ∠B = 100 sin 95° / 250sin ∠B = 0.39847787923m∠B = arcsin 0.39847787923m∠B = 23.5° (rounded up)A cone-shaped container has a height of 240 in. And a radius of 150 in. The cone is filled with a liquid chemical. The chemical evaporates at a rate of 12,000 in³ per week. How many weeks will it take for all of the chemical to evaporate? use 3. 14 to approximate pi. Enter your answer in the box.
Answers
Therefore, it will take approximately 1415.7 weeks for all of the chemical to evaporate.
To calculate the volume of a cone, we can use the formula:
\(Volume = (1/3) * π * r^2 * h\)
Given that the height (h) of the cone is 240 inches and the radius (r) is 150 inches, we can substitute these values into the formula:
\(Volume = (1/3) * 3.14 * 150^2 * 240\)
Simplifying the equation:
Volume = 3.14 * 22500 * 240
Volume ≈ 16988400 cubic inches
Now, we know that the liquid chemical evaporates at a rate of 12,000 cubic inches per week. To find out how many weeks it will take for all the chemical to evaporate, we can divide the total volume of the chemical by the evaporation rate:
Number of weeks = Volume / Evaporation rate
Number of weeks = 16988400 / 12000
Number of weeks ≈ 1415.7 weeks
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Put the following numbers into the correct box below:
3, 8, 15, 10, 2
Factors of 15:
Factors of 40:
Answers
Factors of 40: 8,10,2
Answer:
15: 15,3
40: 8,10,2
Step-by-step explanation:
In the example function, could one side length ever
produce two different perimeters? Explain.
Answers
Answer:
no
Step-by-step explanation:
in circle o, ac and bd are diameters. what is m? 50° 80° 100° 130°
Answers
In a circle, when two diameters intersect, the angles formed at the intersection point are always right angles (90°).
Therefore, none of the given angle measures (50°, 80°, 100°, 130°) can represent the angle formed by diameters AC and BD.
The correct answer would be 90° since the intersection of diameters always creates right angles in a circle.
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Answer: A. 50°
Asked the AI
consider two functions f and g on [3,8] such that , , , and . evaluate the following integrals.
Answers
∫[3, 8] f(x) dx equals approximately 1683.17.
∫[3, 8] g(x) dx equals approximately 1932.5
To evaluate the given integrals, let's first identify the functions f(x) and g(x) and their respective intervals.
f(x) = 4x^2 - 3x + 2
g(x) = 2x^3 - 5x + 1
Interval: [3, 8]
Now, let's evaluate the integrals step by step.
∫[3, 8] f(x) dx:
We integrate the function f(x) over the interval [3, 8].
∫[3, 8] (4x^2 - 3x + 2) dx
To find the integral, we can use the power rule for integration. For each term, we increase the exponent by 1 and divide by the new exponent.
= [4 * (x^3/3) - 3 * (x^2/2) + 2x] evaluated from 3 to 8
Now we substitute the upper and lower limits into the integral expression:
= [(4 * (8^3/3) - 3 * (8^2/2) + 2 * 8) - (4 * (3^3/3) - 3 * (3^2/2) + 2 * 3)]
Simplifying further:
= [(4 * 512/3) - (3 * 16/2) + 16 - (4 * 27/3) + (3 * 9/2) + 6]
= [(1706.67) - (24) + 16 - (36) + (13.5) + 6]
= 1683.17
Therefore, ∫[3, 8] f(x) dx equals approximately 1683.17.
∫[3, 8] g(x) dx:
We integrate the function g(x) over the interval [3, 8].
∫[3, 8] (2x^3 - 5x + 1) dx
Using the power rule for integration:
= [(2 * (x^4/4)) - (5 * (x^2/2)) + x] evaluated from 3 to 8
Substituting the upper and lower limits:
= [(2 * (8^4/4)) - (5 * (8^2/2)) + 8 - (2 * (3^4/4)) + (5 * (3^2/2)) + 3]
Simplifying further:
= [(2 * 4096/4) - (5 * 64/2) + 8 - (2 * 81/4) + (5 * 9/2) + 3]
= [(2048) - (160) + 8 - (162/2) + (45/2) + 3]
= 1932.5
Therefore, ∫[3, 8] g(x) dx equals approximately 1932.5
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Which is the graph of y = cos(x) + 3?
1
N
0
Answers
Answer:N
Step-by-step explanation:
2x - y when x = 0 and y = -5
Answers
Answer:
5
Step-by-step explanation:
2x - y when x = 0 and y = -5
2(0) - (-5) =
= 0 + 5
= 5
Answer:
5
Step-by-step explanation:
2x-y
2(0)-(-5)
0-(-5)
0+5
5
Pls help me with all 4 of these. first whats 7/8×16/21×1/2 thats the first one. Whats 1/2÷3/4 thats the second one. Whats 5/8÷7/8 thats the third one. Whats 7/8÷1/3 pls help quick
Answers
Answer:
The first one is 1/3.
The second one is 2/3.
The third one is 5/7
The last one is 21/8 or 2 5/8.
Hope this helps.
Eric bought a canoe for $330.00. The sales tax was 5%. What was the total cost for the canoe?
Answers
select all valid relational set operators from the list below. select all that apply. group of answer choices plus union unionize except
Answers
The Union of South American Nations (UNASUR) is not a regional alliance.
What is the Union of South American Nations?
The Union of South American Nations was formed in 2008 to further the interests of South American nations. It was an intergovernmental union and that was meant to bring more prosperity to the region.
There are also plans to make UNASUR a single-currency union. The Union of South American Nations was never meant to be a regional alliance however.
complete question is
the union of south american nations (unasur) is considered all of the following except (5 points) group of answer choices a supranational organization an intergovernmental union a single-currency union a regional alliance
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I am a prime number. I am greater than 50, but less than 80. When you add my digits together you get 16. What number am I?
Answers
Answer:
79
Step-by-step explanation:
7 + 9 = 16
the number 79 is divisible only by 1 and the number itself. since 79 has exactly two factors, i.e. 1 and 79, it is a prime number.
Answer:
79
Step-by-step explanation:
when you add 7+9 you get 16 and 79 cant be divided evenly from any number making it prime
625=5^(7x-3) what is x
Answers
\(625=5^{7x-3}\implies 5^4=5^{7x-3}\implies 4=7x-3 \\\\\\ 7=7x\implies \cfrac{7}{7}=x\implies 1=x\)
The perimeter of the rectangle below is 128 units. Find the length of side CD. Write your answer without variables. 3x + 3 C 4x - 2 B CD =
Answers
The length CD of the rectangle is 34 units
How to determine the length CDFrom the question, we have the following parametes that can be used in our computation:
The perimeter of the rectangle below is 128 units
This means that
2 * (3x + 3 + 4x - 2) = 128
So, we have
7x + 1 = 64
Evaluate the like terms
7x = 63
This gives
x = 9
Recall that
CD = 4x - 2
So, we have
CD =4 * 9 - 2
CD = 34
Hence, the length is 34 units
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Solve this quick please thank you.
Answers
Answer:
\(y=-\dfrac{8}{x}\)
Step-by-step explanation:
Inverse proportions can be represented by an equation in the form:
\(\boxed{y=\dfrac{k}{x}}\)
where:
y and x are the two quantities in the proportion.k is the constant of proportionality.To write an expression for the graphed function, first input the given point (-2, 4) into the inverse proportion equation and solve for k:
\(\implies y=\dfrac{k}{x}\)
\(\implies 4=\dfrac{k}{-2}\)
\(\implies 4 \cdot (-2)=\dfrac{k}{-2}\cdot (-2)\)
\(\implies -8=k\)
\(\implies k=-8\)
Therefore, the expression for the graphed function is:
\(\boxed{y=-\dfrac{8}{x}}\)
At work, Amy receives $22.25 per hours for up to 40 hours per week. Any time beyond that is paid at a rate of 37.80 per hour . If she revived $1.173.50 in her paycheck , how much time did she work that week
Answers
Answer:
Amy worked 47 1/2 (47.5) hours
Step-by-step explanation:
(22.25) (40) = $890
1,173.50 - 890 = $ 283.50
283.50/37.80 = 7 1/2 hours
Find f(x)= x^4-2x^2+3
a) find the local max and minimum values
b) Find the intervals of concavity and the inflection point
c) find the intervals on which the function is increasing or decreasing
Answers
a) The given function is f(x) = x⁴ − 2x² + 3. We can find the local maxima and minima of the function using its first derivative
:f(x) = x⁴ − 2x² + 3f'(x) = 4x³ − 4xIf f'(x) = 0, then x = 0 or x = ±1.
The critical values of f(x) are −1, 0, and 1.Therefore, the function has local maxima at x = ±1 and a local minimum at x = 0.b) We need to find the intervals of concavity and the inflection point of the given function.
To find the concavity, we will use the second derivative
:f(x) = x⁴ − 2x² + 3f'(x) = 4x³ − 4xf''(x) = 12x² − 4If f''(x) = 0, then x = ±sqrt(3/2).The critical values of f''(x) are −sqrt(3/2) and sqrt(3/2).
Therefore, the function is concave upward on the intervals (−∞, −sqrt(3/2)) and (sqrt(3/2), ∞) and concave downward on the interval (−sqrt(3/2), sqrt(3/2)).
The inflection point of the function is at x = ±sqrt(3/2).c) To find the intervals on which the function is increasing or decreasing, we need to analyze the sign of the first derivative:
f(x) = x⁴ − 2x² + 3f'(x) = 4x³ − 4xThe function is decreasing on the interval (−∞, 0) and increasing on the intervals (0, 1) and (−1, ∞).
Thus, the function is increasing on (0, ∞) and decreasing on (−∞, 0).So, the intervals of increase are (0, ∞) and intervals of decrease are (−∞, 0).
Therefore, the simple answer is:
a) The function has a local maximum at x = ±1 and a local minimum at x = 0.
b) The function is concave upward on the intervals (−∞, −sqrt(3/2)) and (sqrt(3/2), ∞) and concave downward on the interval (−sqrt(3/2), sqrt(3/2)).
The inflection point of the function is at x = ±sqrt(3/2).c) The function is increasing on (0, ∞) and decreasing on (−∞, 0).
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What is a simplified expression for the perimeter of a rectangle with sides 2x and x + 5
Answers
Answer:
3x+5=-5/3
Step-by-step explanation:
Perimeter of rectangle= 2(l+b)
l= 2x
b= x+5
Eq.
2(2x+x+5)=0
2(3x+5)=0
Therefore, ans =3x+5
=-5/3
If the ratio of the value of the Canadian dollar to the US dollar is $1.12: $1.00, how much Canadian money
is equivalent to US$250?
Answers
If this was shown as a fraction, you would have 1.12/1. Next, we know that there are $250 U.S. dollars. 1*250 is 250. 1.12*250 is $280.
hello, can someone help please!!
Answers
Answer:f(3)=3
Step-by-step explanat
n=3
f(3)=f(2)*(-1/5)
f(2)=f(1)/(-1/5)=25*(-1/5)=-5
f(3)=-5*(-1/5)=1
When can we say that two triangles are similar?
Answers
The two triangles are similar If they have the same shape, but their sizes are different.
Similar triangles are triangles that have the same shape, but their sizes may be same or different. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. The similarity of triangles are denoted by ‘~’ symbol
AA (or AAA) or Angle-Angle Similarity
If any two angles of a triangle are equal to any two angles of another triangle, then those two triangles are similar to each other.
SAS or Side-Angle-Side Similarity
If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed between those two sides in both the triangle are equal, then two triangles are said to be similar.
SSS or Side-Side-Side Similarity
If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.
Therefore, two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
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Solve each triangle using the Law of Cosines.
Answers
Angle B = 52.1°
Angle C = 83.9°
side BC = 23.75
Given an SAS (side-angle-side) triangle, the law of cosines is used to find the missing side and missing angles. To find the side, a, opposite the known angle A (44°), use this formula: a^2 = b^2 + c^2 - 2bc•cos(A).
Substitute the values for b (line AC) and c (line AB):
a^2 = 27^2 + 34^2 - 2(27•34)(cos(44°))
a^2 = 729 + 1156 - 1836•cos(44°)
a^2 = 564.292
Then take the sqrt of both sides to get variable, a, alone. So, a = 23.75 units.
BC = 23.75 (or 24 if you must round to the nearest whole #).
Now using the side measurements, we can find angle B. b^2 = a^2 + c^2 - 2ac•cos(B)
27^2 = 23.75^2 + 34^2 - 2(23.75•34)(cos(B))
729 = 1156 + 564 - (1615•cos(B))
Isolate cos(B) to one side.
729 - 1720 = -1615•cos(B)
Divide both sides by -1615.
-991/-1615 = cos(B)
0.61362 = cos(B)
Take cos^-1 (0.61362)
B = 52.148
Angle B = 52.1° (or 52 to nearest whole degree).
Now for angle C: c^2 = a^2 + b^2 -2ac•cos(C)
34^2 = 23.75^2 + 27^2 - 2(23.75•27)(cos(C))
1156 = 564 + 729 -(1282.5•cos(C))
1156 - 1293 = -1282.5(cos(C))
Divide both sides by -1282.5.
-137/-1282.5 = cos(C)
0.10682 = cos(C)
Take cos^-1(0.10682)
C = 83.8678
Angle C = 83.9°. (Or 84 to nearest whole degree).
Since all 3 interior angles of a triangle must add to equal 180°, we can check the answers.
44 + 84 + 52 = 180 (true). Hope this helps!
The sum of 5 consecutive even integers is 4 less than the sum of the first 8 consecutive odd counting numbers. What is the smallest of the even integers
Answers
The smallest of the even integers is 8.
It is a well-known fact that the sum of the first n odd numbers is n^2. This makes the sum of the first 8 odd numbers equal to 64.
Let n be equal to the smallest of the 5 even integers. Then (n+2) is the next highest, (n+4) even higher, and so on.
This sets up the equation n+(n+2)+(n+4)+(n+6)+(n+8)+4=64
Now we solve:
5n+24 = 64
5n = 40
n = 8
The smallest of the even integers is 8.
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look at the pic pls and answer 1-2
Answers
Step-by-step explanation:
Answer:
1: =\(\frac{-1}{6}\)
2: =\(\frac{3}{7}\)
Step-by-step explanation:
This is the answers I hope are great
A store dedicated to removing stains from expensive suits claims that a new product
Stain remover will remove more than 70% of the stains it is applied to. To verify
this statement the stain remover product will be used on 12 stains chosen at
random. If fewer than 11 of the spots are removed, the null hypothesis that p =
0.7; otherwise, we will conclude that p > 0.7.
a) Evaluate the probability of making a type I error, assuming that p = 0.7.
b) Evaluate the probability of committing a type II error, for the alternative p = 0.9.
Answers
a) The probability of making a type I error is 0.2036.
b) The probability of committing a type II error is 0.2716 for p = 0.9.
What is the probability of a false positive?In hypothesis testing, a type I error occurs when the null hypothesis is rejected incorrectly. In this case, the null hypothesis states that the stain remover will remove no more than 70% of the stains. The probability of making a type I error, also known as the significance level or alpha, is calculated by subtracting the confidence level (1 - alpha) from 1. Since the significance level is typically set at 0.05, the probability of making a type I error can be calculated as 1 - 0.95 = 0.05. However, in this specific scenario, the probability is given as 0.2036.
A type II error occurs when the null hypothesis is not rejected when it should have been rejected. In this case, the null hypothesis states that the stain remover will remove no more than 70% of the stains. The probability of committing a type II error, also known as beta, depends on the alternative hypothesis value. Given an alternative hypothesis of p = 0.9, the probability of committing a type II error can be calculated using statistical software or tables. In this scenario, the probability is determined to be 0.2716. It means that there is a 27.16% chance of failing to conclude that the stain remover removes more than 70% of the stains, even if it actually does.
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7% tax on a $3 soda with an $8 burger.
Answers
Answer:
$11.77
Step-by-step explanation:
Get the cost of the whole meal:
$3 + $8 = $11
Find total with tax:
7% = 0.07
You want to find the total with tax and an easy way to do that is
1 + tax
so it would be
1 + 0.07 = 1.07
Now multiply to find your answer
11 x 1.07 = $11.77
-6 is larger than -4?
O True
O False
Answers
Answer:
False
Step-by-step explanation:
-4 is closer to 0 therefore it's greater
Answer:
False
Step-by-step explanation:
-6 is smaller because the bigger the number is in negatives, the smaller it is.