Differentiation of the given function f(x)=sinx/(1+tanx) is equal to
(cos³x -sin³x) / (cos²x)(1 + tanx)².
As given in the question,
Given function : f(x) = sinx /(1 + tanx )
Let u = sinx , v = ( 1 + tanx)
Differentiate the given function with respect to x
du/dx = cosx
dv/dx = sec²x
= 1/cos²x
(d/dx)(f(x)) = (d/dx)(sinx /(1 + tanx ))
= ( d/dx) (u / v)
= [v (du/dx) -u (dv/dx)] / (v)²
= [(1+tanx)(cosx) -(sinx)(1/cos²x)] / (1 + tanx)²
= [cos²x(cosx + sinx) -sinx]/ (cos²x)(1 + tanx)²
= [cos³x +sinx(cos²x -1)] / (cos²x)(1 + tanx)²
= (cos³x -sin³x) / (cos²x)(1 + tanx)²
Therefore, differentiation of the given function f(x)=sinx/(1+tanx) is equal to
(cos³x -sin³x) / (cos²x)(1 + tanx)².
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About how much is 1224.53 divided by 36.02?
Find the volume of this triangular prism.
Be sure to include the correct unit in your answer.
8 yd
K
5
7 yd
7 yd
➜
The volume of this triangular prism 7yd x 7yd x 8yd is calculated as 196 [tex]yd^3\\[/tex] as per answered with the correct unit.
What is a prism?A prism is a kind of a polyhedron in geometry that has n number of parallelogram faces that connect the n-sided polygon basis, the second base, which is a translated duplicate of the present first base, and the n faces.
The bases are all translated into all cross-sections that are parallel to them.
The volume of this prism can be found by applying the formula
1/2 Area x Height
= 1/2 x 7 x 7 x 8
= 196 [tex]yd^3\\[/tex]
What is the equation for a prism’s volume?V=Bh
V=Bh, where B can be said as the base area and h as the height, is the formula for a prism’s volume. The prism has a rectangular base.
The total area that any kind of prism takes up in three dimensions is known as its volume. It is defined in mathematically as the result of the base’s area and length.
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what determines the type of feedback?
answer asap for brainlist
Answer:
A
Step-by-step explanation:
if you feel cold your body will tell your brain or give feedback to make you think or say its cold
Use the given special right triangle to find the value of cos 7 21 XV3 3 T
We have:
[tex]\cos (\frac{\pi}{6})=\frac{\sqrt[]{3}}{2}[/tex]And
[tex]\cos (\frac{\pi}{3})=\frac{1}{2}[/tex]After that, we proceed as follows:
[tex]\sin (\frac{\pi}{3})=\frac{x\sqrt[]{3}}{2x}\Rightarrow\sin (\frac{\pi}{3})=\frac{\sqrt[]{3}}{2}[/tex][tex]\cos (\frac{\pi}{3})=\frac{x}{2x}\Rightarrow\cos (\frac{\pi}{3})=\frac{1}{2}[/tex][tex]undefined[/tex]Please help me correct my problem
Answer:
you accidentally put x+6 for the 1st part
Please hurry due today
Which relation is a function?
can somebody quickly answer this?
Lorraine prepared a 2.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.25 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars can Lorraine fill?
By using conversion factor, if Lorraine prepared a 2.5 gallon pot filled with tomatoes to be canned in jars and each jar will hold 1.25 quarts of tomatoes, then Lorraine can fill 8 jars
The quantity of tomatoes prepared by Lorraine = 2.5 gallon
The quantity of tomatoes can be filled in one jar = 1.25 quarts
We know
1 gallon = 4 quarts
First convert the quantity of tomatoes prepared by Lorraine from gallon to quarts
2.5 gallon = 2.5×4 = 10 quarts
How many jars can Lorraine fill = The quantity of tomatoes prepared by Lorraine/The quantity of tomatoes can be filled in one jar
we have to use division
= 10/1.25
= 8 jars
Hence, if Lorraine prepared a 2.5 gallon pot filled with tomatoes to be canned in jars and each jar will hold 1.25 quarts of tomatoes, then Lorraine can fill 8 jars
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F(x)=(1/2)=2^x
exponential functions
[tex] \frac{1}{2} = {2}^{x} \\ {2}^{ - 1} = {2}^{x} \\ x = - 1[/tex]
ATTACHED IS THE SOLUTION
What else would need to be congruent to show that ABC=DEF by SAS?
Answer:
D). Angle B ≈ Angle E
Step-by-step explanation:
ASA means that for the relation to be true, there not only has to be the 3 given proportionate values, but 2 have to be angles and 1 has to be a side.
Since we already have the 1 side, option 1 and 2 are voided.
Then since we already have Angle A and D option 3 is as well, so through this we know the answer is number 4 or Angle B = Angle E
Hope this helps.
Which of the following rational fractions is graphed below?
Help please!
The following rational fractions is graphed below?
f(x) = 1/ is the rational function seen in the given graph (x - 4)
How Are Graphs of Asymptotes Functions Interpreted?
The vertical asymptote of the graph is located at x = 4.
Let's determine each function's vertical asymptote.
We set the denominator equal to 0 to determine the vertical asymptote.
A) x + 4 = 0\sx = -4
That's incorrect
B) 4x = 0 x = 0 Invalid
C) The denominator is erroneous since it lacks a variable.
D) x - 4 = 0\sx = 4
So, this is true.
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Warm-UpMatch the math vocabulary to parts of the expression w+ 5w. Two tiles will not be used.TilestermexponentconstantexpressionequationvariablecoefficientPairsw2 + 5wthe win w2 + 5wthe 2 in w2 + 5Wthe 5 in w2 + 5wthe w? or the 5w in w2 + 5wSubmit
We are given w^2 + 5w and we are asked to identify the terms for each of its parts.
First, let's start with w. The letter w is used to represent an unknown value. Thus, it is called a variable.
ext, 2. Here, 2 is useda as an exponent of w in the first term.
Meanwhile, 5 is used as a multiplier or a numerical coefficient of w in the second term.
Finally, the expression w^2 + 5w is
is the quotient of two natural numbers is always a rational number a true or false statement
Answer:
True
Step-by-step explanation:
Solve for x.
5x - 4 > 12
OR 12x + 5 ≤ -4
By using the method of addition, the equation is 12x + 1.
What is addition?Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation. The sum is the entire value, and the addends are the integers that are being added. The mathematical operation of addition is the process of adding two or more numbers together to determine the total, or sum.
Given that,
5x - 4 > 12 adding 4 to both sides;
5x - 4+ 4 > 12 + 4
5x > 16 dividing both sides by 5;
x > 16/5
12x + 5-4
12x + 1
Therefore, the equation is 12x + 1.
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Consider the following total revenue function for a hammer. R = 36x − 0.01x2 (a) The sale of how many hammers, x, will maximize the total revenue in dollars? x = hammers Find the maximum revenue. $ (b) Find the maximum revenue if production is limited to at most 1000 hammers. $
The sales of the number of hammers that give the maximum revenue of 32400 is 1800
How to determine the number of sale of hammersThe equation of the revenue function is given as
R = 36x − 0.01x2
Rewrite the equation properly as a quadratic function
So, we have the following equation
R = 36x − 0.01x^2
Differentiate the above function
So, we have the following equation
R' = 36 - 0.02x
Set the differentiated function to 0
So, we have the following equation
36 - 0.02x = 0
This gives
0.02x = 36
Divide both sides by 0.02
So, we have
x = 1800
How to find the maximum revenue?In (a), we have
36 - 0.02x = 0
0.02x = 36
x = 1800
Substitute x = 1800 in R = 36x − 0.01x^2
So, we have
R = 36 x 1800 − 0.01 * 1800^2
Evaluate
R = 32400
Hence, the maximum revenue is 32400
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determine the coordinates of S(-7,1)after a reflection in the line y=3
This just means that the y coordinate will always be 3 for all coordinates of x that means that the y coordinate of the point ( -7,1) will change to
(-7,3)
DEEPER The scales shown are used to compare the weights of apples, tangerines, grapefruits, and bananas. How many tangerines
will balance one apple?
Justify your answer using a linear system. Let the weights of apples, tangerines, grapefruits, and bananas be represented by a, t,
g, and b respectively.
Equation for first picture:
Equation for second picture:
Equation for third picture:
Using a system of equations, it is found that 4 tangerines will balance one apple.
The equations are given as follows:
First balance: a + t = g.Second balance: b + t = a.Third balance: 2g = 3b.What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.
For this problem, the variables are given as follows, considering the situation described:
Variable a: weight of an apple.Variable t: weight of a tangerine.Variable g: weight of an grapefruit.Variable b: weight of an banana.For the first picture, one apple and one tangerine balance one grapefruit, hence:
a + t = g.
For the second picture, one banana and one tangerine balance one apple, hence:
b + t = a.
For the third picture, two grapefruits balance three bananas, hence:
2g = 3b.
g = 1.5b.
Replacing on the first equation, we have that:
a + t = 1.5b.
From the second equation, we have that:
b = a - t.
Hence, replacing on the first:
a + t = 1.5(a - t)
1.5a - 1.5t = a + t
0.5a = 2t
a = 4t
Hence 4 tangerines will balance one apple.
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Suppose an account pays 6% interest that is compounded annually. At the beginning of each year, $2,000 is deposited into the account (starting with $2,000 for the first year).
Using the future value formula, it is found that the value of the account after the tenth deposit is of $26,361.59.
What is the future value formula?The future value formula is given by:
[tex]V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right][/tex]
In which:
P is the payment.n is the number of payments.r is the interest rate.For this problem, the parameters are given as follows:
P = 2000, r = 0.06, n = 10.
Hence the value of the account will be of:
[tex]V(10) = 2000\left[\frac{(1 + 0.06)^{10} - 1}{0.06}\right][/tex]
V(10) = $26,361.59.
What is the missing information?The complete problem is:
"Suppose that there is an account that pays 6% interest that is compounded annually. At the beginning of each year, $2,000 is deposited into the account (starting with $2,000 for the first year).
What will be the value of the account after the tenth deposit if no withdrawals or additional deposits are made?"
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What is the sum of the first 5 numbers in the series 1+2+4+8+16+32+...?16313263
Given data:
The series is 1 + 2 + 4 + 8 + 16 + 32 + ....
The given series is G.P because the common ratio for GP is,
[tex]C\mathrm{}R\text{ = }\frac{a_2}{a_1}[/tex]Here, the common ratio is 2.
Sum of the first five numbers ,
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]Here, a is first term that is 1
r is common ratio that is 2
n is the number
Therefore, sum is given as
[tex]S_5=\frac{1(2^5-1)}{2-1}[/tex][tex]\begin{gathered} S_5=\frac{32-1}{1} \\ \text{ = 31} \end{gathered}[/tex]Thus, the sum of first five terms is 31
The correct option is (2).
Write an equation of the line passing through the point A(3,-1) that is parallel to the line y=1/3x+10
Answer:
[tex]y+1=\frac{1}{3}(x-3)[/tex]
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the line we want to find is 1/3.
Using point-slope form, the equation is
[tex]y+1=\frac{1}{3}(x-3)[/tex]
Given f(x) = x³ + kx + 13, and the remainder when f(x) is divided by x + 1 is
22, then what is the value of k
The value of k = -10 in f(x).
What is polynomial?Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.
What is remainder?The amount "left over" after a calculation is the remainder. The integer that remains after multiplying one integer by another to create an integer quotient is known as the remnant in mathematics.
Given that,
f(x) = x³ + kx + 13
The remainder when f(x) is divided by x + 1 is 22,
Here, the f(x) is divided by x+1
Hence, x = -1
Substitute x = -1 in f(x)
22 = f(x) = x³ + kx + 13
22 = f(-1) = (-1)³ + k(-1) + 13
22 = -1 –k +13
22 = -k +12
K = -10
Therefore, the value of k = -10 in f(x).
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A quality control company was hired to study the length of meter sticks produced by a certain company. The team carefully measured the length of many many meter sticks, and the distribution seems to be slightly skewed to the right with a mean of 100.06 cm and a standard deviation of 0.1 cm. (a) What is the probability of finding a meter stick with a length of more than 100.17 cm?
(b) What is the probability of finding a group of 10 meter sticks with a mean length of less than 100.03 cm?
(c) What is the probability of finding a group of 44 meter sticks with a mean length of more than 100.08 cm?
(d) What is the probability of finding a group of 50 meter sticks with a mean length of between 100.05 and 100.07 cm?
(e) For a random sample of 24 meter sticks, what mean length would be at the 92nd percentile?
Using the normal distribution and the central limit theorem, the probabilities are calculated as follows:
a) One meter stick greater than 100.17 cm: 0.1357 = 13.57%.
b) Group of 10 with mean less than 100.3: 0.1711 = 17.11%.
c) Group of 44 with mean greater than 100.08: 0.0918 = 9.18%.
d) Group of 50 with mean between 100.05 and 100.07: 0.5222 = 52.22%.
e) 92nd percentile of sample of 24: 100.09.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the calculated z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
Considering the Central Limit Theorem, the z-score formula can be given as follows:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The mean and the standard deviation of the lengths are given as follows:
[tex]\mu = 100.06, \sigma = 0.1[/tex]
For item a, we have that n = 1 and the probability is one subtracted by the p-value of z when X = 100.17, hence:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{100.17 - 100.06}{\frac{0.1}{\sqrt{1}}}[/tex]
Z = 1.1
Z = 1.1 has a p-value of 0.8643.
1 - 0.8643 = 0.1357.
For item b, we have that n = 10 and the probability is the p-value of Z when X = 100.03, hence:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{100.03 - 100.06}{\frac{0.1}{\sqrt{10}}}[/tex]
Z = -0.95
Z = -0.95 has a p-value of 0.1711.
For item c, we have that n = 44 and the probability is one subtracted by the p-value of Z when X = 100.08, hence:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{100.08 - 100.06}{\frac{0.1}{\sqrt{44}}}[/tex]
Z = 1.33.
Z = 1.33 has a p-value of 0.9082.
1 - 0.9082 = 0.0918 = 9.18%.
For item d, we have that n = 50 and the probability is the p-value of Z when X = 100.07 subtracted by the p-value of Z when X = 100.05, hence:
X = 100.07:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{100.07 - 100.06}{\frac{0.1}{\sqrt{50}}}[/tex]
Z = 0.71.
Z = 0.71 has a p-value of 0.7611.
X = 100.05:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{100.05 - 100.06}{\frac{0.1}{\sqrt{50}}}[/tex]
Z = -0.71.
Z = -0.71 has a p-value of 0.2389.
0.7611 - 0.2389 = 0.5222 = 52.22%.
For item e, we have that n = 24, and the 92th percentile is X when Z = 1.405, hence;
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]1.405 = \frac{x - 100.06}{\frac{0.1}{\sqrt{24}}}[/tex]
x - 100.06 = 1.405 x 0.0204
X = 100.09.
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is the median and mean equal? if not which is greater, explain your reasoning
Answer: The median and mean of height of students is not equal, the median is greater.
Step-by-step explanation:
Definition of Median:
Median is the middle value in the picture. To find the median, order the numbers and see which one is in the middle value of the list.
in this picture, first, we order the numbers in numerical order:
1,1,1,2,2,3,3,5,6,6
Find the middle number:
1,1,1,2,2,3,3,5,6,6
As above, 3 is the middle number, then we find which bar represents the median of height of students:
1+1+1+2+2+3 = 10 students
Referring back to the chart, if we add the first 2 bars together, we will get 6+2 = 8 students, but the median number is 10 students, that means the median will be at the third bar, median of height of students = 62-64.
Definition of Mean:
Mean is the sum of the numbers divided by the number of numbers.
In this picture, the Mean will be
(2+6+5+6+3+3+2+1+1+1) / 10
= 3 students
which means the mean height of students = 60-62.
4: (x+5)=1:2
[tex]4 \div x + 5 = 1 \div 2[/tex]
4 is to (x + 5) and 1 is to 2
Step-by-step explanation:
i2o2k2wkekekekk2k2o2o2o2o2o292
Which values of a make the solution of the equation 3(2x-4)=4(ax-2) positive? Select all that apply
PLEASE HELP!!!!
Answer:
u did not addd the pic
Step-by-step explanation:
Answer: 1.3660254037844
-0.36602540378444
Step-by-step explanation:
h(t) = − 4.9 t^2 + 226t + 283
The Maximum height of the object is 2888.9 feet which is at 23.06 seconds
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
Let h represent the height of an object after t seconds. Given that:
h(t) = -4.9t² + 226t + 283
The maximum height is at h'(t) = 0, hence:
h'(t) = -9.8t + 226
-9.8t + 226 = 0
9.8t = 226
t = 23.06 s
h(23.06) = -4.9(23.06)² + 226(23.06) + 283 = 2888.9
Maximum height is 2888.9 ft
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Please show work
I will mark brainliest
Answer:
A: y = 10
B: ∠A = 42; ∠C = ∠D = 138
Step-by-step explanation:
Given vertical angles A and B, with A marked 5y-8 and B marked 42, you want to know the value of y and the measures of supplementary angles C and D.
A. Value of yVertical angles A and B are congruent, so we have ...
∠A = ∠B
5y -8 = 42
5y = 50 . . . . . . . add 8
y = 10 . . . . . . . divide by 5
B. Angle measuresAs we noted above, angle A has the same measure as vertical angle B:
∠A = 42
Angle C forms a linear pair with angle B, so is supplementary:
∠C = 180 -∠B = 180 -42
∠C = 138
Angle D is a vertical angle to angle C (and is also supplementary to angle B).
∠D = 138
An angle measures 88.8° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:Hence, the measure of angle whose measure is 32∘ less than its supplement is 74∘.
Step-by-step explanation:
Using truth tables
24) All businessmen wear suits.
Aaron wears a suit.
Therefore, Aaron is a businessman.
A) Valid
B) Invalid
Find the answer to the green box give your answer in simplest form
Apply right triangle proportions:
[tex]\frac{16}{x}=\frac{x}{20}[/tex]20 (16) = x (x)
320 = x^2
√320 = x
x = 8√5
Assume that 600 births are randomly selected and 26 of the births are girls. Use subjective judgment to describe the
number of girls as significantly high, significantly low, or neither significantly low nor significantly high.
Choose the correct answer below.
A. The number of girls is significantly low.
B. The number of girls is neither significantly low nor significantly high.
C. The number of girls is significantly high.
D. It is impossible to make a judgment with the given information.
With the aid of subjective judgment, we can describe the number of girls as; A. The number of girls is significantly low.
How to interpret subjective judgement?Subjective judgement is simply defined as something that is subjective is based on personal opinions and feelings rather than on facts.
Now, we are told to assume that 600 births are randomly selected and 26 of the births are girls.
Now, we see that the total number of births are assumed as 600.
Now, since only 26 of that size are seen to be girls, then it means that;
Percentage that are girls = (26/600) * 100 = 4.33%
Thus, using subjective judgement we see that the percentage that are girls is so low that it is even lower than 5%. Thus, we can say that The number of girls is significantly low.
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