Answers
3.
[tex]y=\sec^3x+\cot^2(2x)[/tex]
Use the chain rule:
[tex]y'=(\sec^3x)'+(\cot^2(2x))'[/tex]
[tex]y'=3\sec^2x(\sec x)'+2\cot(2x)(\cot(2x))'[/tex]
[tex]y'=3\sec^2x(\sec x\tan x)-2\cot(2x)\csc^2(2x)(2x)'[/tex]
[tex]y'=3\sec^3x\tan x-4\cot(2x)\csc^2(2x)[/tex]
4.
[tex]y=\sin(cos(3x))[/tex]
Same as before:
[tex]y'=(\sin(\cos(3x)))'[/tex]
[tex]y'=\cos(\cos(3x))(\cos(3x))'[/tex]
[tex]y'=-\cos(\cos(3x))\sin(3x)(3x)'[/tex]
[tex]y'=-3\cos(\cos(3x))\sin(3x)[/tex]
Related Questions
x^2 = 8x - 15
.......................
Answers
Answer: x= 5
Step-by-step explanation: Lets solve by completing the square.
You first need to get -15 by itself.
x^2-8x=15 Now you need to complete the square my finding a perfect constant that will go with x^2-8x, then add it to the other side containing -15 to balance the equation out.
-8x/2= -4^2=16 This will be the perfect square.
x^2-8x+16 = -15 + 16
(x-4)^2 = 1 factor into a binomial, then use the square root on both sides.
√ x-4 ^ 2 = √ 1
x-4 = 1
x=5
Given the equation StartFraction 2 x + 2 Over y EndFraction = 4 w + 2 what is the value of x?
Answers
Question:
Given the equation (2x + 2)/y = 4w + 2.
What is the value of x?
Answer:
x = 2wy + y - 1
Step-by-step explanation:
Given
(2x + 2)/y = 4w + 2
Required
Find x
To find the value of x; the following steps will be used.
First, Multiply both sides by y
y * (2x + 2)/y = (4w + 2) * y
2x + 2 = 4wy + 2y
Subtract 2 from both sides
2x + 2 - 2 = 4wy + 2y - 2
2x = 4wy + 2y - 2
Multiply both sides by ½
½ * 2x = ½(4wy + 2y - 2)
x = ½(4wy + 2y - 2)
Open bracket
x = ½ * 4wy + ½ * 2y - ½ * 2
x = 2wy + y - 1
Hence, the value of x is 2wy + y - 1
Answer:
B
Step-by-step explanation:
I took the test
On the first day of school, each student is given $0.50 to attend. On day two, each student earns $1.00. on day 3, $2.00, etc. How much do students earn on the 9th day
Answers
Answer:
255.50
Step-by-step explanation:
If each day the number is doubled, then all you must do is keep on doubling to the ninth day and then add it all together
day 2- $1.00
day 3- $2.00
this means every day the amount each student is given doubles from the day before.
day 4- $4.00
day 5- $8.00
day 6- $16.00
day 7- $32.00
day 8- $64.00
day 9- $128.00
so on the 9th day the students would earn $128.00
day 9- $128.00
Question 11 of 15
Micah is filling up his cone-shaped cup with water. The cup (as shown) has a diameter of 72 millimeters and a slant height of 45
millimeters. How much water can Micah fill in his cup?
Answers
Answer:
36.644 mL . . . . depending on your value of π (see below)
Step-by-step explanation:
The height of Micah's cup is found from the radius and slant height. The radius is half the diameter, so is 36 mm. Then the height h is ...
45² = 36² +h²
h = √(45² -36²) = 27 . . . . . mm
The volume is given by the formula ...
V = (1/3)πr²h
V = (1/3)π(36 mm)²(27 mm) = 11664π mm³
For π = 3.14
11664(3.14) mm³ ≈ 36,625 mm³ = 36.625 mL
For π = 3.14159265
11665π mm³ = 36,644 mm³ = 36.644 mL
_____
Comment on units
A unit of measure used for relatively small volumes, especially of liquid, is milliliters (mL). 1 mL = 1000 mm³.
Answer:
The answer is 11664pimm^3
Step-by-step explanation:
Select the correct symbol to compare the rates.
22 miles in 20 minutes 38 miles in 30 minutes
Answers
Answer:
<
Step-by-step explanation:
22/20=1.1
38/30=1.27
Answer:
<
Step-by-step explanation:
Complete A and B for 5-8 points.
Answers
Answer:
a) 4 hours
b) 11 am
Step-by-step explanation:
So say the number of hours is x
a) 72 + 6x = 96
6x = 24
x = 4
b) 7am + 4 hours = 11am
You score a 65% on your AP Statistics Exam and a 78% on your Economics Exam. The AP Statistics scores were normally distributed with an average of 60% and a standard deviation of 6%. The Economics scores were also normally distributed with an average of 75% and standard deviation of 2.5%. In which class did you perform better relative to the class average? Be sure to justify your answer.
Answers
Answer:
His economics grade had a higher z-score, so you performed better relative to the class average in economics.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In which class did you perform better relative to the class average?
In whichever class you had the higher z-score.
Statistics:
Scored 65, mean 60, standard deviation 6. So [tex]X = 65, \mu = 60, \sigma = 6[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{65 - 60}{6}[/tex]
[tex]Z = 0.83[/tex]
Economics:
Scored 78, Mean 75, Standard deviation 2.5. So [tex]X = 78, \mu = 75, \sigma = 2.5[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{78 - 75}{2.5}[/tex]
[tex]Z = 1.2[/tex]
His economics grade had a higher z-score, so you performed better relative to the class average in economics.
How many unique ways are there to arrange the letters in the word PRIOR?
Answers
Answer:
60
Step-by-step explanation:
Answer:
it is 60
Step-by-step explanation:
This area model shows 50 X 38 Which number is missing from the model
Answers
Answer:
69
Step-by-step explanation:
When you cough,the radius of your trachea (windpipe) decreases,affecting the speed S of the air in the trachea. If r0 is the normal radius of the trachea, the relationship between the speed S of the air and the radius r of the trachea during a cough is given by a function of the form
S(r) = (r0 - r) ar^2
where a is positive constant. Find the radius r for which the speed of the air is greatest.
Answers
Answer: 2r(0)/3.
Step-by-step explanation:
So, we are given one Important data or o or parameter in the question above and that is the function of the form which is given below(that is);
S(r) = (r0 - r) ar^2 -----------------------------(1).
We will now have to differentiate S(r) with respect to r, so, check below for the differentiation:
dS/dr = 2ar (r0 - r ) + ar^2 (-1 ) ---------;(2).
dS/dr = 2ar(r0) - 2ar^2 - ar^2.
dS/dr = - 3ar^2 + 2ar(r0) ------------------(3).
Note that dS/dr = 0.
Hence, - 3ar^2 + 2ar(r0) = 0.
Making ra the subject of the formula we have;
ra[ - 3r + 2r(0) ] = 0. -------------------------(4).
Hence, r = 0 and r = 2r(0) / 3.
If we take the second derivative of S(r) too, we will have;
d^2S/dr = -6ar + 2ar(0). -------------------(5).
+ 2ar(0) > 0 for r = 0; and r = 2r(0)/3 which is the greatest.
Answer:
[tex]r =\frac{2r_{0}}{3}[/tex]
Step-by-step explanation:
We need to take the derivative of S(r) and equal to zero to maximize the function. In this conditions we will find the radius r for which the speed of the air is greatest.
Let's take the derivative:
[tex]\frac{dS}{dr}=a(2r(r_{0}-r)+r^{2}(-1))[/tex]
[tex]\frac{dS}{dr}=a(2r*r_{0}-2r^{2}-r^{2})[/tex]
[tex]\frac{dS}{dr}=a(2r*r_{0}-3r^{2})[/tex]
[tex]\frac{dS}{dr}=ar(2r_{0}-3r)[/tex]
Let's equal it to zero, to maximize S.
[tex]0=ar(2r_{0}-3r)[/tex]
We will have two solutions:
[tex]r = 0[/tex]
[tex]r =\frac{2r_{0}}{3}[/tex]
Therefore the value of r for which the speed of the air is greatest is [tex]r =\frac{2r_{0}}{3}[/tex].
I hope it helps you!
Factor.
Z^2- 3z – 18
Answers
Answer:
(z-6)(z+3)
Step-by-step explanation:
Answer:
Step-by-step explanation:
z^2-6z + 3z -18
z(z-6)+3(z-6)
(z+3)(z-6)
What is the volume of a sphere with a diameter of 6 m, rounded to the nearest tenth of a cubic meter?
Answers
Answer:113 cubic meter
Step-by-step explanation:
Diameter=6
Radius=r=6/2
Radius=r=3
π=3.14
Volume of sphere=4/3 x π x r x r x r
Volume of sphere=4/3 x 3.14 x 3 x 3 x 3
Volume of sphere=(4x3.14x3x3x3) ➗ 3
Volume of sphere=339.12 ➗ 3
Volume of sphere=113.04
Volume of sphere =113 cubic meter
brainliest quick!
Aiden wanted to model -15 + 15 = 0 on the number line. He first drew an arrow 15 units long starting from zero that pointed to the left. He then draws another arrow 15 units long starting from zero that points to the right. What error did Aiden make?
A. The first arrow he drew should have pointed to the right to represent -15.
B. The second arrow he drew should have pointed to the left to represent 15.
C. The first arrow he drew should have started at -15 instead of 0.
D. The second arrow he drew should have started at -15 instead of 0.
Answers
Answer:
c
Step-by-step explanation:
Answer:
it's D
Step-by-step explanation:
The number never goes over 0 so there is no need to put anything above 0
Given f(x) = -4x + 7 and g(x) = x, choose
the expression for (fºg)(x).
Answers
Answer:
-4x^2+7x
Step-by-step explanation:
Multiply -4x+7 and x.
You get -4x^2+7x.
Which goes with which
Answers
Solve for a given 2e^a =4b
Answers
Answer:
a = ln (2b)
Step-by-step explanation:
2e^a =4b
Divide each side by 2
2/2 e^a =4/2b
e^a = 2b
Take the natural log of each side
ln(e^a) = ln(2b)
a = ln (2b)
Find the volume of a block of woods
Answers
Answer:volume=125 cm^3
Surface area=150 cm^2
Step-by-step explanation:
Part A:
volume=length x width x height
volume=5 x 5 x 5
Volume=125 cm^3
Part B:
Surface area=6x5x5
Surface area=150 cm^2
What’s the correct answer for this?
Answers
Answer:
C
Step-by-step explanation:
HJN IS SIMILAR TO PQN
Find the supplement of an angle that measures 20 degrees.
A) 50 degrees
B) 70 degrees
C) 90 degrees
D) 160 degrees
Answers
Answer:
160 degrees
Step-by-step explanation:
Answer:I think it is D
Step-by-step explanation:
Three black beads, two red beads, and a yellow bead are arranged in a line. What is the probability that no black bead is adjacent to the yellow bead?
Answers
Answer:
Probability of no black bead is adjacent to the yellow bead is = 0.966
Step-by-step explanation:
First to arrange all the beads without restrictions = 6! = 720
Probability the black bead is adjacent to Yellow bead = 4!/6! = 24 /720
= 0.0333
Probability of no black bead is adjacent to the yellow bead is
= 1- Probability the black bead is adjacent to Yellow bead
= 1-0.033
= 0.966
what are the steps for using integar tiles to evaluate the expression 45 divided by 15
Answers
Answer:
1. Gather 45 tiles
2. Split them up into groups of 15. Your answer will be the amount of piles you end up with. Hope this helps!
list all the factor means use divisibility rules of 102,232
Answers
Answer:
102,232 = 2·2·2·13·983
Step-by-step explanation:
102,232 ends in 32, so is divisible by 4
102,232/4 = 25558 ends in 2, so is divisible by 2
25558/2 = 12779
is not even, so is not divisible by 2
has a sum of digits mod 9 of 8, so is not divisible by 3 or 9
does not end in 0 or 5, so is not divisible by 5
gives the result 1277-2·9 = 1259; 125-2·9 = 107; 10-2·7 = -4, which is not zero, so 12779 is not divisible by 7
gives the result (1+7+9)-(2+7) = 8, which is not divisible by 11, so 12779 is not divisible by 11
gives the result 1277 +4·9 = 1313, which is divisible by 13, so 12779 is divisible by 13
12779/13 = 983 needs to be tested for divisibility by primes between 17 and 31, namely 17, 19, 23, 29, 31. It is not divisible by any of these, so this is the last prime factor of 102,232:
102,323 = 2·2·2·13·983
_____
Divisibility rules:
Note that for any transformation rule, the rule can be repeated on the reduced result. The digits of a sum of digits can be summed, for example.
2: ends in even digit
3: sum of digits is divisible by 3
5: ends in 0 or 5
7: subtracting 2 times the last digit from the rest is divisible by 7
11: difference of sums of alternate digits is divisible by 11
13: there are several rules. A couple of useful ones are
the sum of 4 times the last digit and the remaining number will be divisible by 13 (used above)the difference of the sums of alternate groups of 3 digits will be divisible by 13 (232-102 = 130, for the number above; is divisible)17: subtracting 5 times the last digit from the rest is divisible by 17
19: the sum of 4 times the last 2 digits and the remaining number will be divisible by 19
23: the sum of 3 times the last 2 digits and the remaining number will be divisible by 23
29: the sum of 9 times the last 2 digits and the remaining number will be divisible by 29
31: subtracting 3 times the last digit from the rest is divisible by 31
Calcula el 23 % de 175
Answers
Answer:40.25
Step-by-step explanation:
23% of 175
23/100 x 175
(23 x 175)/100
4025/100=40.25
Find the radius of Circle M, if the area of a sector is 36.07 cm^2 and the central angle of that sector is 58º. Round your answers to the hundredths place if necessary
Answers
Answer:
r = 5.97 cm
Step-by-step explanation:
The area of the sector is given by the following equation:
[tex]A = r*S = 2\pi*r^{2}*\frac{58}{360}[/tex]
Where:
r: is the radius
A: is the area
The radius is:
[tex]r = \sqrt{\frac{A}{2*\pi*58/360}} = \sqrt{\frac{36.07 cm^{2}}{2*\pi*58/360}} = 5.97 cm[/tex]
Therefore, the radius of Circle M is 5.97 cm.
I hope it helps you!
What is the sum in simplest form I ready diagnostic please hurry
Answers
example:
The value of x is 22
Step-by-step explanation:
We are given that there are two numbers
First number is x
second number is 35
The sum of x and 35 is 57
so, we get equation as
now, we can solve solve x
So, subtract both sides by 35
What are prime number
Answers
A prime number is a special number because it means that it only has one factor pair and that factor pair is always 1 and the number itself.
In other words, prime numbers are the numbers
divisible by 1 and the number itself.
For example, let us take 2.
2 has only two factors and those are 1 and 2 so it's prime.
Similarly, 7 is also a prime number because it has only two factors
and these are 1 and the number itself which is 7.
Answer:
A number that is only divisible by itself and 1
Step-by-step explanation:
B(4,8) and C(8,0) are the endpoints of a line segment. What is the midpoint M of that line
segment?
Write the coordinates as decimals or integers.
Answers
Answer:
(6,4)
Step-by-step explanation:
I just did quick math in my head.
What is the circumference of the following circle?
9 cm
Answers
Answer:
9π or 28.27 cm
Step-by-step explanation:
The circumference formula is 2πr or dπ. The diameter is 9 cm so we multiply 9 with pi to get the answer.
The value of the circumference of the given circle is 9π cm OR 28.278 cm
Calculating circumference of a circleFrom the question, we are to determine the circumference of the circle.
The circumference of a circle can be calculated by using the formula,
C = πd
Where C is the circumference of the circle
and d is the diameter
From the diagram,
d = 9 cm
Therefore,
Circumference of the circle = π × 9
Take π = 3.142
Then,
Circumference of the circle = 28.278 cm
Hence, the value of the circumference of the given circle is 9π cm OR 28.278 cm
Learn more on Calculating circumference of a circle here: https://brainly.com/question/12823137
1. To measure the resting heart rate of an animal biologist use the function h(m) = 530m-C), where h
is resting heart rate in beats per minute, given the mass m in pounds.
Part A: What is a feasible domain for the function him?
Answers
Answer:
Step-by-step explanation:
In mathematics, the domain or set of departure of a function is the set into which all of the input of the function is constrained to fall. It is the set X in the notation f: X → Y. Since a function is defined on its entire domain, its domain coincides with its domain of definition, the subset of the domain for which the function associates an image. However this coincidence is no longer true for a partial function since the domain of definition of a partial function can be a proper subset of the domain.
faz um bom tempo que não faço expressões numéricas,vcs podem me ajudar!
Answers
Answer:
English Plz
Step-by-step explanation:
