The length of the arc of the circle is 3.67 meters
What is an arc?The arc of a circle is a part of the circumference that makes up the circle
How to determine the length of the arc?From the question, we have the following parameters
Diameter, d = 14 meters
Central angle = π/6 radians
Start by calculating the radius of the circle using
Radius, r = Diameter/2
This is so because radius is half the diameter
So, we have
r = 14 meters/2
Evaluate the quotient of 14 meters and 2
r = 7 meters
The length of the arc of the circle is then calculated using
L = Radius * Central angle
Substitute known values in the above equation
L = 7 meters * π/6
Evaluate the product of 7 and π/6
L = 3.67 meters
Hence, the length of the arc of the circle is 3.67 meters
Read more about arc lengths at:
https://brainly.com/question/2005046
#SPJ1
Find the surface area of the figure. Round to the nearest hundredth of a unit. Let a = 1.9,b = 0.1, and c = 2
Answer:
I believe its 20.8, but I may be wrong
Step-by-step explanation:
Simplify Negative 3 over 2 divided by 9 over 6. −4 −1 4 1
Answer:
Step-by-step explanation: -3/2 divided by 9/6
= -3/2 multiply (to divide fractions we multiply by their recipical) 6/9
Then, simplify
= -3/3 = 1
Answer: -1
Hope this helps lol
The simplified result is -1. The correct option is b.
Given that:
Expression, -3/2 ÷ 9/6
To solve the given expression, follow as:
Rewrite the division as multiplication by the reciprocal of the second fraction.
-3/2 ÷ 9/6 = -3/2 × (6/9)
Now, simplify the fractions:
-3/2 × (6/9) = -3/2 × (2/3)
-3/2 × (6/9) = - (3 × 2)/(2 × 3)
-3/2 × (6/9) = -6/6
Finally, the simplified expression is -6/6. However, further simplify it by dividing the numerator and denominator by their greatest common divisor, which is 6:
-6/6 = -1
So, the simplified result is -1. The correct option is b.
Learn more about Divide here:
brainly.com/question/29464370
#SPJ3
Complete question:
Simplify Negative 3 over 2 divided by 9 over 6.
a. −4
b. −1
c. 4
d. 1
If the hypotenuse is c=a√2, then 6=a√2. In inches, what is the value of a?
The value of a is 3√2 inches if it is given that the hypotenuse is c = a√2 and 6 = a√2. This can be obtained by using Pythagoras' theorem.
Calculate the value of a:This question can be solved using Pythagoras' theorem,
If in a right angled triangle, hypotenuse is the longest side of the triangle and always opposite to the angle 90°, height and base are the two shorter sides which are adjacent to the angle 90°.
If hypotenuse = c, height = a and base = b then,
⇒ hypotenuse² = height² + base²
⇒ c² = a² + b²
Here in the question it is given that,
Hypotenuse of the triangle is c = a√2 6 = a√2 in inches ⇒ c = 6 Height and base is equal and both has the value of a ⇒ height = a and base = aBy using the Pythagoras' theorem we can write that,
⇒ hypotenuse² = height² + base²
⇒ 6² = a² + a²
⇒ 36 = 2a²
By dividing both sides of the equation by 2,
⇒ 18 = a²
⇒ a² = 18
By taking square on both side of the equation,
⇒ a = 3√2 inches
Hence the value of a is 3√2 inches if it is given that the hypotenuse is c = a√2 and 6 = a√2.
Learn more about Pythagoras' theorem here:
brainly.com/question/9005379
#SPJ1
The residual plot for a data set is shown below...
Based on the residual plot, which statement best explains whether the regression line is a good model for the data set and why?
A. The regression line is not a good model because there is no pattern in the residuals.
B. The regression line is a good model because the residuals are randomly distributed.
C. The regression line is not a good model because only one point in the residual plot is on the x-axis.
D. The regression line is a good model because there is one point in the residual plot on the x-axis.
Based on the residual plot given, the statement that describes if the model is good is B. The regression line is a good model because the residuals are randomly distributed.
Why is the residual line a good model?For a model to be considered ideal or good, the residuals from the model should be randomly distributed in an equal manner around the regression line.
The residual plot shows that the residuals are randomly distributed which means that the regression line is a good model.
Find out more on residuals at https://brainly.com/question/1447173.
#SPJ1
help please.
Malaysia police traffic department claims that 54% of fatal car accidents are caused by driver error. A researcher studies 30 randomly selected accidents and founds that 14 were caused by driver error. Using a = 0.05, is that Malaysia police traffic department's statement is true?
Answer:
The Malaysia police departments statement was true, because 14/30 is extremely close to 54% (roughly 15.5/30).
Type: Probability
Please rate this answer based on how helpful it was!Solve -7(m-1)= -(3m-1)
Please give work
Answer:
m = 3/2
Step-by-step explanation:
-7(m-1)= -(3m-1)
-7m + 7 = -3m + 1
-4m = -6
m = 3/2
Check.
-7(m-1)= -(3m-1)
-7(3/2 - 1) = -(3*3/2 - 1)
-7(1/2) = -(4.5 - 1)
-3.5 = -3.5
Use the distributive property to multiply −7 by m−1.
−7m+7=−(3m−1)To find the opposite of 3m−1, find the opposite of each term.
−7m + 7 = −3m −( − 1 )The opposite of −1 is 1.
−7m + 7= −3m + 1Add 3m to both sides.
−7m + 7 + 3m = 1Combine −7m and 3m to get −4m.
−4m + 7 = 1Subtract 7 from both sides.
−4m = 1 − 7Subtract 7 from 1 to get −6.
−4m = −6Divide both sides by −4.
m = -6/-4Reduce the fraction -6/-4 to its lowest expression by extracting and canceling −2.
Answer: m=3/4 ✅
In a city of 56,000 people, there are 21,000 people under 25 years of age. What percent of the population is under 25 years of age?
Answer:
37.5
Step-by-step explanation:
So whenever you want to find "x" percent of a number, you just do: [tex]\frac{x}{100} * n = \text{x\% of n}[/tex]. You're essentially converting the percentage to it's decimal value by dividing by 100.
Given this information, we're solving for x, instead of x% of n. In this case n = 56,000, and x% of 56,000 is 21,000
[tex]\frac{x}{100} * 56000 = 2100[/tex]
Divide both sides by 56,000
[tex]\frac{x}{100} = \frac{21,000}{56,000}[/tex]
Multiply both sides by 100
[tex]x = 100(\frac{21,000}{56,000})[/tex]
Simplify:
[tex]x = 37.5\%[/tex]
This can be generally thought of as:
[tex]x=100(\frac{part}{whole})[/tex]
where part = partial amount, or how much is after finding what x% is of the whole amount, but in this case we know what it is, we just don't know what the "x" percent is.
Find g(x), where g(x) is the translation 2 units left and 13 units up of f(x)=–7x+7.
Answer:
[tex]g(x)=-7x+6[/tex]
Step-by-step explanation:
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function:
[tex]f(x)=-7x+7[/tex]
Translation of 2 units left:
[tex]\implies f(x+2)=-7(x+2)+7[/tex]
Translation of 13 units up:
[tex]\implies f(x+2)+13=-7(x+2)+7+13[/tex]
Simplifying:
[tex]\implies g(x)=-7(x+2)+7+13[/tex]
[tex]\implies g(x)=-7x-14+7+13[/tex]
[tex]\implies g(x)=-7x+6[/tex]
Learn more about graph transformations here:
https://brainly.com/question/28041916
https://brainly.com/question/27930491
The width of a rectangle is 9 less than twice its length. If the area of the rectangle is 96
cm ^2 , what is the length of the diagonal?
Thee diagonal of the rectangle is 13.86 cm long.
What is the length of the diagonal of rectangle?We are given that;
Width of a rectangle is 9 less than twice its length. Thus, if length is L, then;
W = 2L - 9
Area formula for a rectangle is;
A = Length * Width
We are given area of rectangle = 96 cm²
Thus;
L(2L - 9) = 96
2L² - 9L = 96
2L² - 9L - 96 = 0
Using online quadratic equation calculator gives;
L = 9.53 cm
Thus;
W = 2(9.53) - 9
W = 19.06 - 9
W = 10.06 cm
The diagonal of the triangle will be gotten from Pythagoras theorem;
D = √(9.53² + 10.06²)
D = √192.0245
D = 13.86 cm
Thus, we conclude that the diagonal of the rectangle is 13.86 cm long.
Read more about Rectangle Diagonal at; https://brainly.com/question/7071655
#SPJ1
There is a set of 12 cards numbered 1 to 12. A card is chosen at random. Event A is choosing a number less
than 6. Event B is choosing a number divisible by 3. A diagram is given below.
(Can you help with #4 if you know it:)
The number of permutations of picking 4 pens from the box is 30.
There are six different unique colored pens in a box.
We have to select four pens from the different unique colored pens.
We have to find in how many different orders the four pens can be selected.
What is a permutation?A permutation is the number of different arrangements of a set of items in a particular definite order.
The formula used for permutation of n items for r selection is:
[tex]^nP_r = \frac{n!}{r!}[/tex]
Where n! = n(n-1)(n-2)(n-3)..........1 and r! = r(r-1)(r-2)(r-3)........1
We have,
Number of colored pens = 6
n = 6.
Number of pens to be selected = 4
r = 4
Applying the permutation formula.
We get,
= [tex]^6P_4[/tex]
= 6! / 4!
=(6x5x4x3x2x1 ) / ( 4x3x2x1)
= 6x5
=30
Thus the number of permutations of picking 4 pens from a total of 6 unique colored pens in the box is 30.
Learn more about permutation here:
https://brainly.com/question/14767366
#SPJ1
A coin is flipped, and a number cube is rolled. What is the probability of getting heads on the coin and a number less than 3 on the number cube?
a.one eighth
b. one sixth
c. one fourth
d. one half
=============================================================
Explanation:
The probability of getting heads is 1/2 because there's one side we want out of two sides total
The probability of getting less than 3 is 2/6 = 1/3 since we have two sides we want (rolling a "1" or a "2") out of six sides total.
Multiply the two mentioned fractions: 1/2 times 1/3 = 1/6
1/6 can be written as "one sixth", but I prefer the first format better since it's shorter.
---------------
If you are a visual learner, you can make a table with 2 rows and 6 columns, or vice versa (6 rows and 2 columns). The order doesn't matter.
The two rows represent the events Heads or Tails. The 6 columns show the different outcomes on the number cube. We have 6*2 = 12 different outcomes of rolling a die and flipping a coin.
Of those 12 outcomes, shade in 2 boxes to represent getting heads and either a "1" or "2". Refer to the diagram below.
We have 2 shaded rectangles out of 12 total to get 2/12 = 1/6
The visual representation of a table like this may help show why we multiplied the fractions 1/2 and 1/3 to get the answer. Hint: think of area = length*width.
The probability of getting heads on the coin and a number less than 3 on the number cube is 1/6, Option A is correct.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
A coin is flipped, and a number cube is rolled.
We need to find the probability of getting heads on the coin and a number less than 3 on the number cube.
The probability of getting heads when flipping a coin is 1/2
The probability of getting less than 3 is 2/6 = 1/3 since we have two sides
Now the probability of getting heads on the coin and a number less than 3 on the number cube
The product of 1/2 and 1/3
1/2×1/3
1/6
Hence, the probability of getting heads on the coin and a number less than 3 on the number cube is 1/6, Option A is correct.
To learn more on probability click:
https://brainly.com/question/11234923
#SPJ2
Cos(11*)cos(19*) - sin(11*) sin(19*)
Write the expression as a function of one number then find it’s exact value.
Answer:
√3/2
Step-by-step explanation:
This is compound angle of cosine
cos(11+19)
=cos(30)
=√3/2
The function f(x)=58(1.6)x represents the possible bird population in a park x years from now. Each year, the expected number of birds is ____the number the year before.
Answer:
1.6 times or 60% more than
Step-by-step explanation:
The question seems to be asking about the growth factor in the given exponential function.
Exponential functionA generic exponential function will have the form ...
quantity = (initial value) × (growth factor)^(number of intervals)
Comparing this form to the given formula ...
f(x) = 58 × 1.6^x
we see the "growth factor" is 1.6. This is the multiplier from one interval (year) to the next.
Each year the expected number of birds is 1.6 times the number the year before.
__
Additional comment
A growth factor is sometimes expressed in terms of a growth rate, usually a percentage.
growth factor = 1 + growth rate
1.6 = 1 + 0.60 = 1 + 60%
The growth rate of this bird population is 60% per year. Each year, the population is 60% more than the year before.
Answer: 1.6
Step-by-step explanation:
The human eye contains approximately 9.1 x 10^7 rod cells and 4.5 x 10^6 cone cells . Samuel subtracts 9.1-4.5 and says there are about 46,000,000 more rod cells than cone cells in the human eye . Use the drop - down menus to explain why Samuel is incorrect
Samuel is incorrect because he didn't subtract the power of the numbers.
How many more rod cells are there?The number of rod and cone cells in the human eye is written in scientific notation. Scientific notation is used in expressing large numbers in smaller numbers. To write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, 1 x 10² is equivalent to 100
(9.1 x 10^7) - (4.5 x 10^6)
= (9.1 - 4.5) x 10^(7 - 6)
4.6 x 10 = 46
To learn more about scientific notation, please check: https://brainly.com/question/25334755
#SPJ1
Use the formula to find the standard error of the distribution of differences in sample means, x¯1-x¯2. Samples of size 100 from Population 1 with mean 90 and standard deviation 11 and samples of size 85 from Population 2 with mean 71 and standard deviation 15 Round your answer for the standard error to two decimal places. standard error = Enter your answer in accordance to the question statement
Using the Central Limit Theorem, the standard error of the distribution of differences in sample means is of 1.97.
What is the standard error for each sample?According to the Central Limit Theorem, it is given by the standard deviation of the sample divided by the square root of the sample size, hence:
s1 = 11/sqrt(100) = 1.1.s2 = 15/sqrt(85) = 1.63.What is the square root of the distribution of differences?It is given by the square root of the sum of the standard errors of each sample squared, hence:
s = sqrt(1.1² + 1.63²) = 1.97.
More can be learned about the Central Limit Theorem at https://brainly.com/question/16695444
#SPJ1
I
. If the results of a probability experiment can be any integer from 16 to 18 and the
probability that the integer is less than 20 is 0.88, what is the probability that the
integer be 20 or more?
Using the probability concept, considering complementary probabilities, there is a 0.12 = 12% probability that the integer is of 20 or more.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
If two events are complementary, the sum of their probabilities is of 1. In this problem, we have that an integer being less than 20 is complementary to an integer being 20 or more.
We have that:
There is a 0.88 probability that the number is less than 20.There is a x probability that the number is 20 or more.These events are complementary, hence:
0.88 + x = 1
x = 1 - 0.88
x = 0.12
There is a 0.12 = 12% probability that the integer is of 20 or more.
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
Suppose that the sum of the three vectors u, v, and w shown in the figure is the zero vector. If w = 10 find u and v.
a. The value of v is 9.2
b. The value of u is 9.9
What are vectors?Vectors are physical quantities that have both magnitude and direction
How to find the value of vectors u and v?Since we have vectors
u at 70° to the x-axis v at 47° to the x-axis and w = 10 at 15° to the x-axis,We resolve them into component form
So, u = -(ucos70°)i - (usin70°)j
u = -(0.3420u)i - (0.9397u)j
v = -(vcos47°)i + (vsin47°)j
v = -(0.6820v)i - (0.7314v)j
w = (wcos15°)i + (wsin15°)j
w = (0.9659w)i + (0.2588w)j
w = (9.659)i + (2.588)j
Since the sum of the three vectors is zero, we have that
u + v + w = 0
u + v = -w
So,
-(0.3420u)i - (0.9397u)j + [-(0.6820v)i - (0.7314v)j] = -[(9.659)i + (2.588)j]
-(0.3420u)i - (0.9397u)j -(0.6820v)i - (0.7314v)j = -(9.659)i - (2.588)j]
-(0.3420u)i -(0.6820v)i - (0.9397u)j - (0.7314v)j = -(9.659)i - (2.588)j]
-[0.3420u + 0.6820v]i - [0.9397u + 0.7314v]j = -(9.659)i - (2.588)j
Equating i components, we have
-[0.3420u + 0.6820v]i = -9.659i
0.3420u + 0.6820v = 9.659
Dividing through by 0.3420. we have
u + 1.994v = 28.242 (1) and
Also, equating j components, we have
- [0.9397u + 0.7314v]j = -2.588j
0.9397u + 0.7314v = 2.588
Dividing through by 0.9397 we have
u + 0.778v = 2.754 (2)
a. The value of v
Subracring equation (2) from(1),we have
u + 1.994v = 28.242 (1)
-
u + 0.778v = 2.754 (2)
2.772v = 25.488
v = 25.488/2.772
v = 9.19
v ≅ 9.2
The value of v is 9.2
b. The value of uSubstituting v into (1), we have
u + 1.994v = 28.242 (1)
u + 1.994(9.19) = 28.242
u + 18.325 = 28.242
u = 28.242 - 18.325
u = 9.917
u ≅ 9.9
The value of u is 9.2
Learn more about vectors here:
https://brainly.com/question/25705666
#SPJ1
what fraction of four weeks is 8 days
Answer:
For weeks are 28 days, so the fraction is 28/8= 3,5 and the fraction is 7/2
Add 10/12 and 6/10 as a mixed number
Answer:
1 13/30
Step-by-step explanation:
10/12 + 6/10 =
= 5/6 + 3/5
= 25/30 + 18/30
= 43/30
= 30/30 + 13/30
= 1 13/30
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{Equation:}[/tex]
[tex]\mathsf{\dfrac{10}{12} + \dfrac{6}{10}}[/tex]
[tex]\huge\textsf{Solving:}[/tex]
[tex]\mathsf{\dfrac{10}{12} + \dfrac{6}{10}}[/tex]
[tex]\mathsf{= \dfrac{10\div2}{12\div2} + \dfrac{6\div2}{10\div2}}[/tex]
[tex]\mathsf{= \dfrac{5}{6} + \dfrac{3}{5}}[/tex]
[tex]\mathsf{= \dfrac{5\times5}{6\times5} + \dfrac{3\times6}{5\times6}}[/tex]
[tex]\mathsf{= \dfrac{25}{30} + \dfrac{18}{30}}[/tex]
[tex]\mathsf{= \dfrac{25 + 18}{30-0}}[/tex]
[tex]\mathsf{= \dfrac{25 + 18}{30}}[/tex]
[tex]\mathsf{= \dfrac{43}{30}}[/tex]
[tex]\approx\mathsf{1\dfrac{13}{30}}[/tex]
[tex]\huge\textsf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{1\dfrac{13}{30}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
HOW MANY DISTINCT ARRANGEMENTS CAN BE MADE WITH THE LETTERS IN THE
WORD CONNECTION?
There are 151200 distinct ways to arrange the letters of the word CONNECTION
How to determine the number of arrangements?The word is given as:
CONNECTION
In the above word, we have the following parameters:
Total number of characters, n = 10
The repeated letters are:
C's = 2
O's = 2
N's = 3
The number of arrangements of the letters is then calculated as:
Arrangements = n!/(C! * O! * N!)
Substitute the known values in the above equation
Arrangements = 10!/(2! * 2! * 3!)
Evaluate the expression
Arrangements = 151200
Hence, there are 151200 distinct ways to arrange the letters of the word CONNECTION
Read more about permutation at:
https://brainly.com/question/11732255
#SPJ1
What is the answer I need help!
Which function has the greatest y-intercept?
Answer:
Second one from the left
Answer:
b
Step-by-step explanation:
edg 22'
Two trains leave towns 664 miles apart at the same time and travel toward each other. One train travels 16 mih faster than the other. If they meet in 4 hours, what is the rate of each train?
Answer:
I think that I am right. One train is traveling at 75 mph and the other train is traveling at 91 mph
Step-by-step explanation:
question in pictures
The derivatives of the functions are listed below:
(a) [tex]f'(x) = -7\cdot x^{-\frac{9}{2} }- 2\cdot x + 4 - \frac{1}{5} - 5\cdot x^{-2}[/tex]
(b) [tex]f'(x) = \frac{1}{3}\cdot (x + 3)^{-\frac{2}{3} }\cdot (x+ 5)^{\frac{1}{3} } + \frac{1}{3} \cdot (x + 5)^{-\frac{2}{3} } \cdot (x + 3)^{\frac{1}{3} }[/tex]
(c) f'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)²
(d) f'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)]
(e) f'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶
(f) [tex]f'(x) = (\ln x + 1)\cdot [7^{x\cdot \ln x \cdot \ln 7}+7\cdot (x\cdot \ln x)^{6}][/tex]
(g) [tex]f'(x) = -2\cdot \arccos x \cdot \left(\frac{1}{\sqrt{1 - x^{2}}} \right) - \left(\frac{1}{1 + x} \right) \cdot \left(\frac{1}{2} \cdot x^{-\frac{1}{2} }\right)[/tex]
(h) f'(x) = cot x + cos (㏑ x) · (1 / x)
How to find the first derivative of a group of functions
In this question we must obtain the first derivatives of each expression by applying differentiation rules:
(a) [tex]f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}[/tex]
[tex]f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}[/tex] Given[tex]f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4\cdot x - \frac{x}{5} + 5 \cdot x^{-1} - \sqrt[11]{2022}[/tex] Definition of power[tex]f'(x) = -7\cdot x^{-\frac{9}{2} }- 2\cdot x + 4 - \frac{1}{5} - 5\cdot x^{-2}[/tex] Derivative of constant and power functions / Derivative of an addition of functions / Result(b) [tex]f(x) = \sqrt[3]{x + 3} \cdot \sqrt[3]{x + 5}[/tex]
[tex]f(x) = \sqrt[3]{x + 3} \cdot \sqrt[3]{x + 5}[/tex] Given[tex]f(x) = (x + 3)^{\frac{1}{3} }\cdot (x + 5)^{\frac{1}{3} }[/tex] Definition of power[tex]f'(x) = \frac{1}{3}\cdot (x + 3)^{-\frac{2}{3} }\cdot (x+ 5)^{\frac{1}{3} } + \frac{1}{3} \cdot (x + 5)^{-\frac{2}{3} } \cdot (x + 3)^{\frac{1}{3} }[/tex] Derivative of a product of functions / Derivative of power function / Rule of chain / Result(c) f(x) = (sin x - cos x) / (x² - 1)
f(x) = (sin x - cos x) / (x² - 1) Givenf'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)² Derivative of cosine / Derivative of sine / Derivative of power function / Derivative of a constant / Derivative of a division of functions / Result(d) f(x) = 5ˣ · ㏒₅ x
f(x) = 5ˣ · ㏒₅ x Givenf'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)] Derivative of an exponential function / Derivative of a logarithmic function / Derivative of a product of functions / Result(e) f(x) = (x⁻⁵ + √3)⁻⁹
f(x) = (x⁻⁵ + √3)⁻⁹ Givenf'(x) = - 9 · (x⁻⁵ + √3)⁻⁸ · (- 5) · x⁻⁶ Rule of chain / Derivative of sum of functions / Derivative of power function / Derivative of constant functionf'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶ Associative and commutative properties / Definition of multiplication / Result(f) [tex]f(x) = 7^{x\cdot \ln x} + (x \cdot \ln x)^{7}[/tex]
[tex]f(x) = 7^{x\cdot \ln x} + (x \cdot \ln x)^{7}[/tex] Given[tex]f'(x) = 7^{x\cdot\ln x} \cdot \ln 7 \cdot (\ln x + 1) + 7\cdot (x\cdot \ln x)^{6}\cdot (\ln x + 1)[/tex] Rule of chain / Derivative of sum of functions / Derivative of multiplication of functions / Derivative of logarithmic functions / Derivative of potential functions [tex]f'(x) = (\ln x + 1)\cdot [7^{x\cdot \ln x \cdot \ln 7}+7\cdot (x\cdot \ln x)^{6}][/tex] Distributive property / Result(g) [tex]f(x) = \arccos^{2} x - \arctan (\sqrt{x})[/tex]
[tex]f(x) = \arccos^{2} x - \arctan (\sqrt{x})[/tex] Given[tex]f'(x) = -2\cdot \arccos x \cdot \left(\frac{1}{\sqrt{1 - x^{2}}} \right) - \left(\frac{1}{1 + x} \right) \cdot \left(\frac{1}{2} \cdot x^{-\frac{1}{2} }\right)[/tex] Derivative of the subtraction of functions / Derivative of arccosine / Derivative of arctangent / Rule of chain / Derivative of power functions / Result(h) f(x) = ㏑ (sin x) + sin (㏑ x)
f(x) = ㏑ (sin x) + sin (㏑ x) Givenf'(x) = (1 / sin x) · cos x + cos (㏑ x) · (1 / x) Rule of chain / Derivative of sine / Derivative of natural logarithm /Derivative of addition of functions f'(x) = cot x + cos (㏑ x) · (1 / x) cot x = cos x / sin x / ResultTo learn more on derivatives: https://brainly.com/question/23847661
#SPJ1
Once a delay or disability is diagnosed, the best thing to do is to continue to be a family’s knowledgeable and reliable partner in child care.Once a delay or disability is diagnosed, the best thing to do is to continue to be a family’s knowledgeable and reliable partner in child care.
Once you detect that there is a delay or disability, then you should continue to be the reliable partner in child care to the family so this is True.
What should be done when a delay in child development is seen?The observation and screening process can lead to a child care partner discovering a delay or disability.
When this happens, you should report to your supervisor to check if the child is eligible for federal and state programs related to their condition. Whatever the case, you should remain accessible to the family as their partner in child care.
Find out more on child development delays at https://brainly.com/question/5082527
#SPJ1
The ratio of Sadias age to her fathers age is 3:5. The sum of their ages is 96. What is Sadias age.
Answer:
36 years old
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
sum the parts of the ratio , 3 + 5 = 8
divide the sum of their ages by 8 to find the value of one part of the ratio
96 ÷ 8 = 12 ← value of 1 part of the ratio , then
3 parts = 3 × 12 = 36 ← Sadias age
Which statement is true about the voting results?
Answer:
11% more people voted for Candidate B than Candidate A
Step-by-step explanation:
15+6=21
9+23=32
32-21=11
Will give brainliest !!
Type the correct answer in the box.
Which trigonometric expression can be used to find value of x? Replace a and b with the correct values.
(trigonometry)
Answer:
x = 12cos(35)
Step-by-step explanation:
Well you have hyp and adj, meaning cosine. and u have the angle and need the adjacent, so side(cos(theta)).
12cos(35).
Sims waist is 30 inches. He wants to put on more weight and is hoping to gain enough weight to increase his waist size by 8%. How many inches does he want his waist to be?
Sim wants to increase his waist size to 32.4 inches.
How many inches does Sim want his waist to be?Sim wants the increase to be 8% of 30 inches.
The amount of increase Sim wants in his waist size exists
8% × 30 inches.
= 0.08 × 30 inches.
= 2.4 inches.
Adding the wanted increase to his present size would create Sim's waist size to be
30 in + 2.4 in = 32.4 inches.
Sim wants to increase his waist size to 32.4 inches.
Therefore, the correct answer is 32.4 inches.
To learn more about sizes refer to:
https://brainly.com/question/6285404
#SPJ9
Describe in detail how you would create a number line with the following points: 1, 3.25, the opposite of 2, and – (–4fraction of one-half). Please be sure to describe on which tick marks each point is plotted and how many tick marks are between each integer. It may help for you to draw this number line by hand on a sheet of paper first.
The detail Description on how to create a number line with the above points is given below:
What is the Description?Note that we were given the following: points 4, 1, 25, and opposite of 2. The step to take to First draw on Number Line.
Since Numbers with a negative sign are known to be less than zero ( Right of zero is shown by ‘+’ sign and to the left of zero is shown by ‘–’ sign while the + sign numbers can be depicted as simply numbers)
Then:
Draw a line and select some points that is known to have an equal distance and then select and mark a point as zero on that line. The Points to the right of zero will be called positive integers and they are those marked as 1, 2, 3, etc., and also, the points to the left of zero are said to be negative integers and are known to be marked – 1, – 2, – 3, etc.Then take the line to 4 unit on right sides from Zero to depict the point 4.Then Go 3 units to the Left from zero to depict the opposite of 3Then Divide number line between 1 and 2 in four equal parts and then take to 1 part right of point 1.Lastly, divide the number line that is between 0 & -1 into two Equal parts and then take 1 part left of 0.Therefore, The detail Description on how to create a number line with the above points given above is correct:
Learn more about integer from
https://brainly.com/question/17695139
#SPJ1