1. Differentiate the function f(x) = ln (81 sin^2 (x)) f’(x) 2. Differentiate the function P(t) = in ( √t2 + 9) p' (t) 3. if x2 + y2 + z2 = 9, dx/dt = B, and dy/dt = 4, find dz/dt when (x,y,z) = (2,2,1)
dz/dt =
First you will get 4dz
helppppp please ? lol i’m trying to pass summer school
Answer:
B
Step-by-step explanation:
To find the inverse of a function just replace the x and y value
so for f(x) instead of y=√(x-2) it x=√(y-2) --- take this and now solve for y
x=√(y-2)
x²=y-2
x²+2=y
This matches h(x)
Answer: It really is B but I’m confused on your new question I’ll try :(
Step-by-step explanation:
question 10 please
need help
Answer:
Denes Dynamos =
2012 attendance = 34500
2013 attendance = 30705
change = 30705 - 34500= -3795
change percentage = -3795 * 100 / 34500 = -11%
Edgefield Eagles =
2012 = 24100
2013 = 21208
change = -2892
change Percentage = -2892 * 100 / 24100 = -12%
Evaluate:
(i) (3/5)^-2
(ii) (-3)^-3
(iii) (2/7)^-4
Need help please.
Step-by-step explanation:
# 1
\(\: \sf \bigg\lgroup{\dfrac{3}{5}} \bigg\rgroup^{ - 2}\)
\(\begin{gathered}\end{gathered}\)
\({\underline{\underline{\sf{\red{Solution :}}}}}\)
Using the law of exponent :
\( \dashrightarrow{ \sf{{a}^{ - m} = \dfrac{1}{{a}^{m} }}}\)
\(\dashrightarrow\: \sf \bigg\lgroup{\dfrac{3}{5}} \bigg\rgroup^{ - 2} \)
\(\dashrightarrow\: \sf \bigg\lgroup{\dfrac{5}{3}} \bigg\rgroup^{ 2}\)
\(\dashrightarrow\: \sf \bigg\lgroup{\dfrac{5}{3} \times \dfrac{5}{3}} \bigg\rgroup\)
\(\dashrightarrow\: \sf \bigg\lgroup{\dfrac{5 \times 5}{3 \times 3}} \bigg\rgroup\)
\(\dashrightarrow\: \sf \bigg\lgroup{\dfrac{25}{9}} \bigg\rgroup\)
\(\longrightarrow{\underline{\boxed{\sf{\pink{Answer = \dfrac{25}{9}}}}}}\)
#2
\( \sf{\big( - 3 \big)}^{ - 3} \)
\(\begin{gathered}\end{gathered}\)
\({\underline{\underline{\sf{\red{Solution :}}}}}\)
Using the law of exponent :
\( \dashrightarrow{ \sf{{a}^{ - m} = \dfrac{1}{{a}^{m} }}}\)
\( \dashrightarrow{\sf{\big( - 3 \big)}^{ - 3} }\)
\( \dashrightarrow{\sf{\dfrac{1}{{( - 3)}^{3}}}}\)
\( \dashrightarrow{\sf{\dfrac{1}{{( - 3 \times - 3 \times - 3)}}}}\)
\( \dashrightarrow{\sf{\dfrac{1}{{ - 27}}}}\)
\(\longrightarrow{\underline{\boxed{\sf{\pink{Answer = \dfrac{1}{{ - 27}}}}}}}\)
#3
\( \: \sf\bigg\lgroup{\dfrac{2}{7}} \bigg\rgroup^{ - 4}\)
\(\begin{gathered}\end{gathered}\)
\({\underline{\underline{\sf{\red{Solution :}}}}}\)
Using the law of exponent :
\(\dashrightarrow{ \sf{{a}^{ - m} = \dfrac{1}{{a}^{m}}}}\)
\(\dashrightarrow{\sf{\bigg\lgroup{\dfrac{2}{7}} \bigg\rgroup^{ - 4}}}\)
\(\dashrightarrow{\sf{\bigg\lgroup{\dfrac{7}{2}} \bigg\rgroup^{ 4}}}\)
\(\dashrightarrow{\sf{\bigg\lgroup{\dfrac{7}{2} \times \dfrac{7}{2} \times \dfrac{7}{2} \times \dfrac{7}{2}} \bigg\rgroup}}\)
\(\dashrightarrow{\sf{\bigg\lgroup{\dfrac{7 \times 7 \times 7 \times 7}{2 \times 2 \times 2 \times 2}} \bigg\rgroup}}\)
\(\dashrightarrow{\sf{\bigg\lgroup{\dfrac{2401}{16}} \bigg\rgroup}}\)
\(\longrightarrow{\underline{\boxed{\sf{\pink{Answer = \dfrac{2401}{16}}}}}}\)
(3/5)⁻² = (5/3)² = 25/9
(II)(-3)⁻³ = (1/-3)³ = 1/-27
(III)(2/7)⁻⁴ = (7/2)⁴ = 2410/16
-TheUnknownScientist 72
an experiment of flipping a coin was run 200 times with the results shown below. What is the difference between the experimental probability and the theoretical probability of landing on heads?
heads = 140
tails = 60
Theoretical probability describes how likely an event is to occur, and experimental probability describes how frequently an event actually occurred in an experiment.
hope this helps
x-1=-5-x if you know please
Answer:
X will be -2
Step-by-step explanation:
Divide each side by factors that don't contain the variable
3(x+1)=2(x-3) whats the answer
The answer is -9
I dont know the step-by-step used a calculator
Is each triangle a right triangle? Explain.
The triangle shown in the image above that has sides 8, 24, and 25 is a right triangle because it satisfies the Pythagorean theorem.
How to Determine if a Triangle is a Right Triangle?A triangle with sides 8, 24, 25 is a right triangle.
This is because the sides satisfy the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the longest side (the hypotenuse).
In this case, we have:
8² + 24² = 64 + 576 = 640
25² = 625
Since 8² + 24² = 25², the triangle satisfies the Pythagorean theorem, and is therefore a right triangle.
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You are ready to spend your Christmas money! You go to your
favorite store and buy some jewelry. They are running a sale where
everything is $10! You got $130 for Christmas and don't have any
more than that to spend.
Write an inequality to represent how many pieces of jewelry (j)
you can buy.
Answer:
\(10j \leqslant 130\)
\(j \leqslant 13\)
Solve the equation.
2(3x + 8) = - 36 +4
Answer: -8
Step-by-step explanation:
i did the math
Answer:
X= -8
Step-by-step explanation:
2(3X+8)=-36+4
6X+16= -32
6X= -32-16
6X= -48
X= -48/6
X= -8
the wait time at a popular fast food restaurant is uni- formly distributed between 1 and 15 minutes on average. (a) find the probability that you wait less than 6 min- utes. (b) find the probability that you wait between 5 and 10 minutes. (c) what is the expected wait time, and the variance of wait time? (d) if you have waited 5 minutes already, what is the probability you wait an additional 5 minutes?
The following parts can be solved by the concept of probability.
(a) Since the wait time is uniformly distributed between 1 and 15 minutes, the probability of waiting less than 6 minutes is the ratio of the length of the interval between 1 and 6 minutes to the length of the entire interval between 1 and 15 minutes. Therefore, the probability of waiting less than 6 minutes is:
P(wait < 6) = (6 - 1) / (15 - 1) = 5 / 14 ≈ 0.357
(b) Similarly, the probability of waiting between 5 and 10 minutes is the ratio of the length of the interval between 5 and 10 minutes to the length of the entire interval between 1 and 15 minutes. Therefore, the probability of waiting between 5 and 10 minutes is:
P(5 ≤ wait ≤ 10) = (10 - 5) / (15 - 1) = 5 / 14 ≈ 0.357
(c) The expected wait time for a uniform distribution is the average of the minimum and maximum values of the distribution, which is (1 + 15) / 2 = 8 minutes.
To find the variance of the distribution, we use the formula:
Variance = [(b - a)^2] / 12
where a is the minimum value of the distribution (1), b is the maximum value (15). Plugging in these values, we get:
Variance = [(15 - 1)^2] / 12 = 14^2 / 12 = 196 / 12 ≈ 16.33
(d) If you have already waited 5 minutes, the remaining time you need to wait is uniformly distributed between 0 and 10 minutes (since the total wait time is uniformly distributed between 1 and 15 minutes, and you've already waited for 5 minutes). Therefore, the probability of waiting an additional 5 minutes is:
P(wait additional 5 | wait already 5) = (10 - 5) / (15 - 5) = 1/2 = 0.5
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?/1 4. Draw a line representing the relationship between x , the number of hours it takes the painting company to finish the house, and y , the total cost of painting the house. Label the two points from the earlier question on your graph.what is the slope?
We can plot these points on a graph with x on the horizontal axis and y on the vertical axis. Once we plot these points, we can draw a straight line passing through both points.
To calculate the slope of this line, we can use the formula:
slope = (change in y) / (change in x)
In this case, the change in y is $2000 - $1600 = $400, and the change in x is 10 - 8 = 2.
Therefore, the slope of the line is: slope = $400 / 2 = $200 per hour
This means that for every additional hour it takes the painting company to finish the house, the total cost of painting the house increases by $200. In summary, we can draw a line representing the relationship between x and y using the two points provided, and calculate the slope of the line to be $200 per hour.
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Hey there mind answering this questions for me? Thank you .
1. Fruit cost $2 per pound. How many pounds can you buy for $1.50?
2. A pound of apples cost $.85. How many pounds can you buy for $6.00?
Critical Thinking
What is wrong with the sale price in this picture.
SALE!!
Batteries
Now 2 for $3
Before sale
4 for $5
this shipping cost for an order at an online store is 1/10 the cost of the items you order. what is an expression for the total cost of a given order? what are the total cost for orders $43, $79, $95, and $103? $
Answer:
43$= 4.30
79= 7.90
95= 9.50
103= 10.30
all them together 326= 32.60
Step-by-step explanation:
What is the equation of the line that passes through the point (-4, 5) and has an
undefined slope?
Answer:
y = 5 or y = 0x + 5 (they're both the same)
Step-by-step explanation:
y = mx + b
y = 0x + b
5 = 0(-4) + b
5 = 0 + b
b = 5
y = 5 or y = 0x + 5 (they're both the same)
Step-by-step explanation:
an undefined slope is y/0.
not 0/x.
remember, the slope is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
so, if x never changes, we get the undefined slope.
that means it is a vertical line through a point x on the x-axis, and it represents all points for which x = that constant value.
now, we look at our given point, its x-coordinate is -4.
so, the equation of the line is
x = -4
please show work for both thank you!!
Answer:
a. x = 4.8989794855663561963945681494118 or 4.9 rounded
b. x = 8.6023252670426267717294735350497 or 8.6 rounded
Step-by-step explanation:
7² - 5² = x²
49 - 25 = x
49 - 25 = 24
√24 = 4.8989794855663561963945681494118
7² + 5² = x²
49 + 25 = x
49 + 25 = 74
√74 = 8.6023252670426267717294735350497
What are the x-intercept and y-intercept of the line y 4x 5?.
x-intercept and y-intercept of the line y = 4x+5 is -5/4 and 5 respectively.
What is the equation straight line?
The given equation Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The equation of the line is y = 4x+5
So the y-intercept is (x=0)
y = 5
And the x-intercept is (y=0)
4x +5 =0
x = -5/4
Hence, the x-intercept and y-intercept of the line y = 4x+5 is -5/4 and 5 respectively.
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Problem: \ The yellow portion of a circle represents 35%: How many degrees are in the angle formed by the edges of the yellow region?
Answer:
126°
Step-by-step explanation:
Given that the yellow portion covers 35% of the circle, the degree formed by its edges can be calculated as follows:
The degree of a full circle = 360°
To find the degree formed by the edges of the yellow region, we would calculate 35% of 360°:
\( \frac{35}{100}*360 \)
\( \frac{35*360}{100} \)
\( \frac{12600}{100} \)
\( \frac{126}{1} \)
\( 126 \)
126° is formed by the edges of the yellow region.
Find the coordinates for the vertex of the graph of the function y = 3x² – 12x+12.
A (-2, 48)
B. (0, 2)
C. (-2, 0)
D. (2,0)
the data collected from the customers in restaurants about the quality of food is an example of a(n)... select one: variable study. cross-sectional study. experimental study. observational study.
The data collected from the customers in restaurants about the quality of food is an example of a(n); Observational Study
What type of statistical study is used?There are four types of statistical studies namely;
Observational studies
Surveys
Experiments
Meta-analytical studies.
1) An observational study involves observing and recording data on some variable(s) of interest.
2) A (sample) survey uses questioning to gather data.
3) An experiment also referred to as experimental study attempts to give an answer to a statistical question by manipulating all or part of the sample.
Now, we are told that some data was collected from the customers in restaurants about the quality of food.
This is a type of observational study because it involves observing and recording data on an interest which is quality of food
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In the expression 8k + 5. which best describes what 8 represents?
Answer:
it represents a variable
Step-by-step explanation:
The number 8 is the coefficient of the variable k.
What is a coefficient?A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.
Given that the expression is 8k + 5. In the given expression the number 8 is the coefficient of the given expression.
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need help please its a missing assignment and i need to turn it in at midnight
C=pi*d
Where pi is 3.14 and d is the diameter, in this case is 14ft. Find the circumference
\(\begin{gathered} C=\pi\cdot d \\ C=3.14\cdot14ft \\ C=43.96ft \end{gathered}\)Please help I don’t understand this!
Answer:
a.)
Step-by-step explanation:
because 3 to the left is a negative and 2 units up means positive
PLEASE HELP ME!!! I will give the BRAINLIEST for whoever answers it CORRECTLY!
Answer:
Add equations A + B to eliminate y
Then add equations A and C to eliminate y
Step-by-step explanation:
Since all the equations have y with a coefficient of 2, I would eliminate y
Add equations A + B to eliminate y
Then add equations A and C to eliminate y
Answer:
the 3rd choice
The length of a rectangle is 7 cm longer than it's width, x cm. So, write down an equation in term of x, for the length of this rectangle
Answer:
Length = (7 + x)
Step-by-step explanation:
In this question we have to convert the verbal expression to algebraic expression.
Let the width of the rectangle = x cm
"Length of the rectangle is 7 cm longer than it's width"
Length = 7 + Width
Length = (7 + x) cm
Therefore, equation for which length of the rectangle is defined will be,
Length = (7 + x)
Look at the equations below. Find a pair of equations whose lines are perpendicular.
The pair of equations whose lines are perpendicular is (d) y = 1/6x + 3; y = -6x - 3
Find a pair of equations whose lines are perpendicular.from the question, we have the following parameters that can be used in our computation:
The pair of equations
By definition;
The slopes of perpendicular lines are opposite reciporcals
So, we have
(a) -1/3 and -3 false
(b) -3 and -6 false
(c) 3 and 3 false
(d) 1/6 and -6 true
Hence, the equations are (d) y = 1/6x + 3; y = -6x - 3
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A store is offering a 30% discount on shirts. A shirt at the store has an original cost of $25. What is the cost of the shirt, in dollars, after the discount?
The cost of the shirt, in dollars, after the 30% discount is $17.50.
What is discount?
A discount is a reduction in the price of a product or service that is offered by a seller to a buyer. Discounts can be offered for a variety of reasons, such as to attract customers, increase sales, or clear out inventory. Discounts can be expressed as a percentage or a fixed amount, and they can be applied at the time of purchase or deducted from an invoice or bill. Discounts are often used in sales promotions, marketing campaigns, and loyalty programs to incentivize customers to buy or use a product or service.
If a store is offering a 30% discount on shirts that cost $25 originally, then the discount amount is:
30% of $25 = 0.30 x $25 = $7.50
The discount amount is $7.50, so the new price of the shirt after the discount is:
$25 - $7.50 = $17.50
Therefore, the cost of the shirt, in dollars, after the 30% discount is $17.50.
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what is the square root of 38.7
Answer:
6.220932406
Why on Earth would you need that??
Pauline has 35 cups of flour. She makes cakes that requires 2 1/4 cups each. How mant cakes can she bake using the 35 cups of flour?
Answer:
15.56
Step-by-step explanation:
Total flour available=35 cups
Each cake=2 1/4 cups
Find how many cakes Pauline can bake with 35 cups of flour
Let the number of cakes she can bake with 35 cups of flour=x
x=35 cups / 2 1/4 cups
=35÷9/4
=35×4/9
=140/9
=15 5/9 cakes
=15.56 cakes approximately
what is the volume of 3cm and 7cm
Answer:
21
Step-by-step explanation: