Answer:
[tex]\displaystyle \frac{d}{dx}[\sin(9x)] = 9 \cos(9x)[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \sin(9x)[/tex]
Step 2: Differentiate
Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = \cos(9x)(9x)'[/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle y' = 9 \cos(9x)(x)'[/tex]Basic Power Rule: [tex]\displaystyle y' = 9 \cos(9x)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
What is the dual of a ∧ b ∨ c ∧ d?
On interchanging the logical AND operator with logical OR operator and zeroes with ones,
(B'+C).A = (B'.C) + A
Now, According to the question:
Concept:
Duality theorem states that the dual of the Boolean function is obtained by interchanging the logical AND operator with logical OR operator and zeroes with ones. For every Boolean function, there will be a corresponding Dual function.
Calculation:
On interchanging the logical AND operator with logical OR operator and zeroes with ones,
(B'+C).A = (B'.C) + A
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The complete question is this:
Calculate the dual of the Boolean expression (B' + C).A
A company creates containers of mixed nuts using the same ratios of different types of nuts in each container. In a 20 ounce container of the company's mixed nuts, there are 11 ounces of peanuts.
There are 37.8 ounces of almonds in a 42-ounce container of the company's mixed nuts.
We know that the company uses the same ratio of different types of nuts in each container. Therefore, we can use the ratio of peanuts to the total weight in the 20-ounce container to find the weight of almonds in the 42-ounce container.
In the 20-ounce container, 11 ounces of the nuts are peanuts. Therefore, 20-11 = 9 ounces of the nuts are not peanuts.
To find the weight of almonds in the 42-ounce container, we can use the same proportion of non-peanut nuts to the total weight. So,
9 ounces / 20 ounces = x / 42 ounces
Cross-multiplying we get:
9 × 42 ounces = 20 × x
x = 37.8 ounces
So, there are 37.8 ounces of almonds in a 42-ounce container of the company's mixed nuts.
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What is the frequency of the function f(x)? f(x)=3cos(πx)−2 Express the answer in fraction form
Answer:
1/2
Step-by-step explanation:
You want to know the frequency of the function f(x) = 3cos(πx) -2.
FrequencyFor frequency f, the basic function (before vertical scaling or translation) will be written ...
f(x) = cos(2πfx)
That is, we can find the frequency by comparing the arguments of the cosine function:
πx = 2πfx
f = (πx)/(2πx) = 1/2
The frequency of the function is 1/2.
__
Additional comment
You will notice in the attached graph that there is 1/2 period in 1 horizontal unit. A full period takes 2 horizontal units, so the frequency is ...
(1 period)/(2 units) = 1/2 periods/unit.
<95141404393>
-3 + 7 - 2
simplifyyyyyyyyy please someone
Answer:
2
Step-by-step explanation:
-3+7=4
4-2=2
Answer:
2
Step-by-step explanation:
-3 is a negative number so,
-3 + 7 is 4.
Then, 4 - 2 is 2.
So the answer is 2.
12. Sarah uses long division to convert
a rational number 2 to a decimal.
P
Which of the following statements
cannot be true?
A. The decimal form of P
q
terminates with a zero in the
tenths place.
B. The decimal form of P
eventually repeats.
C. The decimal form of never
terminates or repeats.
D. The decimal form ofis 0.
The pic says it all, thanks.
Answer:
Step-by-step explanation:
.
.
.
.
Answer:
The area left is equal to about 2686 [tex]ft^{2}[/tex] (if we will round to the nearest whole number).
Step-by-step explanation:
The area of the backyard that will be left will equal to the area of his backyard minus the area of the circular pool. So we can write it as...
The area left = (area of the backyard) - (area of the pool)
The area left = [tex]60 * 50 - \pi (20 / 2)^{2}[/tex]
The area left = [tex]3000 - 100\pi[/tex]
The area left ≅ 2686 [tex]ft^{2}[/tex]
Mario wait table at a retaurant where he make money by earning tip. One night, two of hi regular cutomer dined at the retaurant. Cutomer A had a total bill of $430. 50 and tipped 20% of the bill. Cutomer B had a total bill of $184. 00 and tipped 25% of the bill. How much did Mario make from the tip of hi two regular cutomer
Mario make total $132.1 from the tip of his two customers.
The amount of tip obtained = total bill × percentage of the bill
Put the respective values in equation depending on the customer A or B
Tip from customer A
Tip = 430.50 × 20%
Now find percentage by multiplication and division on Right Hand Side of the equation
Tip = $86.1
Tip from customer B
Tip = 184 × 25%
Again perform multiplication and division on Right Hand Side of the equation
Tip = $46
Total tip earned = 86.1 + 46
Simply add the two numbers on Right Hand Side of the equation to find the total tip earned
Total tip earned = $132.1
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If f(x) =x - 5 and g(x) = 2x + 3, find values for each of the following.
a. f(g(1)) =
b. g(f (2)) =
c. g(g(0)) =
d. (f 0 9) (-2) =
e. (g o f) (3) =
f. (f o f) (-1) =
When f(x) = x - 5 and g(x) = 2x + 3, the value of f(g(1)) is 0 and the value of g(f (2)) is -2.
what is function ?Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. one-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions
given
a) f(g(1)
g(1) = 5 and f(g(1)) = 0
b) g(f (2))
f(2) = -3
g(f (2)) = -2
so When f(x) = x - 5 and g(x) = 2x + 3, the value of f(g(1)) is 0 and the value of g(f (2)) is -2.
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The graph shows the cost of grapes at a grocery store. What is the slope of the line?
The slope of the line that passes through the graph is 3
How to calculate the slope of the line?From the graph, the points are given as
(0, 0) and (1, 3)
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (0, 0) and (1, 3)
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 0) and (1, 3)
Substitute the known values in the above equation
So, we have the following equation
Slope = (3 - 0)/(1 - 0)
Evaluate
Slope = 3
Hence, the slope of the line is 3
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Find the area of the kite. Round to the nearest tenth.
The area of the kite is 90 sq.m.
Calculation
Area of the kite (quadrilateral) = [tex]\frac{product of their diagonal}{2}[/tex] = [tex]\frac{pq}{2}[/tex]
= [tex]\frac{12m*15m}{2}[/tex] = [tex]\frac{180 sq.m}{2}[/tex] = 90 sq.m.
What is the geometry of a kite?
The diagonals of every kite are orthodiagonal (at right angles), and when convex, they are tangential quadrilaterals (its sides are tangent to an inscribed circle). The quadrilaterals that are orthodiagonal and tangential are precisely convex kites. In addition to the squares, which are special examples of both right kites and rhombi, they also include the right kites, which have two opposite right angles, the rhombi, which have two diagonal axes of symmetry, and the squares.To learn more about kite geometry, refer to https://brainly.com/question/26870235
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The scatterplot below shows the grade 10 students earned on a test and the amount of time each student studied for the test
Which describes the relationship between the number of hours studied and the students grade on the test?
Answer choices
A There is a weak positive relationship between the variables.
B There is a strong negative relationship between the variables.
CThere is a weak negative relationship between the variables.
D There is a strong positive relationship between the variables.
Answer fast please
In the graph, there is a strong positive relationship between the variables. Option D
What is the correlation?We know that the term correlation has to do with how two or more variables are related. The way that the variables are related can be seen from the graph that is shown.
There is a strong positive correlation if we notice that the straight-line of the graph is moving in the positive direction. As we can see from the graph that we have, there is a positive correlation among the variables.
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Hassan lined up the interior angles of the triangle along the line below.
Triangle A B C. Angle C is 112 degrees and angle B is 30 degrees. 2 lines extend from a horizontal line to form 3 angles. From left to right the angles are 38 degrees, question mark, 112 degrees.
What is the measure of the missing angle along the line?
30°
38°
112°
150°
Answer:
A/30 degrees
Step-by-step explanation:
Just took the test and passed it
Answer:
A
Step-by-step explanation:
lol
Yesterday, Camille's Snack Shack went through 1/4 of a bottle of ketchup. If they used 2/3 as much mustard as ketchup, how many bottles of mustard did they go through?
The number of bottles of mustard they went through is given by the equation A = 1/6 of the bottle
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of bottles of mustard be represented as A
Now , the equation will be
The amount of ketchup used by Camille's Snack Shack = ( 1/4 ) of the bottle
Now , the amount of bottle of mustard used = ( 2/3 ) of the bottle of ketchup
Substituting the values in the equation , we get
The number of bottles of mustard used A = ( 2/3 ) of ( 1/4 ) of the bottle
On simplifying the equation , we get
The number of bottles of mustard used A = ( 2/3 ) x ( 1/4 )
The number of bottles of mustard used A = ( 1/6 ) of the bottle
Therefore , the value of A is 1/6
Hence , the number of bottles is 1/6
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A rectangle with two parallel sides is called a
Answer:
Parallelogram!
Step-by-step explanation:
Hope this helps! :3
The drama club is selling candles for a fundraiser. They spend $100 on the candles and sell them for $4.50 each. The inequality x > 50 is the solution to the inequality representing the situation, where x represents the number of candles sold. Which are viable solutions in the context of the situation? Check all that apply. 0 50 50.5 56 60
Answer:
D and E, or 56 and 60
Step-by-step explanation:
The inequality says the value must be greater than or equal to 50, so that can take out the first two (0 and 50), since they do not fit this criteria. 50.5 also does not work, because the club cannot sell half a candle. Therefor, the last two choices are the only ones that make sense in the context of the situation.
Answer:
the answer is D and E, or 56 and 60 :D
Step-by-step explanation:
ind the median and mean of the data set below: 29,8,11,29,29,6,49
Answer:
Mean= 23
Median= 29
Step-by-step explanation:
Plz help timed test I’ll give extra points
Answer:
am not really sure but ig the answer is B
Step-by-step explanation:
Plz help timed test I’ll give extra points
Cherri brought $2,100 computer on an installment plan. She made a $400 down payment, and she has to make a monthly payment for $79. 50 for the next two years. How much interst will she pay
If Cherri brought $2100 computer on an installment plan and made $400 down payment and monthly payment for $79. 50 for the next two years, then the interest amount is $208 .
the cost of the computer is = $2100 ;
the amount paid as down payment is = $400 ;
the amount that will be paid in monthly installment is = $79.50 ;
the time for the loan is = 24 months ;
So , the amount paid as installment is 24 months is = [tex]24 \times79.50[/tex]
= $1908 .
So , the total amount paid by Cherri with installment plan is = [tex]\$1908+\$400[/tex]
= $2308 .
So , the interest amount paid is = [tex]\$2308-\$2100[/tex]
= $208 .
Therefore , Cherri will pay $208 as interest .
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a 10-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 8feet from the base of the building. How high up does the ladder reach?
The ladder would reach a distance of 6 feet up the wall.
The Pythagorean theorem.This is a theorem that can be used to determine the unknown side of a right angled triangle. It is given as:
/hyp/^2 = /opp/^2 + /adj/^2
In the given question, the ladder is placed a against a vertical wall of a building. Given that the bottom of the ladder is 8 feet to the base of the building. Therefore this is would form a right angled triangle, such that the Pythagorean theorem can be applied.
So that, let the height of the ladder on the wall be represented by t. Then;
10^2 = t^2 + 8^2
100 = t^2 + 64
t^2 = 100 -64
= 36
t = (36)^1/2
t = 6 feet
Thus the ladder is placed 6 feet up the vertical wall.
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I need help plz no links
Answer:
look at the picture I sent
Josefina wants to prove that figures d and d are similar.
What seguence of transformation could Josefina perform to prove the figures are similar?
The left shift required to translate from D to D" is 6 units and scale factor for dilation of D" from D' is 2.5.
What is Scale factor?The scale factor is a type of measurement which is used to increase or decrease the size of an object keeping its shape as the same. It can be determined by taking the ratio of the new and the original dimension of the object.
Compare the corresponding vertex of the given figures.
It is given as,
(-5, 0) → (1, 0)
It can be concluded that the graph of D is shifted (1 - (-5)) = 6 units towards left.
The scale factor is given as,
Length of side of D" ÷ Length of side of D'
⇒ 10 ÷ 4 = 2.5
Hence, the required shift and the scale factor are obtained as 6 units and 2.5 respectively.
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What are equivalents in a reaction?
In a reaction the amount f a substance which react with another substance is known as it's equivalent.
The definition of equivalent is "weight in grams of a substance that displaces or combines with one gram of hydrogen."
It is an important part of chemistry and comes under stoichiometry. In every reaction there is a reactant which forms the suitable product and the amount of that is calculated using stoichiometry.
The mole ratio is a typical sort of stoichiometric relationship that compares the amounts in moles of any two components in a chemical process.
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PLEASE HELP ME ILL MARK YOU AS A Brainiest
Answer:
4 + 2 + q - 1 + q = 15
Step-by-step explanation:
P = 4 + 2 + q - 1 + q = 15
Of the 6,960 balloons thrown in a water-ballon fight, 870 were red. At this rate, how many balloons out of 48 would be red? WRITE JUST THE ANSWER WITHOUT UNITS
The number of balloons out of 48 that will be red would be = 3/435
How to calculate the number of red balloons?The number of balloons thrown in a water-ballon fight = 6,960 balloons.
The number of red balloons =870 balloons.
The number of balloons out of 48 that would be red; divide through by two.
= 48/6,960
= 24/3,480
= 12/1740
= 6/870
= 3/435
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frank weighs 160 lbs gains 2 lbs a week, john weighs 208 lbs and loses 3 lbs a week
A. when will they weigh the same, and how much will they weigh
B. Explain clearly
If frank weighs 160 lbs gains 2 lbs a week, john weighs 208 lbs and loses 3 lbs a week.
a. When they will weigh the same is 9.6 dieting days and the amount is 179.2lbs.
b. Based on the calculation both of them has the same amount of weight.
How to find the amount of weight?a. Weight
Let d represent the number of dieting days for this happen.
Since Frank gains 2 lb a day or a total of 2d lbs and John loses 3 lb a day for a total of 3d lbs
So,
John's weight = Frank's weight
Hence,
208 - 3d = 160 + 2d
Combine like terms
208 - 160 = 2d + 3d
48 = 5d
Divide both side by 5d
d = 48/5
d = 9.6 dieting days
The amount the weigh
Using John equation
Weigh = 208 - 3(9.6)
Weigh = 208 - 28.8
Weigh = 179.2 lbs
b. The amount they both weigh is the same as John weigh 179.2ilb and Frank as weigh the same.
Using Frank's equation
Weigh = 160 + 2(9.6)
Weigh = 160 + 19.2
Weigh = 179.2 lbs
Therefore when they will weigh the same is 9.6 dieting days and the amount is 179.2lbs.
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Please help this is due soon and I'm struggling!
1)
a. 4
b. 9
c. -7
d. -23
2)
a. F
b. F
c. T
d. F
3)
a. 100 -66 =34
b. 78 x 3 = 234
c. 36 + 24 = 60
d. 4 x 17 x 3 = 204
21)
a. -9 + (-12)
= - 9 - 12
= - 21
b. -17 + (3)
= -17 + 3
= - 14
c. 24 + ( -11 )
= 24 - 11
= 13
d. - 15 + (-10)
= - 15 - 10
= - 25
e. - 63 + ( -42) + 8
= - 63 - 42 + 8
= - 97
f. 101 + ( -11 ) + ( -100 )
= 101 -11 - 100
= - 10
William is trying to pick out an outfit for the first day of school. He can choose from 2 pairs of pants. 3 t-shirts, and 4 pairs of shoes. How many different outfits does William have to choose from?
Answer:
3
Step-by-step explanation:
because he has 2 pants and they could get washed do he could wear the three shirts and wear the same pants again.
Which equation is graphed here?
Responses
A 2x - y = 122x - y = 12
B x + y = 12x + y = 12
C 2y - x = 122y - x = 12
D 2x + y = 122x + y = 12
E x + 2y = 12x + 2y = 12
The equation of the line passing through (3, 6) and (6, 0) is 2x + y = 12
What is an equation?An equation shows how two or more numbers and variables are related to each other.
The standard linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
The line passes through (3, 6) and (6, 0). Hence:
y - 6 = [(0 - 6)/(6 - 3)](x - 3)
y - 6 = -2(x - 3)
y = -2x + 12
2x + y = 12
The equation of the line is 2x + y = 12
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Tanner has $4.60 in nickels and quarters. If he has 14 more nickels than quarters, how many of each coin does he have?
quarters
nickels
The number of coins of nickels and quarters will be 27 and 13, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Tanner has $4.60 in nickels and quarters. If he has 14 more nickels than quarters.
Let 'x' be the number of nickels and 'y' be the number of quarters. Then the equations are given as,
x = y + 14 ....1
0.05x + 0.25y = 4.60 ....2
From equations 1 and 2, then we have
0.05(y + 14) + 0.25y = 1
0.05y + 0.70 + 0.25y = 4.60
0.30y = 3.9
y = 13
Then the value of 'x' is given as,
x = 13 + 14
x = 27
The number of coins of nickels and quarters will be 27 and 13, respectively.
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How do you find the third side of a triangle that is not right?
The third side of a triangle can be found using the Pythagorean Theorem.
The Pythagorean Theorem states that for a triangle with sides of length a, b, and c (with c being the length of the unknown side) a^2 + b^2 = c^2.
To find the third side of a triangle that is not right, first calculate the lengths of the two known sides. Let's say the lengths of the two known sides are a = 5 and b = 12.
Next, plug the values into the Pythagorean Theorem and solve for c.
[tex]a^2 + b^2 = c^2[/tex]
[tex](5)^2 + (12)^2 = c^2 \\25 + 144 = c^2[/tex]
[tex]169 = c^2[/tex]
Finally, take the square root of both sides to solve for c.
sqrt(169) = c
13 = c
Therefore, the length of the third side is 13.
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