Answer:
\(\displaystyle t = \frac{2 \pi}{3}, \ \frac{4 \pi}{3}\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
FunctionsFunction Notation[Interval Notation] - [Brackets] imply inclusive, (Parenthesis) imply exclusivePre-Calculus
Unit CircleCalculus
Derivatives
Derivative Notation
The definition of a derivative is the slope of the tangent line
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Property [Addition/Subtraction]: \(\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]\)
Derivative Property [Multiplied Constant]: \(\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)\)
Trig Derivative: \(\displaystyle \frac{d}{dx}[sinu] = u'cosu\)
Step-by-step explanation:
Step 1: Define
[Given] q(t) = t + 2sint
[Given] Interval [0, 2π]
[Solve] q'(t) = 0
Horizontal tangent line have a slope of 0Step 2: Differentiate
[Derivative] Basic Power Rule/Trig Derivative [Derivative Prop - Add]: \(\displaystyle q'(t) = 1 \cdot t^{1 - 1} + 1 \cdot 2cost\)[Derivative] Simplify exponent: \(\displaystyle q'(t) = 1 \cdot t^{0} + 1 \cdot 2cost\)[Derivative] Evaluate exponent: \(\displaystyle q'(t) = 1 \cdot 1 + 1 \cdot 2cost\)[Derivative] Multiply: \(\displaystyle q'(t) = 1 + 2cost\)Step 3: Solve
[Derivative] Substitute in function value: \(\displaystyle 0 = 1 + 2cost\)[Subtraction Property of Equality] Isolate t term: \(\displaystyle -1 = 2cost\)Rewrite: \(\displaystyle 2cost = -1\)[Division Property of Equality] Isolate trig t term: \(\displaystyle cost = \frac{-1}{2}\)[Equality Property] Inverse Trig: \(\displaystyle t = cos^{-1}(\frac{-1}{2})\)Evaluate [Unit Circle, Interval]: \(\displaystyle t = \frac{2 \pi}{3}, \ \frac{4 \pi}{3}\)Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
HELP ME ASAP!!!
Question 3(Multiple Choice Worth 5 points)
(04.04 MC)
If a sprinkler waters 1 over 15 of a lawn in 1 over 3 hour, how much time will it take to water the entire lawn?
5 hours
15 hours
18 hours
45 hours
It would take 5 hours.
1/15 of the lawn in 1/3 hours means it takes 1 hour to water 3/15 of the lawn aka 1/5
1/5 of the lawn in 1 hour would mean it takes 5 hours to finish watering the entire lawn.
Translate the following into an algebraic expression: The product between -3 and the sum of 9 and a number, y.
Answer:
Step-by-step explanation:
(-3) x (9+y)=
Jane and johnny are running a race. Jane's speed is 1/4 that of Johnny's.
What is Johnny's speed compared to Jane?
Explain.
25%
50%
150%
400%
The right response is 400%. In other words, Johnny moves at four times the pace of Jane.
We must compare the speeds of Johnny and Jane in relation to one another in order to get their ratio. According to the issue, Jane moves at a pace that is 1/4 that of Johnny. In other words, Jane moves at a speed that is one-fourth that of Johnny.
We may compare the speeds as a fraction to figure out the ratio:
Johnny's speed divided by Jane's speed equals 4/1.
This indicates that Johnny is moving at a speed that is four times that of Jane. We can express Johnny's speed as 400% of Jane's speed in percentage terms.
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B=(3,5,6,9) and C=(2,4,6,8) Find (A). A/B (B). B/C C. A/C (D). C/A
Answer:
The question isn't clear. Can you provide more information or context? What is A? Is it a set or a number? Without this information, I can't provide a meaningful answer.
On monday, Maggie ran n miles. On tuesday, she ran 90% of the number of miles that she ran on Monday. On wednesday,she ran 50% of the miles that she ran on Tuesday
Answer:
+ 0.5 then 1.5 n
Step-by-step explanation:
A company is making concrete blocks. The blocks are in the form of right trapezoidal prisms and have the dimensions shown. What is the volume of one block? Show your work
Please help I give 40 brainly
Answer:
9180 (cm³)
Step-by-step explanation:
area of cross-section (trapezium) = 0.5 X (12 + 22) X 9
= 0.5 X 34 X 9 = 153 cm²
then multiply that by the length (60)
153 X 60 = 9180 (cm³)
Ms. Wilson surveyed her class of 36 students about their favorite ice cream flavors.
• Two-thirds of the students preferred chocolate ice cream.
• One-fourth of the students preferred strawberry ice cream.
• The rest preferred vanilla ice cream.
How many students preferred vanilla ice cream?
Answer:
1 student.
Step-by-step explanation:
Two thirds of the students preferred chocolate ice cream:
2/3 of 36 is 24 students.
One fourth of the students preferred strawberry ice cream:
1/4 of 36 is 9.
9+24= 35
--------------------------------------------------------------------------------------
36-35=1
Only one student preferred vanilla ice-cream.
Answer:
1
Step-by-step explanation:
2/3 × 36
= 24 students preferred Choclate Ice cream
1/4 × 36
= 9 students prefer strawberry ice cream
total students who prefer Chocolate or Strawberry
9+24
=35
Remaining students
36-35
=1
only 1 student preferred vanilla ice cream
Which equation results from adding the equations in this system?
-8x+8y=8
3x-8y=-18
Answer:
-5x=-10
Step-by-step explanation:
Adding both equations will result in this
Obwód narysowanego obok sześciokąta wynosi 72 cm. Oblicz długości wszystkich jego boków.
Answer:
72 cm ze wszystkich stron
Step-by-step explanation:
promień jest równy bokom kształtu.
A tank of gas cost about $32.25 on a midsize car if the tank holds 15 gallons what is the cost per gallon?
Answer:
$483.75
Step-by-step explanation:
32.25 x 15 = 483.75
If I'm wrong, please kill me ;-;
how many whole are there in 4/6
The total number of whole number between -4 and 6 are 7 that are 0,1,2,3,4,5,6.
What is an example of a whole number?Whole numbers are the complete set of natural numbers plus '0'. Examples include: 0, 11, 25, 36, 999, 1200, and so on. Learn more about numbers by clicking here.
Is every whole number an integer?Integers supplement this set of numbers because they include negatives, but otherwise follow the same rules. As a result, all whole numbers are integers (because they are all positive integers), but not all integers are whole numbers (because some are negative).
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What will be the new position of the given point (3, 5) after translation of 2 units left and 3 units up?
Answer:5 8
Step-by-step explanation:left 2 up 3
HELP Cornell makes 11/12 of a gallon of Tuscan white bean soup. He eats equal portions of the soup for 5 days, with no soup remaining after the fifth day. How many gallons of soup did Cornell eat each day? If necessary, enter your answer as a fraction. gallons
Solution:
Note that:
11/12 gallons of soup = 5 daysUsing cross multiplication:
11/12 gallons of soup = 5 days=> 11 gallons of soup = 5 x 12 days=> 11 gallons of soup = 60 daysUsing the division property of equality.
11 gallons of soup = 60 days=> 11/60 gallons of soup = 60/60 days=> 11/60 gallons of soup = 1 dayEach day, Cornell ate 11/60 gallons of soup.
The amount of gallons of soup Cornell ate each day was 11/60
How to interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.
Thus, if 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.
Division, thus, can be interpreted as equally dividing the number that is being divided in total \(x\) parts, where \(x\) is the number of parts the given number is divided.
Thus, \(a \div b\) = a divided in b equal parts.
Also, we can write: \(a \div b = a \times \dfrac{1}{b}\)
(it is since a = a times 1 so \(a/b = 1 \times (a/b) = (1/b) \times a\))
For the given case, we're given that:
Total amount of soup Cornell ate in 5 days = 11/12 gallons.
Cornell ate equal amount of soup each day.
Due to this equal amount of soup eating, we can use division.
The amount of soup Cornell ate each day = 11/12 divided in 5 equal parts
The amount of soup Cornell ate each day = \(\dfrac{11}{12} \div 5 = \dfrac{11}{12} \times {1}{5} = \dfrac{11}{60}\)
Thus, the amount of gallons of soup Cornell ate each day was 11/60
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Give a pair of corresponding angles, a pair of alternate interior angles, and a pair of alternate exterior angles.
A pair of corresponding angles, alternate interior angles, and alternate exterior angles include the following:
Corresponding angles: ∠1 ≅ ∠5.
Alternate interior angles: ∠4 ≅ ∠6.
Alternate exterior angles: ∠2 ≅ ∠8
What are corresponding angles?In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines:
∠1 ≅ ∠5
By applying the alternate interior angles theorem to parallel lines m and n, we have the following congruent angles:
∠4 ≅ ∠6
By applying the alternate exterior angles theorem to parallel lines m and n, we have the following congruent angles:
∠2 ≅ ∠8
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what is the product of the complex number 3-4i and 6+I where I =-1
Answer:
15-20i
Step-by-step explanation:
Hello,
When l =-1
6+l = 6-1 = 5
and 5(3-4i)=15-20i
Thanks
please help asap!
Find x. Round to the nearest tenth: 12 cm 22 cm 420 x = [?]° Law of Sines: sin A sin c sin B b a C с Enter
Answer: 21.4 answer 21.406 is correct you just need to round to the nearest tenth!
Step-by-step explanation:
Clue is a board game in which you must deduce three details surrounding a murder. In the original game of Clue, the guilty person can be chosen from 6 people, and there are 6 different possible weapons and 9 possible rooms. At one point in the game, you have narrowed the possibilities down to 4 people, 5 weapons, and 7 rooms. What is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices, and the guess being correct? Enter a fraction or round your answer to 4 decimal places, if necessary.
Answer:
the required probability is 0.0071
Step-by-step explanation:
Given the data in the question;
we have narrowed the possibilities down to 4 people, 5 weapons, and 7 rooms.
so total number of combinations for the narrowed down metrics is computed as follows;
using multiplication rule:
⇒ 4 × 5 × 7 = 140 ways
Now, the probability of making a random guess from our narrowed down choices as well as getting the guess correct will be;
⇒ 1 / 140
{ assuming that the narrowed down choices have within it the correction combination }
= 0.007142 ≈ 0.0071 { four decimal place }
∴ the required probability is 0.0071
You sailed 0.055 units to the left and found treasure at 0.085 units find where the ship started
using the data on this scatter plot
Answer:
\( - 8(45) + 482 = - 360 + 482 = 122\)
Write 27 + 21 as a product using the GCF as one of the factors.
Consider the polynomial
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
Combine all like terms and enter the coefficients for each term into the blanks below
The required coefficients are:4, -1, -11, and 7.
Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.
In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.
In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.
We need to consider the polynomial:
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:
4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn
Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2
Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn
Taking the coefficients of the constant terms6 + 2 - 1 = 7
Therefore, the required coefficients are:4, -1, -11, and 7.
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The International Coffee Association has reported the mean daily coffee consumption for U.S. residents as 1.65 cups. Assume that a sample of 38 people from a North Carolina city consumed a mean of 1.84 cups of coffee per day, with a standard deviation of 0.85 cups. In a two-tail test at the 0.05 level, could the residents of this city be said to be significantly different from their counterparts across the nation?
Answer:
The calculated value t = 1.3788 < 2.0262 at 0.05 level of significance
the null hypothesis is accepted
There is no significant difference between their counterparts across the nation
Step-by-step explanation:
Step(i):-
Given that the mean of the U.S residents = 1.65
Given that the size of the sample 'n' = 38
Mean of the sample = 1.84
Given that the standard deviation of the sample (S) = 0.85
Step(ii):-
Null hypothesis:H₀:
There is no significant difference between their counterparts across the nation
Alternative Hypothesis:-H₁:
There is a significant difference between their counterparts across the nation
Test statistic
\(t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }\)
\(t = \frac{1.84-1.65}{\frac{0.85}{\sqrt{38} } }\)
t = 1.3788
Degrees of freedom
ν = n-1 = 38-1 = 37
t₀.₀₅ ,₃₇ = 2.0262
The calculated value t = 1.3788 < 2.0262 at 0.05 level of significance
Null hypothesis is accepted
Final answer:-
There is no significant difference between their counterparts across the nation.
2% Drug
3% Mass Merchants
11%
Vending
Stores
16% Gąs
Stations
24% Fountain
44% Grocery
Stores
Based on the pie chart, the four largest locations for soft drink sales
account for approximately what percentage of total soft drink sales in
the year under consideration?
Answer: 95%
Step-by-step explanation:
With the information provided, the four largest merchants are Grocery Stores, Fountain, Gas Stations, and Vending Stores.
These stores each make up 44%, 24%, 16%, and 11%, respectively.
The sum of these percentages is 95%. Thus, the four largest locations for soft drink sales make up 95% of soft drink sales.
PLEASE HELL I NEED THIS ONE FAST PLEASE
Which statement is true about the decimal expansion of ? 3/7
O A. It is a rational number because it is a terminating decimal.
○B. It is an irrational number because it is not a terminating decimal.
○C. It is a rational number because after reaching a remainder of 3 for the second time the quotient will start repeating.
O D. It is an irrational number because after reaching a remainder of 3 for the second time the quotient will start repeating.
Answer:
A is the answer because divide 7 divided by 3 a
A product costs $70 today, how much will the product cost in t days if the price is reduced by $5 a day
Answer:
P ($)=70-5(t)
Where p = price at t days
t = number of days
Step-by-step explanation:
The product price initially = $70
Now, every day , it reduces $5
The rate=$5 per day reduction
The price in the days will be determined by the formula below
P ($)=70-5(t)
Where p = price at t days
t = number of days
So let's assume it's on the second day
The price after the second day
P($) = 70-5(2)
P($) = 70-10
P($)= $60
The price after two days will be reduced to $60
What’s the range of A and B and both
This is of Both
Range = Highest - Lowest data
Range = 45 - 10
Range = 35
Only A
Range = 45 - 10
Range = 35
Only B
Range = 40 - 15
Range = 25
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in the fruit bowl there are 12 bananas 8 apples and 4 oranges. do for every one orange there are ___ bananas
For every 1 orange in the fruit bowl there are three bananas.
According to the question,
We have the following information:
In the fruit bowl there are 12 bananas, 8 apples and 4 oranges.
Now, in order to find the number of bananas in this fruit bowl for 1 orange can be as written below:
4 oranges = 12 bananas
Now, to find the number of bananas for 1 orange, we will divide the total number of bananas by the number of oranges.
So, we have the following expression:
1 orange = 12/4 bananas
1 orange = 3 bananas
Hence, for every 1 orange in the fruit bowl there are three bananas.
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Name each type of special quadrilateral that can meet the given condition.
exactly one pair of congruent sides.
Choose the correct answer below.
Trapezoid
parallelogram and kite
trapezoid and isosceles trapezoid
isosceles trapezoid
kite and isosceles trapezoid
Magdalene creates the scale drawing shown of a rectangular field.
7.2 cm
Scale
1 cm = 4.5m
3 cm
What is the area, in square meters (m²), of the actual field?
The scale of the drawing is 1 cm = 4.5 m. This means that each centimeter in the drawing represents 4.5 meters in the actual field. The length of the field in the drawing is 7.2 cm, so the actual length of the field is 7.2 cm × 4.5 m/cm = 32.4 m. The width of the field in the drawing is 3 cm, so the actual width of the field is 3 cm × 4.5 m/cm = 13.5 m. The area of a rectangle is found by multiplying its length by its width, so the area of the actual field is 32.4 m × 13.5 m = 437.4 m²
Note :- I'm sorry to bother you but can you please mark me BRAINLEIST if this ans is helpfull
Number of Customers
The scatter plot shows the relationship between the average
number of nightly customers and the number of months since a
restaurant opened. The equation represents the linear model for
this data
300
270-
240-
y = 5x + 120
210-
180
What does the number 5 in the equation mean in this context?
Average nightly customers
150
O The restaurant has been open for 5 months
.
120
The average number of customers per night
increased by 5 each month
90
60
There were 5 customers per night when the
restaurant opened
30
O
There were 5 customers per month after the
restaurant was open 120 months.
8
9
10
Time (months)
For every 5 months the restaurant has been open,
there are 120 more customers per night
Answer:
The average number of customers per night increased by 5 each month.
Step-by-step explanation:
hope this helps! :)