Answers
Answer:
Q = 30
Step-by-step explanation:
Since this is a right triangle we can use trig functions
We know the opposite side and the hypotenuse
sin Q = opp / hypotenuse
sin Q = 7/14
Taking the inverse sin of each side
sin ^-1 (sin Q) = sin ^-1(7/14)
Q =30
Answer:
30 degrees
Step-by-step explanation:
Related Questions
What is the factored form of the binomial expansion 625x4 – 3,000x3y + 5,400x2y2 – 4,320xy3 + 1,296y4?
(5x – 6y)4
(5x + 6y)4
(25x – 36y)2
(25x + 36y)2
Answers
Answer:
(5x – 6y)^4
Step-by-step explanation:
Given
[tex]625x^4 - 3000x^3y + 5400x^2y^2 - 4320xy^3 + 1296y^4[/tex]
Required
The factored form
Solving (a): (5x – 6y)^4
Expand using pascal triangle;
Exponent 4 is represented as: 1 4 6 4 1. So, we have:
[tex](5x - 6y)^4 = 1 * (5x)^4 + 4 * (5x)^3 * (-6y) + 6 * (5x)^2 * (-6y)^2 + 4 * (5x) * (-6y)^3 + 1 * (-6y)^4[/tex]
Expand:
[tex](5x - 6y)^4 = 1 * 625x^4 + 4 * 125x^3 * (-6y) + 6 * 25x^2 * 36y^2 + 20x * (-216y^3) + 1 * (1296y^4)[/tex]
Remove brackets
[tex](5x - 6y)^4 = 625x^4 - 3000x^3y + 5400x^2y^2 - 4320xy^3 + 1296y^4[/tex]
Hence, (a) is correct
The average cost when producing x items is found by dividing the cost function, C(x), by the number of items,x. When is the average cost less than 100, given the cost function is C(x)= 20x+160?
A) ( 2, infinit)
B) (0,2)
C) (-infinit,0) U (2,infinit)
D) (- infinit,0] U [2,infinit)
Answers
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Answer:
A) (2, ∞) . . . . or C) (-∞, 0) ∪ (2, ∞) if you don't think about it
Step-by-step explanation:
We want ...
C(x)/x < 100
(20x +160)/x < 100
20 +160/x < 100 . . . . . separate the terms on the left
160/x < 80 . . . . . . . subtract 20
160/80 < x . . . . . multiply by x/80 . . . . . assumes x > 0
x > 2 . . . . . . simplify
In interval notation this is (2, ∞). matches choice A
__
Technically (mathematically), we also have ...
160/80 > x . . . . and x < 0
which simplifies to x < 0, or the interval (-∞, 0).
If we include this solution, then choice C is the correct one.
_____
Comment on the solution
Since we are using x to count physical items, we want to assume that the practical domain of C(x) is whole numbers, where x ≥ 0, so this second interval is not in the domain of C(x). That is, the average cost of a negative number of items is meaningless.
Describe a rule for the transformation.
Answers
Answer: 90° counterclockwise
Step-by-step explanation:
At the Arctic weather station, a warning light turns on if the outside temperature is below -25 degrees Fahrenheit. Which inequality models this situation?
t > -25
t < -25
t ≤ -25
t ≥ -25
Answers
Answer:
t≥-25
Step-by-step explanation:
this is becuaset ≥ -25 shows that it can not fall under -25, but can be equal to -25.
Simplify (1 - sin x)(1 + sin x).
0 1
O cos^2 x
O sin^2 x
O tan^2 x
Answers
1-sin^2(x)=cos^2(x)
please help
abd=58 and bdc=32 what is the measure of adb
Answers
Answer:
<ADB = 61degrees
Step-by-step explanation:
From the diagram shown, triangle ADB is isosceles since they projected out from the chord AD. Hence;
<ABD + <ADB + <BAD = 180
Since <ADB = <BAD, then;
<ABD + <ADB + <ADB = 180
Given that:
<ABD = 58degrees
58 + 2<ADB = 180
2<ADB = 180 - 58
2<ADB = 122
<ADB = 122/2
<ADB = 61degrees
Answer90 degrees
Step-by-step explanation:
In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is with a standard deviation of days. Assume the data to be approximately bell-shaped.
Required:
a. Between what two values will approximately 68% of the numbers of days be?
b. Estimate the percentage of customer accounts for which the number of days is between 18 and 46.
c. Estimate the percentage of customer accounts for which the number of days is between 11 and 53.
Answers
that’s what i put
What is the derivative of x^2?
Answers
Answer:
[tex]\displaystyle \frac{d}{dx}[x^2] = 2x[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x^2[/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle \frac{dy}{dx} = 2x^{2 - 1}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = 2x[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
What is the product? (–3s + 2t)(4s – t)
Answers
Answer:
[tex] - 12 {s}^{2} + 11st - 2 {t}^{2}[/tex]Step-by-step explanation:
(–3s + 2t)(4s – t)
= -3s (4s - t) + 2t(4s - t)
[tex] = - 12 {s}^{2} + 3st + 8st - 2 {t}^{2} [/tex]
[tex] = - 12 {s}^{2} + 11st - 2 {t}^{2} (ans)[/tex]
Answer: -12s^2 + 11st -2t^2
Step-by-step explanation:
= (-3s + 2t)(4s - t)
= -12s^2 + 3st + 8st -2t^2
= -12s^2 + 11st -2t^2
Answer Provided by GauthMath please heart and comment thanks if you like.
Anyone willing to help on this worksheet?
Answers
Answer:
I am pretty sure it's #2 but wait for more ansawers because im not 100% sure.
Step-by-step explanation:
Answer:
Same I think it's B but I'm not entirely sure
Step-by-step explanation:
I NEED MAJOR HELP WITH THIS QUESTION
Instriction; using the following image, solve for tbe trigonometry ratios of < D and < F .
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Since the triangle is right angled ; we can solve for x using Pythagoras :
x = hypotenus ; hence ;
x² = opposite² + adjacent²
x² = 15² + 8²
x² = 225 + 64
x² = 289
x = √289
x = 17
Using Trigonometry :
Sin D = side opposite D / hypotenus = 8/17
Cos D = side Adjacent D / hypotenus = 15 / 17
Tan D = side opposite D / Adjacent side = 8/15
Sin F = side opposite F / hypotenus = 15/17
Cos F = side Adjacent F / hypotenus = 8 / 17
Tan F = side opposite F / Adjacent side = 15/8
how all work.
A) What is the average rate of change of the function g(x) = 14x + 6 over the interval [0, 5]?
B) What is the average rate of change of the function g(x) = 3(2x) - 6 over the interval [0,5]?
C) How does this compare to your Answers for Problem 4?
Answers
Answer:
Here we can only answer A and B.
For a given function f(x), the average rate of change in a given interval [a, b] is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
A) we have g(x) = 14*x + 6, and the interval [0, 5], the average rate of change is:
[tex]r = \frac{g(5) - g(0)}{5 - 0} = \frac{(14*5 + 6) - (14*0 + 6)}{5} = \frac{14*5}{5} = 14[/tex]
The average rate of change is 14.
B) We have g(x) = 3*(2x) - 6
we can rewrite this as:
g(x) = 3*2*x - 6 = 6x - 6
And we want to find the rate of change in the interval [0, 5]
is:
[tex]r = \frac{g(5) - g(0)}{5 - 0} = \frac{(6*5 - 6) - (6*0 - 6)}{5} = 6[/tex]
Consider the series ∑n=1∞5n2+n.
The general formula for the sum of the first n terms is Sn=
. Your answer should be in terms of n.
The sum of a series is defined as the limit of the sequence of partial sums, which means
∑n=1∞5n2+n=limn→∞(
)=
.
Select all true statements (there may be more than one correct answer):
A. Most of the terms in each partial sum cancel out.
B. The series converges.
C. The series is a p-series.
D. The series is a telescoping series (i.e., it is like a collapsible telescope).
E. The series is a geometric series.
Answers
(a) Decompose the summand into partial fractions:
[tex]\dfrac5{n^2+n} = \dfrac5{n(n+1)} = \dfrac an+\dfrac b{n+1}[/tex]
[tex]\implies 5=a(n+1)+bn=(a+b)n+a[/tex]
[tex]\implies a+b=0\text{ and }a=5 \implies b=-5[/tex]
[tex]\implies\displaystyle\sum_{n=1}^\infty\frac5{n^2+n} = 5\sum_{n=1}^\infty\left(\frac1n-\frac1{n+1}\right)[/tex]
The n-th partial sum for the series is
[tex]S_n = 5\displaystyle\sum_{k=1}^n\left(\frac1k-\frac1{k+1}\right)[/tex]
which can be simplified significantly by examinging consective terms in the sum:
[tex]\displaystyle S_n = 5\left(1-\frac12\right) + 5\left(\frac12-\frac13\right) + 5\left(\frac13-\frac14\right) + \cdots + 5\left(\frac1{n-1}-\frac1n\right) + 5\left(\frac1n-\frac1{n+1}\right)[/tex]
[tex]\implies S_n = \boxed{5\left(1-\dfrac1{n+1}\right)}[/tex]
(b) Using the result of (a), you then get
[tex]\displaystyle\sum_{n=1}^\infty\frac5{n^2+n} = \lim_{n\to\infty}\boxed{5\left(1-\frac1{n+1}\right)} = \boxed{5}[/tex]
(c) As shown in (a), the partial sum is simplified because of the reasons given in options A and D, and the result of (b) says that B is also correct.
Answer:
Part a. [tex]\displaystyle S_n = 5 - \frac{5}{n + 1}[/tex]
Part b. [tex]\displaystyle \lim_{n \to \infty} (5 - \frac{5}{n + 1}) = 5[/tex]
Part c. A, B, and D
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringPre-Calculus
Partial Fraction DecompositionCalculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]Limit Property [Addition/Subtraction]: [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]Sequences
Series
Definition of a convergent or divergent seriesTelescoping Series: [tex]\displaystyle \sum^\infty_{n = 1} (b_n - b_{n + 1}) = (b_1 - b_2) + (b_2 - b_3) + (b_3 - b_4) + ... + (b_n - b_{n + 1}) + ...[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n}[/tex]
Step 2: Rewrite Sum
Factor: [tex]\displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n} = \sum^\infty_{n = 1} \frac{5}{n(n + 1)}[/tex]Break up [Partial Fraction Decomposition]: [tex]\displaystyle \frac{5}{n(n + 1)} = \frac{A}{n} + \frac{B}{n + 1}[/tex]Simplify [Common Denominator]: [tex]\displaystyle 5 = A(n + 1) + Bn[/tex][Decomp] Substitute in n = 0: [tex]\displaystyle 5 = A(0 + 1) + B(0)[/tex]Simplify: [tex]\displaystyle 5 = A[/tex][Decomp] Substitute in n = -1: [tex]\displaystyle 5 = A(-1 + 1) + B(-1)[/tex]Simplify: [tex]\displaystyle 5 = -B[/tex]Solve: [tex]\displaystyle B = -5[/tex][Decomp] Substitute in variables: [tex]\displaystyle \frac{5}{n(n + 1)} = \frac{5}{n} + \frac{-5}{n + 1}[/tex]Simplify: [tex]\displaystyle \frac{5}{n(n + 1)} = \frac{5}{n} - \frac{5}{n + 1}[/tex]Substitute in decomp [Sum]: [tex]\displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n} = \sum^\infty_{n = 1} \bigg( \frac{5}{n} - \frac{5}{n + 1} \bigg)[/tex]Step 3: Find Sum
Find Sₙ terms: [tex]\displaystyle \sum^\infty_{n = 1} \bigg( \frac{5}{n} - \frac{5}{n + 1} \bigg) = (5 - \frac{5}{2}) + (\frac{5}{2} - \frac{5}{3}) + (\frac{5}{3} - \frac{5}{4}) + (\frac{5}{4} - 1) + ... + ( \frac{5}{n} - \frac{5}{n + 1}) + ...[/tex]Find general Sₙ formula: [tex]\displaystyle S_n = 5 - \frac{5}{n + 1}[/tex]Find Sum [Take limit]: [tex]\displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n} = \lim_{n \to \infty} S_n[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n} = 5 + 0[/tex]Simplify: [tex]\displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n} = 5[/tex]∴ the sum converges by the Telescoping Series.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Convergence Tests (BC Only)
Book: College Calculus 10e
The speed of train A is 6 mph slower than the speed of train B. Train A travels 190 miles in the same time it takes train B to travel 220 miles. Find the speed of each train.
Answers
Answer:
train A=38mph train B=44mph
Step-by-step explanation:
Setting up a table:
s t d
A x 190/x 190
B x+6 220/x+6 220
Train A was 6mph slower as shown in the table, so to make it easier, train a is identified as x, train b would be x+6
Their distances are put in their respective column.
You find time from distance divided by speed.
So time would be written as such.
Since you know they take the same amount of time, for the equation, you connect them with an equal sign. Cross multiply to something like:
190(x+6)=220x
190x+1140=220x
1140=30x
x=38
You plug this in and get the speed for train A as 38, and train B as 44.
Hope this helps ^^
Salma invested $8000 in a fund for 6 years and was paid simple interest. The total interest that she received on the investment was $1400. As a percentage, what was the annual interest rate of her investment? If necessary, refer to the list of financial formulas.
Answers
Answer: I don’t know lol maybe 1460
Step-by-step explanation:
PLEASE CORRECT BEFORE ANSWERING I AM HAVING TROUBLE GETTING THINNGS RIGHT SO PLEASE HELP
Answers
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Answer:
3
Step-by-step explanation:
AB is 1 unit long.
A'B' is 3 units long.
The scale factor is the ratio of these lengths:
scale factor = A'B'/AB = 3/1 = 3
ABC is dilated by a factor of 3 to get A'B'C'.
Find the length of XW.
Answers
Answer:
XW = 78
Step-by-step explanation:
Both triangles are similar, therefore based on triangle similarity theorem we have the following:
XW/XZ = VW/YZ
Substitute
XW/6 = 104/8
XW/6 = 13
Cross multiply
XW = 13*6
XW = 78
There are 84 students in a speech contest. Yesterday, 1/4 of them gave their speeches. Today, 3/7 of the remaining students gave their speeches. How many students still haven't given their speeches?
Answers
Answer:
36
Step-by-step explanation:
Total students un the contest = 84
Number of students who gave their speech yesterday:-
[tex] \frac{1}{4} \: of \: total \\ = \frac{1}{4} \times 84 \\ = 21[/tex]
so 21 students gave their speech yesterday
remaining students = 84 - 21= 63
Number of students who gave their speech today:-
[tex] \frac{3}{7} \: of \: remaining \\ = \frac{3}{7} \times 63 \\ = 27[/tex]
Number of students who have given their speech:-
= 21 + 27
= 48
Number of students who still haven't given their speech :-
= total - 48
= 84 - 48
= 36
First turn 1/4 and 3/7 into common denominators and add; 7/28+12/28=19/28
Subtract: 28/28-19/28=9/28
To find how many remain multiply: 9/28*84= 27
Fill in the missing number to make these fractions equivalent
Answers
Step-by-step explanation:
1. 12/18/3 = 4/6....!!!
Answer:
6
Step-by-step explanation:
I would first simplify the fraction on the left:
12/18 = 2/3
Then:
2/3 = 4/x
2x/3 = 4
2x = 4*3
x = 4*3/2
x = 12/2
x = 6
(2/3)x-1=27/8,find x
Answers
Answer:
x = 105/16
Step-by-step explanation:
2/3x - 1 = 27/8
Add 1 to each side
2/3x - 1+1 = 27/8+1
2/3x = 27/8 + 8/8
2/3x = 35/8
Multiply each side by 3/2
3/2 * 2/3x = 35/8 *3/2
x = 105/16
What is the slope of the line shown below?
Answers
Answer:
2
Step-by-step explanation:
Given two points on the line, we can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 7 - -3)/(3 - -2)
= (7+3)/(3+2)
= 10/5
=2
The answer is 2
please help me with this question.
Answers
Please help me thank you!!!
Answers
Answer:
B
Step-by-step explanation:
To solve this use a unit circle (see pic)
Go to the 300 degree
Then look at the y coordinate (y coordinate because it's cosine)
Which matches with answer choice B
write two properties of 1
Answers
The identity property of 1 says that any number multiplied by 1 keeps its identity. In other words, any number multiplied by 1 stays the same. The reason the number stays the same is because multiplying by 1 means we have 1 copy of the number. For example, 32x1=32.
Whoever gets this problem right with proper work shown will get brainliest
Answers
Answer:
100 % or 1
Step-by-step explanation:
There are two dice
Each dice has a possible roll of 1,2,3,4,5,6
The possible sums are 2,3,4,5,6,7,8,9,10,11,12
The probability of getting a sum greater than 1 is 100 % or 1 since the outcomes are all greater than 1
Hope this helps
Which of the following functions is graphed below?
20
15
10
-8-84
-2
42
-5
-10
-15
-20
Answers
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Answer:
D.
Step-by-step explanation:
The linear portion of the curve is in the region x ≥ 2. The only function defined that way is the one in choice D.
If a snowball melts so that its surface area decreases at a rate of 8 cm2/min, find the rate (in cm/min) at which the diameter decreases when the diameter is 11 cm. (Round your answer to three decimal places.)
Answers
Answer:
Step-by-step explanation:
I'm going to go through this as I would when teaching it to my students for the first time. This is a super simple one, so it shouldn't be too hard. Begin with what you know:
A snowball is a sphere. Since we are told that the surface area is changing (decreasing, to be exact), it would make sense to know the formula for the surface area of a sphere:
[tex]S=4\pi r^2[/tex] where r is the radius. Let's take the derivative of this using implicit differentiation to see what it is we need to solve this:
[tex]\frac{dS}{dt}=4\pi*2r\frac{dr}{dt}[/tex], where dr/dt is the rate at which the radius is changing. If we look at the problem, we are looking for the rate at which the DIAMETER is changing. So instead of using the radius in the original formula, we need to write it in terms of the diameter. We know that
d = 2r so
[tex]r=\frac{d}{2}[/tex] and we will put that into the formula for r to get:
[tex]S=4\pi(\frac{d}{2})^2[/tex] and simplify a bit:
[tex]S=4\pi(\frac{d^2}{4})[/tex] and the 4's cancel each other out, leaving us with simply:
[tex]S=\pi d^2[/tex] Now let's take the derivative:
[tex]\frac{dS}{dt} =\pi 2d\frac{dD}{dt}[/tex] where the rate of the surface area is -8 ("decreasing" rate makes this number a negative) when the diameter is 11. Filling in:
[tex]-8=\pi(2)(11)\frac{dD}{dt}[/tex] and solving for the rate at which the diameter is changing:
[tex]\frac{dD}{dt}=-\frac{8}{22\pi}[/tex] , which rounds to
[tex]\frac{dD}{dt}=-1.142\frac{cm}{min}[/tex] and again, the negative means that the diameter is decreasing.
write your answer in simplest radical form
Answers
Answer:
n = 2
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 30 = n / 2 sqrt(3)
2 sqrt(3) tan 30 = n
2 sqrt(3) * sqrt(3)/3 = n
2 = n
We have to find,
The required value of n.
Now we can,
Use the trigonometric functions.
→ tan(θ) = opp/adj
Let's find the required value of n,
→ tan (θ) = opp/adj
→ tan (30) = n/2√3
→ n = 2√3 × tan (30)
→ n = 2√3 × √3/3
→ n = 2√3 × 1/√3
→ [n = 2]
Thus, the value of n is 2.
At the gas station, each liter of gas costs $3 but there's a promotion that for every beverage you purchase you save $0.20 on gas.
Answers
In the context of the Pearson r correlation coefficient, the absolute size of r is the:_____.
a. coefficient that indicates the measurement scale that applies to two variables.
b. direction of the relationship between two variables.
c. strength of the relationship between two variables.
d. curvilinear relationship between two variables.
Answers
Answer:
strength of the relationship between two variables.
Step-by-step explanation:
The Pearson r correlation Coefficient used to measure the relationship or association between two variables. The correlation Coefficient, R ranges between - 1 and 1. As it provides information on both the strength and type of the relationship. The type of relationship could be positive or negative.
The absolute size of r measures Tha strength of the relationship as it ignores the sign. As the Pearson r value moves closer to 1, the higher the strength of the relationship.
