Answers
Given:
The right traingle ABC with side measurements.
Required:
\(\text{ Determine which of two acute angle has cosine of }\frac{4}{5}.\)Explanation:
First draw a figure
We need here cosine law
\(cosC=\frac{a^2+b^2-c^2}{2ab}\)So, we have a = 8, b = 10 and c = 6.
So, cosine of acute angle C
\(\begin{gathered} cosC=\frac{a^2+b^2-c^2}{2ab} \\ cosC=\frac{8^2+10^2-6^2}{2\times8\times10} \\ cosC=\frac{64+100-36}{160} \\ cosC=\frac{128}{160} \\ cosC=\frac{4}{5} \end{gathered}\)Answer:
\(\text{ Acute angle }C\text{ has cosine }\frac{4}{5}.\)
Related Questions
A rubber ball is dropped from a height of 10 feet onto a hard surface. After the first bounce, the ball is 6 feet in the air and continues to follow a sequence of bounces. Assume the distances from the ground form a geometric sequence. What is the total DOWNWARD vertical distance the ball has traveled after it hits the surface the 5th time?
Answers
Answer:
The total DOWNWARD vertical distance the ball has traveled after it hits the surface the 5th time is 23.056 feet.
Step-by-step explanation:
Geometric sequence:
The nth term is a product of the previous(nth-1) term and the common ratio. That is:
\(a_n = qa_{n-1}\)
In which q is the common difference.
Sum of the first n terms of geometric sequence:
The sum of the first n terms of a geometric sequence is given by:
\(S_n = \frac{a_1(1-q^n)}{1-q}\)
A rubber ball is dropped from a height of 10 feet onto a hard surface.
This means that \(a_1 = 10\)
The ball is 6 feet in the air and continues to follow a sequence of bounces
This means that \(q = \frac{6}{10} = 0.6\)
What is the total DOWNWARD vertical distance the ball has traveled after it hits the surface the 5th time?
This is \(S_5\). So
\(S_5 = \frac{10(1-0.6^5)}{1-0.6} = 23.056\)
The total DOWNWARD vertical distance the ball has traveled after it hits the surface the 5th time is 23.056 feet.
Please give me the correct answer.
Answers
Answer:
33
Step-by-step explanation:
Pls help will mark brain list
Answers
Answer: B
Step-by-step explanation:
I did this before and got a 100%.
Please help! Provide an answer with an explanation to my question & you will receive a 100 points for one question! :)
Answers
Answer:
B
Step-by-step explanation:
Standard deviation is the average distance away from the mean, thus B is correct
21 is 72% of which number
Answers
Answer:
29.12
Step-by-step explanation:
You would need to set up a proportion to do this...
is actually "x", which oddly enough is the 100%.
we also know that 72% of "x" is 21, hmmm what the heck is "x"?
\(\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 21& 72 \end{array} \implies \cfrac{x}{21}~~=~~\cfrac{100}{72} \implies\cfrac{ x }{ 21 } ~~=~~ \cfrac{ 25 }{ 18 } \implies 18x=(21)(25) \\\\\\ x=\cfrac{(21)(25)}{18}\implies x=\cfrac{175}{6}\implies x=29\frac{1}{6}\implies x=29.1\overline{666}\)
Write (i-1)^(i+1) as a+bi.
Answers
The rectangular form of the power of the complex number is equal to - 0.095 + i 10.546.
How to find the rectangular form of the power of a complex number
In this problem we must determine the rectangular form, that is, a number of the form a + i b, where a, b are both real numbers, of the power of a complex number, whose exponent is also a complex number. This can be done by complex number properties. First, write the entire number:
\((i - 1)^{i + 1}\)
Second, use the De Moivre's formula:
√2 · [cos [(i + 1) · 3π / 4] + i sin [(i + 1) · 3π / 4]]
√2 · [cos (i 3π / 4 + 3π / 4) + i sin (i 3π / 4 + 3π / 4)]
Third, expand the trigonometric functions:
√2 · cos (3π / 4) · cos (i 3π / 4) - √2 · sin (3π / 4) · sin (i 3π / 4) + i √2 · sin (3π / 4) · cos (i 3π / 4) + i √2 · cos (3π / 4) · sin (i 3π / 4)
- cos (i 3π / 4) + sin (i 3π / 4) + i cos (i 3π / 4) - i sin (i 3π / 4)
Fourth, eliminate the imaginary term within the trigonometric functions:
- cosh (3π / 4) + i sinh (3π / 4) + i cosh (3π / 4) - i² sinh (3π / 4)
[- cosh (3π / 4) + sinh (3π / 4)] + i [sinh (3π / 4) + cosh (3π / 4)]
(- 5.321 + 5.226) + i (5.226 + 5.321)
- 0.095 + i 10.546
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ramone takes care of animals. he charges $12 per day for dogs and $5 per day for cats. in one month he earned $108. he took care of 3 times as many cats as dogs. how much of the money ramone earned was from taking care of cats?
Answers
ANSWER:
$60
STEP-BY-STEP EXPLANATION:
In this case we must propose a system of equations to be able to find the answer:
Let x be the number of dogs and y the number of cats, with the statement we propose the following equations
\(\begin{gathered} 12x+5y=108 \\ 3x=y\rightarrow x=\frac{y}{3} \end{gathered}\)we replace and we have:
\(\begin{gathered} 12\cdot\frac{y}{3}+5y=108 \\ 4y+5y=108 \\ 9y=108 \\ y=\frac{108}{9} \\ y=12 \end{gathered}\)Now, knowing that I take care of 12 cats, we can know how much I collect because for each cat he charges $ 5
\(12\cdot5=60\)In total I charge $ 60 with the cats
What is the answer?
2/5 + 3/4
Answers
Take LCM
5×4=20Now
2/5+3/48+15/2023/20Answer:
23/20
Step-by-step explanation:
2/5 + 3/4
LCM = 5 * 4 = 20
=》2/5 * 4/4 = 8/20
=》3/4 * 5/5 = 15/20
So,
2/5 + 3/4
= 8/20 + 15/20
= 23/20
_________
Hope it helps ⚜
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Determine whether the given binomial is a factor of the polynomial following it. If it is a factor, then factor the polynomial completely.
x+2, x³+4x²-4x-16
Answers
Answer:
x+2 is a factory = (x +4)(x +2)(x -2)Step-by-step explanation:
You want the complete factorization of x³ +4x² -4x -16.
Factor by pairsPairing terms of the given polynomial, we have ...
(x³ +4x²) -(4x +16)
Factoring each pair gives ...
x²(x +4) -4(x +4)
= (x² -4)(x +4)
Difference of squaresThe factorization of x² -4 is found using the form for factoring the difference of squares:
a² -b² = (a +b)(a -b)
x² -4 = (x +2)(x -2)
Note that x+2 is a factor here.
Complete factorizationThe complete factorization of the given polynomial is ...
x³ +4x² -4x -16 = (x +4)(x +2)(x -2)
This is confirmed by the graph, which shows zeros at x = -4, -2, 2.
1 7/8 divided by 3/4 can someone please help me
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2. Use KFC to divide fractions. KEEP the first term, FLIP the second and CHANGE to multiplication.
3. 15/8 x 4/3 = 60/24 = 2 1/2
Answer:
1 7/8
Step-by-step explanation:
Find the value of x.
helllppp
tysm
Answers
Answer:
Step-by-step explanation:
In the Gaussian integral, how does the left side of this equation equal the right side? An answer would be really appreciated, thank you.
Answers
the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.
How do we calculate?
using completing the square method:
Starting with the left side of the equation:
∫\(e^(^-^x^2)\) dx
\(e^(^-^x^2) = (e^(^-x^2/2))^2\)
∫\((e^(^-^x^2/2))^2 dx\)
let u = √(x²/2) = x = √(2u²).
dx = √2u du.
∫ \((e^(^x^2/2))^2 dx\)
= ∫ \((e^(^-2u^2)\)) (√2u du)
The integral of \(e^(-2u^2)\)= √(π/2).
∫ \((e^(-x^2/2))^2\) dx
= ∫ (√2u du) \((e^(-2u^2))\\\)
= √(π/2) ∫ (√2u du)
We substitute back u = √(x²/2), we obtain:
∫ \((e^(-x^2/2))^2\)dx
= √(π/2) (√(x²/2))²
= √(π/2) (x²/2)
= (√π/2) x²
A comparison with the right side of the equation shows that they are are equal.
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. 3F furniture dealer has always sold its merchandise through 4 company-operated stores. Last year sales were birr 1million and net profit was 8% of sales. Fixed costs were birr 170,000. As a result of shifting population and increased competition, the four locations have become less desirable. 3F is considering eliminating its retail stores in favor of door-to-door selling. It is estimated that sales would increase by 25% and net profit by birr 30,000. Fixed costs would increase by birr 30,000 because operations would be moved to a low-rent warehouse. Required a) What was the break-even point under the old situation? b) What will be the break-even point under the proposed situation? c) What birr sales volume must be obtained under the proposed plan to make as much profit as last year?
Answers
a) The break-even point under the old situation is 680000.
b) The break-even point under the proposed situation is 806451.
c) Birr sales volume must be obtained under the proposed plan to make as much profit as last year is 1129032.
a) The break-even point under the old situation:
100000 * a - 170000 = 1000000 * 8%
a = 25% (Profit rate)
x.a = 170000
x = 680000
b) The break-even point under the proposed situation:
1250000 * b - 170000 -30000 = 80000 + 30000
b = 24.8%
x.b = 20000
x = 806451
c) Birr sales volume must be obtained under the proposed plan to make as much profit as last year :
x.b - 200000 = 80000
x.b = 28000
x = 1129032
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How do i round 3,842,532 to the nearest 1,000?
Answers
Answer:
until you only look at the thousands and hundreds place and if the hundred is 5 or more you round the thousands up one
so 3,842,532 rounded the the nearest 1000 is 3,843,000
—————
1000
Reduce
960633
————-
250
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
\(x = 2 \sqrt{3y} \)
\(x = 0\)
\(y = 7\)
; about the y-axis
Answers
on this one, we proceed the same as the other, we start off by graphing them, Check the picture below. Now, we have a solid horizontal line at y = 7, that'd be our boundary, and a parabola that has a vertex at the origin, that's our other boundary, from 0 to 7.
In this case, is a solid area from the curve to the axis of rotation, so we can simply use the "disk" method to get the volume, lemme do it in the same way as "area under the curve", assuming h(y) = 0 for the axis of rotation
\(\textit{area under the curve}\\ \stackrel{f(y)}{2\sqrt{3y}}~~ - ~~\stackrel{h(y)}{0}\qquad \implies 2\sqrt{3y} \\\\\\ \displaystyle\int_{0}^7\pi \left( 2\sqrt{3y} \right)^2 dy\implies \int_{0}^7\pi(12y)dy\implies 12\pi \int_{0}^7 y\cdot dy \\\\\\ 12\pi \cdot \left. \cfrac{y^2}{2} \right]_{0}^7\implies12\pi \cdot \cfrac{49}{2}\implies 294\pi\)
A rectangle has a height of 362 and a width of 464 + 26 -6 what is the area?
Answers
Answer:
175,208 square units
Step-by-step explanation:
Lets calculate the width first:
464 + 26 - 6 = 484
The area is equal to the length times the width, so
362 x 484 = the area
= 175,208 square units
What is an equation of the line that passes through the points (6, -7)(6,−7) and (-6, 3)(−6,3)? Put your answer in fully reduced form.
Answers
Given:
A line passes through the points (6,-7) and (-6,3).
To find:
The equation of line.
Solution:
If a line passes through two points \((x_1,y_1)\text{ and }(x_2,y_2)\), then the equation of line is
\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)
The line passes through the points (6,-7) and (-6,3). So, the equation of line is
\(y-(-7)=\dfrac{3-(-7)}{-6-6}(x-6)\)
\(y+7=\dfrac{3+7}{-12}(x-6)\)
\(y+7=\dfrac{10}{-12}(x-6)\)
\(y+7=-\dfrac{5}{6}(x-6)\)
Using distributive property, we get
\(y+7=-\dfrac{5}{6}(x)-\dfrac{5}{6}(-6)\)
\(y+7=-\dfrac{5}{6}x+5\)
Subtract 7 from both sides.
\(y=-\dfrac{5}{6}x+5-7\)
\(y=-\dfrac{5}{6}x-2\)
Therefore, the equation of line is \(y=-\dfrac{5}{6}x-2\).
what is the most effluence first step to isolate the variable term on one side of this equation -9x=-4x+5
Answers
g count the worst-case number of operations performed by the following pseudocode segment. assume that all possible data sets are equally likely. preconditions: x
Answers
G count the maximum number of operations that the next pseudocode segment might possibly complete. Assume that the likelihood of all potential data sets is equal. preconditions: x
x(x + 1)/2 = O(x^2)
The pseudocode segment given has two nested for loops. The outer loop is iterating over the variable x, while the inner loop is iterating over variable i. G count the maximum number of operations that the next pseudocode segment might possibly complete. Assume that the likelihood of all potential data sets is equal. Each loop iteration is increasing the variable z by 1. In total, this will result in x*(x+1) / 2 operations being performed. This is equal to O(x^2), which is the worst-case number of operations.
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is sangwoo a psychopath,sociopath or both
Answers
Answer:
both, and I didn't know other people watch the anime
Answer:
He's both lol
Step-by-step explanation:
I need help with this
Answers
Answer:
x = 16
Step-by-step explanation:
Step 1: We know DF - DE = EF
9x - 39 - 47 = EF
Step 2: Simplify
9x - 86 = EF
Step 3: Set the equation equal to 3x + 10
9x - 86 = 3x + 10
6x = 96
x = 16
Therefore x is equal to 16
Answer:
58
Step-by-step explanation:
DE + EF = DF
47+ 3x+10 = 9x-39
Combine like terms
57 +3x = 9x-39
Subtract 3x from each side
57+3x-3x = 9x-3x-39
57 = 6x-39
Add 39 to each side
57+39 = 6x-39+39
96 = 6x
Divide by 6
96/6 = 6x/6
16 =x
We want the length of EF
EF = 3x+10
= 3*16 +10
= 48+10
= 58
Write the number 16408 in words.
Answers
Answer:
Step-by-step explanation:
Sixteen thousand, four hundred and eight
Hope this helps!
"I think you have been doing a great job, but you haven't been signing many people up for our new service feature. I want you to set a goal of signing up 25% of your new customers for our new service feature."
Representative: "If I get 96 new customers that means I have to get __________ of them to sign up for the new service feature."
Answers
What is the surface area of the rectangular prism below?
Answers
Answer:
Step-by-step explanation:
The surface area of a rectangular prism calculator gives us the answer: A = 2 * l * w + 2 * l * h + 2 * w * h = 2 * 8 ft * 6 ft + 2 * 8 ft * 5 ft + 2 * 6 ft * 5 ft = 236 ft² .
A ratio of two angles is 5 to 3 and their sum is 180 degrees. Find the measure of each angle. The find their complements. Make a sketch, set up the corresponding equation and solve it.
Answers
Answer:
112.5
67.5
Step-by-step explanation:
We know the ratio is:
5:3
So, we can write it as:
5x+3x=180, with 5x being one angle, and 3x being the other
combine like terms
8x=180
divide both sides by 8
x=22.5
5(22.5)=112.5
3(22.5)=67.5
So, one angle is 112.5 and the other is 67.5.
Hope this helps!
Math whizzes assemble! this is a tough one, this is a question on my study guide its a screenshot, any help would be appreciated.
Answers
Answer:
14
Step-by-step explanation:
Knowing the first triangle is isosceles, and given the degree is 69.
We can find the top left angle as 180-69-69=42
42 combine with another angle to make a right angle
90-42=48.
The second triangle is also isosceles, so to find 2
we can use 180-42=138 (supplementary angles rule)
and given 10x-8=138
10x=140
x=14
The volume of this cube is 4,913 cubic inches. What is the surface area of this cube?
Answers
Answer:
1734
Step-by-step explanation:
1. cube root the volume
2. square that number
3. multiply by 6 sides
What is true about the function f(x) = -3|x+2| - 1 ?A) It has a Maximum at -1 when x=2B) It has a Minimum at -1 when x=-2C) It has a Maximum at -1 when x=-2D) It has a Minimum at -1 when x=2
Answers
First we will graph the function,
So we have a maximum at -1 when x = -2
Jerome solves the inequality y–2 ⩽ 9 in one step, writing y ⩽ 11 as the solution. What property best justifies the step he used to solve the inequality?
A. multiplication or division property of inequality
B. addition or subtraction property of inequality
C. distributive property
Answers
In the formula for the area of a circle, what gets multiplied by r?
Answers
Answer:
A. r²
Step-by-step explanation:
The formula for the area of a circle is π r²,
thus the π is multiplied by the r²