Based on the calculations, the height of this ravine is equal to 143.95 feet.
Given the following data:
Height of ravine = 100 feet.How to calculate the length of rope.First of all, we would assign a variable to the height of the ravine, which is 100 feet tall.
Let the height of ravine be h.
Note: We would choose 46° as a measure for angle A.
From the image attached, we would determine the length of the hypotenuse by using Cosine trigonometric:
[tex]Cos A=\frac{Adj}{Hyp} \\\\Cos 46=\frac{100}{h} \\\\0.6947=\frac{100}{h}\\\\h=\frac{100}{0.6947}[/tex]
h = 143.95 feet.
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PLEASEE answerrrrrr
Is ( – 1, – 5) a solution to this system of equations? 7x+2y=13 4x+4y=14
Answer:
yes
Step-by-step explanation:
help me please. I'll give brainly, thank u >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Answer:
a
Step-by-step explanation:
the solution to the system is at the point of intersection of the linear equations.
the lines intersect at (- 4, 3 )
then solution is (- 4, 3 )
Real Numbers: Mastery Test
Answer:
exuse me but i dont see the questions
Step-by-step explanation:
If in a certain year, 400 000 high school seniors took a test in the NSAT and 240 000 scored above the cut-off score, what is the cut-off score for that year?
Answer:
160 000
Step-by-step explanation:
400 000 - 240 000 = 160 000
What are the domain and range of g of x equals the square root of the quantity x plus 4?
D: [4, ∞) and R: [0, ∞)
D: (–4, ∞) and R: (–∞, 0)
D: [–4, ∞) and R: [0, ∞)
D: (4, ∞) and R: (–∞, 0)
Using it's concept, it is found that the domain and range of the function are given by:
D: [–4, ∞) and R: [0, ∞)
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In this problem, the function is:
[tex]g(x) = \sqrt{x + 4}[/tex]
The square root function does not exist for negative values, hence the domain is represented by:
[tex]x + 4 \geq 0 \rightarrow x \geq -4[/tex]
The range of the square root function is [tex]x \geq 0[/tex], which remains the same as there are no vertical translations.
Hence the correct option is given by:
D: [–4, ∞) and R: [0, ∞)
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Answer: C) D: [–4, ∞) and R: [0, ∞)
Step-by-step explanation:
In the following figure, the square ABCD is inscribed in the circle centered at point P. What is the area of the circle?
Answer:
[tex]A_{Circle} \approx 39.24\: units^2[/tex]
Step-by-step explanation:
Square ABCD is inscribed in a circle with center P such that BC = 5 units.
BD will be diagonal of the square as well as diameter of the circle.
[tex]BD = BC\times\sqrt 2[/tex]
[tex]\implies BD = 5\sqrt 2[/tex]
-> Diameter of the circle [tex](d) = 5\sqrt 2[/tex]
-> Radius of the circle [tex](r) = 2.5\sqrt 2=3.535\: units[/tex]
[tex]A_{Circle} =\pi(r)^2[/tex]
[tex]\implies A_{Circle} =3.14(3.535)^2[/tex]
[tex]\implies A_{Circle} =3.14(3.535)^2[/tex]
[tex]\implies A_{Circle} =39.2381465[/tex]
[tex]\implies A_{Circle} \approx 39.24\: units^2[/tex]
Roman Civilization began in 509 B.C. and ended in 476 A.D. How long did Roman Civilization last?
Answer:
Add 509 and 476; The Roman Era lasted for a total of 985 years from 509 B.C to 476 A.D.
Step-by-step explanation:
Type the correct answer in the box. round your answer to the nearest tenth. events m and n are independent events. in this scenario, if p(m) = 0.46 and p(m and n) = 0.138, then p(n) = .
The probability helps us to know the chances of an event occurring. The probability of event n occurring is 0.3.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
We know that for two independent events the probability of the two events occurring simultaneously is written as,
[tex]P(A \cap B) = P(A)\cdot P(B)[/tex]
Now, as we know the probability of event m occurring also we know the probability of both events occurring simultaneously, therefore, the probability of event n occurring can be written as,
[tex]P(A \cap B) = P(A)\cdot P(B)\\\\P(m \cap n) = P(m)\cdot P(n)\\\\0.138 = 0.46 \times P(n)\\\\P(n) = 0.3[/tex]
Hence, the probability of event n occurring is 0.3.
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Find the measure of the missing angle in this triangle
Answer:
c = 40degrees
Step-by-step explanation:
the sum of a triangle should be 180 degrees
you need to ad 80+60 which is 140 then minus 140 from 180 which is 40 so 40 degrees is the measurement of angle c
A pool supply company sells 50-pound buckets of chlorine tablets. A customer believes that the company may be underfilling the buckets. To investigate, an inspector is hired. The inspector randomly selects 30 of these buckets of chlorine tablets and weighs the contents of each bucket. The sample mean is 49.4 pounds with a standard deviation of 1.2 pounds. The inspector would like to know if this provides convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds, so he plans to test the hypotheses H0: μ = 50 versus Ha: μ < 50, where μ = the true mean weight of all 50-pound buckets of chlorine tablets. The conditions for inference are met. The test statistic is t = –2.74 and the P-value is between 0.005 and 0.01. What conclusion should be made at the significance level, Alpha?
Reject H0. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.
Reject H0. There is not convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.
Fail to reject H0. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.
Fail to reject H0. There is not convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.
The answer is: Reject H0. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.
Your coach bought 12 hamburgers and 6 large fries for your team for
dinner. Each hamburger cost $1.75. He spend $30. Write and solve
an equation to determine the cost c of a large fry.
Answer:
$1.5
Step-by-step explanation:
12 x 1.75 + 6c = 30
21 + 6c = 30
6c = 30 - 21
6c = 9
c = 9/6
c = 1.5
Answer:
do face reveal
Step-by-step explanation:
we don't talk about bruno
SHORT EASY QUESTION PLS HELP)
Find the exact volume if the radius is 7 inches and the height is 18 inches.
Answer:
V≈2770.88Step-by-step explanation:
The radious is 7 inches, that means the diameter is 14 inches.
The height is 18 inches. so...
V=πr2h=π·72·18≈2770.88472
So hence, your answer is
V≈2770.88-------------------------------------------------------------------------------------------------------------
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Have a great day!
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What is the run of a 50% slope with a rise of 50 feet?
a
Answer: 25
Step-by-step explanation: because 50% of 50 is 25
pleaseeee check picture its about finding area of triangle.
Answer:
13.75 is your answer
Step-by-step explanation:
find area of whole triangle 5.5*7*1/2=19.25
Find area of blank spot 5.5*2*1/2=5.5
Subtract 19.25-5.5=13.75
Can y’all please solve this
Find the 51st term of the arithmetic sequence 29,9, -11, ...
Answer:
Step-by-step explanation:
29-9=20
9-(-11)=20
50×-20=-1000
-1000+29=-971
What is the formula of area of circle when diameter is given?
Answer:
[tex]\pi (\frac{diameter}{2} )^{2}[/tex]
Step-by-step explanation:
The formula is pretty similar to the standard equation, π·r², since the diameter is just the radius times two.
Hope that helps! :)
find the percentage profit in each case cost price 500 selling price 550
Answer:
0.1 or 10%
Step-by-step explanation:
Cost: 500
Sell: 550
550-500 = 50
50/500 = 0.1 OR 10%
Therefore, the percentage profit for each sale is 10% of the original wholesale price.
Answer:
10%
Step-by-step explanation:
profit=buyingpirce _selling price
550_500=50
%profit=profit\buyingprice×100
50\500×100=10%
Last year, there were n pies baked for the bake sale. This year, there were 228 pies baked. Using , write an expression for the total number of pies baked in the two years.
Pls help dont need an explanation just an answer
Answer:
[tex]\boxed{\text{Slope = 5}}[/tex]
[tex]\boxed{\text{y-intercept = 1}}[/tex]
Step-by-step explanation:
To find the slope of the line, we must pick any two points on the line. Using those two points, we will calculate the Rise and the Run. Then, we will use the slope formula (Rise/Run) to find the slope. The y-intercept is the intersection of the point on the y-axis.
[tex]\text{My chosen points: (0,1) and (1,6)}[/tex]
[tex]\text{Rise = 5; Run = 1}[/tex]
≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
[tex]\text{Slope}= \dfrac{\text{Rise}}{\text{Run}}[/tex]
➡ [tex]\bold{Slope = \frac{5}{1} = \underline{5}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Rise = 5; Run = 1}][/tex]
[tex]\underline{........................................................................................................................}[/tex]
[tex]\text{Intersection on y-axis:} \ (0,1)[/tex]
➡ [tex]\text{y-intercept} \rightarrow (0,\bold{ 1}) \rightarrow \bold{\underline{{1}}}}[/tex]
≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
Consider the following initial-value problem. Y'' − 5y' = 8e4t − 4e−t, y(0) = 1, y'(0) = −1 find ℒ{f(t)}, for f(t) = 8e4t − 4e−t. (write your answer as a function of s. )
The Laplace transform of the non-homogeneous second order differential equation is [tex]\mathcal {L} \{f(t)\} = \frac{4\cdot (s+6)}{s\cdot (s-4)\cdot (s+1)\cdot (s-5)} +\frac{1}{s} -\frac{1}{s\cdot (s-5)}[/tex].
How to determine the Laplace transform of a non-homogeneous second order differential equationA Laplace transform is a frequency-based algebraic substitution method used to determine the solutions of differential equations in a quick and efficient manner.
In this question we shall use the following Laplace transforms:
[tex]\mathcal {L} \{f(t) + g(t)\} = \mathcal {L} \{f(t)\} + \mathcal {L}\{g(t)\}[/tex] (1)
[tex]\mathcal {L} \{\alpha\cdot f(t)\} = \alpha\cdot \mathcal {L} \{f(t)\}[/tex] (2)
[tex]\mathcal{L} \left\{y^{(n)} \right\} = s^{n}\cdot \matcal {L}\{f(t)\}-s^{n-1}\cdot y(0) -...-y^{(n)}(0)[/tex] (3)
[tex]\mathcal {L} \{e^{-a\cdot t}\} = \frac{1}{s+a}[/tex] (4)
Now we proceed to derive an expression fo the Laplace transform of the solution of the differential equation:
[tex]y'' -5\cdot y' = 8\cdot e^{4\cdot t}-4\cdot e^{-t}[/tex]
[tex]s^{2}\cdot \mathcal {L}\{f(t)\}-5\cdot y(0) - y'(0) - 5\cdot s \cdot \mathcal {L} \{f(t)\} +5\cdot y(0) = \frac{8}{s-4}-\frac{4}{s+1}[/tex]
[tex]\mathcal {L} \{f(t)\} = \frac{4\cdot (s+6)}{s\cdot (s-4)\cdot (s+1)\cdot (s-5)} +\frac{1}{s} -\frac{1}{s\cdot (s-5)}[/tex]
The Laplace transform of the non-homogeneous second order differential equation is [tex]\mathcal {L} \{f(t)\} = \frac{4\cdot (s+6)}{s\cdot (s-4)\cdot (s+1)\cdot (s-5)} +\frac{1}{s} -\frac{1}{s\cdot (s-5)}[/tex]. [tex]\blacksquare[/tex]
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The Laplace transform Y'' − 5y' = 8e4t − 4e−t when y(0) = 1, y'(0) = −1 for f(t) = 8e4t − 4e−t would be [tex]\frac{4(s+6)}{s.(s-4)(s+1).(s-5)} + \frac{1}{s} - \frac{1}{s.(s-5)}[/tex].
What is Laplace transform?A Laplace transform is a frequency-based algebraic substitution method used to determine the solutions of differential equations quickly and efficiently.
The Laplace transform
L[ f(t) + g(t) ] = Lf(t) + Lg(t)
Also,
L [[tex]y^{n}[/tex]] = [tex]s^{n} . L[ f(t) ] - s^{n-1} .y(0) .....y^{n}(0)[/tex]
We have
Y'' − 5y' = 8 . e^4t − 4 . e−t
[tex]s^{2} . L[ f(t) ] - 5. y(0)- y'(0) .....y^{n}(0)[/tex]
y(0) = 1, y'(0) = −1
for f(t) = 8e4t − 4e−t.
= [tex]\frac{8}{s-4} - \frac{4}{s+1}[/tex]
L [f(t)] = [tex]\frac{4(s+6)}{s.(s-4)(s+1).(s-5)} + \frac{1}{s} - \frac{1}{s.(s-5)}[/tex]
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What is the angle measure θ in degrees such that cos(θ) = 2/16? Round your answer to the nearest degree.
Answer: 83 degrees
Step-by-step explanation:
In order to find theta, you must take the arccosine of both sides. The arccosine eliminates the cosine, and extracts the argument. Therefore:
[tex]cos(x)=\frac{2}{16} =\frac{1}{8}[/tex]
[tex]arccos(cos(x))=arccos(\frac{1}{8} )=x[/tex]
Use a calculator the find the arccosine of 1/8. Its nearly impossible to find the exact answer without one:
[tex]x=arccos(\frac{1}{8} )[/tex]
[tex]x=83[/tex]
Write the equation for the cosine function for the ferris wheel ride, with where h, is the height in meters, and t, is the time in minutes.
The cosine function for the ferris wheel ride is an illustration of a sinusoidial function
The equation of the Ferris wheel is y = -190cos(π / 120 t) + 195
How to determine the cosine function?A cosine function is represented as:
y = Acos(Bt - C) + D
From the complete question, the diameter of the ferris wheel is 380 feet.
The amplitude represents the radius, and this is calculated as:
A = 380/2
A = 190
The function becomes:
y = 190cos(Bt - C) + D
The period of the function is:
T = 2π / B
From the complete question, one full rotation is completed in 4 minutes.
Convert the time to seconds
T = 4 * 60
T = 240.
So, we have:
240 = 2π / B
Divide both sides by 2
120 = π / B
Make B the subject
B = π / 120
The function becomes
y = 190cos(π / 120 t - C) + D
From the question, the ferris wheel is 195 feet above the ground.
This represents the vertical shift.
So, we have:
D = 195
The function becomes
y = 190cos(π / 120 t - C) + 195
Also, we have:
The lowest point is at t = 0 and the function is a negative cosine function
So, we have:
C = 0
The function becomes
y = -190cos(π / 120 t) + 195
Hence, the cosine function is y = -190cos(π / 120 t) + 195
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[tex]solve \: the \: following \: problems \: below[/tex]
please answer it correctly I need It now
please none sense report
Answer:
1. Find the circumference, then multiply that by 120 turns.
Formula for circumference;
C = 2πr
But, we need to find the radius which is 1/2(half) of the diameter, so,
D/2 = R
D = Diameter
R = Radius
20/2 = 10 is the radius.
Plug in values now:-
C = 2(3.14) x 10
C = 6.28 x 10
C = 62.8 is the circumference, now we multiply this by 120 to get the total amount of centimetres it'll go.
62.8(120)
= 7,536 cm it'll go.
2. Find the circumference, then multiply that by 750 turns/revolutions.
C = 2πr
Find radius,
D/2 = R
50/2 = 25 is the radius.
Plug in values now:-
C = 2(3.14) x 25
C = 6.28 x 25
C = 157 cm it'll go.
3. Same thing, find circumference then compare values.
Given that radius is 10,
Use the formula for circumference;
C = 2πr
Replace values:-
C = 2(3.14) x 10
C = 6.28 x 10
C = 62.8 cm is the circumference of the first circle.
Now the second circle, (use same formula)
C = 2πr
Find radius,
D/2 = R
10/2 = 5 is the radius.
Replace values:-
C = 2(3.14) x 5
C = 6.28 x 5
C = 31.4 cm is the circumference for the second circle.
Now subtract the second circle's circumference from the first:
62.8 - 31.4
= 31.4, 31.4 cm is how much greater the second circle is than the first.
4 - 5. Find circumference, (using circumference formula)
C = 2πr
Find radius,
D/2 = R
760/2 = 380
Replace values:-
C = 2(3.14) x 380
C = 6.28 x 380
C = 2,386.4 km is the distance he'll travel.
If he wants to travel around it with 2,000 km, he'll need to travel at least once.
Solve the system using linear combination.
41
S 5x + 3y
Зх бу
9
We want to eliminate the variable y. What number should we multiply times the first
equation, so that when we add the two equations, we can eliminate the variable y?
Answer:
Delta does not have a relative extreme in the equation, so it is variable y It can not be true
Step-by-step explanation:
[tex]s = 5x + 3y[/tex]
There is an answer
The rest of the equation that has no substituted delta is not true, so the prime variables have relative extremes.
Jasmyn and Samantha go to the mall to go shopping. Jasmyn buys a new t-shirt that is $24.99 and Samantha buys a new pair of pants that are $48.99. If sales tax is 6%, how much will they have to pay total for the t-shirt and pants including tax?
The total cost of both items is $ ____
Answer:
78.42
Step-by-step explanation:
[tex]1.06(24.99 + 48.99)[/tex]
[tex]1.06 \times 73.98 = 78.42[/tex]
help me please I will mark as brainlist
Answer:
[tex] \frac{ \alpha + \beta + \gamma }{ - d} [/tex]
Step-by-step explanation:
If we simplify that fraction, we get
[tex] \frac{ \alpha + \beta + \gamma }{ \alpha \beta \gamma } [/tex]
Keep that in mind.
If y, a ,b are zeroes of the cubic polynomial, then that means
[tex](x - \alpha )(x - \beta )(x - \gamma )[/tex]
make up the polynomial.
Notice that leading xoeffeicent will be 1, so the roots will multiply to
[tex] - d[/tex]
so
[tex] \alpha \beta \gamma = - d[/tex]
which gives us
[tex] \frac{ \alpha + \beta + \gamma }{ - d} [/tex]
Proof:
Consider the function
[tex](x - 2)(x - 3)(x - 5)[/tex]
The roots are 2, 3, 5.
D is -30 so we get
Using the value,
[tex] \frac{2 + 3 + 5}{ 30} = \frac{1}{3} [/tex]
If we use the orginal equation, we get
[tex] \frac{1}{6} + \frac{1}{10} + \frac{1}{15} = \frac{10}{30} = \frac{1}{3} [/tex]
Answer:
Hey,mate
Notice that leading xoeffeicent will be 1, so the roots will multiply to
The roots are 2, 3, 5.
[tex]\sqrt{2} \sqrt{3} \sqrt{5}[/tex]
D is -30
Trey decides to raise the price of his tomatoes from $5 a basket to $6 a basket. What is the percent of the increase?
Answer:
(6-5)/5=20% increase
Step-by-step explanation:
There are 250 wolves in a national park. the wolf population is increasing at a rate of 16% per year. write an exponential model to represent the situation. use the model from problem 1 to determine how long it will take the wolf population in the national park to reach 1000. round the answer to the nearest hundredth.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ A=250(1 + 0.16)^{t}\implies A=250(1.16)^t \\\\[-0.35em] ~\dotfill[/tex]
[tex]A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &1000\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ 1000=250(1.16)^t\implies \cfrac{1000}{250}=1.16^t\implies 4=1.16^t \\\\\\ \log(4)=\log(1.16^t)\implies \log(4)=t\log(1.16) \\\\\\ \cfrac{\log(4)}{\log(1.16)}=t\implies \stackrel{\textit{about 9 years and 4 months}}{9.34\approx t}[/tex]