A cable hangs between two poles of equal height and 30 feet apart. set up a coordinate system where the poles are placed at x=−15 and x=15, where x is measured in feet. the height (in feet) of the cable at position x i
The length of the cable is the number of units on it.
The cable is 35.26 feet long
How to determine the cable lengthThe function is given as:
[tex]h(x) = 15\cos(x/15)[/tex]
For all the lengths, we have the following differential equation
[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + (\frac{dy}{dx})^2} \, dx[/tex]
So, we have:
[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + (15 * \frac{1}{15} * \tanh^2(\frac{x}{15}))} \, dx[/tex]
Evaluate
[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + \tanh^2(\frac{x}{15})} \, dx[/tex]
This gives
[tex]Length = \int\limits^{15}_{-15} {\sqrt{cosh^2(\frac{x}{15})} \, dx[/tex]
Evaluate the exponents
[tex]Length = \int\limits^{15}_{-15} {cosh(\frac{x}{15}) \, dx[/tex]
The above function is an even function.
So, we have:
[tex]Length = 2\int\limits^{15}_{0} {cosh(\frac{x}{15}) \, dx[/tex]
Integrate
[tex]Length = 2 * [\frac{sinh(\frac{x}{15})}{1/15}]|\limits^{15}_{0}[/tex]
Simplify
[tex]Length = 30 * [\sinh(\frac{x}{15})]|\limits^{15}_{0}[/tex]
Expand
[tex]Length = 30 * [\sinh(\frac{15}{15}) - \sinh(\frac{0}{15})][/tex]
Solve
[tex]Length = 35.26[/tex]
Hence, the length of the cable is 35.26 feet
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tickets for a football match are sold at $30 for adults and $15 for children a company bought 28 tickets if x of these tickets were for adults, write in terms of x a. the number of tickets for children b. the amount spent on tickets for adults c. the amount spent on tickets ...
The number of tickets for children is represented by '28-x' and the amount spent on tickets for adults is '$30x'. The amount spent on tickets for children is '$15*(28-x)'.
Explanation:We will use the concept of algebraic expressions to solve this question. If we represent the number of adult tickets as x, we know that the total number of tickets is 28. Hence, the number of children tickets can be represented as 28-x. The cost of a ticket for adults is $30, so the amount spent on adult tickets can be represented as $30x. Similarly, as the cost of a ticket for children is $15, the amount spent on children tickets can be represented as $15*(28-x).
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The number of ticket for children is (28 - x), the amount spent on tickets for adults would be $30x, and the total amount spent on tickets would be $30x + $15(28 - x).
Explanation:If a company bought 28 tickets and x of these tickets were for adults, then:
a. The number of tickets for children would be 28 - x. This is because from the total number of tickets purchased, we subtract the number of adult tickets to find the number of children's tickets.
b. The amount spent on tickets for adults would be $30x. This is because each adult ticket costs $30 and there are x number of adults.
c. To find out the total amount spent by the company, we will multiply the number of adult tickets by the price of an adult ticket ($30x) and add this to the product of the number of children tickets (28 - x) and the price of a child's ticket ($15). Therefore, the total spent would be $30x + $15(28 - x).
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Quadrilateral ABCD is inscribed in a circle. What is the measure of angle A? Enter your answer in the box. m∠A= ° A quadrilateral inscribed in a circle. The vertices of the quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle A is labeled as left parenthesis 3 x plus 6 right parenthesis degrees. The angle C is labeled as left parenthesis x plus 2 right parenthesis degrees.
The measure of angle A in a cyclic quadrilateral ABCD, where the measure of angle A is (3x + 6) degrees and the measure of angle C is (x + 2) degrees, is determined to be 135 degrees.
Explanation:Given that quadrilateral ABCD is inscribed in a circle, it follows from the properties of cyclic quadrilaterals that the sum of the opposite angles of such a quadrilateral is always 180 degrees. Therefore, if the measure of angle A is represented by the expression (3x + 6) degrees and the measure of angle C is represented by the expression (x + 2) degrees, then we can set up an equation that (3x + 6) + (x + 2) = 180. Solving this equation gives x = 43. Using x = 43, substitute it into 3x + 6 to get the value of angle A, which is equal to 135 degrees.
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Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.2, 0.4, and 0.4, respectively. what is the expected number of books a customer will purchase? the standard deviation of the customer's book purchases is
The expected number of books a customer will purchase is 1.2 books, and the standard deviation of their book purchases is approximately 0.78 books.
To find the expected number of books a customer will purchase,
use the formula for the expected value (also known as the mean) of a random variable:
Expected Value (μ) = Σ (x × P(x))
Where:
μ is the expected value.
x represents the possible values of the random variable (in this case, 0, 1, and 2).
P(x) is the probability associated with each value of x.
Probability of purchasing 0 books (P(0)) = 0.2
Probability of purchasing 1 book (P(1)) = 0.4
Probability of purchasing 2 books (P(2)) = 0.4
Now, calculate the expected value:
μ = (0 × 0.2) + (1 ×0.4) + (2 × 0.4)
μ = 0 + 0.4 + 0.8
μ = 1.2
To find the standard deviation (σ) of the customer's book purchases,
use the formula for the standard deviation of a discrete random variable:
Standard Deviation (σ) = √[Σ((x - μ)² × P(x))]
Where:
σ is the standard deviation.
x represents the possible values of the random variable.
μ is the expected value.
P(x) is the probability associated with each value of x.
In this case, you already calculated μ as 1.2, and you have the probabilities P(0), P(1), and P(2).
Now, calculate the standard deviation:
σ = √[((0 - 1.2)² × 0.2) + ((1 - 1.2)² × 0.4) + ((2 - 1.2)² × 0.4)]
σ = √[(1.44 ×0.2) + (0.16 × 0.4) + (0.64 × 0.4)]
σ = √[0.288 + 0.064 + 0.256]
σ = √0.608
σ ≈ 0.78
Therefore, the expected number and the standard deviation of books a customer will purchase is 1.2 books and approximately 0.78 books respectively.
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if x2 = 49 the only possible answer for x is 7
While the equation x² = 49 suggests that x = 7, it also has a negative solution, x = -7. Both solutions can be verified by substitution into the original equation, proving they are correct through resulting identities.
The equation x² = 49 has two solutions in the realm of real numbers, not just x = 7. To find the values of x that satisfy the equation, we take the square root of both sides. Since the square root of a number has both a positive and a negative value, the solutions are x = 7 and x = -7. To verify these solutions, we can substitute them back into the original equation to confirm that they work, demonstrating identities such as 7² = 49 and (-7)² = 49.
How much would $500 invested at 7% interest compounded annually be worth after 5 years?
Find the points on the curve y = 2x3 + 3x2 − 12x + 9 where the tangent line is horizontal.
the points on the curve [tex]y = 2x^3 + 3x^2 - 12x + 9 are (-2,29) \; and \; (1,2)[/tex]where the tangent line is horizontal.
Given :
The equation of the curve is [tex]y=2x^3\:+\:3x^2\:-\:12x\:+\:9[/tex]
Given tangent line is horizontal . Tangent line is horizontal when slope =0
Slope is nothing but the derivative.
So we find out x values where derivative =0
Lets take derivative for the given curve y
[tex]y=2x^3+3x^2-12x+9\\y'=2(3x^2)+3(2x)-12\\y'=6x^2+6x-12[/tex]
Now we set the derivative =0 and solve for
[tex]6x^2+6x-12=0\\Divide\; whole \; equation \; by \; 6\\x^2+x-2=0\\(x+2)(x-1)=0\\x+2=0, x=-2\\\\x-1=0, x=1[/tex]
So , the slope =0 when x=1 and x=-2
Now we find out the points . Use the original function
[tex]y=2x^3\:+\:3x^2\:-\:12x\:+\:9\\x=-2\\2\left(-2\right)^3+3\left(-2\right)^2-12\left(-2\right)+9=29\\(-2,29)\\\\x=1\\2\left(1\right)^3+3\left(1\right)^2-12\left(1\right)+9=2\\(1,2)[/tex]
the points on the curve [tex]y = 2x^3 + 3x^2 - 12x + 9 are (-2,29) \; and \; (1,2)[/tex]where the tangent line is horizontal.
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A sphere with a radius of 3 cm has the same volume as a cone with a radius of 6 cm. What is the height of the cone?
A) 2 cm
B) 3 cm
C) 4 cm
D) 5 cm
Try this option:
[tex]if \ the \ volume \ of \ the \ sphere \ is \ the \ same \ one \ as \ a \ cone, \ then \ V_s=V_c; \ <=> \ \frac{4 \pi}{3}*3^3=\frac{1}{3} \pi*6^2*h_c; \ => \ h_c=3(cm)[/tex]
answer: B
B) 3 cm
Vsphere = [tex]\frac{4}{3}\pi r^{3} = \frac{4}{3}\pi(3)^{3} = 36\pi[/tex]
Vcone =
1
3
πr2h
36π =
1
3
π(6)2h
36π = 12πh
h = 3
Thus, the height is 3 cm.
Alternatively, the two equations could be set equal to each other and solved for the unknown height of the cone.
226Ra has a half-life of 1599 years. How much is left after 1000 years if the initial amount was 10 g?
Find the inverse of this 3x3 matrix. [1 5 2]
[ 1 1 7]
[0 -3 7]
Answer:
A
Step-by-step explanation:
⎡−25 26 −33⎤
⎥ 4 −4 5 ⎥
⎥ 3 −3 4 ⎦
PLEASE HELPS NEED THIS DONE BEFORE 3 O CLOCK
1)Jerome noticed the following house numbers on his street:
305, 318, 331, 344
The house numbers follow a pattern. Which expression can be used to determine the nthnth house number on his street?
A) 292 +13n
B) 292n
C) 292n + 13
D) 13(n + 292)
2) A polynomial expression is shown below.
(mx+8)(2x−4)
The expression is simplified to:
−6x2+28x−32-6x2+28x-32
What is the value of m?
A) 3
B) 4
C) -3
D) -4
3) What is the domain of the function shown below? (PICTURE AT BOTTOM)
A) 2
B) −8 ≤ x <3and 4 ≤ x <8
C) −8 ≤ x < 8
D) −7 ≤ x ≤ 7
Answer:
Jerome noticed the following house numbers on his street:
Answer 292 +13n
A polynomial expression is shown below. What is the value of m?
Answer -3
What is the domain of the function shown below
Answer −8 ≤ x <3and 4 ≤ x <8
ONLY ANSWER IF YOU KNOW THE ANSWER Which shows a correct order to solve this story problem? The Johnson Chair Factory used 165.6 pounds of nails in 6 weeks. The Martinez Table Factory used 154.2 pounds of nails in 6 weeks. How many pounds of nails did the two factories use altogether in one week? A. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Add the two amounts. B. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Add the two amounts. Step 4: Multiply the sum by 2. C. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Divide the two amounts by 6. D. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Multiply the two amounts by 6.
Answer:
A if you look close at the story you will learn alot! hope this helps!
J is 25 more than 3 help???
For which k will the graph of f(x)=x^2−kx+k^2 cross the x-axis twice?
The cylinder shown has a volume of π in3. Find the volume of a cone with the same base and height as the cylinder.
Answer:
Step-by-step explanation:
Alright, lets get started.
Suppose the height of cylinder is h and radius of base is r.
The volume of cylinder will be : [tex]\pi r^2h[/tex]
The cone is of same height means h and same base means radius will be r.
The formula of volume of cone is : [tex]\frac{1}{3} \pi r^2h[/tex]
It means the volume of cone is one third of the volume of cylinder.
The volume of cylinder is given as π.
So, the volume of cone will be : [tex]\frac{\pi }{3}[/tex] : Answer
Hope it will help :)
Look at the figure. How can you prove ∆ABD and ∆ACD are congruent?
A. ∆ABD ≅ ∆ACD by the SAS Postulate.
B. It is not possible to determine if the triangles are congruent.
C. ∆ABD ≅ ∆ACD by the SSS Postulate.
Answer: The correct option is (B). It is not possible to determine if the triangles are congruent.
Step-by-step explanation: We are given to select the correct option by which we can prove that ∆ABD and ∆ACD are congruent.
As shown in the figure,
In ∆ABD and ∆ACD, we have
∠ADB = ∠ADC = 90°,
AD is the common side.
So, one angle and the adjacent side of one triangle are congruent to the corresponding angle and the adjacent side of the other triangle.
That is, to prove that the two triangles are congruent, we need one of the following two conditions:
(i) BD = CD
or
(ii) ∠BAD = ∠CAD.
Since none of these two are given, so we cannot determine the congruence of the two triangles.
Therefore, it is not possible to determine if the triangles are congruent.
Thus, option (B) is correct.
How many triangles are with two sides each 6 inches long and one angle measure of 90°.
The description relates to an isosceles right triangle.
An isosceles right triangle can be described as the triangle that has two sides that are both equal while it also has an angle that will be 90° which is the right angle.
In this case, the two equal sides are given as 6 inches while it also has an angle of 90°. Therefore, it's an isosceles right triangle.
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how many rootes are in f(x)=(x^2-3x+1)^2
2
5
6
9
Solve for C. See photo
Write the explicit formula for the geometric sequence.
64, 32, 16, 8, ...
A) an = 8 · 4n-1
B) an = 8 · 2n-1
C) an = 32 · 0.5n-1
D) an = 64 · 0.5n-1
Answer:
D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]
Step-by-step explanation:
The answer is D because it is the only answer that has an=64 and a decimal, 64 is your first term and the sequence is getting smaller
AND OR
Answer:
D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]
Step-by-step explanation:
Explicit Formula: an = a1 · dn-1
a1 = 64, d = 0.5
an = 64 · 0.5n-1
Gas prices in Cook county are at $3.30 per gallon. If a market scientist predicts a 20% increase in the price of gas in the coming month, what will the price of gas be?
The price of the gas is $3.96.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Gas prices in Cook-County are at $3.30 per gallon.
If a market scientist predicts a 20% increase in the price of gas in the coming month,
that means,
100 + 20% = 120% increase = 1.2 in decimals.
The price of gas,
= 3.30 + 3.30 x 1.2
= 3.96
Therefore, the new price is $3.96.
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The formula for the volume of a cube is V(s) = s3 where s is the side length of the cube. In which quadrant(s) is the graph of the function V(s)?
Answer:
The answer is A: Quadrant 1
Step-by-step explanation:
On Edge :)
Select two rations that are equivalent to 3: 12.
Milli plans to rent a room for her birthday party for $40. The catering charge is $12 per person but there is no charge for Milli's meal since she is the guest of honor. If Milli has $100 to spend on her birthday party, what is the maximum number of friends Milli can invite?
Kelly is having a party. She wants to make punch. The recipe for punch uses 3 pints of pineapple juice, 5 cups or orange juice, 1/4 gallon of lemonade, and 1 quart of apricot nectar. Kelly says her recipe will make 20 cups of punch. Is Kelly correct? Explain your answer. How does one arrive at the answer? Are all the ingredients added? Is anything multiplied?
Evaluate the integral. (use c for the constant of integration.) 7 ln(x)/ x sqrt(5 + (ln(x))^2) dx
The expression for the integral [tex]\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex] after the evaluation is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].
Given an integral expression:
[tex]\text{I}=\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]
This can be written as:
[tex]\text{I}=7\int\frac{ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]
It is required to find the integral value.
Let u = 5 + (ln (x))²
Differentiate.
[tex]du=2ln(x)*\frac{1}{x} dx[/tex]
Or [tex]\frac{du}{2} =\frac{lnx}{x} dx[/tex]
Substitute the values.
[tex]\text{I}=7\int\frac{1}{\sqrt{u} } \frac{du}{2}[/tex]
[tex]\text{I}=\frac{7}{2} \int\frac{1}{\sqrt{u} }du[/tex]
[tex]\text{I}=\frac{7}{2} (2\sqrt{u} )+C[/tex]
Substitute back the value of u.
[tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex]
Hence the value of the integral is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].
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Please try this, I forget absolutely everything about rhombuses. Thanks for all the help, shouldn't be too hard
Treys online music club charges a monthly rate of $20 plus $0.80 per song download. Debs online music club charges a monthly rate of $21 plus $0.60 per song download. For what number of songs will the monthly charge be the same for both clubs? How much will it cost?
Answer:
For 5 songs the monthly charge be the same for both clubs.
It will cost $ 24.
Step-by-step explanation:
Let, for x songs, the monthly charges are same for both clubs,
Given,
For Treys online music club,
Monthly rate = $ 20,
Additional Charges for a song = $ 0.80,
⇒ Additional Charges for x song = $ 0.80x,
Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song
= 20 + 0.80x
Now, for Debs online music club,
Monthly rate = $ 21,
Additional Charges for a song = $ 0.60,
⇒ Additional Charges for x song = $ 0.60x,
Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song
= 21 + 0.60x
Hence, we can write,
[tex]20 + 0.80x = 21 + 0.60x[/tex]
[tex]0.80x - 0.60x = 21 - 20[/tex]
[tex]0.20x = 1[/tex]
[tex]\implies x = \frac{1}{0.20}=5[/tex]
Hence, for 5 songs the monthly charge be the same for both clubs.
Also, the cost for 5 songs = 20 + 0.80 × 5 = 20 + 4 = $ 24
2x - y + 3z = -9
x + 3y - z = 10
3x + y - z = 8
find the ordered triple
given right triangle XYZ what is the value of tan 60°
Answer:
√3
Step-by-step explanation:
got 100%