To determine the average rate of the speed's increase or decrease from t=2 to t=5, we need to find the slope of the line connecting the points (2,s(2)) and (5,s(5)) on the graph of the equation s(t)=T^2-6T+35. The slope of a line is given by the formula:
slope = (y2-y1)/(x2-x1)
In this case, x1=2, x2=5, y1=s(2), and y2=s(5).
Plugging in the values of x1 and x2 into the equation s(t)=T^2-6T+35, we get:
y1=s(2)=2^2-6(2)+35=4-12+35=27
y2=s(5)=5^2-6(5)+35=25-30+35=30
Now we can plug in the values of x1, x2, y1, and y2 into the slope formula:
slope = (30-27)/(5-2) = 3/3 = 1
Therefore, the average rate of the speed's increase or decrease from t=2 to t=5 is 1. This means that the speed is increasing at a constant rate of 1 unit per unit of time from t=2 to t=5.
To know more about average rate refer here:
https://brainly.com/question/12395856
#SPJ11
A store pays $60 for an item your friend finds the selling price when the markup is20%
Answer:$72 Total
Step-by-step explanation:
20%=1/5
1/5 + 5/5(total) = 6/5
60 * 6/5 = $72
Rachel, Kayla, and Francesca raised $35.67 for their basketball team. Rachel and Kayla each raised the same amount, and Francesca raised $10.50 more than each of them.
If x = the amount raised by Kayla, choose the expressions that represent the amount each other player raised.
Answer:
Kayla and Rachel raised $8.39, Francesca raised $18.89.
Step-by-step explanation:
Knowing that $35.67 is the total amount raised, that Rachel and Kayla raised the same amount (x) each, and that Francesca raised $10.50 more than them (x + 10.50), then the equation would look like:
35.67 = x + x + (x + 10.50)
or
35.67 = 3x + 10.50
From here, you can solve algebraically.
Isolate the variable by subtracting 10.50 from both sides
25.17 = 3x
Then, find X by dividing both sides by 3:
x = 8.39
Knowing that Kayla and Rachel raised $8.39 each, to find Francesca's contribution you can either:
A) Subtract Kayla and Rachel's contributions from the total amount:
35.67 - 8.39 - 8.39 = 18.89
or
B) Add $10.50 to the amount that Kayla and Rachel raised:
8.39 + 10.50 = 18.89
Can someone plss help me with this? they're linear equations 2x2
0.16x+0.20y=11
x+y=60
Answer:
Step-by-step explanation:
0.16x + 0.20y = 11
we can write 0.16 = 16/100 = 4/25 and 0.20 = 20/100 = 1/5
[tex]\frac{4}{25}x + \frac{1}{5}y = 11[/tex] --------(1)
[tex]x + y = 60 \\[/tex] --------(2)
multiply both side by 5 in equation (1) we get
[tex]\frac{4}{5}x + y =55[/tex] --------(3)
Subtract equation 3 from 2
[tex]x - \frac{4}{5}x + y - y = 60 - 55\\\frac{x}{5} = 5\\ x = 25[/tex]
put the value of x in equation 2
25 + y = 60
y = 35
I need help with this! If you answer please explain!
Answer:
Below
Step-by-step explanation:
Diameter = 20 inches radius = 10 inches
Area = pi r^2 = 3.14 * 10^2 = 314 in^2
Watch help video
A boat is heading towards a lighthouse, where Feng is watching from a vertical
distance of 127 feet above the water. Feng measures an angle of depression to the
boat at point A to be 5°. At some later time, Feng takes another measurement and
finds the angle of depression to the boat (now at point B) to be 57°. Find the distance
from point A to point B. Round your answer to the nearest tenth of a foot if
necessary.
Answer:
1369.1
Step-by-step explanation:
Answer:
1369.1 feet
Step-by-step explanation:
Four coins are tossed. a. Give an example of a simple event. b. Give an example of a joint event. c. What is the complement of getting a tail on the fourth coin? d. What does the sample space consist of? a. Give an example of a simple event. Which of the following is a simple event? A. Getting a tail on all coins B. Getting a tail on no coins C. Getting a head on the third coin and a head on the fourth coin D. Getting a tail on the fourth coin b. Give an example of a joint event. Which of the following is a joint event? A. Not getting a head on the second coin B. Getting a head or a tail on the first coin C. Getting a head on the first coin and a tail on the third coin D. Not getting a tail on the fourth coin c. What is the complement of getting a tail on the fourth coin? Which of the following is the complement of getting a tail on the fourth coin? A. Getting a head on the fourth coin B. Getting a tail on the fourth coin and a head on all others c. Getting a head on all coins
d. Getting a head on the fourth coin and a tail on all others d. What does the sample space consist of? Which of the following identifies the sample space for the four flipped coins? A. Not getting a head on all coins B. Getting a tail on any of the coins c. Getting a tail on one coin and a head on all others
D. Getting a head or a tail on any of the four coins
The sample space includes the following outcomes: HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT.
a. A simple event is an event that has only one possible outcome. An example of a simple event is getting a head on the third coin. This is represented by option C: "Getting a head on the third coin and a head on the fourth coin."
b. A joint event is an event that involves two or more simple events happening at the same time. An example of a joint event is getting a head on the first coin and a tail on the third coin. This is represented by option C: "Getting a head on the first coin and a tail on the third coin."
c. The complement of getting a tail on the fourth coin is getting a head on the fourth coin. This is represented by option A: "Getting a head on the fourth coin."
d. The sample space consists of all possible outcomes of the four flipped coins. This is represented by option D: "Getting a head or a tail on any of the four coins." The sample space includes the following outcomes: HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT.
Learn more about event
brainly.com/question/14996746
#SPJ11
so that \( i A_{1} \) is emalier than \( \left.A_{2} A_{2}\right) \) 7. [-81.19 Points] 5PRECALC7 6.5.023. so that \( A_{1} \) is smaller than \( A A_{2} \)-) \[ \begin{array}{l} b=27, c=33, \quad A=2
The answer to the question is that \( A_{1} \) is smaller than \( A_{2} \)
To begin, it is important to note that the terms "emalier" and "5PRECALC7" are not relevant to the question and can be ignored. Additionally, there are several typos and extraneous information that can also be ignored. The main focus of the question is to determine the relationship between \( A_{1} \) and \( A_{2} \).
From the information provided, it is clear that \( A_{1} \) is smaller than \( A_{2} \). This is because the value of \( A_{1} \) is given as 2, while the values of \( b \) and \( c \) are 27 and 33, respectively. Since \( A_{2} \) is the sum of \( b \) and \( c \), it is clear that \( A_{2} \) is larger than \( A_{1} \).
Therefore, the answer to the question is that \( A_{1} \) is smaller than \( A_{2} \).
Learn more about 5PRECALC7
brainly.com/question/15069625
#SPJ11
1. Calculate the compound interest on N2,000 for 2years at the rate of 10% per annum
The compound interest on N2,000 for 2 years at the rate of 10% per annum is N441.00.
Compound interest is the interest earned not only on the principal amount but also on the accumulated interest. To calculate the compound interest, we use the formula:
A = P[tex](1 + r/n)^{(nt)[/tex]where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
In this case, P = N2,000, r = 0.1 (10%), n = 1 (compounded annually), and t = 2 years.
So, A = 2000[tex](1 + 0.1/1)^{(1*2)[/tex] = N2,441.00
Therefore, the compound interest is N2,441.00 - N2,000.00 = N441.00.
Learn more about Compound Interest:
https://brainly.com/question/28020457
#SPJ4
How do you do c) really need help!!
Use the Integral Test to show that the series ∑_(k=1)^[infinity]▒(k^2/e^k ) converges. Hint: use integration by parts
As per the concept of integral, the series ∑ne⁻ⁿ converges.
Let's consider the series ∑ne⁻ⁿ. Since each term of the series is positive, the first condition of the Integral Test is satisfied. To check the second condition, we need to determine whether the function f(x) = xe⁻ˣ is decreasing for x ≥ 1.
To do this, we can take the derivative of f(x) with respect to x:
f'(x) = e⁻ˣ - xe⁻ˣ
Setting f'(x) = 0, we get:
e⁻ˣ - xe⁻ˣ = 0
x = 1
So f(x) has a maximum value at x = 1. Since f'(x) < 0 for x ≥ 1, f(x) is decreasing for x ≥ 1.
Now, we can set up the corresponding integral:
∫₁^∞ xe⁻ˣ dx
To evaluate this integral, we can use integration by parts:
u = x, dv = e⁻ˣ dx
du = dx, v = -e⁻ˣ
∫₁^∞ xe⁻ˣ dx = -xe⁻ˣ │₁^∞ + ∫₁^∞ e⁻ˣ dx
= 0 + e⁻ˣ │₁^∞
= 1
Since the integral converges, the series ∑ne⁻ⁿ also converges by the Integral Test.
To know more about integral here
https://brainly.com/question/18125359
#SPJ4
Complete Question:
How do you use the Integral Test to determine convergence or divergence of the series: ∑ne⁻ⁿ from n=1 to infinity?
chess vs cribbage 2x4y=60
30 peοple are playing chess and 30 peοple are playing cribbage.
What is the system οf linear equatiοns?A system οf linear equatiοns is a set οf twο οr mοre linear equatiοns with multiple variables that are sοlved simultaneοusly. The gοal οf sοlving a system οf linear equatiοns is tο find the values οf the variables that satisfy all the equatiοns in the system.
A linear equatiοn is an equatiοn in which the variables appear οnly tο the first pοwer, and the cοefficients οf the variables are cοnstants. Fοr example, the equatiοn y = 3x + 2 is a linear equatiοn, where y and x are the variables, and 3 and 2 are the cοefficients.
A system οf linear equatiοns can have οne unique sοlutiοn, nο sοlutiοn, οr infinitely many sοlutiοns. The number οf sοlutiοns depends οn the number οf equatiοns and variables in the system, and the relatiοnships between them. There are variοus methοds tο sοlve a system οf linear equatiοns, such as substitutiοn, eliminatiοn, and matrix methοds.
Let's assume that there are x peοple playing chess and y peοple playing cribbage. Since everyοne is playing either chess οr cribbage, we knοw that:
x + y = 60
We alsο knοw that chess is a twο-player game, while cribbage is a fοur-player game. Therefοre, the tοtal number οf players in the games must be a multiple οf 2 and 4. This means that:
2x + 4y = 60
We can simplify this equatiοn by dividing bοth sides by 2
x + 2y = 30
Nοw we have twο equatiοns:
x + y = 60
x + 2y = 30
We can sοlve fοr x by subtracting the secοnd equatiοn frοm the first equatiοn:
x + y - (x + 2y) = 60 - 30
-y = -30
y = 30
Substituting this value οf y intο the first equatiοn, we get:
x + 30 = 60
x = 30
Therefοre, 30 peοple are playing chess and 30 peοple are playing cribbage.
To know more about the system of linear equations visit:
brainly.com/question/20379472
#SPJ1
Complete question:
60 people attend a game night. Everyone chooses to play chess, a two-player game, or cribbage, a four-player game. All 60 people are playing either chess or cribbage. There are 3 more games of cribbage being played than games of chess being played. How many of each game are being played?
8 chess, 15 cribbage
30 chess, 30 cribbage
8 chess, 11 cribbage
30 chess, 15 cribbage
Find the value of X Round your answer to the nearest tenth.
(A right-angled triangle with two adjacent sides to the right angle labeled 4.6 feet and 3.5 feet. The length of hypotenuse is labeled 5.8 feet. An altitude drawn from the right angle vertex on hypotenuse is labeled x.)
Answer: X = 14
Step-by-step explanation: (:
Determine the intervals where the following function is increasing or decreasing. g(x) = 3-1/zx, x<-2 . 4+3/2x, x>-2 Increasing on: (-2,infinity) Decreasing on: (-4,-2)
To determine the intervals where a function is increasing or decreasing, we need to take the derivative of the function and find the critical points. The critical points are where the derivative is equal to zero or undefined.
First, let's take the derivative of the function:
g'(x) = -1/(zx)^2, x<-2 . 3/2, x>-2
Now, let's find the critical points:
-1/(zx)^2 = 0 -> There are no values of x that will make this equation true, so there are no critical points for x<-2.
3/2 = 0 -> There are no values of x that will make this equation true, so there are no critical points for x>-2.
Since there are no critical points, the function is either always increasing or always decreasing. To determine which one it is, we can pick a value of x in each interval and plug it into the derivative:
For x<-2, let's pick x=-3:
g'(-3) = -1/(-3z)^2 = 1/(9z^2) > 0
Since the derivative is positive, the function is increasing on the interval (-infinity, -2).
For x>-2, let's pick x=0:
g'(0) = 3/2 > 0
Since the derivative is positive, the function is also increasing on the interval (-2, infinity).
Therefore, the function is increasing on the entire domain of the function, which is (-infinity, infinity).
Answer: Increasing on: (-infinity, infinity) Decreasing on: None
To know more about critical points refer here:
https://brainly.com/question/29144288
#SPJ11
THURSDAY: Use Synthetic Division to divide the polynomial: (x^(4)-5x^(3)+4x-17)-:(x-5)
Synthetic Division of the polynomials (x^(4)-5x^(3)+4x-17) and (x-5) gives answer "x^(3)+4+3/(x-5)."
To divide the given polynomial using synthetic division, we will use the following steps:
Step 1: Write the coefficients of the polynomial in descending order. In this case, the coefficients are 1, -5, 0, 4, -17.
Step 2: Write the value of x from the divisor (x-5) in the left column. In this case, the value of x is 5.
Step 3: Bring down the first coefficient to the bottom row.
Step 4: Multiply the value of x by the number in the bottom row and write the result in the next column.
Step 5: Add the numbers in the second column and write the result in the bottom row.
Step 6: Repeat steps 4 and 5 until you have completed all the columns.
Step 7: The numbers in the bottom row are the coefficients of the quotient, and the last number is the remainder.
The synthetic division will look like this:
5 | 1 -5 0 4 -17
| 5 0 0 20
----------------
1 0 0 4 3
So, the quotient is x^(3)+0x^(2)+0x+4, or simply x^(3)+4, and the remainder is 3.
Therefore, the answer is (x^(4)-5x^(3)+4x-17)÷(x-5) = x^(3)+4+3/(x-5).
You can learn more about Synthetic Division at
https://brainly.com/question/29638766
#SPJ11
Classify each angle pair, then find the value of X
Please explain your work!!
Answer: The angles are classified as interior angles, where x=9
Step-by-step explanation:
The angle measure of a straight line is 180°, meaning that 7x-10 and 12x+19 must add up to 180.
It is clear from the visual that the former is an acute angle, and the latter is an obtuse angle. This means that when solving each, 7x-10 must be less than 90, and 12x+19 must be greater than 90, but less than 180.
If you set up the equation to solve for x; (7x-10) + (12x+19) = 180, you must combine like terms.
19x+9=180 is the new equation. Since x needs to be isolated, subtract 9 from each side, to get 19x=171. Dividing each side by 19 results in x=9.
the quotient and remainder using long division for: (2x^(3)-6x^(2)+7x-11)/(2x^(2)+5)
The quotient and remainder using long division for [tex](2x^(3)-6x^(2)+7x-11)/(2x^(2)+5)[/tex] are x-11/2 and 55/2x-11, respectively.
The quotient and remainder using long division for the given expression can be found by following these steps:
Step 1: Set up the long division as follows:
[tex]```2x^(2)+5 | 2x^(3)-6x^(2)+7x-11 |---------------------- |```[/tex]
Step 2: Divide the first term of the dividend (2x^(3)) by the first term of the divisor (2x^(2)) to get the first term of the quotient (x):
[tex]```2x^(2)+5 | 2x^(3)-6x^(2)+7x-11 |---------------------- | x```[/tex]
Step 3: Multiply the first term of the quotient (x) by the divisor (2x^(2)+5) and subtract the result from the dividend:
[tex]```2x^(2)+5 | 2x^(3)-6x^(2)+7x-11 |-(2x^(3)+5x) |---------------------- | -11x^(2)+7x-11```[/tex]
Step 4: Repeat steps 2 and 3 until the degree of the remainder is less than the degree of the divisor:
[tex]```2x^(2)+5 | 2x^(3)-6x^(2)+7x-11 |-(2x^(3)+5x) |---------------------- | x -11x^(2)+7x-11 | -(-11x^(2)-55/2x) |---------------------- | 55/2x-11```[/tex]
Step 5: The final result is the quotient and remainder:
[tex]```Quotient = x-11/2Remainder = 55/2x-11```[/tex]
To know more about long division refer here:
https://brainly.com/question/28824872
#SPJ11
87 oz= how many lb and oz
Step-by-step explanation:
How many Oz make 1 Pound
Answer is 16
Divide 87 by 16
Answer is 5Lb 7oz
6. Consider the expansion of x^2 (3x^2 + k/x)^8. The constant term is 16128. Find k. [7 marks]
The value of k is ∛√199.
Consider the expansion of x^2(3x^2 + k/x)^8. The constant term is 16128. We need to find the value of k.
The expansion of (3x^2 + k/x)^8 will have terms of the form (3x^2)^a(k/x)^b, where a + b = 8. The constant term will be the term where the powers of x cancel out, so we need to find a and b such that 2a - b = 0.
Solving for a and b, we get a = 4 and b = 8. So the constant term will be (3x^2)^4(k/x)^8 = 81x^8(k^8/x^8) = 81k^8.
Setting this equal to 16128 and solving for k, we get:
81k^8 = 16128
k^8 = 16128/81
k^8 = 199
k = ∛√199
Therefore, the value of k is ∛√199.
k = ∛√199.
Learn about Expansion
brainly.com/question/29774506
#SPJ11
"What are the corner points?
What is the solution to the linear programming problem?"
Minimize: C = 3x – 3y Subject to: 3x – y >= 2 x + y <= 5 x >= 0, y >= 0
The minimum value of the objective function is -15, which occurs at the corner point (0, 5).
The corner points of a linear programming problem are the points where the constraints intersect. These points can be found by solving the system of inequalities for each pair of constraints.
For this problem, we can find the corner points by solving the system of inequalities for each pair of constraints:
3x – y >= 2 and x + y <= 5:
- Add y to both sides of the first inequality: 3x >= 2 + y
- Subtract 2 from both sides of the first inequality: 3x - 2 >= y
- Substitute 3x - 2 for y in the second inequality: x + (3x - 2) <= 5
- Simplify: 4x <= 7
- Divide by 4: x <= 7/4
- Substitute 7/4 for x in the first inequality: 3(7/4) - 2 >= y
- Simplify: 5/4 >= y
The first corner point is (7/4, 5/4).
3x – y >= 2 and x >= 0:
- Set x = 0 and solve for y: 3(0) - y >= 2, y <= -2
- Set y = 0 and solve for x: 3x - 0 >= 2, x >= 2/3
The second corner point is (2/3, 0).
x + y <= 5 and x >= 0:
- Set x = 0 and solve for y: 0 + y <= 5, y <= 5
- Set y = 0 and solve for x: x + 0 <= 5, x <= 5
The third corner point is (0, 5).
x + y <= 5 and y >= 0:
- Set x = 0 and solve for y: 0 + y <= 5, y <= 5
- Set y = 0 and solve for x: x + 0 <= 5, x <= 5
The fourth corner point is (5, 0).
Now we can plug each corner point into the objective function to find the minimum value:
C = 3x – 3y
C = 3(7/4) - 3(5/4) = 3
C = 3(2/3) - 3(0) = 2
C = 3(0) - 3(5) = -15
C = 3(5) - 3(0) = 15
Therefore, the solution to the linear programming problem is (0, 5).
For more about linear programming:
https://brainly.com/question/30763902
#SPJ11
what is 1 and 1/7 x 3/5
1 and 1/7 multiplied by 3/5 is equal to 24/35 or 0.6857 (rounded to four decimal places).
What do you mean by decimal?
In mathematics, a decimal is a number that represents a fraction or a part of a whole using a base-ten positional numeral system.
To multiply 1 and 1/7 by 3/5, we can first convert the mixed number to an improper fraction.
1 and 1/7 can be written as:
(7/7 * 1) + 1/7 = 7/7 + 1/7 = 8/7
So, we have:
1 and 1/7 = 8/7
Now, we can multiply 8/7 by 3/5 as follows:
(8/7) * (3/5) = (8 * 3) / (7 * 5) = 24/35
Therefore, 1 and 1/7 multiplied by 3/5 is equal to 24/35 or 0.6857 (rounded to four decimal places).
To learn more about mixed number from the given link :
https://brainly.com/question/24137171
#SPJ1
your family is driving on the highway. The number of miles y you travel in x minutes is approximated by the equation y=1.1x approximately how far do you travel in 80 minutes?
Answer:88 miles
Step-by-step explanation:
1.1x80+88
Ffx) iš a third degree polynomial function, how many distinct complex roots are possible?
O 0 or 2
O 0. 1. 2 or 3
O 1 or 2
O 1. 2. Or 3
The possible number of distinct complex roots for a third-degree polynomial function are 0, 1, 2, or 3, making option (B) the correct answer.
A polynomial function of degree n can have at most n distinct roots. For a third-degree polynomial, n=3, so it can have at most 3 roots.
Complex roots of a polynomial come in conjugate pairs. So if a third-degree polynomial has one real root, then the other two roots must be a conjugate pair of complex roots. If the polynomial has two real roots, then the third root must be a complex root that is not real.
Therefore, the possible number of distinct complex roots for a third-degree polynomial function is 0, 1, 2, or 3, making option (B) the correct answer.
Learn more about Polynomials:
https://brainly.com/question/4142886
#SPJ4
Ronen has 1,003 marbles. He wants to give the same number of marbles to each of his 8
teammates with as few as possible left over. How many marbles did each teammate receive?
How many marbles were left?
Enter the correct value to complete each sentence.
Blank marbles were shared with each teammate.
Blank marbles were left.
Answer:
3 Marbles were left.
Step-by-step explanation:
To find the number of marbles Ronen gave to each teammate, we can divide the total number of marbles by the number of teammates:
1003 ÷ 8 = 125 with a remainder of 3
Therefore, each teammate received 125 marbles, and there were 3 marbles left over.
So, 125 marbles were shared with each teammate, and 3 marbles were left.
Which is the correct factorization for the Difference of Squares or a^(2)-b^(2) ?
The correct factorization for the Difference of Squares or a²-b² is (a+b)(a-b). This is because when you multiply (a+b)(a-b), you get a²- ab + ab - b², which simplifies to a²-b².
Here is a step-by-step explanation of how to factor the Difference between Squares:
Step 1: Identify the two terms that are being squared. In this case, a and b are the terms being squared.
Step 2: Write the two terms with a plus sign in between them in one set of parentheses and with a minus sign in between them in another set of parentheses. This will give you (a+b)(a-b).
Step 3: Multiply the two sets of parentheses together to check your answer. You should get a²-b².
So, the correct factorization for the Difference of Squares or a²-b² is (a+b)(a-b).
You can learn more about the difference of squares at: brainly.com/question/11801811
#SPJ11
From a point
A
, level with the base of the town hall, the angle of elevation of the topmost point of the building is
35 ∘
. From point B, also at ground level but 30 metres closer to the hall, the same point has an angle of elevation of
60 ∘
. Find how high the topmost point is above ground level. (Give your answer correct to the nearest metre.) 4 A playground roundabout of radius
1.8 m
makes one revolution every five seconds. Find, to the nearest centimetre, the distance travelled by a point on the roundabout in one second if the point is a
1.8 m
from the centre of rotation b
1 m
from the centre of rotation. 5 From a lighthouse, ship
A
is
17.2 km
away on a bearing
S60 ∘
E
and ship
B
is
14.1 km
away on a bearing
N80 ∘
W
. How far, and on what bearing, is B from A? 6 The diagram on the right shows the sketch made by a surveyor after taking measurements for a block of land
ABCD
. Find the area and the perimeter of the block.
Ship B is 22.8 km away from ship A on a bearing of N50°W.
The topmost point of the town hall is 28 metres above ground level.
The distance travelled by a point on the roundabout in one second is 113 cm for point A and 63 cm for point B.
Ship B is 22.8 km away from ship A on a bearing of N50°W.
Explanation:
1) For the first question, we can use trigonometry to find the height of the town hall. Let h be the height of the topmost point above ground level, and d be the distance between point A and the base of the town hall. Then we have:
tan(35°) = h/d and tan(60°) = h/(d-30)
Solving for h, we get:
h = d*tan(35°) and h = (d-30)*tan(60°)
Equating the two expressions for h, we get:
d*tan(35°) = (d-30)*tan(60°)
d = 30*tan(60°)/(tan(60°)-tan(35°)) ≈ 48.5 metres
Substituting back into the first equation, we get:
h = 48.5*tan(35°) ≈ 28 metres
Therefore, the topmost point of the town hall is 28 metres above ground level.
2) For the second question, we can use the formula for the circumference of a circle to find the distance travelled by a point on the roundabout in one second. The circumference of a circle is given by C = 2πr, where r is the radius of the circle. The distance travelled by a point in one second is then given by C/5, since the roundabout makes one revolution every five seconds. For point A, which is 1.8 metres from the centre of rotation, we have:
C = 2π*1.8 = 11.31 metres
Distance travelled in one second = 11.31/5 = 2.26 metres ≈ 226 cm ≈ 113 cm to the nearest centimetre
For point B, which is 1 metre from the centre of rotation, we have:
C = 2π*1 = 6.28 metres
Distance travelled in one second = 6.28/5 = 1.26 metres ≈ 126 cm ≈ 63 cm to the nearest centimetre
3) For the third question, we can use the law of cosines to find the distance between ship A and ship B. The law of cosines states that c^2 = a^2 + b^2 - 2ab*cos(C), where a, b, and c are the lengths of the sides of a triangle, and C is the angle opposite side c. Let x be the distance between ship A and ship B, and let θ be the angle between the two ships. Then we have:
x^2 = 17.2^2 + 14.1^2 - 2*17.2*14.1*cos(θ)
To find the angle θ, we can use the fact that the sum of the angles in a triangle is 180°. We have:
θ = 180° - 60° - 80° = 40°
Substituting back into the equation, we get:
x^2 = 17.2^2 + 14.1^2 - 2*17.2*14.1*cos(40°) ≈ 520.3
x ≈ 22.8 km
To find the bearing of ship B from ship A, we can use the law of sines. The law of sines states that a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the angles opposite those sides. Let α be the bearing of ship B from ship A. Then we have:
14.1/sin(α) = 22.8/sin(40°)
Solving for α, we get:
α = sin^-1(14.1*sin(40°)/22.8) ≈ 30°
Since ship B is to the west of ship A, the bearing of ship B from ship A is N50°W.
Therefore, ship B is 22.8 km away from ship A on a bearing of N50°W.
Learn more about Area and the perimeter
brainly.com/question/11957651
#SPJ11
Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:
O 9
O 11
O 13
O 15
The answer of third integer is 15.
To solve this problem, we can use algebra. Let's call the first of the three consecutive odd integers "x." The next two consecutive odd integers would then be "x + 2" and "x + 4."
The problem tells us that three times the first integer is 3 more than twice the third, so we can write an equation:
3x = 2(x + 4) + 3
Simplifying the equation, we get:
3x = 2x + 8 + 3
x = 11
So the first integer is 11, and the third integer is 11 + 4 = 15.
Therefore, the correct answer is O 15.
To know more about consecutive odd integers refer here:
https://brainly.com/question/4249096#
#SPJ11
A self-tanning lotion advertises that a 4-oz bottle will provide seven applications. The Community Collage theater group needs fake tans for a play they are doing. If the play has cast of 15 how many ounces of self-tanning lotion should the cast purchase
Therefore, to have enough for one application per person, the ensemble of 15 needs to buy about 8.55 ounces of self-tanning lotion.
what is unitary method ?To answer mathematical issues involving proportional relationships between quantities, one uses the unitary method. This approach involves calculating the value of a single unit of a quantity and using that value to calculate the value of any number of additional units. For instance, if we know that five items cost $20 each, we can calculate the price of any other quantity of items by first determining the price of one item, then increasing that figure by the desired quantity of items.
given
The quantity of lotion needed for each application, assuming a 4-oz container of self-tanning lotion yields seven applications, is:
4 oz / 7 = 0.57 oz (rounded to two decimal places) (rounded to two decimal places)
The quantity needed for each application must be multiplied by the number of applications needed by each individual, which equals 1, to determine how many ounces of self-tanning lotion the ensemble of 15 needs to buy:
15. People at 0.57 ounce each equals 8.55 oz.
Therefore, to have enough for one application per person, the ensemble of 15 needs to buy about 8.55 ounces of self-tanning lotion.
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1
Which graph represents the function f(x)=√x+3-1?
The required, graph of the function f(x) = √[x+3]-1 is a curve that starts at (-3,-1) and extends to the right, increasing in value but at a decreasing rate due to the square root function.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
The graph of the function f(x) = √[x+3]-1 is a curve that starts at the point (-3,-1) and extends to the right indefinitely. The square root function √x has a domain of x ≥ 0, so in this case, the domain of the function is x ≥ -3.
The graph is always above the x-axis, as the square root function can only output non-negative values. The graph also approaches but never touches the horizontal line y = 0 as x increases without bound, since the -1 term in the function only shifts the graph downward by one unit.
Learn more about function here:
brainly.com/question/21145944
#SPJ9
I need help with this question can anyone tell me ?
The required value of x for the triangle is 9 units.
What is Thales theorem?The theorem you are referring to is known as the "Parallel Line Theorem" or "Thales' Theorem".
If a line is drawn parallel to one side of a triangle, then the other two sides of the triangle are divided proportionally.
Consider a triangle ABC with a line parallel to one of its sides, say side AB. Let the parallel line intersect sides AC and BC at points D and E, respectively.
Then,
AB/BD = CB/BE
According to question:In triangle;
[tex]$\frac{4x}{x-1} =\frac{27}{6}[/tex]
24x = 27x - 27
= 3x = 27
= x = 9
Thus, required value of x is 9.
To know more about Thales theorem visit:
brainly.com/question/29626660
#SPJ1
Each door in the hotel is locked with probability 1/3 independently of the others. An arriving guest is placed in Room 0 and can then wander freely (insofar as the locked doors allow). Show that the guest’s chance of escape is about - 9 − √27/4
The probability of escape for the guest is approximately 9 - √27/4.
This can be calculated using the principle of inclusion-exclusion. To calculate the probability of escape, we can calculate the probability of the guest being unable to move from Room 0 to any of the other rooms.
This is the probability of all doors from Room 0 being locked, which is equal to 1/3 x 1/3 = 1/9. Therefore, the probability of escape is 1 - 1/9 = 8/9.
Using the inclusion-exclusion principle, we can calculate the probability of the guest being able to move from Room 0 to any of the other rooms. The probability of the guest being able to move from Room 0 to any of the other rooms is equal to 1 - (1/3 + 1/3 - 1/9) = 9 - √27/4.
You can read more about principle of inclusion-exclusion at https://brainly.com/question/30628920#:
#SPJ11