The coordinates of p so that p partitions segment ab in the part-to-whole ratio of 1 to 5 with a(-9, 3) and b(1, 8) is (-44/6, 23/6).
To find the coordinates of point P, we can use the following formula:
P = ( (5 x Ax + 1 x Bx) / 6 , (5 x Ay + 1 x By) / 6 )
Here, Ax and Ay are the x and y coordinates of point A, and Bx and By are the x and y coordinates of point B. By plugging in the values we have, we get:
P = ( (5 x (-9) + 1 x 1) / 6 , (5 x 3 + 1 x 8) / 6 )
P = ( (-45 + 1) / 6 , (15 + 8) / 6 )
P = ( -44/6 , 23/6 )
So the coordinates of point P are (-44/6, 23/6).
To check if we got the right answer, we can measure the distance between A and P and the distance between P and B, and make sure that the ratio is indeed 1 to 5. We can use the distance formula for this:
Distance between A and P:
√( (-9 - (-44/6))² + (3 - 23/6)² )
= √( (35/6)² + (5/6)² )
= √( 1225/36 + 25/36 )
= √( 1250/36 )
= 5/6 x √(50)
Distance between P and B:
√( (1 - (-44/6))² + (8 - 23/6)² )
= √( (55/6)² + (41/6)² )
= √( 3025/36 + 1681/36 )
= √( 4706/36 )
= 5/6 x √(94)
The ratio of the distance between A and P to the distance between P and B is:
(5/6 x √(50)) / (5/6 x √(94)) = √(50/94)
Simplifying this gives us:
√(50/94) = √(25/47)
The ratio of the distances is indeed 1 to 5, which confirms that our answer for the coordinates of P is correct.
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2 PART QUESTION PLS HELP Harris has a spinner that is divided into three equal sections numbered 1 to 3, and a second spinner that is divided into five equal sections numbered 4 to 8. He spins each spinner and records the sum of the spins. Harris repeats this experiment 500 times.
Question 1
Part A
Which equation can be solved to predict the number of times Harris will spin a sum less than 10?
A) 3/500 = x/15
B) 12/500 = x/15
C) 12/15 = x/500
D) 3/15 = x/500
QUESTION 2
Part B
How many times should Harris expect to spin a sum that is 10
or greater?
_______
Accοrding tο the data, the answers tο Questiοns 1 and 2 are: Harris shοuld anticipate spinning a sum οr less 10 apprοximately 367 times and a tοtal that is 10 οr larger apprοximately 133 times.
What are a fοrmula and an equatiοn?Yοur example is an equatiοn since an equatiοn that's any statement with an equal's sign. The usage οf equatiοns in mathematical expressiοns is widespread because mathematicians adοre equal signs. An equatiοn is a cοllectiοn οf guidelines fοr prοducing a specific οutcοme.
Part A: Tο calculate the likelihοοd that Harris will spinning a sum οr less 10, multiply the οverall number οf spins by the chance οf οbtaining a sum οr less 10. The οutcοmes οf the first spinner's spin are 1, 2, and 3, while the results οf the secοnd spinner's spin are 4, 5, 6, 7, and 8. Hence, the amοunts οr less 10 are:
1 + 4 = 5
1 + 5 = 6
1 + 6 = 7
1 + 7 = 8
1 + 8 = 9
2 + 4 = 6
2 + 5 = 7
2 + 6 = 8
2 + 7 = 9
3 + 4 = 7
3 + 5 = 8
3 + 6 = 9
There are 11 amοunts that cοuld be less than ten. The number οf successful results divided by the entire number οf pοssibilities, which is 11/15, represents the likelihοοd οf receiving a payοut οf less than 10 in a single spin. Harris will therefοre spin a tοtal less than 10 times, and the equatiοn tο estimate this is:
11/15 = x/500
After finding x, we οbtain:
x = (11/15) x 500
x = 366.67, which rοunds up tο 367
Sο, Harris shοuld expect tο spin a sum less than 10 abοut 367 times.
Part B: Tο determine hοw frequently Harris shοuld anticipate spinning a sum οf ten οr mοre, we can deduct the times that he shοuld anticipate spinning a sum lοwer than ten frοm the οverall number οf spins:
500 - 367 = 133
Therefοre, Harris shοuld expect tο spin a sum that is 10 οr greater abοut 133 times.
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A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5 years, and standard deviation of 1.3 years.
If you randomly purchase one item, what is the probability it will last longer than 6 years?
Answer:
Step-by-step explanation:
Let X be the lifespan of an item. We are given that X is normally distributed with a mean of μ = 5 years and a standard deviation of σ = 1.3 years.
We want to find the probability that an item will last longer than 6 years. Let Y be the random variable that represents the lifespan of an item in excess of 6 years, i.e. Y = X - 6. Then we want to find:
P(Y > 0)
Using the properties of normal distribution, we can standardize Y to get a standard normal variable Z:
Z = (Y - μ) / σ = (X - 6 - 5) / 1.3 = (X - 11) / 1.3
So we want to find:
P(Z > (6 - 11) / 1.3) = P(Z > -3.85)
Using a standard normal distribution table or calculator, we can find that the probability of Z being greater than -3.85 is very close to 1 (in fact, it is essentially 1). Therefore, the probability of an item lasting longer than 6 years is essentially the same as the probability of Y being greater than 0, which is 1.
Therefore, the probability that a randomly purchased item will last longer than 6 years is approximately 1.
calculate the following limits?
1=
2=
3=
The values are [tex]\lim_{x \to {\(-2}^{-}[/tex] [tex]f(x) = \frac{1}{h}[/tex]
[tex]\lim_{x \to {\(-2}^{+}[/tex] [tex]f(x) = 3[/tex] and [tex]\lim_{x \to {\(2}[/tex] [tex]f(x) =[/tex] 3
What is limits?The concept of limits is used to describe the behavior of a function as its input approaches a certain value.
[tex]\lim_{x \to {\(-2}^{-}[/tex] [tex]f(x) = \lim_{h \to \o[/tex] [tex]f(-2-h)[/tex] = [tex]\lim_{h \to \o[/tex] [tex]\frac{1}{(-2-h)+2}[/tex]
[tex]\lim_{h \to \o[/tex] [tex]\frac{1}{h}[/tex]
(So, Does not exist)
[tex]\lim_{x \to {\(-2}^{+}[/tex] [tex]f(x)[/tex] = [tex]\lim_{h \to \o[/tex] [tex]f(-2+h)[/tex]
[tex]\lim_{h \to \o[/tex] [tex]3(-2+h)+9[/tex] = 3
(So, Does not exist)
[tex]\lim_{x \to {\(-2}[/tex] [tex]f(x)[/tex] = 3×(-2) +9 = -6+9= 3
(So, Does not exist)
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I will mark you brainiest!
Determine the MOST PRECISE name for the quadrilateral below.
A) rhombus
B) parallelogram
C) square
D) trapezoid
E) kite
The answer is A, rhombus.
begin by finding the area under the curve from to , . this area can be written as the definite integral
The area under the curve y = 1/ (x^2 + 6x -16) from x = t to x = 6 is 1/10( ln(4) - 1/10 ln(t+8))
To find the area under the curve y = 1/ (x^2 + 6x -16) from x = t to x = 6, where t > 2, we need to evaluate the definite integral:
∫[t,6] 1/ (x^2 + 6x -16) dx
To solve this integral, we can use partial fraction decomposition. First, we factor the denominator:
x^2 + 6x -16 = (x+8)(x-2)
Then, we can write:
1/ (x^2 + 6x -16) = A/(x+8) + B/(x-2)
Multiplying both sides by (x+8)(x-2), we get:
1 = A(x-2) + B(x+8)
Setting x = -8, we get:
1 = A(-10)
So, A = -1/10.
Setting x = 2, we get:
1 = B(10)
So, B = 1/10.
Therefore, we can write:
1/ (x^2 + 6x -16) = -1/10(x+8) + 1/10(x-2)
Substituting this into the integral, we get:
∫[t,6] 1/ (x^2 + 6x -16) dx = ∫[t,6] (-1/10(x+8) + 1/10(x-2)) dx
Integrating, we get:
= [-1/10 ln|x+8| + 1/10 ln|x-2|] from t to 6
= 1/10 ln|6-2| - 1/10 ln|t+8|
= 1/10 ln(4) - 1/10 ln(t+8)
Therefore, the area is: 1/10( ln(4) - 1/10 ln(t+8))
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_____The given question is incomplete, the complete question is given below:
begin by finding the area under the curve from to y = 1/ (x^2 + 6x -16) from x = t to x = 6, t>2 this area can be written as the definite integral
the set is a basis of the space of upper-triangular matrices. find the coordinates of with respect to this basis.
The set is a basis of the space of upper-triangular matrices. The coordinates of with respect to this basis is B⁻¹ × p
In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients that includes only the operations of addition, subtraction, multiplication, and power of variables with a positive integer. Polynomials appear in many areas of mathematics and science. For example, they are used to create polynomial equations that encode a wide variety of problems, from elementary word problems to complicated scientific problems; they are used to define polynomial functions that appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial circles and algebraic varieties, which are central concepts in algebra and algebraic geometry.
According to the Question:
Converting the polynomials into vectors by taking their coordinate vectors with respect to the standard basis of P³, {1, x, x²}.
Thus B = [-1, 0, -2], [-2, 3, -4], [-2, 9, -8].
And p is [-6, 21, -24].
⇒ [p(x)]B = B⁻¹ × p
Complete Question:
the set B = [tex]\left[\begin{array}{ccc}1&1&\\0&0\end{array}\right][/tex], [tex]\left[\begin{array}{ccc}0&1\\0&-1\end{array}\right][/tex], [tex]\left[\begin{array}{ccc}0&0&\\0&-2\end{array}\right][/tex] is a basis of the space of upper triangular 2 × 2 matrices . Find the coordinates of
M = [tex]\left[\begin{array}{ccc}-6&-3&\\0&-5&\end{array}\right][/tex] with the respect to this basis.
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lighting, inc. uses direct labor hours as a basis for allocating overhead. next year's estimated total overhead is $180000 and direct labor hours are predicted to be $30000 hours. the average labor cost is $10 per. what is the predetermined overhead rate
Answer:
The predetermined overhead rate is calculated as follows:
Predetermined overhead rate = Estimated total overhead / Estimated total direct labor hours
In this case, the estimated total overhead is $180,000, and the estimated total direct labor hours are 30,000. Therefore:
Predetermined overhead rate = $180,000 / 30,000 hours
Predetermined overhead rate = $6 per direct labor hour
So, the predetermined overhead rate is $6 per direct labor hour.
what is 8 x 1 ????????????
Answer:8
Step-by-step explanation:8x1=8
Angela is riding on a circular Ferris wheel that has a 59-foot radius. After boarding the Ferris wheel, she traveled a distance of 44.3 feet along the arc before the Ferris wheel stopped for the next rider.
a) Make a drawing of the situation and illustrate relevant quantities.
b) The angle that Angela swept out along the arc had a measure of how many radians?
c) The angle that Angela swept out along the arc had a measure of how many degrees?
a) Drawing of the situation is shown in below figure.
b) 0.75 radians
c) 42.97 degrees
Define the term conversion?Conversion is the process of changing a value from one unit or system of measurement to another.
a) The situation of the drawing: The center of the Ferris wheel is labeled "O", and its radius is 59 feet. Angela boards the Ferris wheel at point A and travels a distance of 44.3 feet along the arc to point B. The angle that she sweeps out along the arc is labeled θ.
(Drawing of the situation is shown in below figure)
b) The length of an arc of a circle by the formula: s = rθ
Given, the radius of the circle is 59 feet and the length of the arc that Angela travels is 44.3 feet. So,
θ = s / r
θ = 44.3 / 59
θ ≈ 0.75 radians
Therefore, the angle that Angela sweeps out along the arc has a measure of approximately 0.75 radians.
c) To convert radians to degrees, we use the formula:
θ (in degrees) = θ (in radians) × 180 / π
θ (in degrees) = 0.75 × 180 / π
θ (in degrees) ≈ 42.97 degrees
Therefore, the angle that Angela sweeps out along the arc has a measure of approximately 42.97 degrees.
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a) Drawing of the situation is shown in below figure.
b) 0.75 radians
c) 42.97 degrees
Conversion is the process of changing a value from one unit or system of measurement to another.
a) The situation of the drawing: The center of the Ferris wheel is labeled "O", and its radius is 59 feet. Angela boards the Ferris wheel at point A and travels a distance of 44.3 feet along the arc to point B. The angle that she sweeps out along the arc is labeled θ.
(Drawing of the situation is shown in below figure)
b) The length of an arc of a circle by the formula: s = rθ
Given, the radius of the circle is 59 feet and the length of the arc that Angela travels is 44.3 feet. So,
θ = s / r
θ = 44.3 / 59
θ ≈ 0.75 radians
Therefore, the angle that Angela sweeps out along the arc has a measure of approximately 0.75 radians.
c) To convert radians to degrees, we use the formula:
θ (in degrees) = θ (in radians) × 180 / π
θ (in degrees) = 0.75 × 180 / π
θ (in degrees) ≈ 42.97 degrees
Therefore, the angle that Angela sweeps out along the arc has a measure of approximately 42.97 degrees.
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Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form.
The line is perpendicular to the line defined by y = 4x-8 and passes through the point(8,3).
Answer:
[tex]y=-\frac{1}{4}x+5[/tex]
Step-by-step explanation:
Given the point (8,3) and slope of 4, we can write an equation in point-slope form.
We know that any line perpendicular to another line has a opposite reciprocal. The opposite reciprocal of 4 is [tex]-\frac{1}{4}[/tex].
Now, to write this in point slope form.
Point slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
New equation:
[tex]y-3=-\frac{1}{4}(x-8)[/tex]
Simplify:
[tex]y=-\frac{1}{4}x+5[/tex]
Here is the equation :)
if cot0=3/4 and the terminal point determined by 0 is in quadrant 3, then
If cotθ = 3/4 then cosθ = -3/5 is the right option according to the rules of trigonometry.
What is Trigonometry?Trigonometry is a branch of mathematics that deals with the study of relationships between the sides and angles of triangles. It is primarily concerned with the study of the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent, and their applications in various fields such as engineering, physics, and navigation.
What are angles of triangle?A triangle is a three-sided polygon, and its angles are the angles formed by the intersection of its sides. The sum of the angles in a triangle is always 180 degrees.
First, we know that cot(0) = adjacent / opposite = 3/4.
In quadrant 3, the adjacent side is negative and the opposite side is positive, so we can draw a right triangle in quadrant 3 with adjacent side -3 and opposite side 4.
The hypotenuse can be found using the Pythagorean theorem.
h² = adjacent²+ opposite²
h² = (-3)^2 + 4^2
h²= 9 + 16
h² = 25
h = 5
So we have a right triangle in quadrant 3 with adjacent side -3, opposite side 4, and hypotenuse 5.
Using the definitions of the trigonometric functions, we can find the values of the other functions:
sin(0) = opposite / hypotenuse = 4/5
cos(0) = adjacent / hypotenuse = -3/5
tan(0) = opposite / adjacent = -4/3
csc(0) = hypotenuse / opposite = 5/4
sec(0) = hypotenuse / adjacent = -5/3
cot(0) = adjacent / opposite = 3/4 (given)
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HELP ASAP PLEASE! What is the arc length of an arc with radius 18 inches and central angle 22°? Leave the answer in terms of n. Show your work.
Answer:
arc length = 2.2π inches
Step-by-step explanation:
arc length is calculated as
length = circumference of circle × fraction of circle
= 2πr × [tex]\frac{22}{360}[/tex] ( r is the radius )
= 2π × 18 × [tex]\frac{22}{360}[/tex] ( cancel 18 and 360 by 18 )
= 2π × [tex]\frac{22}{20}[/tex]
= [tex]\frac{44}{20}[/tex] π
= 2.2π inches
Cookies are on sale! Today each cookie costs
$
0.75
$0.75dollar sign, 0, point, 75 less than the normal price. Right now if you buy
7
77 of them it will only cost you
$
2.80
$2.80dollar sign, 2, point, 80!
Write an equation to determine the normal price of each cookie
(c)
(c)left parenthesis, c, right parenthesis.
The correct answer is:
The equation is [tex]7(c-0.75) = 2.80[/tex], and the regular price of a cookie is [tex]c =\$1.15[/tex].
Explanation:
c is the regular price of a cookie. We know that today they are $0.75 less than the normal price; this is given by the expression [tex]c-0.75[/tex].
We also know if we buy 7 of them, the total is $2.80. This means we multiply our expression, [tex]c-0.75[/tex], by 7 and set it equal to $2.80:
[tex]7(c-0.75) = 2.80[/tex]
To solve, first use the distributive property:
[tex]7 \times c-7\times0.75 = 2.80[/tex]
[tex]7c-5.25 = 2.80[/tex]
Add 5.25 to each side:
[tex]7c-5.25+5.25 = 2.80+5.25[/tex]
[tex]7c = 8.05[/tex]
Divide each side by 7:
[tex]7c\div7 = 8.05\div7[/tex]
[tex]c = \$1.15[/tex].
The name of a U.S. state is spelled out with letter tiles. Then the tiles are placed in a bag, and one is picked at random. What state is spelled out if the probability of picking the letter O is 1/2? , 3/8?, 1/3?. (need 3 answers with explanations)
Answer:
Ohio
Colorado
Oregon
Step-by-step explanation:
1/2 of the letters in Ohio are O)
3/8 letters in Colorado are O)
2/6 letters in Oregon are the letter O which Is 1/3
is 2/1 more than 1?
Answer: yes 2/1 is more than one
Step-by-step explanation: 2/1 is equivalent to 2 while 1 is just 1
Answer:
No! 2/1 is less then 1 because when devided, your answer will be -2 which is less then 1.
Which function produces a range of {−11,−5,1,7,13} given a domain of {−2,0,2,4,6}
f(x) = 3x − 5
f(x) = −3x + 4
f(x) = x + 2
f(x) = −5x + 3
we can see, the function f(x) = 3x - 5 produces the desired range for the given domain.
What is Domain?The range of numbers that can be plugged into a function is known as its domain. The x values for a function like f make up this collection.(x). A function's range is the collection of values it can take as input. After we enter an x number, the function outputs this set of values.
According to question:The function that produces the range of {−11,−5,1,7,13} given a domain of {−2,0,2,4,6} is:
f(x) = 3x - 5
To see why, we can plug in each value from the domain into the equation and see if it produces the corresponding value in the range:
f(-2) = 3(-2) - 5 = -11
f(0) = 3(0) - 5 = -5
f(2) = 3(2) - 5 = 1
f(4) = 3(4) - 5 = 7
f(6) = 3(6) - 5 = 13
As we can see, the function f(x) = 3x - 5 produces the desired range for the given domain.
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Ciara has $4,300 in savings. If she deposits the money into a long-term savings account with 2.13% APY and monthly compounding, what will the accrued value of her account be in five years?
find the following answers
Answer:
hope it helps
Step-by-step explanation:
based on the given condition formulate
Can someone please help
Answer:
1.11
2.4
3.5
pls correct me if I'm wrong
Answer:
38. (b) 11
39. (c) 4
40. (c) 5
Step-by-step explanation:
38.)
[tex]\implies \: \sf \sqrt{3xx - 8} = 5 \\ \\ \implies \: \sf 3xx - 8 = {(5)}^{2} \\ \\ \implies \: \sf 3xx - 8 = 25 \\ \\ \implies \: \sf 3xx = 25 + 8 \\ \\ \implies \: \sf 3xx = 33 \\ \\ \implies \: \sf xx = \dfrac{33}{3} \\ \\ \implies \: \sf xx = 11\\ [/tex]
Hence, Required answer is option (b) 11.
39.)
[tex]\implies \: \sf \sqrt{4xx -7 } - 3 = 0 \\ \\ \implies \: \sf \sqrt{4xx - 7} = 3 \\ \\ \implies \: \sf 4xx - 7 = {(3)}^{2} \\ \\ \implies \: \sf 4xx - 7 = 9 \\ \\ \implies \: \sf 4xx = 9 + 7 \\ \\ \implies \: \sf 4xx = 16 \\ \\ \implies \: \sf xx = \dfrac{16}{4} \\ \\ \implies \: \sf xx = 4 \\ [/tex]
Hence, Required answer is option (c) 4.
40.)
[tex]\implies \: \sf \sqrt{6xx + 6} - 6 = 0 \\ \\ \implies \: \sf \sqrt{6xx + 6} = 6 \\ \\ \implies \: \sf 6xx + 6 = {(6)}^{2} \\ \\ \implies \: \sf 6xx + 6 = 36 \\ \\ \implies \: \sf 6xx = 36 - 6 \\ \\ \implies \: \sf 6xx = 30 \\ \\ \implies \: \sf xx = \dfrac{30}{6} \\ \\ \implies \: \sf xx = 5 \\ [/tex]
Hence, Required answer is option (c) 5.
Xochitl spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7425 feet. Xochitl initially measures an angle of elevation of 19 degrees to the plane at point A.
At some later time, she measures an angle of elevation of 37 degrees to the plane at point B. Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary.
The plane travels a distance of 11710 feet from point A to point B.
Why are trig ratios important?
As specified by the definition of a right-angled triangle's side ratio, trigonometric ratios are the values of all trigonometric functions. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.
The figure representing the situation is given below.
From triangle AOC,
tan 19° = AC / OC
tan 19° = 7425 / OC
OC = 7425 / tan 19°
OC = 21563.77 feet
Similarly for triangle BOD,
tan 37° = BD / OD
tan 37° = 7425 / OD
OD = 7425 / tan 37°
= 9853.31 feet
AB = CD
= OC - OD
= 21563.77 feet - 9853.31 feet
= 11,710.46 feet
≈ 11710 feet
Hence the distance plane travelled from point A to point B is 11710 feet.
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pls help !! i will mark brainilest
Answer:
m = 2/3
Step-by-step explanation:
Answer:
[tex] \frac{2}{3} [/tex]
Step-by-step explanation:
slope is
[tex] m = \frac{rise}{run} = \frac{y 2 - y1}{x2 - x1} [/tex]
(0,0) & (3,2)
[tex] m = \frac{2 - 0}{3 - 0} = \frac{2}{3} [/tex]
A boat is heading towards a lighthouse, whose beacon-light is 139 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 5 degrees.
What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary.
The bοat's hοrizοntal distance frοm the lighthοuse (and the shοre) is apprοximately 1592.53 feet.
What is trigοnοmetryTrigοnοmetry is οne οf the mοst impοrtant branches in mathematics that finds huge applicatiοn in diverse fields. The branch called “Trigοnοmetry” basically deals with the study οf the relatiοnship between the sides and angles οf the right-angle triangle.
Hence, it helps tο find the missing οr unknοwn angles οr sides οf a right triangle using the trigοnοmetric fοrmulas, functiοns οr trigοnοmetric identities. In trigοnοmetry, the angles can be either measured in degrees οr radians. Sοme οf the mοst cοmmοnly used trigοnοmetric angles fοr calculatiοns are 0°, 30°, 45°, 60° and 90°.
We can use trigοnοmetry tο sοlve fοr the hοrizοntal distance. Let x be the hοrizοntal distance frοm the bοat tο the lighthοuse.
Then, tan(5°) = οppοsite/adjacent = 139/x
Sοlving fοr x, we get:
x = 139/tan(5°) ≈ 1592.53 feet
Therefοre, the bοat's hοrizοntal distance frοm the lighthοuse (and the shοre) is apprοximately 1592.53 feet.
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What is the answer? Need help!!!
there are 24total customers seated at 4 tables in a restaurant each table is the same size and has the same number of customers tell whether each statement is truth or false
Find the area of a triangle with base 1 2/3 inches and height 5 inches?
Answer:
The area of the triangle is 9.8 inches.
HERE IS THE SEQUENCE OF NUMBERS 3,6,11,18,27...
FIND THE NTH TERM OF THE SEQUENCE
3, 6, 11, 18, 27, 38, 51 , Next term 51 in the sequence is nth term .
What does math sequence mean?
An arrangement of numbers in a specific order is referred to as a sequence. The sum of the components of a sequence, on the other hand, is what is referred to as a series.
SEQUENCE 3,6,11,18,27...
the series follows the odd counting.
for example:
we have odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, etc.
now
3 + 3 = 6
6 + 5 = 11
we can see adding odd numbers in a series results in the solution of the proceeding number of series.
similarly,
11 + 7 = 18
18 + 9 = 27
27 + 11 = 38
now adding 13 to 38 according to the series will result in the next number.
38 + 13 = 51
hence, 51 is the next number in the series.
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Use the given acceleration function to find the velocity vector v(t), and position vector r(t). Then find the position at time t = 4.
a(t) = eti − 6k
v(0) = 2i + 9j + k, r(0) = 0
The velocity vector and position vector and position vector at t=4 is r(4) = (e₄+2)i+36j - 44k.
a(t) = eti - 6k
Since we know that v(t) = ∫ a(t) dt
= ∫ (eti - 6k) dt
= ∫6ti-6tk+c
where c is the arbitrary vector valued constant
since it is given that
v(0) = 2i + 9j + k
therefore from above
v(0) = e * 0i - 6(0) * k + c
2i + 9j + k =i+c
C= i +9j+k
therefore,
v(t) = eti - 6tk + i + 9j + k
= (et + 1) * i + 9j + (- 6t + 1) * k
Since we know that velocity vector can be found by integration of acceleration vector.
Since, v(t) = (et + 1) * i + 9j + (- 6t + 1) * k
and we know that
R(t) = ∫ v(t)dt
= ∫ of [(a + 1)i + 9j+(-6t + 1)k]dt =(a+t)i+9tj+(-3ta+t)k+C
where C is an arbitrary vector constant.
Now,
Since it given that r(0)=0 therefore
r(0) =(e0+1)+9(0)j)+(-3(0)2+0)x+C
0=2i+ C
C= -2i
therefore
r(t)= (et+t)i+9tj+(-3t+t)k-2i
r(t)=(a+t-2)1+9tj+(-3t+t)k
Since we know that position vector can be found by integration of velocity vector
r(4) = (e4+4-2)i+9(4)j + (-3(4)+4)k
r(4) = (e4+2)1+36j-44k
Now we have found the velocity vector and position vector and position vector at t=4 which are as follows:
v(t) =(et+1)i+9j+(-6t+1)k
r(t) =(et+t-2)i+9tj+(-3t2+t)k
r(4) = (e₄+2)i+36j - 44k
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2. Suppose a coin is dropped from the top of the Empire State building in New York, which is 1,454 feet tall. The position function for free-falling objects is: s(t) = −16t^2 + v0t + s0 , where v0 is the initial velocity and s0 is the initial position.
A. Determine the position and velocity functions for the coin.
B. Determine the average velocity of the coin on the interval [1, 3].
C. Find the instantaneous velocities when t =1 and t = 3.
D. At what time is the instantaneous velocity of the coin equal to the average velocity of the coin found in part B?
E. What is the name of the theorem that says there must be at least one solution to
part D?
F. Find the velocity of the coin just before it hits the ground.
find the velocity function from the derivative of s
v=s'=-32t+vo
set that equal to 64, solve for time t.
In your average velocity, you should have had a negative distance, which would have made a negative velocity (meaning downward). see the original equation for the negative sign.
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32 Select the correct answer from each drop-down menu. Let c(g) be the total cost, including shoe rental, for bowling g games at Pin Town Lanes. c (g) 5g + 3 So, c(6) = __(14,30,8,33)__ This means that__(6games,total cost of 6,6 per game)__ the __(number of games is 14, total cost is 30, total cost is 33,games are 8 each__
correct answer is
c(6) = 33This means that the total cost of 6 games (including shoe rental) is $33.Explain equationA mathematical statement that demonstrates the equivalence of two expressions is known as an equation. It has two sides that are divided by an equal symbol. Each side of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and logarithms.
c(6) = 5(6) + 3 = 30 + 3 = 33
This means that the total cost of 6 games (including shoe rental) at Pin Town Lanes is $33.
Therefore, the correct answer is:
c(6) = 33This means that the total cost of 6 games (including shoe rental) is $33To know more about logarithms, visit:
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determine if the transformation is one to one and/or onto. justify your answers. give an explanation for each of these properties.
To determine whether a transformation is one-to-one or onto, one must analyze its behavior and properties, such as passing the horizontal line test for one-to-one or checking if the range equals the codomain for onto.
In mathematical terms, a transformation refers to a function that maps elements from one set, called the domain, to another set, called the range. A transformation is said to be one-to-one if no two distinct elements in the domain are mapped to the same element in the range. This means that each element in the range is associated with a unique element in the domain.
On the other hand, a transformation is onto if every element in the range is mapped to by at least one element in the domain. In other words, for each element in the range, there exists at least one element in the domain that maps to it.
To determine whether a transformation is one-to-one or onto, one can analyze its properties and behavior. For example, a transformation is one-to-one if and only if it passes the horizontal line test. This means that no two points in the domain map to the same point on a horizontal line. To determine if a transformation is onto, one can check if the range of the transformation equals the codomain.
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The given question is incomplete, the complete question is:
How to determine the transformation is one to one and/or onto?