Graph the six terms of a finite series where a1 = −3 and r = 1.5.
Answers
For the given series:
[tex]a_{1}=-3 \\ r=1.5 [/tex]
Each term of the geometric series is obtained by multiplying the previous term by common ratio.
So the next terms will be:
-4.5, -6.75, -10.125, -15.1875, -22.78125
The general formula for the G.P would be:
[tex] a_{n}=-3(1.5)^{n-1} [/tex]
On plotting the series, the result will be like this:
Answer:
the answer is C
Step-by-step explanation:
Related Questions
YOOO!!!!NEEED IMMEDIATE HELP!!!!!!!!!!!!
Answers
Transformations:
1) Reflect the graph across the x-axis: f(x) changes sign:
h(x)=-f(x)→h(x)=-sqrt(x)
2) and shift it upward 3 units: We must add 3 units to the function:
g(x)=h(x)+3→g(x)=-sqrt(x)+3
Answer: Option C. g(x)=-sqrt(x)+3
Write an expression for the total Surface Area (SA) of a rectangular prism whose base is a square with side of length x and height of y.
Answers
S.A = 2x ^ 2 + 2x *y + 2x * y
Rewriting we have:
S.A = 2x ^ 2 + 4x *y
S.A = 2 (x ^ 2 + 2x * y)
Where,
x: side length of a square base
y: height of the prism
Answer:
an expression for the total Surface Area (SA) of a rectangular prism is:
S.A = 2 (x ^ 2 + 2x * y)
Please help asap!!!!!!!!!!!!
Answers
Hope this helps.
The correct answer is C: - 50
The Square Root of 625 is 25, so B and D can be eliminated
Since the negative is outside of the square root, it is not possible for it to be positive (It is also impossible to square root a negative number), so that eliminated A., leaving you with the correct answer, C.
I hope this helps ^^
This week, sandy was out sick on monday and tuesday. Last week, Jared was out sick on Thursday and Friday. The week before, Elisa was out sick on Wednesday and Thursday. What generalization can you make about these three students absents? Can you make a second generalization?
Answers
A generalization is a broad statement or an idea that is applied to a group of people or things. Most often, generalizations are not entirely true, because usually, the pattern they see in the relationship of a certain group of individuals or situations does not apply. In our example, where Elisa, Sandy, and Jared got sick and were absent from school for two days straight, within the 3 week period, we can make the following generalizations patterns:
1) There is an outbreak of sickness in the school for 3 consecutive weeks.
2) The said sickness lasts for two days.
Two mechanics worked on a car. the first mechanic worked for 10 hours, and the second worked for 15 hours. together they charged a total of 1800. what was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour ?
Answers
Total money earned:
[tex]10x + 15y = 1800[/tex]
Sum of hourly rates:
[tex]x + y = 155[/tex]
To solve this, you solve for one equation first, substitute it in the second, then input it back into the first equation. I will first be solving for x.
[tex]x + y = 155 \\ x = 155 - y[/tex]
Input this into the other equation to find y:
[tex]10(155 - y) + 15y = 1800 \\ 1550 - 10y + 15y = 1800 \\ 5y = 250 \\ y = 50[/tex]
Input y into the first equation:
[tex]x + 50 = 155 \\ x = 105[/tex]
The first mechanic charges $105 per hour and the second mechanic charges $50 per hour.
The rates charged per hour by the first and second mechanics will be $105 and $50.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that two mechanics worked on a car, the first mechanic worked for 10 hours, and the second worked for 15 hours. together they charged a total of 1800.
Suppose x is the hourly rate for the first mechanic and y is the hourly rate of the second.
If the total money earned is 1800.
10x + 15 y = 1800 ---- (1)
If both have their individual rates the sum of the hourly rate is,
x+ y = 15 -------- (2)
Rearrange the equation,
x = 155- y
Substitute the value of x in equation 1 we get,
10x + 15 y = 1800
10(155-y) + 15y = 1800
1150 - 10y + 15y = 1800
5y = 250
y = 50
Substitute the value of y in equation 2 we get,
x = 155- y
x= 155 - 50
x = 105
Thus, the rates charged per hour by the first and second mechanics will be $105 and $50.
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PLZ help
which inequality does the graph represent
Answers
For -2 on the number line, we can see a hollow circle. This means that -2 is not included in the interval, eliminating the possibilities of greater and equal than or less and equal than (≥ and ≤).
The graph will have to use the original greater than symbol (>) or less than symbol (<).
The graph represents all numbers less than -2. Thus, the final inequality will be
x < -2.
The inequality the graph represent is y > x - 2.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions. An inequality is a mathematical statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). Inequalities are used to describe relationships between quantities or to express constraints or conditions.
We are given that;
The number line
Now,
The slope of the line is 1 and the y-intercept is -2,
so we can write y = x - 2 for the equation of the line.
The line is dashed, so we know that y is not equal to x - 2.
The region above the line is shaded, so we know that y is greater than x - 2.
Therefore, by the inequality the answer will be y > x - 2.
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find the height of the triangle
Answers
We'll do the sine trig. identity, as it is the most effective.
Given an angle '[tex] \alpha [/tex]' in a right triangle, '[tex]sin( \alpha )[/tex]' is defined as the opposite side of the triangle to the given angle, over the triangle's hypotenuse.
So, for this setup:
[tex]sin(20)= \frac{x}{10} [/tex]
Now, we solve for x:
[tex]x=10sin(20)=3.42[/tex]
So, answer is 3.4
sin theta = opposite / hypotenuse ; where theta =20 ; h = 10
sin (20) = x / 10
x = 3.42
The answer is the fourth one, 3.42
During boot camp, the drill sergeant measured the weight of the men in his unit. he found the average weight of the men to be 142 pounds and the standard deviation 14 pounds. the data is normally distributed. find the interval in which 68% of the data lies. what is the probability that a man picked at random from the unit will weigh more than 170 pounds? that he will weigh less than 128 pounds?
Answers
mean=142
standard deviation=14
a] Find the interval in which 68% of the data lies:
P(x<X)=68%=0.68
the z-score associated with this probability is:
P(z<Z)=0.47
but :
z=(x-mu)/sig
thus;
0.47=(x-142)/14
solving for x we get:
x=148.58
thus 68 percent of the data lie below 148.58
b]what is the probability that a man picked at random from the unit will weigh more than 170 pounds?
x=170
thus
P(x>170) will be:
z=(170-142)/14
z=2
Thus
P(x>170)=1-P(z<2)
=1-0.9772
=0.0228
c] that he will weigh less than 128 pounds?
P(x<128)
z=(128-142)/14
z=(-14/14)=-1
Thus
P(z<-1)=0.1587
To find the interval of 68% of the data, use the empirical rule. The probability a man weighs more than 170 lbs or less than 128 lbs can be found using the normal distribution curve.
Explanation:To find the interval in which 68% of the data lies, we can use the concept of the empirical rule. According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean.
Since the standard deviation is 14 pounds and the mean is 142 pounds, one standard deviation above the mean is 142 + 14 = 156 pounds, and one standard deviation below the mean is 142 - 14 = 128 pounds.
Therefore, the interval in which 68% of the data lies is from 128 pounds to 156 pounds.
The probability that a man picked at random from the unit will weigh more than 170 pounds can be found by calculating the area under the normal distribution curve to the right of 170 pounds.
The probability that a man picked at random from the unit will weigh less than 128 pounds can be found by calculating the area under the normal distribution curve to the left of 128 pounds.
Which polar coordinates represent the point plotted on the graph? Select all that apply. (2 answers)
a. (-4, 90 degrees)
b. (4, 90 degrees)
c. (4, -90 degrees)
d. (-4, 270 degrees)
e. (-4, -270 degrees)
Answers
Answer: The correct options are (b) and (d).
Explanation:
It the polar form [tex]r^2=x^2+y^2[/tex], where
[tex]x=r\cos \theta,y=r\sin \theta[/tex]
The polar coordinate are in the form of [tex](r,\theta)[/tex].
From the given figure it is noticed that the value of r is 4 and [tex]\theta=\frac{\pi}{2}[/tex] or [tex]90^{\circ}[/tex] .
So the point is defined as [tex](4,90^{\circ})[/tex] and option b is correct.
The value,
[tex](r\cos \theta, r\sin \theta)=(0,4)[/tex]
Check the each option if we get the same value then that option is correct.
For option a.
[tex](r\cos \theta, r\sin \theta)=(-4\cos 90^{\circ} , -4\sin 90^{\circ})=(0,-4)[/tex]
Therefore option (a) is incorrect.
For option c.
[tex](r\cos \theta, r\sin \theta)=(4\cos (-90)^{\circ} , 4\sin (-90)^{\circ})=(0,-4)[/tex]
Therefore option (c) is incorrect.
For option d.
[tex](r\cos \theta, r\sin \theta)=(-4\cos (270)^{\circ} , -4\sin (270)^{\circ})\\(-4\cos (360-90)^{\circ} , -4\sin (360-90)^{\circ})=(0,4)[/tex]
Therefore option (d) is correct.
For option (e).
[tex](r\cos \theta, r\sin \theta)=(-4\cos (-270)^{\circ} , -4\sin (-270)^{\circ})\\(-4\cos (270)^{\circ} , 4\sin (270)^{\circ})=(0,-4)[/tex]
Therefore option (e) is incorrect.
Answer:
1. A
2. B, D
3. A, D, E
4. C
5. A
Step-by-step explanation:
What is the end behavior of the polynomial function? PLEASE HELP!!!
Answers
We have then that:
x ---> - inf then,
y -----> - inf
Answer:
option 4
Here is the explanation:
x ---> - inf then,
y -----> - inf
So in the graph, the choices given will give this answer and it is the 4th option.
If f(x) = 1000(3)x and g(x) = 8x. Which statement is true? A) None are true. B) as x → ∞, f(x) < g(x). C) as x → ∞, f(x) = g(x). D) as x → ∞, f(x) > g(x).
Answers
Answer: f(x) > g(x).
If f(x) = 1000(3)x and g(x)=8x
fx=3000x
f=3000x/x
f=3000
g(x)=8x
g=8x/x
g=8
For whatever amount of X (positive), the statement f(x) > g(x) is true.
Write the equation in standard form using integers y=4x+5
Answers
On a 10 item test, three students in prof. miller's advanced chemistry seminar received scores of two, five, and eight, respectively. for this distribution of test scores, standard deviation is equal to the square root of
Answers
In order to calculate the standard deviation, first, you need to calculate the mean of the scores:
m = (2 + 5 + 8) / 3
= 15 / 3
= 5
Then, find the variance: subtract the mean from each value, square the results, sum them up and divide it by the number of scores.
(2 - 5)² = 9
(5 - 5)² = 0
(8 - 5)² = 9
Therefore:
v = (9 + 0 + 9) / 3
= 18 / 3
= 6
The standard deviation is the square root of the variance:
σ = √6
= 2.45
In conclusion, the standard deviation can be calculated by the formula:
[tex]\sigma = \sqrt{ \frac{\sum(v - m)^{2} }{n} } [/tex]
The standard deviation for the given test scores can be calculated by finding the mean, computing the squared differences from the mean, averaging those squared differences to get the variance, and then taking the square root of that variance. The standard deviation for the scores is approximately 2.449.
The student is likely seeking assistance with the concept of standard deviation, which is a measure of dispersion or distribution around the mean in a set of data. The question at hand requires calculating the standard deviation for a small dataset consisting of three scores from a chemistry seminar. To find the standard deviation, one would first need to calculate the mean of the test scores, then find the variance by averaging the squared differences between each score and the mean, and finally, take the square root of the variance.
Step-by-step Calculation:
Calculate the mean (average) of the scores: (2 + 5 + 8) / 3 = 15 / 3 = 5.Find the squared differences from the mean: (2 - 5)² + (5 - 5)² + (8 - 5)² = 3² + 0² + 3² = 9 + 0 + 9.Calculate the variance: (9 + 0 + 9) / 3 = 18 / 3 = 6.The standard deviation is the square root of the variance: √(6) = 2.449The standard deviation of the test scores in Prof. Miller's advanced chemistry seminar is approximately 2.449.
Please help me find the value of x in the triangle in the link!
Answers
The sum of the interior angles of all triangles is 180 degrees; you can find x by setting the sum of the two unknown angles, x, and 98 equal to 180 and solving algebraically.
180 = 98 + x + x
180 = 98 + 2x
82 = 2x
41 = x
Answer:
x = 41
WILL GIVE BRAINLIEST OF YOU ANSWET ALL
50 points plus 49 with brainliest
Answers
Lateral Surface Area = 2π×2×15 = 188.49555921539 feet2
Total Surface Area = 213.62830044411 feet2
(Figure A)
Base Surface Area = 2π×52 = 157.07963267949 feet2
Lateral Surface Area = 2π×5×17 = 534.07075111026 feet2
Total Surface Area = 691.15038378975 feet2
(Figure B)
Base Surface Area = 2π×82 = 402.12385965949 feet2
Lateral Surface Area = 2π×8×22 = 1105.8406140636 feet2
Total Surface Area = 1507.9644737231 feet2
(Figure C)
Answer:
his answer is right.
Two consecutive positive odd integers have a product of 63. what is the smaller number
Answers
Through trial and error, you can find that 7*9 = 63 so we see that 7 is the smaller number. Or you can factor 63.
-----------------------------------
The way your teacher probably wants you to do it is through algebra
x = smaller number
x+2 = next highest number
x*(x+2) = 63
x^2+2x = 63
x^2+2x-63 = 0
At this point, we can use the quadratic formula or factor. Factoring may be easier
x^2+2x-63 = 0
(x+9)(x-7) = 0
x+9=0 or x-7 = 0
x = -9 or x = 7
Toss out x = -9 because the instructions state that the integers must be positive.
The only valid answer is x = 7.
If x = 7, then x+2 = 7+2 = 9
So,
x*(x+2) = 63
7*9 = 63
where 7 is the smaller factor.
Given: KLMN is a parallelogram m∠K : m∠KLM=1:3 LF ⊥ KN , LD ⊥ NM Find: m∠FLD
Answers
<NKL = <LMN = X
<KLM = <KNM = 3X
So, 2(x+3x) = 360°
80x = 360°
x = 45°
The figure LFND is another quadrilateral where:
<LFN = <NDL =90°
<FND = 3x
So, (90×2)+3x+ (angle FLD) = 360°
Angle FLD = 360° - 180° - (3×45)°
= 360° - 315°
= 45°
The measure of the angle m∠FLD is 45 degrees.
What is parallelogram?A parallelogram is a special type of quadrilateral that has equal and parallel opposite sides. The given figure shows a parallelogram ABCD which as AB parallel to CD and AD parallel to BC.
In a parallelogram, opposite angles are equal and since it is a quadrilateral, the angles add up to 360°.
[tex]\rm \angle NKL = \angle LMN = X\\\\\angle KLM = \angle KNM = 3X\\\\ 2(x+3x) = 360\\\\ 80x = 360\\\\ x=\dfrac{360}{80}\\\\ x = 45[/tex]
The figure LFND is another quadrilateral where:
[tex]\rm \angle LFN = \angle NDL =90\\\\ \angle FND = 3x[/tex]
The measure of the, m∠FLD is;
[tex]\rm (90\times 2)+3x+ (angle\ FLD) = 360\\\\m \angle\ FLD = 360- 180- (3\times 45)\\\\ m \angle\ FLD = 360 - 315\\\\ m \angle\ FLD = 45[/tex]
Hence, the measure of the angle m∠FLD is 45 degrees.
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If a person uses $700 in credit with an interest of 14%,what is that person going to owe after three billing cycles with simple interest
Answers
14%
This boils down to ----------- interest per month: a monthly rate of 0.0117.
12 mo
Thus, after 3 months, the amount owed, including the original $700, would be $700 + 3($700)(0.0117) = $724.57.
I really need help with these questions:
Use basic identities to find the simplified expression-
1. (cos^2 x + sin^2 x) / (cot^2 x - csc^2 x)
2. cosine θ^2 / sine θ^2 + csc θ sin θ
Explanations would be greatly appreciated
Answers
(cos^2 x + sin^2 x) / (cot^2 x - csc^2 x)
The numerator becomes 1 since addition order matters not.
1 / (cot^2 x - csc^2 x)
If we factor the denominator out a negative
1 / -(csc^2 x - cot^2 x)
Consider sin^2 x + cos^2 x = 1. Divide both sides by sin^2 x to get
1 + cot^2 x = csc^2 x
Subtract both sides by cot^2 x to get 1 = csc^2 x - cot^2 x.
Replace the denominator
1 / -(1) = -1
For cos^2 θ / sin^2 θ + csc θ sin θ, we use cscθ = 1/sinθ and cosθ/sinθ = cotθ so
= cos^2 θ / sin^2 θ + 1
= cot^2 θ + 1
We use 1 + cot^2 θ = csc^2 θ to simplify this to
= csc^2 θ
Answers: -1
csc^2 θ
[tex]\bf sin^2(\theta)+cos^2(\theta)=1 \qquad \qquad cot(\theta)=\cfrac{cos(\theta )}{sin(\theta)} \qquad csc(\theta)=\cfrac{1}{sin(\theta)}\\\\ -------------------------------\\\\ \cfrac{cos^2(x)+sin^2(x)}{cot^2(x)-csc^2(x)}\implies \cfrac{1}{\frac{cos^2(x)}{sin^2(x)}-\frac{1}{sin^2(x)}}\implies \cfrac{1}{\frac{cos^2(x)-1}{sin^2(x)}} \\\\\\ \cfrac{1}{\frac{-[1-cos^2(x)]}{sin^2(x)}}\implies \cfrac{1}{\frac{-[\underline{sin^2(x)}]}{\underline{sin^2(x)}}}\implies \cfrac{1}{-1}\implies -1[/tex]
2)
[tex]\bf \cfrac{cos^2(\theta )}{sin^2(\theta )}+csc(\theta )sin(\theta )\implies \cfrac{cos^2(\theta )}{sin^2(\theta )}+\cfrac{1}{sin(\theta )}\cdot sin(\theta ) \\\\\\ \cfrac{cos^2(\theta )}{sin^2(\theta )}+1\implies \cfrac{cos^2(\theta )+sin^2(\theta )}{sin^2(\theta )}\implies \cfrac{1}{sin^2(\theta )}\implies csc^2(\theta )[/tex]
A footbridge is in the shape of an arc of a circle. the bridge is 10 ft tall and 27 ft long, horizontally. what is the radius of the circle that contains the bridge? round your answer to the nearest tenth.
Answers
The radius of the circle that includes the footbridge, given the bridge's arc length and height, is 14.1 ft.
Explanation:The problem relates to the geometry of a circle, specifically the concept of the arc length and radius. Given the arc length (L) and the height of the arc (h), we can use these to find the radius (r) of the circle using the formula r = L²/(8h) + h/2.
Here, the arc length is the horizontal length of the footbridge, which is 27 ft and the height h is the height of the bridge, 10 ft.
Substituting these values into the formula we get:
r = (27² ft)/(8*10 ft) + 10 ft/2 = 729/80 + 5 = 14.1 ft
So, to the nearest tenth of a foot, the radius of the circle that includes the footbridge is 14.1 ft.
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The measure of an angle is 27°. what is the measure of a complementary angle?
Answers
Because 27 + 63 = 90
The measure of a complementary angle to a 27 degree angle is 63 degrees because two angles are complementary if their measures add up to 90 degrees. This is calculated by subtracting the given angle from 90.
Explanation:The measure of an angle is given as 27°, and you are asked to find the measure of a complementary angle. In mathematics, two angles are considered complementary if their measures add up to 90 degrees. Therefore, to find the measure of a complementary angle, you subtract the given angle from 90 degrees.
So, to solve this problem, you would simply subtract 27 from 90.
The calculation would look like this:
90-27 = 63. Therefore, the measure of the complementary angle is 63°.
The relative locations of a swing set, a garden, and a sandbox in Gina's backyard are shown in the diagram.
What is the distance between the sandbox and garden?
Enter your answer as a decimal in the box. Round only your final answer to the nearest foot.
Answers
Let us suppose the distance between the sandbox and garden is x feet.
Apply the sine law in the given triangle, we have
[tex]\frac{x}{\sin 65^{\circ}}=\frac{36}{\sin 104^{\circ}}\\ \\ \text{On coss multiplying, we get}\\ x\sin 104^{\circ}=36\sin 65^{\circ}\\ \\ x=\frac{36\sin 65^{\circ}}{\sin 104^{\circ}}\\ \\ x\approx 33.6[/tex]
Therefore, in the nearest foot, the distance between the sandbox and garden is 34 foot.
Answer:
Hello! The correct answer is 34 ft.
Step-by-step explanation:
I am just confirming!
An airplane left Miami, FL. At the same time another plane left Santiago, Chile. The two planes flew toward each other at rates of 625 mph and 575 mph. If Miami and Santiago are 4200 miles apart, how long will it take until the planes pass each other?
Answers
Plane 1(625): Took 23 hours to arrive.
Plane 2(575): Took 25 hours to arrive.
Therefore, the answer should be from 23-25 hours to arrive or if looking for middle number, 24 hours exactly.
Hope this helps.
Find the surface area of a sphere with radius, r = 11 in.
Surface Area = ________ in^2
(Type an exact answer in terms of pi.)
Answers
Sphere Surface Area = 484 PI
In Miami the number of accidents increased by 20% over a four year period.how many accidents were there in 2013 if there were 5120 in 2009
Answers
4+3x-ax=9-7x+bx
PLEASE HELP
Answers
a=−bx+10x−5x
Answer:
[tex]x=\frac{5}{(10-a-b)}[/tex]
Step-by-step explanation:
4+3x-ax=9-7x+bx
take all variable terms at one side and all constant terms at one side,
3x+7x-bx-ax=9-4
10x-ax-bx=5
x(10-a-b)=5
[tex]x=\frac{5}{(10-a-b)}[/tex]
what is the value of x, if the volume of the cone is 12piem^3
Answers
12π=πx²h/3
12=x²h/3
36=x²h
36/h=x²
x=6/√h=(6√h)/h
3. A vacuum robot is in a room and charging at position (0, 5). Once charged, it begins moving on a northeast path at a constant speed of 1/2 foot per second along the line 4 − 3 = −15. After 60 seconds, it turns right 90° and travels in the new direction.
a. What are the coordinates of the point at which the robot made the turn?
b. Find an equation for the second line on which the robot traveled.
c. If after turning, the robot travels 80 seconds along this line, how far has it traveled from its starting position?
d. What is the equation of the line the robot needs to travel along in order to return and recharge? How long will it take the robot to get there?
Show your work
Answers
a)
The robot made the turn at the point (-20, 15).
b)
The equation of the second line on which the robot traveled is:
y = (4/3)x + 35.
c)
The distance between the starting position and the final position is 20.51 feet.
d)
The equation of the line the robot needs to travel along in order to return and recharge is y = (-3/4)x + 5.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
a.
To find the coordinates of the point at which the robot made the turn, we need to determine its position after traveling for 60 seconds along the initial northeast path.
The distance the robot covers in 60 seconds is:
distance
= speed x time
= (1/2) x 60 = 30 feet
The initial path has a slope of -3/4 (since it passes through (4, -3) and
(0, 5)), so the robot's new path after turning right will have a slope of the negative reciprocal of -3/4, which is 4/3.
We know that the robot traveled 30 feet along the initial path, so we can use the slope and distance traveled to find the endpoint of the initial path:
y = mx + b, where m is the slope and b is the y-intercept
-3 = (-3/4)(4) + b
b = 0
So the equation of the initial path is y = (-3/4)x.
The endpoint of the initial path is (-20, 15) (since the initial path passes through (0, 5) and (-20, 15)).
The robot made the turn at the point (-20, 15).
b.
Since the robot turned right, its new path will be perpendicular to the initial path.
We know the robot's position after turning (i.e., the endpoint of the initial path), so we can use this point and the slope of the new path to find the equation of the new path.
The slope of the new path is 4/3, so the equation of the new path is:
y - 15 = (4/3)(x + 20)
Simplifying this equation, we get:
y = (4/3)x + 35
The equation of the second line on which the robot traveled is:
y = (4/3)x + 35.
c.
From the last equation in part (b), we have:
9(y - 5)² = 29 - 16x² - 12x
Taking the square root of both sides and solving for y, we get:
y = 5 ± √((29 - 16x^2 - 12x)/9)
Since the robot is traveling along the new path for 80 seconds, we want to find y when t = 80.
Substituting t = 80 into the equation for y and simplifying, we get:
y = 5 + √(17/9)
So the robot's final position is approximately (20.50, 6.63).
The distance between the starting position and the final position is:
distance
= √((20.50 - 0)² + (6.63 - 5)²)
= √(421.17)
= 20.51 feet.
d.
The robot needs to travel along a path that is perpendicular to the second line on which it traveled in order to return to its starting position.
The slope of the second line is 4/3, so the slope of the path back to the starting position is -3/4 (the negative reciprocal of 4/3).
We know the robot's final position and the slope of the desired path, so we can use the point-slope form to find the equation of the path:
y - 5 = (-3/4)(x - 0)
Simplifying this equation, we get:
y = (-3/4)x + 5
So the equation of the line the robot needs to travel along in order to return and recharge is y = (-3/4)x + 5.
Setting the two equations equal to each other and solving for x, we get:
(4/3)x + 35 = (-3/4)x + 5
Multiplying both sides by 12 to eliminate fractions, we get:
16x + 420 = -9x + 60
Solving for x, we get:
x = -16.8
Substituting this value of x into either equation, we get:
y = (4/3)(-16.8) + 35
y = 13.60
So the intersection point is approximately (-16.8, 13.60).
To find how long it will take the robot to get there, we can use the distance formula between the robot's final position and the intersection point:
distance = √((-16.8 - 20.50)² + (13.60 - 6.63)²) ≈ 40.49 feet.
Since the robot travels at a constant speed of 1/2 foot per second, it will take approximately 80.98 seconds (rounded to two decimal places) for the robot to return and recharge.
Thus,
The robot made the turn at the point (-20, 15).
The equation of the second line on which the robot traveled is:
y = (4/3)x + 35.
The distance between the starting position and the final position is 20.51 feet.
The equation of the line the robot needs to travel along in order to return and recharge is y = (-3/4)x + 5.
Learn more about equation of a line here:
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Which is least expensive per oz rounded to the nearest cent: 20 oz for $1.79 or 2 lb 2 oz for $2.59?
A.) 20 oz
B.) 2 lb 2 oz
C.) Neither
Answers
11.17 = 11.2
2 lb 2 oz / 2.59 = 0.82
0.82 = 0.8
So the answer is B) 2 lb 2 oz.
Hope this Helps!
Answer:
B.) 2 lb 2 oz
Step-by-step explanation:
$1.79 for 20 ounces gives us
1.79/20 = $0.0895 ≈ $0.09 per ounce.
1 lb = 16 oz.; this means that 2 lb = 2(16) = 32 oz.
$2.59 for 2 lb 2 oz then gives us
2.59/34 = $0.07617647059 ≈ $0.08 per ounce.
The second choice is cheaper by 1 cent.
A fish tank contains 18 goldfish and 22 guppies. If you randomly select 2 fish, what is the probability that they are both goldfish?
Answers
Answer:
b
Step-by-step explanation: