The ratio of gallons of high-gloss sold to the total gallons sold is,
D. 33 : 57
What are ratio and proportion?In its most basic form, a ratio is a comparison between two comparable quantities.
There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.
If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.
Given, The hardware store sold 33 gallons of flat paint and 57 gallons of high-gloss paint.
Therefore, The ratio of flat paint : high-gloss paint = 33 : 57.
learn more about proportion here :
https://brainly.com/question/7096655
#SPJ2
which overlapping triangles are congruent by ASa
A cab company charges an initial rate of $2.50 for a ride, plus $0.40 for each mile driven. What is the equation that models the total fee for using this cab company? Write into an equation and then graph it.
Answer:
The equation that models the total fee for using this cab company
[tex]y=\$2.50+\$0.40\times x[/tex]
Step-by-step explanation:
Initial rate charged by company = $2.50
Amount charged for an each mile = $0.40
Let the miles cover during a ride = x
Total cost of ride can given as = y
The equation that models the total fee for using this cab company
[tex]y=\$2.50+\$0.40\times x[/tex]
The graphical interpretation equation in an image.
A scuba diver descends at a rate of 40 feet per minute. How many feet will the scuba diver move in 2 minutes?
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. (1 point) 4, -14, and 5 + 8i
The required polynomial function is x⁴ - 67x² + 1450x - 4984 = 0 with 4 degrees with real coefficients.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The zeros are given in the question as 4, -14, and 5 + 8i
The required polynomial function of minimum degree with real coefficients whose zeros include those listed above.
For the zero 4, you can write (x-4)
For the zero -14, you can write (x+14)
For the zero 5+8i since it is complex it will be accompanied by its conjugate 5-8i
So, you can write (x-(5+8i) and (x-(5-8i)) =(x²-10x+89)
(x - 4)(x + 14)(x² - 10x + 89)
Expanding the expression, we get
x⁴ - 67x² + 1450x - 4984 = 0
Learn more about the polynomial here:
brainly.com/question/11536910
#SPJ5
Tom went to his car in the morning and saw that a car or truck had bumped into it during the night, causing a lot of damage. What is the most likely outcome of this situation?
His finance company will reduce his interest.
His insurance company will lower his monthly payments.
His insurance company will pay for damages.
His finance company will increase his interest.
Answer:
His insurance company will pay for damages.
Step-by-step explanation:
An insurance is a form of contract that permits an individual to transfer the responsibilities of a financial loss to an insurance company. The company bears the risk of the financial loss. Small amount of money are collected from their clients and summed together to pay for losses that the client may encounter in the future. Insurance safeguards an individual and his property from losses, misfortune, hazards or theft. Covered losses are paid for by the insurance company thereby reducing the financial costs for the individual. Examples include auto insurance , health insurance, disability insurance, and life insurance.
Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below: Two rectangular tiles, rectangle PQRS with vertices at P 1, 1. Q is at 8, 1. R is at 8, 5. S is at 1, 5. Rectangle JKLM with vertices J at 4, 1. K is at 8, 1. L is at 8, 4. M is at 4, 4. Which statement is correct? The two tiles are not similar because segment SP is to segment SR is 4:7 and segment MJ is to segment ML is 1:3. The two tiles are similar because segment PQ is to segment QR is 4:3 and segment JK is to segment KL is also 4:3. The two tiles are similar because segment SR is to segment ML is 7:4 and segment PQ is to segment JK is also 7:4. The two tiles are not similar because segment PQ is to segment QR is 7:4 and segment JK is to segment KL is 4:3.
A line has a slope of 5 and a y-intercept of 4 what is the equation in slope intercept form
Write your answer using integers proper fraction and improper fractions in simplest form
What is h(10) equal to?
Ricardo is constructing a line through point P that is perpendicular to line m. He has already constructed the arc shown.
He places his compass on point X to construct an arc.
What must be true about the width of the compass opening when Ricardo draws the arc?
It must be less than 1/2XY.
It must be equal to XY .
It must be equal to PX .
It must be greater than 12XY.
Answer:
It must be greater than 1/2XY.
Step-by-step explanation:
We draw an arc from point X below the arc that passes through X and Y. Keeping our compass the same width, we will draw another arc from point Y below, intersecting the first arc.
If the width of the compass is not set to more than 1/2XY, then the two arcs will not intersect and we will not complete our construction.
Perpendicular lines are lines that meet at 90 degrees.
The true statement about the width of the compass is that: (d) It must be greater than 1/2XY.
From the question, we understand that he has drawn arc XY already.
The next step is to draw an arc less than the width of XY, but greater than half width XY.
This will ensure that the arcs bisect one another.
Hence, the true option is (d).
Read more about perpendicular lines at:
https://brainly.com/question/12206864
A club with 15 women and 12 men need to form a committee that consists of a president, a vice president, a secretary, and a treasurer. how many committees are possible…
a. if the committee must have two women and two men?
Martin drives to work at a speed of 45 miles per hour. It takes him about 2 hours and 15 minutes to get to work. If gas costs $2.75 per gallon and Martin’s car gets 25 miles per gallon, about how much does Martin spend on gas to get to work?
2.25 * 45 = 101.25 miles to work
101.25 / 25 = 4.05 gallons of gas
4.05 * 2.75 = $11.14 total cost of gas
The height of a rocket a given number of seconds after it is released is modeled by h (t) = 6t2 + 32t + 10. What does t represent?
Answer: t represents the the number of seconds after rocket is released.
Step-by-step explanation:
Given: The height of a rocket a given number of seconds after it is released is modeled by [tex]h (t) = 6t^2 + 32t + 10[/tex].
Here h (height) is the dependent variable , which depends on the number of seconds after rocket is released (independent variable).
Since the independent variable in the function is t, then t must represents the the number of seconds after rocket is released.
The variable t represents the number of seconds that have passed since the rocket was released.
How to identify what a variable represents?Here we know that the height of a rocket a given number of seconds after it is released is modeled by:
h(t) = 6*t^2 + 32*t + 10
So this is a function that relates height with time in seconds, we know that the function models the height, so we must have that:
[h(t)] is equivalent to height.
This means that the other variable, t, must be related to time in seconds.
Then we can conclude that the variable t represents the number of seconds after the rocket has been released.
If you want to learn more about motion equations, you can read:
https://brainly.com/question/605631
1. What is the area of a parallelogram whose vertices are A(−1, 12) , B(13, 12) , C(2, −5) , and D(−12, −5) ?
2.
Each small square on the grid is 1 ft².
Which estimate best describes the area of this figure?
25 ft²
35 ft²
50 ft²
65 ft²
In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 189.7 pounds in the summer, including clothing and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 41.4 pounds. Weights are not Normally distributed, especially when the population includes both men and women, but they are not very non-Normal. A commuter plane carries 27 passengers.
What is the approximate probability (±0.0001) that the total weight of the passengers exceeds 5511 pounds?
The only way I can think of to solve this problem is to assume normal distribution.
Since the total weight excess 5511, hence the weight per passenger is at least:
x = 5511 / 27 = 204.1 pounds
Solve for the z score:
z = (x – u) / s
z = (204.1 – 189.7) / 41.4
z = 0.35
From the standard probability tables, the P value using right tailed test is:
P = 0.3632
graph and solve the system
3x+6y-12= 0
x + 2y = 8
Evaluate exactly the value of the integral from negative 1 to 0 of the product of the cube of the quantity 2 times x to the 4th power plus 8 times x and 4 times x to the 3rd power plus 4, dx. Your work must include the use of substitution and the antiderivative.
Answer:
-162
Step-by-step explanation:
Integration by substitution is a technique in calculus where a change of variables is made to simplify the integral by expressing it in terms of a new variable, making the integration easier to manage.
To evaluate the following integral, use the method of substitution:
[tex]\displaystyle \int_{-1}^0 (2x^4 + 8x)^3 (4x^3 + 4) \;\text{d}x[/tex]
Let u = 2x⁴ + 8x.
Differentiate u with respect to x using the power rule for differentiation by multiplying each term by its exponent and then subtracting 1 from the exponent:
[tex]\dfrac{\text{d}u}{\text{d}x}=4 \cdot 2x^{4-1}+1\cdot 8 x^{1-1}[/tex]
[tex]\dfrac{\text{d}u}{\text{d}x}=8x^{3}+8[/tex]
Rewrite it so that dx is on its own:
[tex]\text{d}u=8x^{3}+8\;\text{d}x[/tex]
[tex]\text{d}x=\dfrac{1}{8x^{3}+8}\;\text{d}u[/tex]
Change the limits of integration from x to u:
[tex]\begin{aligned}x=-1 \implies u&=2(-1)^4 + 8(-1)\\&=2(1)-8\\&=2-8\\&=-6\end{aligned}[/tex]
[tex]\begin{aligned}x=0 \implies u&=2(0)^4 + 8(0)\\&=2(0)-0\\&=0-0\\&=0\end{aligned}[/tex]
Rewrite the integral in terms of u:
[tex]\begin{aligned}\displaystyle \int_{-1}^0 (2x^4 + 8x)^3 (4x^3 + 4) \;\text{d}x&=\int_{-6}^0 u^3 (4x^3 + 4) \cdot \dfrac{1}{8x^{3}+8}\;\text{d}u\\\\&=\int_{-6}^0 u^3 (4x^3 + 4) \cdot \dfrac{1}{2(4x^{3}+4)}\;\text{d}u\\\\&=\int_{-6}^0\dfrac{u^3}{2} \;\text{d}u\end{aligned}[/tex]
Integrate with respect to u using the power rule for integration by adding 1 to the exponent of each term and then dividing by the new exponent:
[tex]\begin{aligned}\displaystyle \int_{-6}^0\dfrac{u^3}{2} &=\left[\dfrac{u^{3+1}}{2 \cdot (3+1)}\right]^0_{-6}\\\\&=\left[\dfrac{u^{4}}{8}\right]^0_{-6}\\\\&=\dfrac{(0)^4}{8}-\dfrac{(-6)^4}{8}\\\\&=0-\dfrac{1296}{8}\\\\&=-162\end{aligned}[/tex]
Therefore, the value of the given integral is -162.
What is m∠JNM?
Enter your answer in the box.
°
we know that
Vertical angles are a pair of opposite and congruent angles formed by intersecting lines
In this problem
m∠JNM=m∠KNL -------> by vertical angles
so
[tex](4x+6)\°=(7x-21)\°[/tex]
Solve for x
[tex]7x-4x=6+21\\3x=27\\x=9\°[/tex]
Find the value of m∠JNM
m∠JNM=[tex](4x+6)\°[/tex]
substitute the value of x
m∠JNM=[tex](4*9+6)\°[/tex]
m∠JNM=[tex]42\°[/tex]
therefore
the answer is
m∠JNM=[tex]42\°[/tex]
Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins. Helena has 17 cups of flour and 4.5 cups of sugar available for baking.
Which combination of loaves of bread and batches of muffins could Helena bake?
Answer:
Helen can make 2 loaves of bread and 4 batches of muffins.
Step-by-step explanation:
Let x be the number of loaves of bread
Let y be the number of batches of muffins
As per the given requirement of flour, the equation becomes:
[tex]3.5x+2.5y=17[/tex] .......(1)
As per the given requirement of sugar, the equation becomes:
[tex]0.75x+0.75y=4.5[/tex] .....(2)
Multiplying equation (1) with 0.3 and subtracting (2) from (1)
[tex]1.05x+0.75y=5.1[/tex] now subtracting (2) from this we get
=> [tex]0.3x=0.6[/tex]
So, x = 2
And as [tex]3.5x+2.5y=17[/tex] ; so substituting x = 2 here we get
[tex]3.5(2)+2.5y=17[/tex]
[tex]7+2.5y=17[/tex]
[tex]2.5y=17-7[/tex]
[tex]2.5y=10[/tex]
So, y = 4
Hence, there will be 2 loaves of bread and 4 batches of muffins.
Parker bought a student discount card for the movies. The card cost $7 and and allows him to buy movie tickets for $5.50. After one month, Parker has spent $89.50 total. How many tickets has he bought since getting the discount card?
A) 12 tickets
B) 14 tickets
C) 15 tickets
D) 16 tickets
the total cost of a bus ride and a ferry ride is $8.00. in one month, bus fare will increase by 10% and ferry fare will increase by 25%. the total cost will then be 9.25. how much is the current bus fare?
Jacqui has grades of 79 and 76 on her first two algebra tests. if she wants an average of at least 71, what possible scores can she make on her third test?
A division of a company produces income tax apps for smartphones. each income tax app sells for $9. the monthly fixed costs incurred by the division are $25,000, and the variable cost of producing each income tax app is $4. (a) find the break-even point for the division.
The equation for profit is income – cost:
Profit = Income – Cost
Let us say that x is the number of sold amount
Profit = 9 x – (25,000 + 4 x)
Profit = 5 x – 25,000
Breakeven point occurs when Profit = 0, hence:
5 x = 25,000
x = 5,000
The breakeven is when 5,000 people uses the income tax app
Triangle LMN is located at L(2,3), M(1,2), and N(4,4). The triangle is then transformed using the rule (x+5, y+2) to form the image L’M’N. What are the new coordinates of L’,M’, and N’?
Given:- L (2, 3), M (1, 2), and N make up the triangle known as LMN (4, 4). The image L'M'N' is created by first transforming the triangle according to the rule
To Locate:
What are L's, M's, and N's new coordinates?Solution:-
Rule for Points = (x + 2) on the x-axis.
Thus, the new x-points axis's are as follows:
L' = 2 + 5 = 7
M' = 1 + 5 = 6
N' = 4 + 5 = 9 .
and, Rule for y - axis Points = (y + 2) .
Therefore, New y - axis points of new ∆ are :-
L' = 3 + 2 = 5
M' = 2 + 2 = 4
N' = 4 + 2 = 6 .
Hence, New coordinates of L', M', and N' :-
L' = (7 , 5)
M' = (6, 4)
N' = (9, 6)
Find out more:
show that the point of trisection for the line connecting the points (-5,12) and (-1,12) is the midpoint of the line connecting the...
To learn more about coordinates refer to
brainly.in/question/15118408
#SPJ2
Find the solution of the square root of the quantity of x plus 3 plus 4 equals 6, and determine if it is an extraneous solution
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
We have been given an equation [tex]\sqrt{x+3}+4=6[/tex]. We are asked to find the solution of our given equation.
[tex]\sqrt{x+3}+4-4=6-4[/tex]
[tex]\sqrt{x+3}=2[/tex]
Now, we will square both sides of our given equation.
[tex]x+3=2^2[/tex]
[tex]x+3=4[/tex]
[tex]x+3-3=4-3[/tex]
[tex]x=1[/tex]
To see whether [tex]x=1[/tex] is an extraneous solution or not, we will substitute [tex]x=1[/tex] in our given equation as:
[tex]\sqrt{1+3}+4=6[/tex]
[tex]\sqrt{4}+4=6[/tex]
[tex]2+4=6[/tex]
[tex]6=6[/tex]
Since both sides of our given equation are equal, therefore, [tex]x=1[/tex] is a solution for our given equation.
What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit? 20.6 units 22.7 units 25.6 units 27.6 units
we know that
the perimeter of a polygon is the sum of the length sides
in this problem we have a triangle
so
the polygon has three sides
Let
[tex]A(-5,4)\\B(1,4)\\C(3,-4)[/tex]
the perimeter is equal to
[tex]P=AB+BC+AC[/tex]
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Step 1
Find the distance AB
[tex]A(-5,4)\\B(1,4)[/tex]
substitutes the values in the formula
[tex]d=\sqrt{(4-4)^{2}+(1+5)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(6)^{2}}[/tex]
[tex]dAB=6\ units[/tex]
Step 2
Find the distance BC
[tex]B(1,4)\\C(3,-4)[/tex]
substitutes the values in the formula
[tex]d=\sqrt{(-4-4)^{2}+(3-1)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(2)^{2}}[/tex]
[tex]d=\sqrt{68}[/tex]
[tex]dBC=8.25\ units[/tex]
Step 3
Find the distance AC
[tex]A(-5,4)\\C(3,-4)[/tex]
substitutes the values in the formula
[tex]d=\sqrt{(-4-4)^{2}+(3+5)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(8)^{2}}[/tex]
[tex]d=\sqrt{128}[/tex]
[tex]dAC=11.31\ units[/tex]
Step 4
Find the perimeter
the perimeter is equal to
[tex]P=AB+BC+AC[/tex]
substitutes the values
[tex]P=6+8.25+11.31=25.56\ units=25.6\ units[/tex]
therefore
the answer is
[tex]25.6\ units[/tex]
: A bookstore owner is conducting market research to forecast sales for the coming year. The bookstore is open 360 days a year and out of the 1,200 people who pass the store each day, 8% of them enter the store and make a purchase. The average amount of each sale is $18. What is the estimated amount of sales for the coming year?
Answer:
622,080
Step-by-step explanation:
thanks me later
PLEASE HELP ASAP: A particle is moving with velocity v(t) = t2 – 9t + 18 with distance, s measured in meters, left or right of zero, and t measured in seconds, with t between 0 and 8 seconds inclusive. The position at time t = 0 sec is 1 meter right of zero, that is, s(0) = 1.
The average velocity over the interval 0 to 8 seconds
The instantaneous velocity and speed at time 5 secs
The time interval(s) when the particle is moving right
The time interval(s) when the particle is
going faster
slowing down
Find the total distance the particle has traveled between 0 and 8 seconds
Answer:
1) Average velocity = 10/3 m/s
2) Instantaneous velocity = -2 m/s
Speed = 2 m/s to the left
3) (0, 3) ∪ (6, 8]
4) Going faster: (3, 4.5) ∪ (6, 8]
Slowing down: (0, 3) ∪ (4.5, 6)
5) Total distance = 35.67 m (nearest hundredth)
Step-by-step explanation:
The relationships between position (displacement), velocity and acceleration are:
[tex]\boxed{\boxed{\begin{array}{c}\textbf{POSITION (s)}\\\\\text{Differentiate} \downarrow\qquad\uparrow\text{Integrate}\\\\\textbf{VELOCITY (v)}\\\\\text{Differentiate}\downarrow\qquad\uparrow \text{Integrate}\\\\\textbf{ACCELERATION (a)}\end{array}}}[/tex]
Given a particle is moving with velocity v(t) = t² - 9t + 18, to find its position s(t) we can integrate v(t):
[tex]\begin{aligned}\displaystyle s(t)=\int v(t)\;\text{d}t&=\int(t^2-9t+18)\;\text{d}t\\\\&=\dfrac{t^{2+1}}{2+1}-\dfrac{9t^{1+1}}{1+1}+18t+C\\\\&=\dfrac{t^{3}}{3}-\dfrac{9t^{2}}{2}+18t+C\end{aligned}[/tex]
As s(0) = 1, then:
[tex]\begin{aligned}s(0)=\dfrac{(0)^{3}}{3}-\dfrac{9(0)^{2}}{2}+18(0)+C&=1\\0-0+0+C&=1\\C&=1\end{aligned}[/tex]
Therefore, the position function s(t) is:
[tex]\large\boxed{s(t)=\dfrac{t^3}{3}-\dfrac{9t^2}{2}+18t+1}[/tex]
Given a particle is moving with velocity v(t) = t² - 9t + 18, to find its acceleration a(t) we can differentiate v(t):
[tex]\begin{aligned}a(t)=\dfrac{\text{d}}{\text{d}t}[v(t)]&=2\cdot t^{2-1}-1\cdot9t^{1-1}+0\\&=2t-9\end{aligned}[/tex]
Therefore, the acceleration function a(t) is:
[tex]\large\boxed{a(t)=2t-9}[/tex]
[tex]\hrulefill[/tex]
Question 1To find the average velocity over the interval [0, 8], use the formula:
[tex]\textsf{Average Velocity}=\dfrac{s(t_2)-s(t_1)}{t_2-t_1}[/tex]
In this case:
t₁ = 0t₂ = 8Calculate the position at t₁ and t₂ by substituting t = 0 and t = 8 into s(t):
[tex]s(0)=\dfrac{(0)^3}{3}-\dfrac{9(0)^2}{2}+18(0)+1}=1[/tex]
[tex]s(8)=\dfrac{(8)^3}{3}-\dfrac{9(8)^2}{2}+18(8)+1}=\dfrac{83}{3}[/tex]
Therefore:
[tex]\textsf{Average Velocity}=\dfrac{s(8)-s(0)}{8-0}=\dfrac{\frac{83}{3}-1}{8}=\dfrac{10}{3}\; \sf m/s[/tex]
Therefore, the average velocity is 10/3 m/s.
[tex]\hrulefill[/tex]
Question 2To find the instantaneous velocity at t = 5 seconds, substitute t = 5 into v(t):
[tex]\begin{aligned}v(5)&=(5)^2-9(5)+18\\&=25-45+18\\&=-2\end{aligned}[/tex]
So, the instantaneous velocity at t = 5 seconds is -2 m/s.
Speed is a scalar quantity that measures how fast an object is moving regardless of its direction. Therefore, speed is the magnitude of velocity:
[tex]\textsf{Speed}=|v(5)|=|-2|=2\;\sf m/s[/tex]
Therefore, the speed at t = 5 is 2 m/s to the left.
[tex]\hrulefill[/tex]
Question 2The particle changes direction when v(t) = 0.
[tex]\begin{aligned}v(t)&=0\\\implies t^2-9t+18&=0\\t^2-6t-3t+18&=0\\t(t-6)-3(t-6)&=0\\(t-3)(t-6)&=0\\\\t-3&=0\implies t=3\\t-6&=0\implies t=6\end{aligned}[/tex]
Therefore, the particle changes direction at t = 3 and t = 6.
We know that the position of the particle at t = 0 is 1 meter right of zero. Therefore:
It is moving to the right in the interval (0, 3).It is moving to the left in the interval (3, 6).It is moving to the right in the interval (6, 8].Therefore, the time intervals between 0 ≤ t ≤ 8 when the particle is moving right is:
(0, 3) ∪ (6, 8][tex]\hrulefill[/tex]
Question 4When a(t) > 0:
[tex]\begin{aligned}a(t)& > 0\\2t-9& > 0\\2t& > 9\\t& > \dfrac{9}{2}\\t& > 4.5\; \sf s\end{aligned}[/tex]
When a(t) < 0:
[tex]\begin{aligned}a(t)& < 0\\2t-9& < 0\\2t& < 9\\t& < \dfrac{9}{2}\\t& < 4.5\; \sf s\end{aligned}[/tex]
Therefore:
Velocity is positive in the interval (0, 3) and (6, 8].Velocity is negative in the interval (3, 6).Acceleration is positive in the interval (4.5, 8].Acceleration is negative in the interval (0, 4.5).(Refer to the attachment).
If velocity and acceleration have the same sign, it means the object is speeding up.
If velocity and acceleration have opposite signs, it means the object is slowing down.
Therefore, the time intervals when the particle is going faster and slowing down are:
Going faster: (3, 4.5) ∪ (6, 8]Slowing down: (0, 3) ∪ (4.5, 6)[tex]\hrulefill[/tex]
Question 5To find the total distance the particle has traveled between 0 and 8 seconds, we need to consider the distance traveled between the intervals when it changes direction.
To do this, find the position of the particle at t = 0, t = 3, t = 6 and t = 8.
[tex]s(0)=\dfrac{(0)^3}{3}-\dfrac{9(0)^2}{2}+18(0)+1=1[/tex]
[tex]s(3)=\dfrac{(3)^3}{3}-\dfrac{9(3)^2}{2}+18(3)+1=23.5[/tex]
[tex]s(6)=\dfrac{(6)^3}{3}-\dfrac{9(6)^2}{2}+18(6)+1=19[/tex]
[tex]s(8)=\dfrac{(8)^3}{3}-\dfrac{9(8)^2}{2}+18(8)+1=\dfrac{83}{3}\approx27.67[/tex]
Therefore, in the interval 0 ≤ t < 3, the particle travels:
[tex]|s(3)-s(0)|=|23.5-1|=22.5\; \sf meters\;(to\;the\;right)[/tex]
In the interval 3 < t < 6, it travels:
[tex]|s(6)-s(3)|=|19-23.5|=4.5\; \sf meters\;(to\;the\;left)[/tex]
In the interval 6 < t ≤ 8, it travels:
[tex]|s(8)-s(6)|=|27.67-19|=8.67\; \sf meters\;(to\;the\;right)[/tex]
So the total distance the particle has traveled between 0 and 8 seconds is:
[tex]\textsf{Total distance}=22.5+4.5+8.67=35.67\; \sf meters[/tex]
Number 28 plz?????!!?!???
Write the equation in the slope-intercept form. 7x − 4y + 8 = 0
Final answer:
To convert the equation 7x - 4y + 8 = 0 to slope-intercept form, solve for y to get y = (7/4)x + 2, with a slope of 7/4 and a y-intercept of 2.
Explanation:
To write the equation 7x − 4y + 8 = 0 in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we want to solve for y. The steps are as follows:
Subtract 7x and 8 from both sides of the equation to isolate terms involving y: -4y = -7x - 8.Divide every term by -4 to solve for y: y = (7/4)x + 2.Thus, the equation of the line in slope-intercept form is y = (7/4)x + 2. Here, the slope is 7/4 and the y-intercept is 2.
On a particular road map 1/2 inch represents 18 miles about how many miles apart are 2 towns that are 21/2 inches apart on this map