Step-by-step explanation:
The particle is at rest when the derivative of x(t), which is its velocity, is zero, i.e.,
[tex]\dfrac{d}{dt}[x(t)] = \dot{x}(t) = 0[/tex]
Since [tex]x(t) = 2t^3 - 21t^2 + 72t - 53,[/tex] its derivative is
[tex]\dot{x}(t) = 6t^2 - 42t + 72[/tex]
Equating this to zero, we get
[tex]6t^2 - 42t + 72 = 0 \Rightarrow t^2 - 7t + 12 = 0[/tex]
This is a familiar quadratic equation whose roots are
[tex]t = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]\;\;\;= \dfrac{7 \pm \sqrt{(7)^2 - 4(1)(12)}}{2}[/tex]
[tex]\;\;\;= \dfrac{7 \pm 1}{2}[/tex]
[tex]\;\;\;= 3\;\text{and}\;4[/tex]
This means that the particle will be at rest at t = 3 and t= 4.
I need help solving please
Answer:
B.
Step-by-step explanation:
Range is all the set y values.
Answer:
See image
Step-by-step explanation:
The range is all of the y-values. Look at the points on the graph, and make a list of all the y's That will be the range.
WILL GIVE BRAINLIEST!!!!
Answer:
$319
Step-by-step explanation:
Usually, sales tax is proportional to the amount of the sale, so if the sales tax is a factor of 22/16 times the original tax, then the sale amount must be 22/16 times the original item cost:
(22/16)·$232 = $319
I need to know the area of this triangle and I would like to have an explanation because I dont know how to do it I know the formula just not how to get the height
Area
[tex]\\ \tt\longmapsto \dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
[tex]\\ \tt\longmapsto \dfrac{1}{2}|(-2)(3+5)+(4)(-5-1)+(-2)(1-3)|[/tex]
[tex]\\ \tt\longmapsto \dfrac{1}{2}|-16-24+4|[/tex]
[tex]\\ \tt\longmapsto \dfrac{1}{2}|-36|[/tex]
[tex]\\ \tt\longmapsto 18units^2[/tex]
What property is used to rewrite (x + 2)(y + z) as y (x + 2) + z (x + 2)
Answer:
Distributive Property
Step-by-step explanation (if you were to show the steps):
(x+2)(y+z) (first expression)
xy + xz + 2y + 2z (Distributive Property of Multiplication)
yx + 2y + zx + 2z (use the Commutative Property of Addition and Commutative Property of Multiplication to group xy (also known as yx) and 2y together, and to group xz (also known as zx) and 2z together)
y(x + 2) + z(x + 2) (use factoring to get the rewritten expression at the end)
The equation of the blue line is y=-x+ 5. Manipulate the orange line by setting the sliders so its slope, m, is -1 and its y-intercept, b, is 5. Which statement describes the system after the changes? O The lines intersect at the same point as before the changes. O The lines intersect at a different point than before the changes. O The lines do not intersect. 0 The lines overlap.
Answer:
D
Step-by-step explanation:
Find the slope of a line paprallel to the line below
if you are in a 200 meter race and finish 19 meters ahead of your opponent, if you were to run the race again, where woild you have to start to end the race in a tie?
Answer:
i haven't done this in years but i'm pretty sure -19 meters
Step-by-step explanation:
You work for a consumer advocacy agency and want to estimate the populations means cost of monthly maintenance on a car. It is assumed that the average monthly cost of maintenance is $210 dollars. In a random sample of 100 cars, you find the average monthly maintenance cost was $185. Assume that the population standard deviation is known to be $125; Use a 0.03 significance level to test the claim that the population mean weight of cost of maintenance differs from 210 lbs. State the null and alternate hypothesis test
A) H0: μ≤185
Ha: μ>185
B) H0: μ≥210
Ha: μ<210
C) H0=210
Ha: μ=185
D) H0: μ=210
Ha: μ ≠ 210
According to the desired test, the hypothesis are given by:
D) H0: μ=210
Ha: μ ≠ 210
At the null hypothesis, it is tested if the population mean is of 210 lbs, that is:
[tex]H_0: \mu = 210[/tex]
At the alternative hypothesis, it is tested if the population mean differs from 210 lbs, that is:
[tex]H_a: \mu \neq 210[/tex]
Hence, the correct option is:
D) H0: μ=210
Ha: μ ≠ 210
A similar problem is given at https://brainly.com/question/25707631
51.33333333 just round it plz
Answer:
51
Step-by-step explanation:
The answer would be 51 because the numbers behind the decimal are below 5
Answer:
51
Step-by-step explanation:
51.33333333 rounds to 51 because 3 is less than 5.
When rounding, always look at the number before the first number in front of the decimal. If it is more than 5, round up. If it is less than, round down.
If 9 out of 20 candies are orange, how many orange candies will there be per 100 candies total?
Answer:
45
Step-by-step explanation:
20 / 9 = 2.222222222223
100 / 45 = 2.222222222223
9 is 45% of 20 and 45 is 45% of 100.
Compute the area of a circle with a diameter of 18 inches.
Answer:
254.34
Step-by-step explanation:
Diameter: 2×radius
Radius:Diameter÷2
Area: pi×radius²
18/2=9
Radius=9
pi=3.14
3.14×9²=254.34
The area is 254.34
For which value of x is inequality 3(1+x)<+6true?
Answer: For in the inequality to be true, X must be less than or equal to 1. That represented as an in equality is X < 1.
x<1 true
Step-by-step explanation:
3(1+x)<+6= 3×1+3×X<+6=3+3x<6 then3x=6-3 solution 3x=3 devide by 3 both sides the answer is x=1 hence x<1 verified
can someone plz help with this FAST
I WILL MARK BRAINLIEST
Answer:
Maria
Step-by-step explanation:
Sean - 2 minutes (1 mile/minute)
Maria - 4 minutes (0.5 miles/minute)
David - 3 minutes (1 mile/minute)
Carrie - 2 minutes (0.5 miles/minute)
I need help asap! Pls :)
Answer:
Step-by-step explanation:
6x + 10 + 2x + 26 = 180
8x + 36 = 180
8x = 144
x = 18
Will give brainliest
Answer:
between midnight and 3am i think
Step-by-step explanation:
I’ll give brainliest to the person who give me the correct answer and pointsss.
Match them
I think the y=ab^x goes with the first graph and the y=logbc goes with the second
Step-by-step explanation:
pictures
Please help I don’t understand!!
Answer:
[tex] \frac{5(x + y)}{ - 8x} [/tex]
Step-by-step explanation:
quotient means division
numerator is the top
denominator is the bottom
product means multiply
sum means add
Which graph represents a function?
Answer:
just the first on. upper left corner
Expand and simplify: (x - 7)(x+7)
Answer:
[tex]x^{2} -49[/tex]
Step-by-step explanation:
Answer:
[tex](x-7)(x+7) =x^2 -7^2 = x^2 -49[/tex]
Step-by-step explanation:
General admission to the fair is $8.00, and rides cost $3.00 each.
Answer:
$24.00
Step-by-step explanation:
8x3=24
Which number is a perfect cube?
O4
O 16
O 24
O 64
Tina wants to sew a piece of fabric into a scarf in the shape of an isosceles triangle as shown in the accompanying diagram what are the values of x and y ?
Answer:
A. x = 96 and y = 42
Step-by-step explanation:
The required measure of the angle x and y is given as x =92° and y = 42°. Option A is correct.
Given that,
Tina wants to sew a piece of fabric into a scarf in the shape of an isosceles triangle as shown in the accompanying diagram what are the values of x and y is to be determined.
A triangle with two sides and two congruent angles that are equal each other is called an isosceles triangle.
Here,
For an isosceles triangle,
The measure of the angle opposite to the equal side is equal, So
y = 42°
Now,
The sum of the angles in the triangle° is equal to 180,
x + y + 42 = 180
x + 42 + 42 = 180
x = 96
Thus, the required measure of the angle x and y is given as x =92° and y = 42°. Option A is correct.
Learn more about the isosceles triangle here: https://brainly.com/question/2456591
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What is the equation of the line that passes through the point (8,-4) and has a slope of 1/2
Answer:
y = 1/2x - 8
Step-by-step explanation:
Assuming that they want the equation in slope intercept form we would use the following form: y = mx + b
where m = slope and b = y intercept.
We are given the slope and a point on the line. We need to find the y intercept. We can do this by plugging in what we are given and then solving for b.
y = mx + b
slope (m) = 1/2
x value of given point (x) = 8
y value of given point (y) = -4
- plug in these values -
-4 = (1/2)(8) + b
now solve for b
multiply 1/2 and 8
-4 = 4 + b
subtract 4 from both sides
-8 = b
So the y intercept (b) is -8
We now plug in the slope and y intercept into slope intercept form
y = mx + b
m = 1/2 and b = -8
y = 1/2x - 8 is the equation of the line that passes through the point (8,-4) and has a slope of 1/2
For more validation refer to the attached image.
[tex]\text{Given that,}\\\\(x_1,y_1) = (8,-4), ~~ \text{and slope, m} = \dfrac 12\\\\\text{Equation with given points,}\\\\y -y_1 = m(x-x_1)\\\\\implies y -(-4) = \dfrac 12 (x-8)\\\\\implies y+4 = \dfrac 12 x - 4\\\\\implies y= \dfrac 12x -4 -4 \\\\\implies y = \dfrac 12 x -8\\\\\implies y = \dfrac{x-16}2\\\\\implies 2y = x -16\\\\\implies x -2y = 16[/tex]
How much money will you spend on these items? Round to the nearest cent.
Shopping List:
2.75 pounds of grapes.
0.8 pounds of garlic
The grapes are $0.89 per pound.
The Garlic is $0.34 per pound. Please Help
Answer:
$2.72
Step-by-step explanation:
2.74x0.89=2.4475
0.8x0.34=0.272
2.447+0.272=2.719, rounded is 2.72
the questions are in the pdfs i really need help
Answer:
Step-by-step explanation:
1) 11 + 11
2) 17 - n
3) x^2
4) 3^3
5) 88 / 8
6) 6 + 11
7) the quotient of 35 and 5
8) the sum of 4 and 5
9) 10 squared
10) 3 less than x
13) p^3 + qp
2^3 + 4(2)
8 + 8 + 16
14) (y^3)z / 3
(5^3)3 / 3
125(3) / 3
375 / 3
125
15) 2 + (j - h)^2
2 + (5 - 3)^2
2 + (2)^2
2 + 4
6
the students in Jake's class , 6 have visited a zoo and 6 have visited a factory 3 students have visited both a zoo and a factory . How many students have visited a zoo but not a factory ?
Answer:
3
Step-by-step explanation:
6 have visited a zoo.
6 have visited a factory.
3 visited both.
Of the 6 who visited a zoo, 3 also visited a factory.
Of the 6 who visited a factory, 3 also visited a zoo.
Here is the list of students:
3 visited a zoo but not a factory.
3 visited a factory but not a zoo.
3 visited both.
Answer: 3
In need of help pls. Try and answer asap.
Answer:
Step-by-step explanation:
∠1 and 85 are supplementary
m∠1 = 180 - 85 = 95°
MATHH QUESTION HELP. mesasuremtns
Answer:
Step-by-step explanation:
Answer:
See image
Step-by-step explanation:
Look at the front side of the building. It's a triangle, with the height given. We can see a right triangle here which means we can use the Pythagorean theorem. a^2 + b^2 = c^2 (a and b are the shorter sides called legs and c is the longest side called the hypotenuse)
20^2 + 13^2 = c^2
400 + 169 = c^2
569 = c^2 square root both sides
Sqrt 569 is approximately 23.85 ft. This is the length from the roof peak down the front edge to the bottom front right corner in the image.
Now, if we consider the roof itself. That edge is now a leg (on the front face it was the hypotenuse). The other leg is the 35 ft width given. So we'll use pythagorean theorem again to find the diagonal
23.85^2 + 35^2 = c^2
568.8 + 1225 = c^2
1793.8 = c^2
Square root both sides of the equation.
Sqrt 1793.8 = c
42.35 ft = c
The diagonal of the roof is just over 42 feet, that is 42.35 feet.
A school has 2880 students. The following information refers to the students:
7/20 are freshmen, 2/9 are juniors, 1/6 are seniors. What fractional part are sophomores?
How many students are sophomores?
Answer:
752
Step-by-step explanation:
7/20 of 2880 = 1008
2/9 of 2880 = 640
1/6 of 2880 = 480
2880 - 1008 - 640 - 480 = 752
A=1/2h(b1+b2) is the formula for the area of a trapezoid. Rewrite the formula for h, and then find the height of the trapezoid that has an area of 78 square inches and base lengths of 5 inches and 8 inches.
Answer:
Let's neaten up that equation a bit:
trapezoid area = height * (sum of the bases) / 2
height = 2 * area / (short base + long base)
height = 2 * 78 / (5 + 8)
height = 156 / 13
height = 12 inches
Source: https://www.1728.org/quadtrap.htm
Step-by-step explanation:
The formula for the height is h = (b1+b2)/2A and the height of the trapezoid is 12 inches
What is area of a trapezoid?A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides.
The area of a trapezoid is expressed as;
A = 1/2( a +b) h
where a and b are the parallel sides and h is the height.
Making h the subject
(a+b)h = 2A
h = 2A/( a+b)
h = 2A( b1 + b2)
A = 78 in²
a = 5 in
b = 8 in
h = 2 × 78/( 8+5)
h = 156/13
h = 12 in
learn more about area of trapezoid from
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