Answer:
4
Step-by-step explanation:
I used a calculator. I put integral values of 3 and 1 and then entered the equation inside absolute value bars
The total distance traveled by the laser beam in the given time interval is required.
The total distance traveled by the laser in the given time interval is 4 feet.
Equation of motionThe given equation is
[tex]v(t)=t^2-4[/tex]
The given time interval is from t = 1 to t = 3 seconds.
In order to find the distance traveled we need to integrate the equation with respect to time and between the given intervals.
[tex]0=t^2-4\\\Rightarrow t=\pm 2=+2[/tex]
The laser will change the direction at [tex]t=2[/tex]
[tex]\int_1^3 v(t)=\int_1^2t^2-4 dt+\int_2^3t^2-4 dt\\\Rightarrow \int_1^3 v(t)=\dfrac{t^3}{3}-4t|_1^2+\dfrac{t^3}{3}-4t|_2^3\\\Rightarrow \int_1^3 v(t)=\left|\dfrac{2^3}{3}-4\times 2-(\dfrac{1^3}{3}-4)+\dfrac{3^3}{3}\right|-\left|4\times 3-(\dfrac{2^3}{3}-4\times2)\right|\\\Rightarrow \int_1^3 v(t)=\dfrac{5}{3}+\dfrac{7}{3}\\\Rightarrow \int_1^3 v(t)=\dfrac{12}{3}\\\Rightarrow \int_1^3 v(t)=4\ \text{m}[/tex]
Since, here distance is asked the absolute value of each integral is used.
Learn more about equation of motion:
https://brainly.com/question/25951773
Serafine went shopping and bought the following items:
SERAFINE'S SHOPPING LIST
1 loaf bread $2.99
1 jar peanut butter $3.19
3 pounds apples $2.59
She had one coupon for $0.25 off and another for $0.40 off. Which expression represents
the total amount she needs to pay?
A
B
$2.99+ $3.19+ $ 2.59+ $0.25 + $0.40
$2.99 + $ 3.19+ $ 2.59+($0.25 - $0.40)
c$2.99+ $3.19+ $ 2.59+(- 50.25 + $0.40)
$2.99+ $3.19+ $2.59+- $0.25)+(- $0.40)
D
Answer:
I am going to assume that D's expression is actually $2.99+$3.19+$2.59+(-$0.25)+(-$0.40)
= $6.18+$2.59-$0.25-$0.40 [Note: (+)*(-)=(-)]
=$8.77-$0.25-$0.40
=$8.52-$0.40
=$8.12
Step-by-step explanation:
The prices of the loaf bread, a jar of peanut butter and 3 pounds of apples will be added. The value of the coupons will be then reduced from the total to get the final total.
please help i’ll give brainliest
Answer:
Matter in living things may pass into nonliving things.
Step-by-step explanation:
please help solve h(t) =-16t^2+40t+20
Answer: el último
Step-by-step explanation:
HELP EMERGENCY PLEASE!!!!
Find the percent of children who answered yes to the survey. Find the percent of children who answered no to the survey. Round each answer to the nearest tenth of a percent.
Answer:
31%
33%
Step-by-step explanation:
I'm not 100% sure. I tried my best.
I got 80% on a major grade. It's not that bad, right?
Answer:
no, that's good
Step-by-step explanation:
I'm pretty sure that's a b, so it's good
Answer:
No thats good cause last year i had a 60% as my major grade but i got 92% this year
Step-by-step explanation:
HURRY 50 POINTS
Which is the correct classification and decimal expansion of StartFraction 5 Over 8 EndFraction?
irrational number, 0.6ModifyingAbove 25 with bar
irrational number, 0.625
rational number, 0.625
rational number, 0.6ModifyingAbove 25 with bar
Answer:
the correct classification and decimal expansion of StartFraction 5 Over 8 EndFraction
=5/8=0.625[irrational number]
Answer:
The correct answer is (b) i believe
Step-by-step explanation:
Have a great day!
Solve for s -5s=−13 .
Answer:
13/4
Step-by-step explanation:
for these types of problems i recommend symbolab
ticket to the school play cost $9 for adults and $6 for students. The Smith Family bought 4 adult tickets and 5 student tickets. The Jones family bought 3 adult tickets and 7 student tickets. What was the difference in the amount spent by the two families?
Answer:
Difference is $3
Step-by-step explanation:
The Jones Family bought 3 adult tickets and 7 student tickets, so they spent 27+42=$69 spent.
The Smith Family bought 4 adult tickets and 5 student tickets, so they spent 36+30=$66 spent.
The difference between them is 69-66=$3.
So, the difference between how much the two families spent is $3.
Answer:
3$
Step-by-step explanation:
Smith family:
9x4=36
5x6=30
total=66$
Jones family:
3x9=27
7x6=42
total=69$
difference=3$
HELP DUE IN 60 MINS!
Round to the nearest tenth
1. Length of HF =??
Round to the nearest tenth
2. Length of EG =??
3. What kind of quadrilateral is this?
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
Kite
Answer:
Use distance formula to find the length of the segments
1. H = (-3, 0), F = (3, 2)
HF = [tex]\sqrt{(3 + 3)^2+2^2} = \sqrt{40}[/tex] = 6.3 (rounded)2. E = (1, 4), G = (-1, -2)
EG = [tex]\sqrt{(-1 - 1)^2+(-2-4)^2} = \sqrt{40}[/tex] = 6.33. We see the diagonals are congruent, opposite sides are parallel.
The above is the property of a rectangle
Find the midpoint and slope of the segment (4, 16) and (–8, 12).
Answer:
The midpoint is (-2,14) and the slope is m=1/3
Step-by-step explanation:
What fractions that are less than 3/5
Answer:
1/8 and 1/12
Step-by-step explanation:
Please help will give brainliest
Answer:
D
Step-by-step explanation:
40% = [tex]\frac{40}{100}[/tex] = [tex]\frac{2}{5}[/tex] ← in simplest form
Then
[tex]\frac{2}{5}[/tex] of $120 = [tex]\frac{2}{5}[/tex] × $120 = 2 × $24 = $48
she pays $120 - $48 = $72
A grocery store recently sold 10 cans of soup, 5 of which were lentil soup. What is the experimental probability that the next can sold will be lentil soup?
Write your answer as a fraction or whole number.
plz halp me
Answer: the answer is 1/2
Step-by-step explanation: I just got the answer form IXL
Answer:
1/2 is the answer
Step-by-step explanation:
1/2
Someone help me solve all this + include working out.
Will mark as brainliest. Thanks
Answer:
We know that P(x) = 30*x^3 + k*x^2 + 1
a) If (3x - 1) is a factor, let's find the value of k.
Because the degree of the original polynomial is 3, and the degree of the factor is 1, we should multiply it by a polynomial of degree 2.
Then:
30*x^3 + k*x^2 + 1 = (3*x - 1)*(a*x^2 + b*x + c)
30*x^3 + k*x^2 + 1 = 3*a*x^3 + 3*b*x^2 + 3*c*x - a*x^2 - b*x - c
30*x^3 + k*x^2 + 1 = 3*a*x^3 + (3*b - a)*x^2 + (3*c - b)*x - c
The terms with the same exponent should be equal, then:
30*x^3 = 3*a*x^3
30 = 3*a
30/3 = a = 10
k*x^2 = (3*b - a)*x^2
k = (3*b - 10)
0*x = (3*c - b)*x
0 = (3*c - b)
b = 3*c
and
1 = -c
then:
c = -1
Replacing this in the equation: b = 3*c
we get: b = -3
Replacing this in the equation for k, we get:
k = (3*b - 10) = (3*-3 - 10) = -19
k = -19
And we can write:
P(x) = (3*x - 1)*(10*x^2 - 3*x - 1)
b) Now we want to write P(x) as a product of its linear factors.
Then we need to factorize the quadratic part:
We need to solve
10*x^2 - 3*x - 1 = 0
We can use the Bhaskara's equation to get the solutions:
[tex]x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4*10*(-1)} }{2*10} = \frac{3 \pm 7}{10}[/tex]
Then the two zeros of that polynomial are
x = (3 + 7)/10 = 1
x = (3 - 7)/10 = - 4/10 = -2/5
So we can write the polynomial as:
10*(x - 1)*(x - (-2/5))
Replacing this in the equation of P(x) we get:
P(x) = (3*x - 1)*10*(x -1)*(x + 2/5)
= 10* (3*x - 1)*(x -1)*(x + 2/5)
So P(x) is written as a product of lineal factors.
C) The zeros of the polynomial are the values of x such that one of the factors becomes equal to zero.
For the first factor, we have a zero at x = 1/3
for the second, we have a zero at x = 1
for the third one, we have a zero at x = -2/5
Pls help timed test I don’t know how to do this and yeah
Explain why each statement is true. 5 + 2 + 3 = 5 + (2 + 3)
Answer:
Associative property of addition. Grouping different addends does not change the sum.
Step-by-step explanation:
5 + 2 + 3 = 5 + (2 + 3)
10 = 5 + (5)
10 = 10
For a function,x cannot what?
a) be zero
b)repeat
c)multiply
d) even
What is the volume of the cereal box?
cereal
(Height)18 in
(Length)3in
(W)12 in
find the perimeter of this four sided figure: 8, 17, 22, x
Answer:
255
Step-by-step explanation:
Once split up you find the are of the rectangle which is 8*17=136
Then since the bottom line is 22, you do 22-8 to find the bottom line of the triangle.
The area of the triangle is 17*14/2=238/2
Hence, 119
Hope it helps!
Answer:
63
Step-by-step explanation:
I hope
Please help if you know the answer please
Find the value of x in the triangle shown below.
Answer:
x = 61°
Step-by-step explanation:
since the triangle is isosceles the two angles opposite 58° are equal so:
x = (180° - 58°)/2 = 61°
Please help I have been stuck for a while now
A gallon of milk costs $3 nowIf the price is increasing 10% per year, how long before a gallon of milk costs $10 a gallon? Round your answer to the nearest thousandth, and you do not need to include units
Answer:
The answer is 33 years.
Step-by-step explanation:
10% of 3 is .3
Just move the decimal to the left.
.3 times 33=9.9
9.9~10
Help !!! Find the product of 5 x 2 and enter it in the so ABCD provided
Answer:
10
Step-by-step explanation:
5*2=10
2+2+2+2+2=10
Help meeee no Decimal answers.
Answer: 1,145,375cm^3
Step-by-step explanation:
Answer: Answer in photo below.
Hope this helps!
PLEASE HELP URGENTLY. Look at the given triangles.
Two triangles are shown
The blue triangle is a right triangle. The vertical leg is labeled with the expression 4 x plus 2. The horizontal leg is labeled with the expression 5 x minus 4. The hypotenuse is labeled with the expression 7 x plus 7.
The red triangle is a right triangle. The vertical leg is labeled with the expression x plus 3. The horizontal leg is labeled with the expression x plus 7. The hypotenuse is labeled with the expression 2 x minus 5.
a. Write an expression in simplest form for the perimeter of each triangle.
b. Write another expression in simplest form that shows the difference between the perimeter of the larger triangle and the perimeter of the smaller triangle.
Step-by-step explanation:
blue: 4x+2+7x+7+5x -4 = 16x +5
red: x+3+x+7+2x-5 = 4x -5
difference: 16x+5 - (4x -5) = 12x +10
The seagull population on a small island in the Atlantic Ocean can be calculated using the formula
P(t) = 5.3/11/?, where P is the population in hundred thousands, and t is in years. What will the seagull
population on the island be after 5 years? (Round to the nearest tenth.)
a. about 41.6 hundred thousand
c. about 172.4 hundred thousand
about 3.7 x 10' hundred thousand d. about 66.5 hundred thousand
The correct relation for the sea gull population is: P(t) = 5.3t^(11/7)
Answer:
d. about 66.5 hundred thousand
Step-by-step explanation:
Given that :
P(t) = 5.3t^(11/7)
Population, P is in hujdred thousand ; t = number of years
Population after 5 years ;
t = 5
P(5) = 5.3 * 5^(11/7)
P(5) = 5.3 * 5^1.5714285
P(5) = 5.3 * 12.542422
P(5) = 66.474840
P(5) = 66.5 (approximately)
Hence, population after 5 years will be about 66.5 hundred thousand.
Mhnaifa can you please help?
Answer:
1: 9
2: i dont know sorry
3: 21/2
Step-by-step explanation:
1: know that the bottom portion of the triangle is 18 the bottom left is 12 and the top left is 6. Now you could say that its six because they look the same size but we cant be sure, and six isnt an option. i dont know how to solve so we're using process of elimination so bare with me. we alread have 12 and 18 and theyre way bigger, it cant be 11 because it wouldnt be that small. so in my mind its 9.
2: n/A
3: because i said so
Answer:
#1
AQ/QC = AP/PBAQ / 18 = 6 / 12AQ = 18/2AQ = 9Option D
#2
x/ 12 = 10 / 24x = 12*10/24x = 5#3
(x - 8)/5 = 2/42(x - 8) = 52x - 16 = 52x = 21x = 21/2Option B
Daniel solves the equation 3(x+1)-5=3x-2 and states that it has no solution. Is he correct?
Explain why and why not.
Answer:
He is incorrect
Step-by-step explanation:
Given
3(x + 1) - 5 = 3x - 2 ← simplify left side
3x + 3 - 5 = 3x - 2
3x - 2 = 3x - 2
Since both sides are equal, then this indicates that the equation has infinite solutions.
HELP ASAP!!!! Rosa has 4 1/2 pounds of pizza dough. She uses 3/4 of a pound for one pizza. How many pizzas could be made from Rosa's dough?
Answer:
6
Step-by-step explanation:
3/4
1 1/2
2 1/4
3
3 3/4
4 1/2
Sorry if this doesn't make sense, I hope I helped though!