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A laser beam moves along a straight line so that its velocity is given by v(t)=r²-4 feet/sec. What is the total distance, in feet, that the laser beam will have traveled between t=1 and t=3 seconds?
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
Simón Plz help me giving brainliest
Answer:
Although this (attached) would be the correct answer always; A would be the most logical one since only one piece is shaded the opposite color.
Hope this Helps!:)
HELP PLEASE 10 POINTS AND BRAINLIEST
Answer:
the first (c) is the answer: ΔABC ≅ ΔPQR
Step-by-step explanation:
Find AM⎯⎯⎯⎯⎯⎯ A M ¯ in the parallelogram if PN⎯⎯⎯⎯⎯ = 8 P N ¯ = 8 and AO⎯⎯⎯⎯⎯ = 5 A O ¯ = 5 .
Step-by-step explanation:
please can you show me a picture of this parallelogram
Simplify: 6^6/6^−3 Leave your answer in exponential form
Answer:
6⁹
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Exponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Exponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{6^6}{6^{-3}}[/tex]
Step 2: Simplify
Exponential Rule [Dividing]: [tex]\displaystyle 6^{6 - -3}[/tex]Rewrite: [tex]\displaystyle 6^{6 + 3}[/tex]Add: [tex]\displaystyle 6^{9}[/tex]Three interior angles of a quadrilateral have measures of 100degree,120degree, and 80 degree. Find the fourth angle measure.
The fourth angle measure is..
Answer:
The fourth angle = 60°
Step-by-step explanation:
the sum of the interior angles of a quadrilateral is 360°.
The fourth angle = 360° - 100° - 120° - 80° = 60°
Zoe runs a market in the city of Manila. Half of the canned drinks in stock were sold out. Zoe bought 68 more canned drinks to restock her supply. If there is a total of 200 cans now, how many canned drinks were in stock initially?
Answer:
264 canned drinks
Step-by-step explanation:
Let
canned drinks in stock initially = x
Canned drinks sold out = 1/2 of x
= 1/2x
Canned drinks remaining in stock = x - 1/2x
= 1/2x
New restock = 68 canned drinks
Total drinks in stock presently = Canned drinks remaining in stock + New restock
200 = 1/2x + 68
200 - 68 = 1/2x
132 = 1/2x
x = 132 ÷ 1/2
= 132 × 2/1
x = 264 canned drinks
canned drinks in stock initially = x = 264 canned drinks
What’s this help pls
How to solve your problem
9−4+3
9x−4+3x9x-4+3x9x−4+3x
Simplify
1
Combine like terms
9−4+3
9x−4+3x{\color{#c92786}{9x}}-4+{\color{#c92786}{3x}}9x−4+3x
12−4
12x−4{\color{#c92786}{12x}}-412x−4
Solution
12−4
SO D
Answer:
Answer is 12x - 4
Step-by-step explanation:
The give equation (9x -4 + 2x) has two x variables, we can take them both and add them together since they are both x's. So you would take 9 + 3 and and it to get 12, then plug in the variable x. Which will make your new equation 12x - 4
The diameter of a circle is 5 centimeters.
What is the circle's circumference? Use a = 3.14
Answer:
centimeters.
Answer:
half of 5 is 2.5
2.5 x 3.14 x 2 = 15.7 cm
Formula of circumference:
2(you just always need this number when finding circumference) x pi(3.14 or 22/7 depending on what they tell you to use) x r(radius, half of your diameter or given radius).
Answer:
15.7
Step-by-step explanation:
circumference = 2 x 3.14 x r ---? 2 x 3.14 x 2.5 = 15.7
Find the gradients for line A and B.
See pic attached
Carlos buys a phone that cost $250. He pays a monthly rate of $75. What is the independent variable of this function ?
Answer: 250+75x
Step-by-step explanation: 250 is the flat charge on the phone, and he pays 75 dollars as a monthly rate. x represents the amount on months.
Thank you for the help
Jamal's car travels an average of 16.7 miles per gallon of gas.
A full tank of gas is 20 gallons. Jamal has driven 292 miles
since he last filled his gas tank. How many more miles can
Jamal expect to travel on this same tank of gas?
Answer:
42 miles
Step-by-step explanation:
20 x 16.7 = 334 miles on a full tank of gas
he drove 292 miles so 334 - 292 = 42 miles left
7. Emily and John will be hiking for 42 hours. Hikers should drink at least 2.7 cups of water for every 2 hours of hiking. How many cups of water should Emily and John drink?
Step-by-step explanation:
in 24 hours they will drink 32.7 cups
in 18 hours they will drink 24.3
32.7+24.3=56.7
Evaluate tan15°=tan(60°_45°)
Answer:
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Step-by-step explanation:
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
5. The length of a rectangular swimming pool is 50 yards, and the width of the pool is 16
yards. What is the approximate length of the diagonal of this pool?
A. 66 yards
B. 2756 yards
C. 52.50 yards
D. 47.37 yards
x^2-2x/x^2-y^2 - 2y-y^2/y^2-x^2
2−1⋅22−12−2−1⋅22−12
Step-by-step explanation:
I NEED HEP ASAP I WILL GIBE BRAINLIEST ANSWER FOR WHOEVER ANSWERES FIRST
Answer:2
Step-by-step explanation:
how do you find the circumcenter of a triangle?
Answer:
draw the perpendicular bisectors of the sides and extend them. The point at which the perpendicular intersects each other will be the circumcenter of that triangle.
Find the volume of a pyramid with a square base, where the area of the base is 16 m^2
and the height of the pyramid is 25.4 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
v = 135.5 cm³
Step-by-step explanation:
v = 1/3bh = 1/3(16)(25.4) = 135.5 cm³
URGENT!!!! BRAINLIEST FOR CORRECT ANSWER!
At the Little Rock Zoo, the cost for one children's ticket is $10 and the cost for one adult's ticket is $13. On Saturday, the zoo had a total of 1,465 people visit the zoo and took in a total of $16,603. How many CHILDREN visited the zoo? (Number Only)
Answer:
1663
Step-by-step explanation:
chris is a 150 pound 5 foot 10 inch 18 year old male and he requires 2,048 calories per day to maintain his weight when he doesn't exercise. When he plays basketball, he burns 231 additional calories per hour. Assuming he want s to maintain his current weight, how many more calories per day does he require if he plays basketball for four hours instead of two hours?
Suppose you and a friend are playing a game that involves rolling a fair die. You roll the die and count how many times you must roll until you roll a 6. Which conditions for a binomial setting have been met for this scenario? Binary? Independent? Number of trials? Same probability?
Answer:
Binary-yes
Independent-yes
Number of trials- No
Same probability-yes
Step-by-step explanation:
Answer:
Binary?
✔ Yes
Independent?
✔ Yes
Number of trials?
✔ No
Same probability?
✔ Yes
Step-by-step explanation:
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Answer:
¡Hola! Lo siento, pero no hablo español. ¡qué tengas un lindo día! También necesito puntos porque soy nuevo.
Step-by-step explanation:
The diameter of a circle is 4cm. Find it area to nearewt tenth.
Answer:
12.6cm
Step-by-step explanation:
12.6 cm²
Area formula: (A = πr²)
If the diameter is 4 cm.. then that would mean the radius is 2 cm because the radius is half of the diameter. So, we already know the radius.. we just have to find the circumference.
Circumference formula: (C = πd) or (C = 2πr)
Finding the circumference : 3.14 × 4 = 12.56 cm
So, we now have the radius and circumference.
Radius = 2 cm
Circumference = 12.56 cm
Finding the Area : 3.14 × 2 × 2 = 12.56 cm²
So, 12.56 rounded to the nearest tenth is 12.6 cm².
Hope this helped! :)
Plzz help will mark brainiest!!!!!!
Answer choices for first box : 4, 20, and 34
answer choices for second box: decrease, preserve, and increase
Answer:
The length of the resulting line is 20 units
and for the second one it would be preserve
Step-by-step explanation:
Hope this helps :)
Sooo... WHy does everyone get so mad over links? Are those not allowed???
Q1
(b) Factorise
x2 – 36
(1 mark)
Answer:
(x+6)(x-6)
Step-by-step explanation:
Given: x²-36
Difference of Squares Formula: x²-a²=(x+a)(x-a)
Since 6²=36: x²-6²=(x+6)(x-6)
Kamal makes $12.00 an hour at his job. Last week he earned $390. Write and solve an equation to determine how many hours Kamal worked last week. Enter the correct answers in the boxes.
Show that cos 30 degree + sin 60 degree / 1+ sin 30 degree + cos 60 degree is equal to cos 30 degree
Answer:
cos 30
Step-by-step explanation:
cos 30 + sin 60 / 1+ sin 30 + cos 60
= root3 / 2 + root3/2 / 1 + 1/2 + 1/2
= root 6/2 by 4/2
= root 6/4
= root 3/2
= cos 30
Answer:
cos 30
Step-by-step explanation: