Answer:
y=2x-1
Step-by-step explanation:
May God bless you and your family during this spring break
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{7}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{2}}}\implies \cfrac{4}{2}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{2}(x-\stackrel{x_1}{2}) \\\\\\ y-3=2x-4\implies y=2x-1[/tex]
Ejercicio Nº 4 Desde la parte superior de un acantilado de 80 metros de altura se dispara horizontalmente una piedra a razón de 8m/s. Calcular: g = 10m/s? 1) el tiempo que permanece en el aire. 2) la distancia horizontal que el cuerpo alcanza. 3) la velocidad con que la piedra alcanza el suelo
Answer:
1) La piedra permanece en el aire en 4 segundos.
2) La piedra alcanza una distancia horizontal de 32 metros.
3) La velocidad de la piedra con la que alcanza el suelo es aproximadamente 40.792 metros por segundo.
Step-by-step explanation:
El problema nos indica un caso de tipo parabólico, el cual consiste en la suma de un movimiento horizontal a velocidad y un movimiento uniforme acelerado por la gravedad desde el reposo.
1) El tiempo total que la piedra permanecería en el aire es tiempo requerido entre la parte superior del acantilado y el fondo. La ecuación cinemática que vamos a utilizar es la siguiente:
[tex]y = y_{o} + v_{o,y}\cdot t +\frac{1}{2}\cdot g \cdot t^{2}[/tex] (Ec. 1)
Donde:
[tex]y_{o}[/tex] - Altura inicial, medida en metros.
[tex]y[/tex] - Altura final, medida en metros.
[tex]v_{o,y}[/tex] - Velocidad vertical inicial de la piedra, meadida en metros por segundo.
[tex]g[/tex] - Aceleración gravitacional, medido en metros por segundo al cuadrado.
[tex]t[/tex] - Tiempo, medido en segundos.
Si sabemos que [tex]y_{o} = 80\,m[/tex], [tex]v_{o,y} = 0\,\frac{m}{s}[/tex] y [tex]g = -10\,\frac{m}{s^{2}}[/tex], entonces encontramos la siguiente función cuadrática:
[tex]-5\cdot t^{2}+80 = 0[/tex] (Ec. 2)
El tiempo en el que la piedra permanece en el aire es:
[tex]t = 4\,s[/tex]
La piedra permanece en el aire en 4 segundos.
2) La distancia horizontal es descrita por la siguiente fórmula cinemática:
[tex]x = x_{o}+v_{o,x}\cdot t[/tex] (Ec. 3)
Donde:
[tex]x_{o}[/tex] - Posición horizontal inicial, medido en metros.
[tex]x[/tex] - Posición horizontal final, medido en metros.
[tex]v_{o,x}[/tex] - Velocidad horizontal inicial de la piedra, medida en metros por segundo.
Si sabemos que [tex]x_{o} = 0\,m[/tex], [tex]v_{o,x} = 8\,\frac{m}{s}[/tex] and [tex]t = 4\,s[/tex], entonces la distancia horizontal alcanzada por la piedra es:
[tex]x = 0\,m + \left(8\,\frac{m}{s}\right)\cdot (4\,s)[/tex]
[tex]x = 32\,m[/tex]
La piedra alcanza una distancia horizontal de 32 metros.
3) En primer lugar, determinamos los componentes vertical y horizontal de la velocidad final de la piedra por medio de las siguientes fórmulas cinemáticas:
Velocidad final horizontal ([tex]v_{x}[/tex]), medida en metros por segundo.
[tex]v_{x} = \frac{x-x_{o}}{t}[/tex] (Ec. 4)
Velocidad final vertical ([tex]v_{y}[/tex]), medida en metros por segundo.
[tex]v_{y} = v_{o,y}+g\cdot t[/tex] (Ec. 5)
Si [tex]x = 32\,m[/tex], [tex]x_{o} = 0\,m[/tex]. [tex]t = 4\,s[/tex], [tex]v_{o,y} = 0\,\frac{m}{s}[/tex] y [tex]g = -10\,\frac{m}{s^{2}}[/tex], los componentes de la velocidad final de la piedra son:
[tex]v_{x} = \frac{32\,m-0\,m}{4\,s}[/tex]
[tex]v_{x} = 8\,\frac{m}{s}[/tex]
[tex]v_{y} = 0\,\frac{m}{s}+\left(-10\,\frac{m}{s^{2}} \right) \cdot (4\,s)[/tex]
[tex]v_{y} = -40\,\frac{m}{s}[/tex]
Por último, determinamos la velocidad final de la piedra por Teorema de Pitágoras:
[tex]v = \sqrt{v_{x}^{2}+v_{y}^{2}}[/tex] (Ec. 6)
[tex]v = \sqrt{\left(8\,\frac{m}{s} \right)^{2}+\left(-40\,\frac{m}{s} \right)^{2}}[/tex]
[tex]v \approx 40.792\,\frac{m}{s}[/tex]
La velocidad de la piedra con la que alcanza el suelo es aproximadamente 40.792 metros por segundo.
In Table 2, at this rate, how much would it cost to buy 9 books?
Answer:
There is no table attached, if you attach is I will gladly help :)
Step-by-step explanation:
HELPPP PLEASEEE
Point P is the center of the cirlce and ∠BDC= 60°. Determine:
a. ∠DBC
b. ∠DAC
c. ∠ACD
d. ∠AEB
e. ∠APB
Answer:
Step-by-step explanation:
Angle CDB=angle BAC=42°(angles subtended by same chord)
CA is diameter,therefore angle ABC=90°(angle subtended by diameter is 90°)
In triangle CBA ,angle ACB=48°[angle
sum property]
Consider the following expressions: A. 34÷23 B. 710÷45 C. 78÷12 D. 34÷13 E. 15÷1115 a. Which expression(s) will result in a quotient that is greater than one? 34÷23 710÷45 78÷12 34÷13 15÷1115
Answer:
A, B, C, and D
Step-by-step explanation:
All the prime numbers
Answer:
13 23 43
Step-by-step explanation:
Prime numbers are numbers that are divisible by 1 and itself or numbers that have only 2 factors which is 1 and itself.
Patrick usually jogs 1 1/2 miles each day but yesterday he jogged only 1/3 as far. How far did he run yesterday?
Answer:
You need to divide 11/2 by 1/3 and you will have you answer
Step-by-step explanation:
In January, the depth of a lake was 1,178 feet. In August, the depth of the lake was 1,001.3 feet. What is the percentage decrease of the depth of the lake from January to August?
Answer:
15%
Step-by-step explanation:
decrease in depth = 1,178 - 1,001.3 = 176.7
percentage decrease = 176.7/1,178 = 0.15 = 15%
9,874.35 - 6490.02
step by step
Answer:
[tex]9874.35 \\ 6490.02 \\ 3384.33[/tex]
The perimeter of a rectangular garden is 90m its breadth is 17m find its length
Answer:
28 m
Step-by-step explanation:
Length = x
90 = 2(17 + x)
17 + x = 90/2 = 45
so
x = 45 - 17 = 28 m
Verify the linear approximation at (0, 0) for
f(x, y) = 7x + 4
5y + 1
â 4 + 7x â 20y
Let f(x, y) = 7x + 4 5y + 1 . Then fx(x, y) = ________
In Ben's apartment complex, residents are fined $9 per day each day the rent is late. Last month, Ben wrote the apartment complex a check for $702 when his monthly rent is only $585. How many days late was Ben's rent?
Answer:
13 days late-poor guy
Step-by-step explanation:
(702-585)/9
117/9
13
The sum of two numbers that are at the ratio of 3:4 is 1001. Find these numbers.
Step-by-step explanation:
x - the part
3x one part(first number)
4x second part (second number)
so u have
3x + 4x = 1001
7x= 1001
x = 1001/7
x= 143. First number : 3x = 3• 143 = 429
Second number : 4x = 4• 143= 572
So, 429 and 572 are the numbers
Two parallel lines are crossed by a transversal.
Parallel lines c and b are cut by transversal a. On line c where it intersects with line a, the uppercase left angle is 80 degrees. On line b where it intersects with line a, the bottom right angle is y degrees.
What is the value of y?
y = 40
y = 80
y = 100
y = 120
Answer 80
Step-by-step explanation:
If the line is a straight line through two parallel lines then the angles of the two intersections should be the same. Basically because they are both on the bottom right they will be the same.
The value of 'y' is 80 degrees. option B
How to determine the value of y
Note that alternate angles are equal
The intersections of a transversal with two parallel lines forms various types of pairs of angles such as
consecutive interior anglesconsecutive exterior angles, corresponding anglesalternate anglesIn this case, the transverse line forms alternate angles of line c and b
Angle at line c = 80 degrees
Angle at line b = y
Since they are alternate angles, y = 80 degrees
Therefore, the value of 'y' is 80 degrees. option B
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Are all sides equal in an Isosceles triangle?
Answer:
No
Step-by-step explanation:
An isosceles triangle is a triangle with two equal/congruent sides. An equalateral triangle has all three sides equal.
“Firms will loss _?_ if the firm shuts down in the short run”
Answer:
The correct answer was C!
Step-by-step explanation:
How many pairs does a liminal have?
Answer:the answer to your intresting question is 3
Step-by-step explanation:
add me to brainiest if you want
A cylinder has a radius of 3 feet and a height of 7 feet. Which of the following can be used to calculate the volume of a cone that fits exactly inside the cylinder?
(3.14)(7%)(3)
03(3.14373)(3)
(3.14)(3)(7)
O
0|(3.1413307
Volume of a cylindre = area base x height
Volume of a cone = 1/3 x area base x height
V cone = 1/3 x pi x r² x h = 1/3 x 3,14 x 3² x 7
what is the elapse time between 10:35am and 1:10pm
2 hours, 35 minutes, and 0 second
Step-by-step explanation:
10 am to 1 pm is 2 hours
and you have the 35 in which you add there for giving you the answer 2 hours, 35 minutes, and 0 second
Answer:
2 hours 35 minutes
Step-by-step explanation:
Classify the number (choose all that apply): 3/4
Answer:
What are the answer choices? I would help but you didn't attach or write them.
Step-by-step explanation:
A campsite provides a locking, rectangular box with the dimensions shown to secure
food from bears. What is the volume?
(PUT NUMBER ONLY)
3 feet
2 feet
5 feet
Answer:
30 feet^3
Step-by-step explanation:
2*5*3=30
V= bhw
Help!
What is the answer to this question?
Answer:
b = 73°
Step-by-step explanation:
They are vertical angles to each other.
factorise [8x^{2}-30x-27=0
Answer:
Step-by-step explanation:
8x² - 30x - 27 = 0
8 = 4 * 2
-27 = -9 * 3
-30 = 4*(-9) + 2*3
so (4x + 3)(2x - 9) = 0
Please explain how to do this
Show working
Answer:
a = 3b/b-3
because combined the expression and leaving alone the variable
Answer:
(A, B) = (4, 12) or (12, 4)
Step-by-step explanation:
An Egyptian fraction is the sum of distinct unit fractions. Here, we're asked to decompose 1/3 into an Egyptian fraction sum of two fractions. There are formulas available when the sum has a numerator value of 2.
Here, the sum is a unit fraction. A reasonable approach is to use 1/(n+1) as the larger portion of 1/n. Then the other portion is 1/(n(n+1)). That is effectively what we end up with here.
__
Multiplying by 3AB gives ...
AB = 3B +3A
Solving for B, we find ...
AB -3B = 3A
B(A -3) = 3A
B = 3A/(A -3)
In order for A-3 to be a factor of A, or equal to 3, we must have ...
A-3 = 1 ⇒ A = 4
A-3 = 3 ⇒ A = 6
A-3 = 3×3 ⇒ A = 4×3
This will give integer values for B when A is one of 4, 6, or 12. In the case of A=6, the two fractions are equal, which is not what you want
The two solutions are ...
(A, B) = (4, 12) or (12, 4)
A parabola has an axis of symmetry at x = 0.5 and one of the x-intercepts is at x=-3. Where is
the other x-intercept?
Answer:
4
Step-by-step explanation:
distance from .5 to -3 is 3.5
now add the same distance to the other side
.5 plus 3.5 is 4
A small can contain 2 cups of soup. do 3 small cans have a greater amount than a 1 - quart container of soup.
Answer:
quarts. 11. fluid ounces = —. 1. 4. — quart. 12. quarts = 6 gallons. 13. 16 pints = gallons. 14. ... How many times must a 1-cup measuring cup be filled to equal 4 pints? 2. Leroy has 2 containers. ... can hold. Write cup, pint, quart, or gallon. 15. a bathtub. 16. a container of orange juice. 17. a juice box. 18. a small milk carton. 1
Step-by-step explanation:
Find the distance between (-7,3) and (-2, 1). Round your
answer to the nearest tenth
Answer:
5.4
Step-by-step explanation:
Using the distance formula:
[tex] \sqrt{ {( - 7 - ( - 2))}^{2} + {(3 - 1)}^{2} } [/tex]
[tex] \sqrt{ {( - 5})^{2} + {2}^{2} } [/tex]
[tex] \sqrt{25 + 4} [/tex]
[tex] \sqrt{29} [/tex]
[tex]5.4[/tex]
The 16th term of an AP is three times the 5th term.If the 12th term is 20 more the 7th term.Find the first term and the common difference
Let's take the first term as a and the common difference be d
The formula to find the nth term of an arithmetic progression is given by :
an = a + ( n - 1 ) dAccording to question, we have :
16th term of an AP is three times the 5th term.➝ a16 = 3 ( a5 )
➝ a + ( 16 - 1 )d = 3 ( a + ( 5 - 1 )d )
➝ a + 15d = 3 ( a + 4d )
➝ a + 15d = 3a + 12d
➝ 15d - 12d = 3a - a
➝ 3d = 2a
➝ 2a = 3d
➝ a = 3d/2ㅤㅤㅤ⸻ ( 1 )
And, the 12th term is 20 more the 7th term.➝ a12 - ( a7 ) = 20
➝ a + ( n - 1 )d -( a + ( n - 1 )d ) = 20
➝ a + ( 12 - 1 )d - + a + ( 7 - 1 )d ) = 20
➝ a + 11d - ( a + 6d ) = 20
➝ a - a + 11d - 6d = 20
➝ 5d = 20
➝ d = 20/ 5
➝ d = 4
Using equation ( 1 )➝ a = 3d / 2
➝ a = ( 3 × 4 ) / 2
➝ a = 12 / 2
➝ a = 6
What is 2.95 expressed as a fraction?
5920
11880
33640
40118
2.95 expressed as a fraction is 59/20.
What is the fraction equivalent?The decimal is made up of a whole number and a non-integer. In order to convert the decimal to a fraction, divide the non-integer by 100 and add it to the whole number.
2 + 95/100
2 19/20
Now multiply the whole number by the denominator, add the numerator and then divide by the denominator. The result is:
59/20
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Solve for m please I will give brainliest
Answer:
m-4n=8 divide both sides by 4.
m-n=2
There are two variables, so this is the simplest form.
Griffin bought 1.2 pounds of almonds for $6.60. His friend, Sam, bought almonds for $0.70 per pound cheaper. Which equation represents the cost, c, Sam paid for x pounds of almonds?
A.c = 4.80x
B. c = 5.50x
C. c = 5.90x
D. c = 7.30x
Answer:
Step-by-step explanation:
A
Answer: C
Step-by-step explanation:
0.70 divided by 1.2=0.59
0.59*1.2= 0.70
c=5.90x