Answer:
It takes the rock approximately 4.96 seconds to reach the ground
Step-by-step explanation:
The given parameters of the rock thrown down from the hot air balloon are;
The (initial) downward velocity with which the rock was thrown down, u = 20 feet/second
The height of the balloon when the rock was thrown down, h = 220 feet
According to the kinetic equation of motion, we have;
h = u·t + (1/2)·g·t²
Where;
h = The height of the rock when it was thrown = 220 ft.
u = The initial velocity of the rock = 20 ft./s
g = The acceleration due to gravity acting on the rock = 9.81 m/s²
t = How long it takes the rock to reach the ground
Plugging in the values gives;
220 = 20·t + (1/2)×9.81×t²
4.905·t² + 20·t - 220 = 0
Therefore;
t = (-20 ± √(20² - 4×4.905×(-220)))/(2 × 4.905)
t ≈ 4.96, or t ≈ -9.04
Therefore, the time it takes the rock to reach the ground, t ≈ 4.96 seconds.
Anty was riding his bike to school at a speed of 12 mph. When he was of the way there, he got a flat tire. His mother drove him the rest of the way at a speed of 48 mph. What was his average speed?
Complete question:
Anty was riding his bike to school at a speed of 12 mph. When he was half of the way there, he got a flat tire. His mother drove him the rest of the way at a speed of 48 mph. What was his average speed?
Answer:
His average speed is 19.2 mph
Step-by-step explanation:
Given;
speed of Anty to school half of the way, v₁ = 12 mph
speed of Anty when his mother drove him half of the way, v₂ = 48 mph
The average speed of Anty is calculated as;
[tex]V_{average} = \frac{Total \ distance }{Total \ time }[/tex]
The value of the average speed is closer to 12 mph than 48 mph because Anty spent more time moving at 12 mph than at 48 mph.
Let the equal distance travel at each speed = 96 miles
Time taken at 12 mph = [tex]\frac{96 \ mile}{12 \ m/h} = 8 \ hours[/tex]
Time taken at 12 mph = [tex]\frac{96 \ mile}{48 \ m/h} = 2 \ hours[/tex]
Average speed = [tex]\frac{Total \ distance}{Total \ time } = \frac{96 \ mile \ + \ 96 \ mile}{2\ hr \ + \ 8\ hr} = \frac{192 \ miles}{10 \ hrs} = 19.2 \ mph[/tex]
Also, you can assume any other equal distance traveled at each speed, the average speed will still be 19.2 mph.
Check: let the equal distance traveled at each speed = 480 miles
Time taken at 12 mph = 480/12 = 40 hours
Time taken at 48 mph = 480/ 48 = 10 hours
Average speed = (480 + 480) / (40 + 10)
= 19.2 mph
Which expression is equivalent to 3x5x5x5x5x5x5?
Anyone help with this?
Answer:
3 degrees
Step-by-step explanation:
They are the same because they are on opposite sides of each other. If u look at the picture, angle a and b are the same size.
Based on the figure, select all true equations.
0
A.cos(42) =
B. cos(48) =
C. sin(42) =
D. sin(48)
E. tan(42) -
F. tan(48) =
Answer:
sin c
Step-by-step explanation:
Based on the figure, The true equations are, B. cos48° = b/c,
C. sin42° = b/c, E. tan42° = b/c and F. tan48° = a/c.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
We know, The sum of all the interior angles in a triangle is 180°.
So, The m∠B = 180° - 90° - 48° = 42°.
Now according to reference angles, we'll obtain the trig ratios.
cos42° = a/c.
cos48° = b/c.
sin42° = b/c.
sin48° = a/c.
tan42° = b/c.
tan48° = a/c.
learn more about trig ratios here :
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Miami is building a ramp with a base of 4 feel and a vertical height of 2 feet what is the length of the ramp round to the nearest tenth
Answer:
2√5
Step-by-step explanation:
By applying Pythagoras (hypotenuse)^2=(Base)^2 +(Height)^2
ava,jayden,edwina,lexi,luis, and trina are helping clean up a hiking trail during the summer. The trail is 10 miles long. Edwina, lexi, and luis plant a tree every 1/4 of a mile along the trail. Write and evaluate a division expression to find the number of trees they will plant.
Answer:
120 trees
Step-by-step explanation:
4x10=40
40x3=120
120 trees will be planted
If 8 subtracted from the product of 3 and a number the result is 10. Find the number
Find the volume of a rectangular prism with the following dimensions:
Length = 5 ft
Width = 4 ft
Height = 10 ft
210 ft3
220 ft3
190 ft3
200 ft3
Answer:
The answer is D, 200
Step-by-step explanation:
Since the formula for the volume of a rectangular prism is V = lwh, we multiple the length, width, and height together. This works for any rectangular prism.
V = lwh = 5 * 4 * 10 = 200
Answer:
200 ft3
Step-by-step explanation:
La velocidad maxima permitida en una autopista es de 120km/h. Se considera infraccion si se sobrepasa segun al rodar el 12% de esa velocidad. A que velocidad como minimo iba un conductor que cometio una infraccion
Answer:
La velocidad mínima a la que debe ir un conductor que cometa una infracción es de:
134.5 Km/hO si se desea un número entero:
135 Km/hStep-by-step explanation:
Para identificar la velocidad que debe levar un conductor para cometer una infracción, se deben tener en cuenta las pautas dadas en el ejercicio:
Velocidad Máxima Permitida: 120 Km/hCausa de infracción: Sobrepasar el 12% de la velocidad máxima.Ahora debemos calcular el 12% de la velocidad máxima permitida y sumarlo a dicha velocidad, con el fin de calcular la velocidad límite justo antes de cometer la infracción:
Velocidad límite antes de la infracción = 120 Km/h + (120 Km/h * 12%)Velocidad límite antes de la infracción = 120 Km/h + 14.4 Km/hVelocidad límite antes de la infracción = 134.4 Km/hCómo puedes ver, cuando el conductor está manejando a 134.4 Km/h está justo al límite antes de cometer una infracción, ya que recuerda que en el enunciado se menciona que "se considera infracción si se sobrepasa según al rodar el 12% de esa velocidad", por lo tanto, la velocidad que debe tener para cometer esa infracción debe ser mayor a la velocidad límite, la cual puede ser 134.5 Km/h, aumentando solo una décima a la velocidad límite, o 135 Km/h si se requiere que la respuesta sea un número entero.
There is a 2-digit number. The sum of its ten digit and the unit digit is 10. Given the unit digit is 3, what is the 2-digit number
Answer:
7
Step-by-step explanation:
According to the Question,
Given, There is a 2-digit number, the unit digit is 3 & The sum of its tens digit, and the unit digit is 10.
Suppose The Number is XY .
Now, We Know X+Y=10 & Y=3 .
So, X+3=10 ⇔ 7 is the number on Tens Place.
And, the Number is 73 .
A laptop computer is purchased for $2050. After each year, the resale value decreases by 30%. What will the resale value be after 4 years?
Use the calculator provided and round your answer to the nearest dollar.
$
Answer:
492.205
$492
Step-by-step explanation:
2050/100 = ?/ 70 <- repeat four times changing 2050 to the new value.
The resale value of the laptop after 4 years will be approximately $492.
How to calculate the resale value?To calculate the resale value "b" of the item after "n" years, we need to apply the annual decrease in value to the original price "a" for each year (n). We can do this using a loop or by using a formula.
b = a x (1 - decrease rate)ⁿ
As per the question, the old value is $2050, the decrease rate is 30%, and the number of years is 4. Plugging these values into the formula gives us:
new value = $2050 x (1 - 0.30)⁴
Simplifying this expression gives us:
new value = $2050 x 0.70⁴
new value = $2050 x 0.2401
Which simplifies to:
new value = $492.205
Rounding this result to the nearest dollar gives us $492.
Therefore, the resale value of the laptop after 4 years will be approximately $492.
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Plzzz help last test of the year marking brainliest
Answer:
108
Step-by-step explanation:
PLS HELP Find the value of x.
A. 30
B. 15
C. 45
D. 6
Answer:
B.
[tex](3x - 15) -(45 - x) = 0 \\ 4x -60 = 0 \\ 4x = 60 \\ x = 15[/tex]
work out the answer of the given fractions 3/12+1/6=
What are the coordinates of V′ for the transformation (T(–3, 1)° D4 )(ΔTUV) of T(–7, –6), U(–8, 3), and V(2, 1)?
Answer:
(5;1)
Step-by-step explanation:
-3 means shift to the right
Change the units up above to the correct answer from (a) to (d)
Answer:
Step-by-step explanation:
1 cm = 10 mm
a) 0.1 cm = 1 mm
1 mm = 1000 m
b) 25000mm = 25 m
1 g = 0.001 kg
c) 7g = 0.007 kg
1ml = 0.000001
d) 30000ml = 0.03 kl
Find the missing angle in this triangle
Answer:
hope it helps
Step-by-step explanation:
124+23+x=180
x+147=180
x=180-147
x=33
Which graphs represent functions with the following key features?
positive on ()
increasing on ()
approaches 0 as x approaches
Graph U
Graph V
Graph W
Graph X
Graph Y
Graph Z
Answer:
Graph U
Step-by-step explanation:
A graph is used to illustrate the relationship between variables.
For graph U:
Graph U is positive on (-∞, ∞). The graph also increases on (-∞, ∞). The graph approaches 0 as x approaches -∞.
For graph V:
Graph V is positive on (-∞, ∞). The graph also increases on (-∞, ∞). The graph is negative as x approaches -∞.
For graph W:
Graph W is positive on (-∞, 0). The graph also increases on (-∞, 0). The graph approaches 0 as x approaches -∞.
For graph X:
Graph X is positive on (-∞, ∞). The graph also increases on (-∞, ∞). The graph is negative as x approaches -∞
For graph Y:
Graph Y is positive on (-∞, ∞). The graph also decreases on (-∞, ∞). The graph approaches 0 as x approaches ∞.
For graph Z:
Graph Z is negative on (-∞, ∞). The graph also decreases on (-∞, ∞). The graph is approaches 0 as x approaches -∞
What is the value of x?
2
to
64°
X =
Answer:
26
Step-by-step explanation:
64 + x = 90 ( whole part axioms )
x = 90 - 64
x = 26
Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let x represent the length of each of the equal pieces of yarn that Julie decides to cut. What is the equation that can be used to determine the total length of all of the yarn that she ends up cutting, y? Is the graph of the equation continuous or discrete?Which description is represented by a discrete graph?
Equation: y = 4x + 7.75
The graph is continuous
Step-by-step explanation:
Julie needs to cut 4 pieces of yarn,
Let x represent the length of each yarn.
4x + 7.75
y represents the total length of all of the yarn that Julie decides to cut.
y = 4x + 7.75
Therefore the required equation that can be used to determine the total length of all of the yarn is:
y = 4x + 7.75
The graph is continuous because the amount of yarn that Julie decides to cut not need to be an integer amount.
hope this help's
find the complement of 63°
Answer:
63=90-63= 27
Bye
I need help on this question can anyone help?
Answer:
The answer is A. the range is the set of all real numbers
POSSIBLE POINTS: 6.67
Directions: Solve for x. Round your answer to the nearest tenth. Make sure you calculator is
in degree mode!
24
46
Y
Show work please
Answer:
x ≈ 33.4
Step-by-step explanation:
Using the sine ratio in the right triangle
sin46° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{24}{x}[/tex] ( multiply both sides by x )
x × sin46° = 24 ( divide both sides by sin46° )
x = [tex]\frac{24}{sin46}[/tex] ≈ 33.4 ( to the nearest tenth )
Please help i'm struggling with this!It's urgent!
Answer:
Step-by-step explanation:
Dilation
WRITE AN EQUATION THAT REPRESENTS THE LINE. USE EXACT NUMBERS.
Answer:
[tex]y=\frac{6}{5}x-5[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)
1) Determine the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Plug in the two given points (0,-5) and (5,1)
[tex]m=\frac{1-(-5)}{5-0}\\m=\frac{1+5}{5-0}\\m=\frac{6}{5}[/tex]
Therefore, the slope of the line is [tex]\frac{6}{5}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{6}{5}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{6}{5}x+b[/tex]
On the graph, we can see that when x is 0, y is equal to -5 (we're also given the point (0,-5). Therefore, the y-intercept of the line is -5. Plug this back into the equation:
[tex]y=\frac{6}{5}x-5[/tex]
I hope this helps!
Answer:
y = 6/5x - 5
Step-by-step explanation:
To find the equation of a linear line you need 2 things: the slope and the y-intercept.
The slope can be found by taking two points and dividing the change in y by the change in x. Using the two points highlighted, the slope would be (1 - -5)/(5-0) = 6/5.
The y-intercept is where the line crosses the y-axis, which on this line is at -5. Then plug in this information into point slope form, y = mx + b, where m is the slope.
So you get y = 6/5x - 5.
Here is standard form too if you need this instead: 6x - 5y = 25
How fast can you screw 800 nails in 60 different random locations
please help with the question above!!
Answer:
5
Step-by-step explanation:
1+2+2+3+3+3+4+5+6+6+7+7
+7+8+9 = 73
73/15 = 4.86667
you add all the numbers and divide by how many numbers there were.
so round it up and it should be 5.
In the trapezium ABCD, AB= 4 cm, BC=9 cm, CD= 16 cm, BCD=90°.
Find AD.
The value of AD will be 15 cm.
[tex] \mathrm{✌TeeNForeveR✌}[/tex]
Which equation is equivalent to
y-1= 5(x+2) ?
Step-by-step explanation:
We can simply by opening the brackets ,
=> y - 1 = 5( x - 2 )
=> y - 1 = 5x - 10
=> y - 5x = -9
=> 5x - y + 9 = 0
Which number is equivalent to 43/12
A 3.583
B.
3.583
C 3.583
D 3.583
Answer:
The answer is 3.583, the 3 is repeating
Step-by-step explanation:
Answer:
3.583 ,with 3 as a reapting decimal
