An object travels back and forth along a straight line. Its velocity, in centimeters per second, is given by the
function v(t)
= 13 sin(pi/(45)t), where t is time in seconds.
What is the maximum velocity of the object?
O 0 cm/s
O 13 cm/s
O 26 cm/s
O 90 cm/s
Answers
A function in mathematics is a relation between two sets such that each element of the first set is matched to exactly one of the second set element
The correct option for the maximum velocity of the object is the option;
13 cm/s
The reason for the selection is as follows:
The known parameters of the motion of the vehicle are:
The type motion of the vehicle = Repetitive back and forth
The path of the motion of the object = Along a straight line
The function that gives the velocity in centimeters per second (cm/s) is given as follows;
[tex]v(t) = \mathbf{13 \cdot sin \left(\dfrac{\pi}{45} \cdot t \right)}[/tex]
Where;
t = The time in seconds (a set of the input variables of the function)
v(t) = The velocity of the object (the output variables of the function)
The velocity of the object, v(t), depends (is given by) on the time t, therefore;
The maximum velocity is given at a particular value of t, which together with [tex]\dfrac{\pi}{45}[/tex] is operated by the sine function
The maximum output value of the sine function = 1, therefore;
[tex]\mathbf{Maximum \ value \ of \ sin \left(\dfrac{\pi}{45} \cdot t \right)_{max}} = 1[/tex]
[tex]The \ maximum \ velocity \ v(t)_{max}} = 13 \times sin \left(\dfrac{\pi}{45} \cdot t \right)_{max} = 13 \times 1 = \mathbf{ 13}[/tex]
The units of the of the function is cm/s
Therefore, the maximum velocity of the object is 13 cm/s
Learn more about functions here:
https://brainly.com/question/23999020
Answer: B. 13 cm/s
Step-by-step explanation:
Related Questions
What is the solution to the expression -2-3-(-4)?
-10 -9 8 7 6 5 4 3 -2 -1 0 1 2
3 4
5 6
+
8 9 10
7
O 5
Answers
Answer:
Umm, I believe your only correct answer for your equation above would be -1.
Step-by-step explanation:
Using the PEDMAS method:
-2 - 3= -5
= -5 - (-4)
-(-4) = 4
= -5 + 4
-5 + 4 = -1
So, your answer would be -1. Hope this helps!
(2t + 1) – (t – 9) = -52 – 8t
Show work ion get it
Answers
Step-by-step explanation:
Open the brackets
2t+1-t+9 = -52-8t
Collect the like terms
2t-t+8t = -52-1-9
9t= -62
Divide both sides by 9
t= -62/9
= -6.88
Approximately -6.9
please help me with this. thanks a lot
Answers
Answer:
Part A)
Approximately 318.1318 meters.
Part B)
Approximately 137.7551 meters.
Step-by-step explanation:
The path of a projectile is given by the equation:
[tex]\displaystyle y = \sqrt{3} x -\frac{49x^2}{9000}[/tex]
Part A)
The range of the projectile will be given by the difference between its starting point and landing point. In other words, its two zeros.
Let y = 0 and solve for x:
[tex]\displaystyle 0 = \sqrt{3}x - \frac{49x^2}{9000}[/tex]
Factor:
[tex]\displaystyle 0 = x\left(\sqrt{3} - \frac{49x}{9000}\right)[/tex]
Zero Product Property:
[tex]\displaystyle x = 0 \text{ or } \sqrt{3} - \frac{49x}{9000} = 0[/tex]
Solve for each case:
[tex]\displaystyle x = 0 \text{ or } x = \frac{9000\sqrt{3}}{49}\approx 318.1318[/tex]
Hence, the range of the projectile is approximately (318.1318 - 0) or 318.1318 meters.
Part B)
Since the equation is a quadratic, the maximum height is given by its vertex. Recall that the vertex of a quadratic is given by:
[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = -49/9000 and b = √3.
Find the x-coordinate of the vertex:
[tex]\displaystyle x = - \frac{(\sqrt{3})}{2\left(\dfrac{-49}{9000}\right)} = \frac{4500\sqrt{3}}{49}[/tex]
Then the maximum height will be:
[tex]\displaystyle \displaystyle \begin{aligned} y\left(\frac{4500\sqrt{3}}{49}\right) &=\sqrt{3} \left(\frac{4500\sqrt{3}}{49}\right) -\frac{49\left(\dfrac{4500\sqrt{3}}{49}\right)^2}{9000} \\ \\ &= \frac{13500}{49} -\frac{6750}{49}\\ \\ &=\frac{6750}{49}\\ \\ &\approx 137.7551\text{ meters}\end{aligned}[/tex]
The maximum height reached by the projectile will be 137.7551 meters.
Oscar's dog house is shaped like a tent. The slanted sides are both 5 feet long and the bottom of the house is 6 feet across. What is the height of his dog house, in feet, at its tallest point?
Answers
Answer:
height is 4ft.
Step-by-step explanation:
I used pathagorus theorem .All explaination is in the pic below.
if 3^2x +1 +8 =27 find x
Pls guys I need now
Answers
Step-by-step explanation:
3x²+1+8=27
3x²+9=2
3x²=27-9
3x²=19
x²=19/3
[tex]x = \frac{ \sqrt[]{19} }{ \sqrt{3} } [/tex]
Answer:
[tex]3^{2x} + 1 + 18 = 27\\ 3^{2x} = 18\\2x = log_{3} 18[/tex]
Step-by-step explanation:
Select all numbers that will round to 800 when rounded to the nearest hundred.
724
767
788
810
850
Answers
Answer:
Anything greater or equal to 750 will be rounded to 800
and anything less than 850 will be rounded to 800,
So the numbers are:-
767
788
810
please help. i need steps and everything
Answers
Answer:
x = 13, y = 24.
Step-by-step explanation:
5x - 8 + 63 + 7x - 31 = 180 (interior alternate angles are equal).
12x + 24 = 180
12x = 180 - 24 = 156
x = 156/12
x = 13.
4y + 27 = 63 + 7x - 31 (interior alternate angles are equal).
4y +27 = 32 +7(13)
4y = -27 +32 + 91
4y = `96
y = 96/4
y = 24.
The length of a rectangle is 15 cm and the width is 8 cm which is the perimeter of the rectangle
Answers
46
Step-by-step explanation:
Perimeter = 2(15 + 8)
Perimeter = 46
Answer:
46 cm
Step-by-step explanation:
To calculate the perimeter of a rectangle, you have to add the length with itself then add the width with itself. After that, you add both of the sums together to get the answer. For this particular question, this is what you have to do.
1.Add the length with itself 15+15=30
2.Add the width with itself 8+8=16
3. Add both sums 30+16=46
In conclusion, the perimeter of the rectangle is 46 centimeters.
At a hotel 3/4 of 100 rooms are occupied today yesterday 4/5 of 100 rooms were occupied on which day were more rooms occupied in by how much
Answers
Answer:
Yesterday 4/5 and by 5 more people
Step-by-step explanation:
Ok so 3/4 of 100 is just 100/4*3, which is 75. 4/5 of 100 is 100/5*4, therefore, equaling 80. So 80 > 75, and when you find by how much more you do 80-75, which is 5. I hope this helps and if you have any questions you can comment them on this answer
Answer:
The answer is 4/5
Step-by-step explanation:
well 3/4 of 100 is 75. 4/5 of 100 is 80.
one fourth is equal to 25. We know that because we divide 100/4 and since there's 3 out of 4 (25x3=75)
one fifth is equal to 20. (100/5 = 20) 4 times 20 equals 80
If 3/4 of x is 45, what is 1/8 of x
Answers
Answer:
15/2
Step-by-step explanation:
3/4(x)=45
x = 45 x 4/3
x = 15 x 4
x = 60
1/8 of 60
=> 15/2
..............................
A goat is grazing outside of a rectangular barn that has dimensions 20 ft by 30 ft.
He's tied to a corner of the barn with a 12 ft rope. Find the grazing area of the goat.
Answers
Answer: 36π
Step-by-step explanation:
Four times Greg's age, decreased by 3 is equal to 3 times Greg's age increased by 7. How old is Greg?
O 9
O 11
O 10
O 8
Answers
Answer:
let Greg's age be X
therefore;
4X - 3 = 3X + 7
4X - 3X = 7 + 3
X = 10
Greg is 10 years old
hope it's helpful
If f(0) = x2 + 2x – 10, what is f(-2)?
Answers
F(-2)
is
x2 + 2x
f(0)
=
x2
+
2x
-
10
Answer:
saiufhiuaewriufidnskjnckj
Step-by-step explanation:
sdibadlhjbvfjhbvfsdbhvfsdjh
Amy owes her mother $76. She pays her mother $14 on Sunday and $24 on Monday. Use an expression to describe the situation.
Answers
Answer:
$38
Step-by-step explanation:
$14+24=38 Amy pays her mom 38 dollars. :)
On Monday it snowed 8 in. On Tuesday the
snow melted 3 in. On Wensday it showed
another 5 in. How much snow
was on the
ground after it snowed on Wednesday?
Answers
Answer:
10in
Step-by-step explanation:
8-3=5
5+5=10
Answer:
10 inches.
Step-by-step explanation:
Assuming that before Monday, there was no snow.
On Monday, it snowed 8 inches, which is a net positive of 8:
0 + 8 = 8in total.
On Tuesday, it melted 3 inches, which is a net negative of 3:
8 - 3 = 5in total.
On Wednsday, it snowed another 5 inches, which is a net positive of 5:
5 + 5 = 10in total.
10 inches total of snow was on the ground on Wednesday.
~
Color the factors of 42 through the maze start at the s box and finish in the f box
Answers
Answer:
1, 2, 3, 6, 7, 14, 21, and 42 are the factors of 42
Step-by-step explanation:
Answer:
Factors of 42 are: 1, 2, 3, 6, 7, 14 and 21
How do I solve this I wanna know so I can do the rest without help pls
x + 5 = 2
Answers
Answer:
-3
Step-by-step explanation:
move the constant to the other side and get
X = 2 - 5
and X = -3
so you would do
-3 + 5 and you would get 2
Solve the following equations:
1. -301 = -3x = 7(4x – 18)
Answers
Answer:
-175/31
Step-by-step explanation:
-301 = -3x = 7(4x – 18)
-301 = -3x = 28x - 126
-301 = 31x = -126
-175 = 31x
x = -175/31
The volume for a cylinder is ________, for a cone is _______, and for a sphere is_______
Answers
Here are the formulas
[tex]\boxed{\sf Volume_{(Cylinder)}=\pi r^2h}[/tex]
[tex]\boxed{\sf Volume_{(Cone)}=\dfrac{1}{3}\pi r^2h}[/tex]
[tex]\boxed{\sf Volume_{(Sphere)}=\dfrac{4}{3}\pi r^3}[/tex]
Answer:
The volume for a cylinder is πr2h, for a cone 1/3hπr², and for a sphere is 4/3πr³
Step-by-step explanation:
I hope this will help you
Please help me with this question, I only need help with c), I already know the others, a) 9pi metres squared, b) 8pi metres squared, and d) 54.5metres squared.
Answers
Answer:
1.06 m²
Step-by-step explanation:
To find the area of the two ends, you need to find the area of the inner circle, then subtract that from the area of the large circle.
As we know, A = πr²
The diameter of the larger circle is 1.8, so the radius is 0.9.
π(0.9)² = 2.54
The diameter of the smaller circle is 1.6, so the radius is 0.8
π(0.8)² = 2.01
2.54 - 2.01 = 0.53 m² (this is for one end)
0.53 x 2 = 1.06 m²
i need help on 39 please help me!
Answers
Answer:
,hjdjhihdihhubxhjx,❤️❤️❤️♥️♥️8.
Find the number of real number solutions for the equation. x2 – 10x + 25 = 0
A. 0
B. 1
C. 2
D. cannot be determined
Answers
Answer:
B. 1
Step-by-step explanation:
Answer:
Option B is correct
The number of real number solutions for the given equation is, 1.
Step-by-step explanation:
Given the equation:
Since, this is a quadratic equation of the form of
where a =1 , b = -10 and c =25.
The discriminant of a quadratic equation is,
then;
Discriminant = = (100-100) = 0
Since, a discriminant of zero means there is only one real solution for x.
Substitute the given values.
Simplify:
x = 5
Therefore, the number of real solution for the given equation is, 1
Choose the correct domain and range for the following graph:
GUYS PLZ HELP !!!
Answers
Write an equation that represents the line.
Use exact numbers. PLEASE HELP
Answers
find the area of the football field when the width is 160 feet
Answers
Answer: 240ft
Step-by-step explanation:
Width:
10(15) + 10
= 150 + 10
= 160
Length:
4(15) + 20
= 60 + 20
= 80
L x W
= 160 + 80
= 240
Choose the appropriate answer based on the given side lengths. 8 cm, 8 cm, 13 cm Equilateral Isosceles Scalene Does not make a triangle
Answers
Answer:
good night
sweet dreams
find (f/g)(x).
f(x)=sqrtx^2-1
g(x)=sqrtx-1
(hurry plz its timed lol)
Answers
Answer:
The correct option is (a)
What is modeled by the graph segmenſ between B and C?
CE
Height
B
C
Time
The height is remaining constant over time,
The time is remaining constant while the height changes.
The height is increasing,
The height is decreasing
Mark this and return
Save and Exit
Next
Submit
Answers
Answer:
Option A is correct.
Step-by-step explanation:
Between B and C, the value of height (y) remains constant, as shown as a horizontal line on the graph.
What happened is 10 times as much as 50
Answers
Answer:
the answer is 500!!
Step-by-step explanation:
10 x 50=500
Answer:
500
Step-by-step explanation:
50*10=500
50 into 10 equals 500
29 dekagrams equals 2900 what
Answers
Answer:
It equals 2900 decigrams
Step-by-step explanation:
29 dekagrams = 290 grams
290 grams = 2900 decigrams
Therefore, 29 dekagrams = 2900 decigrams
The equivalent weight in grams for a given weight in dekagrams is approximately 10 times the weight in dekagrams.
To find the equivalent weight in grams for a given weight in dekagrams, you can use the conversion factor that 1 dekagram (dag) is equal to 10 grams.
Given the information that 29 dekagrams equals 290 grams, you can set up a proportion:
[tex]\(\frac{29 \text{ dag}}{290 \text{ g}} = \frac{1 \text{ dag}}{x \text{ g}}\)[/tex]
Cross-multiplying:
[tex]\(29x = 290 \times 1\)[/tex]
Solving for x:
[tex]\(x = \frac{290}{29}\)\\\\\(x \approx 10\)[/tex]
Therefore, the equivalent weight in grams for a given weight in dekagrams is approximately 10 times the given weight in dekagrams.
To know more about weight, refer here:
https://brainly.com/question/32319871
#SPJ3
Complete Question:
If 29 dekagrams equals 290 grams, what is the equivalent weight in grams for a given weight in dekagrams?