To obtain how fast the ball traveling 2 seconds after it is thrown, we differentiate the position equation with respect to time once;
dh(t) = d (-16[tex]t^{2}[/tex] + 40t +5 )
dt dt
dh(t) = -32t + 40
dt
with t= 2:
h'(2) =-32 (2) +40
h'(2) =-24 ft/s.
What is velocity?Velocity is a vector expression of the displacement that an object or particle undergoes with respect to time . The standard unit of velocity magnitude (also known as speed ) is the meter per second (m/s). Alternatively, the centimeter per second (cm/s) can be used to express velocity magnitude. The direction of a velocity vector can be expressed in various ways, depending on the number of dimensions involved.Velocity is relative. Consider a car moving at 20 m/s with respect to the surface of a highway, traveling northward. If you are driving the car, the velocity of the car relative to your body is zero. If you stand by the side of the road, the velocity of the car relative to you is 20 m/s northward. If you are driving a car at 15 m/s with respect to the road and are traveling northward, and another car moving 20 m/s with respect to the road passes you in the same direction, that other car's velocity relative to you is 5 m/s northward. But if that other car passes you going the opposite way on the road, its velocity relative to you is 35 m/s southward.To learn more about Velocity refer to:
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How to use the distributive property to multiply two variables together
Distributive property states that A × (B + C) = AB + AC. are always equal.
According to the statement
we have to explain the distributive property over multiplication.
Distributive property is the multiplication property.
According to this property, it generalizes the Distributive Law and it tells us that the an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.
It means that From distributive property
A × (B + C) = AB + AC.
These are always equal with each other.
Now we will explain with an example,
Let A = 2, B = 3 and C = 4
Then
2 × (3 + 4) = 2(3) + 2(4).
2 × (7) = 2(3) + 2(4).
14 = 6 + 8.
14 = 14.
It proves that the A × (B + C) = AB + AC.
So, Distributive property states that A × (B + C) = AB + AC. are always equal.
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A group of friends wants to go to the amusement
park. They have no more than $420 to spend on
parking and admission. Parking is $8.75, and
tickets cost $25.75 per person, including tax.
Which inequality can be used to determine x, the
maximum number of people who can go to the
amusement park?
Answer:
The maximum amount of people that can go to the amusement park is 15.
Step-by-step explanation:
First you create an equation to represent the question
8.75+25.75x≤420
You put the less than or equal to sign because 420 is the maximum amount of money.
Now you just solve the equation.
25.75x≤420-8.75
25.75x≤411.25
x≤411.25/25.75
x≤15.9708738
Then you have to round down because you cant have .9 of a person.
So x≤15
Then, Check your solution
8.75+(25.75 x 15)≤420
8.75+386.25≤420
395≤420
That is true. But to make sure that is the maximum add another 25.75
395+25.75≤420
420.75≤420
This is equation is false so, our answer is correct.
The maximum amount of people that can go to the amusement park is 15.
Please explain the answer before, and also help with number line!
The solution to the given inequality is x < -6
For the number line, an open circle will be drawn on the value of -6 and the arrow pointing to the left side.
Number line and inequalityGiven the inequality expression as shown
6x + 6 < -30
Subtract 6 from both sides
6x < -30 - 6
6x < -36
Divide through by 6
x < -36/6
x < -6
For the number line, an open circle will be drawn on the value of -6 and the arrow pointing to the left side.
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HELP ME, IT'S AN EMERGENCY
Answer:
(A) 36°
Step-by-step explanation:
Find intercepted arc (RT):
360° - 288° = 72
*A circle is 360°*
Find angle RST:
An inscribed angle = 1/2 intercepted arc
angle RST = 1/2(72)
Angle RST = 36°
Find the circumference and the area of a circle with diameter equal to 8.6 inches. Use 3.14 for pie.
The circumference and area of the circle are 27. 0 inches and 58. 0 inches square respectively.
How to calculate the circumferenceThe formula for circumference of a circle is given as;
Circumference = 2 π r
We have diameter = 8. 6 inches
Radius = diameter/ 2
Radius = 8.6/2 = 4. 3 inches
Circumference = 2 × 3. 14 × 4. 3 = 27. 0 Inches
The formula for area of a circle = π r ^2
Area = 3. 14 × 4. 3 × 4. 3
Area = 58. 0 Inches square
Thus, the circumference and area of the circle are 27. 0 inches and 58. 0 inches square respectively.
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The perimeter of a rectangle is 99 ft, and the length is twice the width. what are its dimensions?
The dimension of the length and width of the rectangle with the given perimeter are 33ft and 16.5ft respectively.
What are the dimensions of the rectangle?Perimeter of rectangle is expressed as;
P = 2( l + w )
Given that;
Perimeter P = 99ftLet width w = xLength l = 2xWe substitute into the formular above.
P = 2( l + w )
99ft = 2( x + 2x )
99ft = 2x + 4x
99ft = 6x
x = 99ft/6
x = 16.5ft
Width = x = 16.5ft
Length = 2x = 2( 16.5ft ) = 33ft
Therefore, the dimension of the length and width of the rectangle with the given perimeter are 33ft and 16.5ft respectively.
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In convex pentagon $ABCDE$, angles $A$, $B$ and $C$ are congruent and angles $D$ and $E$ are congruent. If the measure of angle $A$ is 40 degrees less than the measure of angle $D$, what is the measure of angle $D$
In a convex pentagon, the measure of angle D is 132°.
What is convex pentagon?If a planar polygon has all the line segments connecting any given pair of its points, it is said to be convex pentagon.
Properties of a Convex Polygon are-
Any polygon whose inner angles are all smaller than 180 degrees is said to be convex.A concave polygon is one in which at least one of the angles is bigger than 180°.A convex polygon's diagonals are located inside the polygon.A polygon is considered convex if the line connecting every pair of its points lies entirely within it.Calculation for the measure of angle D.
The sum of the interior angles = 540°
Let A, B , C = D - 40
And let E = D
So we have
A + B + C + D + E = 540
(D - 40) + (D - 40) + (D - 40) + D + D = 540
5D - 120 = 540
5D = 660
D = 660 / 5
D = 132°
Therefore, the measure of angle D is 132°.
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PLEASE HELP!!!!
This year, the Nature Club made 3 exhibits per month for its annual fair. This year's fair has twice as many exhibits as last year's. How many exhibits were there in last year's fair?
Answer: 18
Step-by-step explanation:
There are 12 months in a year. The club made 3 exhibits each month. 3 times 12 is 36. They made twice as many as last year, so divide 36 by 2 and you get 18.
I hope this helps!
Select the correct answer.
Consider these functions:
f(x) = 4x³ - 10
g(x) = 3x - 4/2
What is the value of g(f2))?
Answer:
3x - 4/2
Step-by-step explanation:
2 result(s) for "f(x) = 4x³ - 10 g(x)
-x^2 +x+6=0 (Please solve by completing the square, and show steps)
The solution to the equation using the completing the square are 2 and -3
Quadratic equationThese are equation that has a leading degree of 2. Given the equation below
-x^2 +x+6=0
This can also be written as
x^2-x-6 = 0
Complete the square
x^2-x = 6
x^2-x+ (1/2)^2 = 6 + (1/2)^2
(x-1/2)^2 = 6 + 1/4
(x+1/2)^2 = 25/4
x+1/2 = ±√25/4
x = 5/2 -1/2 or -5/2-1/2
x = 4/2 or -6/2
x = 2 and -3
Hence the solution to the equation using the completing the square are 2 and -3
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PLEASE HELP 50 POINTS
Step-by-step explanation:
The initial velocity of a particle moving along x−axis is u (at t=0 and x=0) and its acceleration a is given by a=kx.For 19-20, Decide whether the polygons are similar. If so, find the scale factor of Figure A to Figure B.
Answer: Not similar
Step-by-step explanation:
The polygons are not similar because the ratio of the corresponding sides is not equal (30/18 is not equal to 18/8)
3x^2=7x solve the equation
Answer:
3x^2 - 7x =0
x(3x-7) = 0
3x - 7 = 0
3x =7
x= 7/3
The angle measurements in the diagram are represented by the following expressions.
Answer:
Angle A= 30
Step-by-step explanation:
Angle A and B are same side interior
So A + B = 180
x = 8
6(8)-18=30
Answer:23
Step-by-step explanation:
jaja
What is the standard deviation of the data set? 6.5, 11.2, 13, 6.3, 7, 8.8, 7.4
Using it's concept, the standard deviation of the data-set is of 2.39.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.The mean of the data-set in this problem is given by:
M = (6.5 + 11.2 + 13 + 6.3 + 7 + 8.8 + 7.4)/7 = 8.6.
Hence the standard deviation is:
[tex]S = \sqrt{\frac{(6.5-8.6)^2+(11.2-8.6)^2+(13-8.6)^2+(6.3-8.6)^2+(7-8.6)^2+(8.8-8.6)^2+(7.4-8.6)^2}{7}} = 2.39[/tex]
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Find the volume of the composite figure. Round to the nearest tenth if necessary.
The volume of the composite figure is of 425 m³.
What is the volume of a prism?The volume of a prism is given by the base area multiplied by the height.
In this problem:
For the top figure, the base is a square with 5m, with height of 13m.For the bottom figure, the base is a square with 5m, with height of 4m.Hence the volume in m³ is:
V = 5² x 13 + 5² x 4 = 25 x 17 = 425 m³.
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Find the x - and y -intercepts of the graph of the linear equation 2 x plus 3 y is equal to 2x+3y=12
Answer:
x-intercept is 6 [(6, 0) is the point]
y-intercept is 4 [(0, 4) is the point]
Step-by-step explanation:
To find the x-intercept, we can set y equal to 0 and solve for x. This works because the x-intercept is the point of the graph where the line crosses the x-axis (meaning y is equal to 0 at this point. So, if we set y=0 and solve, we get this:
[tex]2x+3(0)=12\\2x=12\\x=6[/tex]
So, the x-intercept is 6; if it is written as a point, it is (6, 0) since y is 0
To find the y-intercept, we can set x equal to 0 and solve for y. This works the same way - x is equal to 0 at the point where the line crosses the y-axis. If we set x=0 and solve, we get this:
[tex]2(0)+3y=12\\3y=12\\y=4[/tex]
So, the y-intercept is 4; if it is written as a point, it is (0, 4) since x is 0
Enter the degree of the polynomial below.
5,5 + 8,2 + 2x - 319 - 8x1 -4,5
Based on the given polynomial, the degree of the polynomial can be calculated to be 1.
what is the degree of the polynomial?the degree of the polynomial is defined as the highest exponential degree or power in a polynomial.
from the above, we see that the highest power is 1 from 8x¹.
the degree of the polynomial is therefore 1.
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Which table represents a quadratic function?
Answer:
A (see attached)
Step-by-step explanation:
There are a couple of things you can look for to see if a table represents a quadratic function:
do the values increase, then decrease, or vice versado the differences have a constant difference.ObservationIn the first of the given tables, the f(x) values start out decreasing, and end up increasing. This is a good indication the table represents a quadratic function.
In the remaining tables, the f(x) values are always increasing.
table 2: differences are always +2 (linear function)table 3: differences are always +4.5 (linear function)table 4: table values have a common ratio of 2 (exponential function)AnalysisThe f(x) values in table 1 have differences of ...
-3, -1, 1, 3
These values have differences of ...
2, 2, 2
The constant "second differences" mean that the function can be represented by a 2nd-degree polynomial, a quadratic. In fact, the equation for this table is ...
f(x) = x² +2
One can convert temperature from kelvin into fahrenheit using the formula . what is the temperature in kelvin corresponding to f degrees fahrenheit?
One can easily convert the temperature using temperature conversion formula given below
K = [tex]\frac{5(F - 32)}{9} + 273.15[/tex]
where F = degrees in Fahrenheit
K = degrees in Kelvin
What is temperature conversion? The measuring units of the temperature recorded in a particular unit can be converted with the aid of a temperature converter. The degree of heat or cold that a solid, liquid, or gas has is expressed by its temperature. A thermometer is used to determine temperature. Although the SI unit for temperature is Kelvin (K), most people measure temperature in Centigrade or Celsius (°C) and Fahrenheit (°F).Know more about temperature conversion https://brainly.com/question/13421795
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What is the percent rate??
Kryton -85 is a radioisotope of krypton that has a half-life of about 10.75years. This isotope is produced by the nuclear fission of uranium and plutonium in nuclear weapons and in nuclear reactors, as well as cosmic rays. An important goal of the Limited Nuclear Test Ban Treaty of 1963 was to eliminate the release of such radioisotopes into the atmosphere. At present, the activity of Krypton -85 in the atmosphere is about 135 mCi.
Using an exponential function, it is found that the decay rate is of 6.24% a year.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.The half-life is of 10.75 years, hence A(10.75) = 0.5A(0) and this is used to find the decay rate r.
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]0.5A(0) = A(0)(1 - r)^{10.75}[/tex]
[tex](1 - r)^{10.75} = 0.5[/tex]
[tex]\sqrt[10.75]{(1 - r)^{10.75}} = \sqrt[10.75]{0.5}[/tex]
[tex]1 - r = (0.5)^{\frac{1}{10.75}}[/tex]
1 - r = 0.9376.
r = 1 - 0.9376.
r = 0.0624.
The decay rate is of 6.24% a year.
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The bars in a _____________ do not touch since data is ______________.
A. bar graph ; continuous
B. bar graph ; discrete
C. histogram ; continuous
D. histogram ; discrete
Answer:
b
Step-by-step explanation:
Bat Graphs represent discrete data. They are spaced and don't touch to represent a discrete value.
Histograms represent continuous data. They are close and connected to represent variation in continuous data.
The distance from the Sun to Mercury is approximately 57910000 km.
Assuming Mercury has a circular** orbit around the Sun, find the distance Mercury travels in orbiting the Sun through an angle of 2.65 radians.
Mercury travels a distance of 153 461 500 kilometers on its orbit.
How much distance did Mercury travel on its orbit?
The statement indicates that Mercury has a circular orbit and indicates the central angle covered by translation. The distance traveled is found by definition of circular arc:
s = (2.65 rad) · (57 910 000 km)
s = 153 461 500 km
Please notice that the radius of translation is the distance from the Sun to Mercury.
Mercury travels a distance of 153 461 500 kilometers on its orbit.
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PLEASE HELP!!!!
Question 8(Multiple Choice Worth 5 points)
(05.02 MC)
Based on the figure below, what is the value of x?
A right angle is shown divided in two parts. The measure of the angle of one part is 20 degrees and the measure of the other part is 5x plus 15 degrees.
A) 1
B) 9
C) 11
D) 15
The value of x from the given figure is 11
Complementary anglesThe sum of two complementary angles is 90 degrees.
The angles shown in the diagram are complementary such that;
20 + 5x + 15 = 90
5x + 35 = 90
5x = 90- 35
5x = 55
x = 55/5
x = 11
Hence the value of x from the given figure is 11
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Compare the graphs of the functions listed below.
Function 1: y = 0.25x2
Function 2: y = 4x2
Function 3: y = -½x2
Function 4: y = -16x2
The graph of
✔ function 1
is the widest.
The graph of
is the narrowest.
Answer:
Function 1 is the widestFunction 4 is the narrowestStep-by-step explanation:
The graph is widest when the coefficient of [tex]x^2[/tex] has the smallest absolute value.
The graph is narrowest when the coefficient of [tex]x^2[/tex] has the largest absolute value.
By comparing the graphs of the functions, function 1: y = 0.25x2 is the widest and function 4: y = -16x2 is the narrowest.
The graph is widest when the coefficient of [tex]x^{2}[/tex] has the smallest absolute value.
The graph is narrowest when the coefficient of [tex]x^{2}[/tex] has the largest absolute value.
The answer lies in the coefficient for the [tex]x^{2}[/tex] term. When the absolute value of the coefficient gets bigger, the graph gets narrower (positive and negative simply show the direction the parabola is pointing, with positive opening up and negative opening down).
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please help asap i am so confused
The table so fined below based on the information given about the function.
How to illustrate the information?The table based on the function given will be:
Plan A. Plan B
Monday. 10. 30
Tuesday. 20. 40
Wednesday. 40. 50
Thursday. 80. 60
Friday. 160. 70
A is illustrated as it's double minutes for each day. B is illustrated by adding 10min each day.
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2(-2-4) = use the distributive property to expand the expression below.
Answer:
-12
Step-by-step explanation:
First, solve in parentheses.
2(-2-4)
=
2(-6)
Next, multiply 2 by -6.
Which equals -12.
So therefore using the distributive property shown above, the answer would be -12.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What is the distributive formula?}[/tex]
[tex]\mathsf{a(b + c)}[/tex]
[tex]\mathsf{= a(b) + a(c)}[/tex]
[tex]\mathsf{= ab + ac}[/tex]
[tex]\huge\textbf{What is the equation?}[/tex]
[tex]\mathsf{2(-2 - 4)}[/tex]
[tex]\huge\textbf{What are we simplifying?}[/tex]
[tex]\mathsf{2(-2 - 4)}[/tex]
[tex]\mathsf{= 2(-2) + 2(-4)}[/tex]
[tex]\mathsf{= -4 - 8}[/tex]
[tex]\mathsf{= -12}[/tex]
[tex]\huge\textbf{How are you going to translate to}\\\\\huge\textbf{easier terms?}[/tex]
[tex]\mathsf{2(-2 - 4)}[/tex]
[tex]\mathsf{= 2(-6)}[/tex]
[tex]\mathsf{= -12}[/tex]
[tex]\huge\textbf{What is the ANSWER to the question?}[/tex]
[tex]\huge\boxed{\mathsf{-12}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
given points (8,6) and ( 8, 0) as the endpoints of a radius ,what is the equation of the circle with center ( 8,6)
The general equation of a circle is written like [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the centre and r is the radius.
Solving the QuestionFirstly, we're given that the centre is (8,6).
Plug this into the general equation:
[tex](x-h)^2+(y-k)^2=r^2\\(x-8)^2+(y-6)^2=r^2[/tex]
We're given this other point on the circumference of the circle, (8,0), which is 6 units away from the center.
Therefore, the radius is 6 units. Plug this into the general equation too:
[tex](x-8)^2+(y-6)^2=r^2\\(x-8)^2+(y-6)^2=6^2\\(x-8)^2+(y-6)^2=36[/tex]
Answer[tex](x-8)^2+(y-6)^2=36[/tex]
slope:
y-intercept:
PLSPLSPLS HELP
Answer:
Slope: 1
Y-intercept: -1
Step-by-step explanation:
The line passes the y-axis at -1, the rise/run, which is used to calculate the slope is 2/2, and it equals to 1, so the slope is 1.
I hope it helps! Have a great day!
bren~
142857/500000 simplified
Using your own examples, explain why all statements are sentences but not all sentences are statements. Clearly indicate which type of non-statement you have used in each case. (Your response should be between 500 and 600 words).
Answer:
0.285714 -> 0.29
Step-by-step explanation: