Answer:
39 feet
Step-by-step explanation:
In this problem, the height of the football at time t is modelled by the equation:
[tex]h(t)=-16t^2+vt+s[/tex]
where:
s = 3 ft is the initial height of the ball
v = 48 ft/s is the initial vertical velocity of the ball
[tex]-32 ft/s^2[/tex] is the acceleration due to gravity (downward)
Substituting these values, we can rewrite the expression as
[tex]h(t)=-16t^2+48t+3[/tex]
Here we want to find the maximum height reached by the ball.
This is equivalent to find the maximum of the function h(t): the maximum of a function can be found requiring that the first derivative of the function is zero, so
[tex]h'(t)=0[/tex]
Calculating the derivative of h(t), we find:
[tex]h'(t)=-32 t+48[/tex]
And imposing it equal to zero, we find the time t at which this occurs:
[tex]0=-32t+48\\t=-\frac{48}{-32}=1.5 s[/tex]
And substituting back into h(t), we can find the maximum height of the ball:
[tex]h(1.5)=-16\cdot (1.5)^2 + 48\cdot 1.5 +3=39 ft[/tex]
Using the vertical motion model, the time when the football reaches maximum height is calculated to be 1.5 seconds. Substituting this into the model, the maximum height of the football is found to be 39 feet.
Explanation:To find the maximum height, we consider the vertical motion model h = -16t^2 + vt + s, where v is initial velocity in feet per second and s is the initial height of the football. The information provided include: initial velocity v = 48 feet/sec and initial height s = 3 feet.
The maximum height reached by the football is achieved when the velocity becomes zero (time at which the ball reaches its highest point). This time can be calculated using the formula t = v / (2 * g), with g being half the coefficient of t^2 (g = 16 feet/sec^2 in this case). Substituting v and g gives us approximately t = 1.5 seconds.
We then substitute this time into our initial equation to find the maximum height. This gives: h = -16*(1.5)^2 + 48*1.5 + 3 = 39 feet. Therefore, the maximum height reached by the football is 39 feet.
Learn more about Maximum Height here:https://brainly.com/question/32771757
#SPJ6
what is the equation of a line that has a slope of -4 and goes through (-1,6)
Answer:
Step-by-step explanation:
Given
slope(m) = - 4
Points ( x1 , y1) = ( - 1 , 6)
Now
The equation of a line is given by
y - y1 = m( x - x1)
y - 6 = - 4 ( x + 1)
y - 6 = -4x - 4
4x + y - 6 + 4 = 0
4x + y - 2 = 0
Hope it helps:)
The equation of the line with a slope of -4 and passing through the point (-1, 6) is y = -4x + 2.
Given that the slope (m) is -4 and the point it passes through is (-1, 6), we can substitute these values into the point-slope form:
y - 6 = -4(x - (-1))
y - 6 = -4(x + 1)
Now, we can distribute the -4 to the terms inside the parentheses:
y - 6 = -4x - 4
Next, we can move the -6 to the other side of the equation by adding 6 to both sides:
y = -4x - 4 + 6
y = -4x + 2
Therefore, the equation of the line is y = -4x + 2.
Learn more about the lines here:
https://brainly.com/question/13738061
#SPJ2
Would you rather read 12 pages every night in a chapter book with 144 pages or read 50 pages 3 times a week in a chapter book with 132 pages? Choose an option you would rather have and provide a mathematical justification as to why you made that choice.
Answer:
Read 12 pages every night in a chapter book with 144 pages.
Thus the first option is the best because you will use fewer number of days to complete the reading.
Step-by-step explanation:
For the first option;
Read 12 pages every night in a chapter book with 144 pages, the number of days taken to complete the book will be;
144/12= 12 days
For the second option
50 pages = 3 times
132 pages = ? ------perform cross product
(132*3)/ 50 =7.92 ≈ 8 times
3 times = 1 week
8 times = ?
(8*1)/3 = 2.64 weeks
1 week =7 days
2.64 weeks=?
2.64*7 = 18.5 days
Thus the first option is the best because you will use fewer number of days to complete the reading.
The function () = 2 + 4 was replaced with ( + ) resulting in the function
() = 2 + 22. What is the value of ?
Let's evaluate explicitly [tex]f(x+k)[/tex]:
[tex]f(x)=2x+4\iff f(x+k)=2(x+k)+4=2x+2k+4[/tex]
If this must equal [tex]2x+22[/tex], we have
[tex]2x+2k+4=2x+22 \iff 2k+4=22 \iff 2k=18 \iff k=9[/tex]
Answer:
For what values of does the equation (2 + 1)^2 + 2 = 10 − 6 have two real and equal roots?
Step-by-step explanation:
For what values of does the equation (2 + 1)^2 + 2 = 10 − 6 have two real and equal roots?
Find the volume to the nearest hundredth using 3.14 instead of pi.
Answer:
48π ≈ 150.72
Step-by-step explanation:
The volume formula is V = 1/3Bh
The base area formula would be πr²
Since 8 is the diameter, 4 would be the radius
Now plug that in, π (4²) = 16π
Now multiply that by the height, 9, and get 144π
Multiply again by 1/3 and you'll get 48π
Answer:
150.72 ft^3
Step-by-step explanation:
The volume of a cone is
V = 1/3 pi r^2 h
We need to get the radius
r = d/2 = 8/2 =4
V = 1/3 (3.14) (4)^2 *9
V = 1/3 (3.14) 16 *9
V =150.72
Rounding to the nearest hundredth
V = 150.72
Which is equivalent to 4!
(4 factorial)?
look at picture
Answer:
C. 24
Step-by-step explanation:
4!=24
Apply factorial rule: n! = 1 * 2 * 3 * ... * n
4! = 1 *2 * 3 * 4
1 *2 * 3 * 4 = 24
4! = 1 *2 * 3 * 4 = 24
4!=24
line n passes through the points (-3 -7.5) and (2 -5) tahlia determined that the equation of line n is y = 0.5x. explain the error Tahlia made while determining her equation. Be sure to include the correct equation in your explanation
Answer:
She forgot to find the y intercept add it in the equation
y = .5x-6
Step-by-step explanation:
First we need to find the slope
m = (y2-y1)/(x2-x1)
= (-5 - -7.5)/ (2 - -3)
=(-5 +7.5)/( 2+3)
= 2.5/5
= 1/2
Substitute into the slope intercept form of the equation
y= mx+b
y= .5x +b
We need to determine b by substituting a point into the equation
-5 = .5(2) +b
-5 = 1+b
Subtract 1 from each side
-5-1 = 1-1+b
-6 = b
y = .5x-6
Answer:
She forgot the y-intercept
y = 0.5x - 6
Step-by-step explanation:
y = 0.5x + c
-5 = 0.5(2) + c
c = -6
Correct equation:
y = 0.5x - 6
The scale factor of triangle ABC to triangle DEF is 6. Which description is correct?
Answer:
None are correct
Step-by-step explanation:
Because triangle ABC is the original as it says in the problem"Triangle ABC TO Triangle DEF" which means the answer should be Triangle DEF is 6 times larger than triangle ABC.
Jennifer set up 15 rows of chairs in the cafeteria for her school's talent competition. In the
first 10 rows, she set up 30 chairs on the left side of the middle aisle and x chairs on the right
side. In the last 5 rows, she set up 20 chairs on the left side of the middle aisle and y chairs
on the right side to make room for the sound crew.
Pick all the expressions that represent how many chairs Jennifer set up.
(300 + 10x) + (100 +5y)
30(x + 10) + 20 (y + 5)
10(30 + x) + 5 (20 + y)
x(10 + 30) + y(5 + 20)
Subtract 8x2 + 3xy + 4y2 from 12x2 + 3xy - 5y2.
Your answer should be a polynomial in standard form.
Answer:
4x² - 9y²
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/Coefficients/DegreesStep-by-step explanation:
Step 1: Define
Set up expression
12x² + 3xy - 5y² - (8x² + 3xy + 4y²)
Step 2: Simplify
Distributive negative: 12x² + 3xy - 5y² - 8x² - 3xy - 4y²Combine like terms (x²): 4x² + 3xy - 5y² - 3xy - 4y²Combine like terms (xy): 4x² - 5y² - 4y²Combine like terms (y²): 4x² - 9y²please give answer ?
Answer:
M=(-8, -3.5)
Step-by-step explanation:
The midpoint formula for two points is [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]. Plugging in our numbers, you get [tex](\frac{-9-7}{2},\frac{-10+3}{2})=(-8, -3.5)[/tex]. Hope this helps!
When ringing up a customer,a cashier needs 10seconds to process payment as well as 1second to scan each item being purchased .How long does it take to ring up a customer with 37 items ? Answer
Answer:
47 seconds
Step-by-step explanation:
It takes 37 seconds to scan 37 items at the rate of 1 second per item. It takes an additional 10 seconds to process the payment. Then the total time is ...
37 +10 = 47 . . . seconds
Suppose a city with population 200,000 has been grown a rate of 4%.If the rate continues,find the population of this city in 19 years?
The two right triangular prisms are similar solids.
The scale factor of the larger prism to the smaller prism
is 3. How do the volumes compare?
The volume changes by 3.
The volume changes by
, or 2
The volume changes by
lo
Answer:
The volume of the larger prims is eight times greater than the smaller prism.Step-by-step explanation:
If the scale factor of the larger prims to the smaller prism is 3, that means each side is triple.
We know the a triangular prims has a volume defined by
[tex]V_{small} =\frac{b \times h_{1} }{2} \times h_{2}[/tex]
If we take that formula as the smaller prism, then the larer prism has a volum of
[tex]V_{large} =\frac{2b \times 2h_{1} }{2} \times 2h_{2}=8(\frac{b \times h_{1} \times h_{2} }{2} )[/tex]
If we compare, we can deduct that
[tex]V_{large}=8V_{small}[/tex]
In words, the volume of the larger prims is eight times greater than the smaller prism.
Answer:
Answer Choice 3
Step-by-step explanation:
on edge 2020
A boat leaves the dock and travels 5 miles due south, then 12 miles due west How far is the boat from the dock?
Answer:
13 miles
Step-by-step explanation:
This problem can be represented as a right angle triangle (shown in the diagram).
The distance of the boat from the dock is the hypotenuse of the triangle, hence, we need to find the hypotenuse of the triangle. To do this, we apply Pythagoras theorem:
[tex]hyp^2 = opp^2 + adj^2[/tex]
where opp = side opposite angle of consideration = 12 miles
adj = side adjacent angle of consideration = 5 miles
Hence:
[tex]hyp^2 = 12^2 + 5^2\\\\\\hyp^2 = 144 + 25 = 169\\\\\\hyp = \sqrt{169}\\ \\\\hyp = 13 miles[/tex]
The boat is therefore, 13 miles from the dock.
Final answer:
To find the distance of the boat from the dock after traveling due south and then due west, apply the Pythagorean theorem to calculate the hypotenuse of a right-angled triangle, resulting in 13 miles.
Explanation:
The question involves finding the distance of the boat from the dock after it has traveled in a two-segment path: 5 miles due south and 12 miles due west. This problem can be solved by using the Pythagorean theorem, which is applied in the context of a right-angled triangle formed by the southward and westward paths of the boat as its legs.
Steps to Calculate Distance:
Represent the boat's journey as a right-angled triangle with the southward and westward paths forming the two legs.
Calculate the hypotenuse of the triangle, which represents the straight-line distance between the boat and the dock.
Use the Pythagorean theorem (a² + b² = c²) to find the distance.
For the distances given (5 miles and 12 miles), the calculation would be [tex]\sqrt{5² + 12²}[/tex]= [tex]\sqrt{169}[/tex] = 13
Therefore, the boat is 13 miles away from the dock after traveling 5 miles due south and 12 miles due west.
urgent !! Convert the following equation to logarithmic or exponential form:
log subscript 49 left parenthesis 7 right parenthesis equals 1 half
Your answer:
49 to the power of 7 equals 1 half
7 to the power of 49 equals 1 half
open parentheses 1 half close parentheses to the power of 7 equals 49
49 to the power of 1 half end exponent equals 7
Answer:
The exponential form is 49 to the power of one-half equals 7 ⇒ 4th answer
Step-by-step explanation:
The exponential equation of [tex]log_{b}(m)=n[/tex] is [tex]b^{n}=m[/tex] , where b is the base, n is the exponent of b and m is the value of [tex]b^{n}[/tex]
Ex: If [tex]log_{3}(81)=4[/tex] , that means b = 3 , n = 4 and m = 81, then its exponential form is [tex]3^{4}=81[/tex]
Now let us solve the question
∵ The equation is [tex]log_{49}(7)=\frac{1}{2}[/tex]
∴ The base is 49
∴ The exponent is [tex]\frac{1}{2}[/tex]
∴ The answer is 7
- Substitute them in the form of the exponential form
∴ The exponential form is [tex](49)^{\frac{1}{2}}=7[/tex]
The exponential form is 49 to the power of one-half equals 7
The given equation is log49(7) = 1/2. To convert it to exponential form, we can write it as 49^(1/2) = 7.
Explanation:The given equation is:
log49(7) = 1/2
To convert this equation to exponential form, we need to remember that logarithms and exponentials are inverse functions. Therefore, we can write the equation as:
491/2 = 7
Hence, the exponential form of the given equation is 49 raised to the power of 1/2 equals 7.
Select the correct description and/or example for each rigid transformation
Answer:
1.reflection
2. translation
3. rotation
4. rotation
5. reflection
Step-by-step explanation:
A 2D image of a 3D figure is most commonly know as what?
Answer:
net
Step-by-step explanation:
A two-dimensional shape has only two measurements and a three-dimensional shape has three measurements.
For example square, the triangle are two-dimensional shapes and cube, prism are three-dimensional shapes.
A 2 D image of a 3 D figure is most commonly know as a net.
A net is a two-dimensional pattern that can be folded to form the three-dimensional figure.
When you cut out the "net", fold it and stick it together you get a three-dimensional shape.
find the surface area of the rectangular prism
Answer:
23 units²
Step-by-step explanation:
height = 2
length = 4
width = 2.5
Formula = 2(wl + lh + hw) ⇒ 2 [(2.5 × 4) + (4 × 2) + (2 ×2.5)] = 23 units²
Hope this helps.
#FORTHEPUPPIES
Would having deadbolt locks on exterior doors affect a homeowner's insurance policy price? Why or why not? Answer in complete sentences.
Answer:
Having a deadbolt lock installed on the exteriors of a building would affect the price of Insurance.
The principles of insurance require that the Insurance Policy Holder or Insured should act as if uninsured. This means that even with an Insurance Policy in place, the owner of this house is required to ensure that all reasonable steps have been taken to secure the house.
This may include having a properly installed lock in place.
The price or insurance premium of a homeowner may go up very significantly if there is no lock installed, that is if the risk is accepted for coverage by the insurance company.
It (the premium that is) may or may not come down if there is a deadbolt lock in place. It all depends on the extent to which the deadbolt lock has reduced the exposure of the Insurance company. Where the deadbolt lock has very significantly reduced the risk, the policyholder may press for a reduction in insurance premium.
In most Homeowners Insurance policy, for a claim concerning theft of insured home items, the policyholder has to provide evidence of forceful entry or exit, showing that the house was reasonably secured to warrant a breaking in or breakout.
Cheers!
The volume inside a rectangular storage room is 2,106 cubic feet. The room is 9 feet high. Find the area of the floor.
Answer:
Area of the floor is 234 feet²
Step-by-step explanation:
To find the area of the floor of a rectangular storage room that is 2,106 cubic feet and has a height of 9 feet , we will follow the steps below;
First, write down the formula for calculating its volume
volume = l×b×h
but area=l×b
volume = area × h
From the question given volume = 2106 cubic feet
height h = 9 feet
volume = area × h
2106 = area × 9
Divide both-side of the equation by 9
2106/9 = area × 9/9
234 = area
area = 234 feet²
Area of the floor is 234 feet²
What is the volume of the rectangular prism?
Answer:210
Step-by-step explanation:
What is the general form of the equation of the line shown?
y - 2 = 0
y + 2 = 0
x - 2 = 0
Answer:
General form of the equation of the line: y-2 = 0
Step-by-step explanation:
The general form of the equation is given by:
y = mx +b where m is the slope and b is the y-intercept.
y-intercepts of the line is the value of y at the point where the line crosses the y-axis(i.e x= 0)
From the given figure;
we can see that the line crosses the y-axis at y =2 and also here the slope is , m= 0
therefore, by definition of y-intercepts
y-intercept (b) = 2
Therefore, the equation of line as shoen in figure is:
y = (0)x + 2
or
y = 2
y-2 = 0
Therefore, the general form of the equation line as shown in the figure is:
y-2 =0
In need of help of these math questions
Answer:
1. 4
2. 6.4
3. 10.0828313253
Explanation:
2.
15/12=1.25
8/1.25=6.4
3. ill write explanation for 3 later im occupied those are the correct answers
problably they want you to round to nearest tenth
On Sunday afternoon, the ratio of adults to children at the park was 1 to 3. There were 48 children at the park.
How many adults were at the park
Answer:
16 adults
Step-by-step explanation:
There were 3 times more children than adults at the park.
That means that dividing the number of children by 3 would give us the number of adults.
48 / 3 = 16
Answer:
16:48 Therefore, 16 adults
Step-by-step explanation:
A fish tank has a length of 4 feet and width of 18 inches. The fish tank is 3 feet high and is filled to within 4 inches of the top of the tank. What is the volume of water in the tank?
The volume of water in the tank, with a length of 4 feet, width of 1.5 feet, and filled to within 4 inches of the top, is approximately 42.667 cubic feet.
To find the volume of water in the tank, we need to calculate the volume of the portion of the tank that is filled with water.
1. First, let's convert all the measurements to the same unit. Since the height of the tank is given in feet and the width is given in inches, let's convert the width to feet.
Given:
- Length = 4 feet
- Width = 18 inches
- Height = 3 feet
- Water level = 4 inches from the top
Converting width to feet:
1 foot = 12 inches
So, 18 inches = 18/12 = 1.5 feet
Now, we have:
- Length = 4 feet
- Width = 1.5 feet
- Height = 3 feet
- Water level = 4 inches from the top
2. Calculate the height of the water in the tank:
Total height of the tank = Height of tank - Distance from the top to the water level
Total height = 3 feet - 4 inches
Total height = 3 feet - (4/12) feet
Total height = 3 feet - 0.3333 feet
Total height = 2.6667 feet
3. Calculate the volume of water using the formula for the volume of a rectangular prism:
Volume = Length × Width × Height
Volume = 4 feet × 1.5 feet × 2.6667 feet
Volume ≈ 16 feet³ × 2.6667
Volume ≈ 42.667 feet³
So, the volume of water in the tank is approximately 42.667 cubic feet.
Can someone please help me answer this question ASAP
Answer:
B. 1
Step-by-step explanation:
3x-1=2
3x=3
x=1
What is the y-intercept in the equation y=4x-3?
Answer:
-3
Step-by-step explanation:
The equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = 4x-3
4 is the slope and -3 is the y intercept
Eight pounds of peanuts cost $24.00. Six pounds of walnuts cost half as much.
Which is more expensive and by how much?
Answer:
peanuts are more expensive by $1.00.
Step-by-step explanation:
∵ The cost of eight pounds of peanuts = $24.00
∴ The cost of one pound of peanuts = [tex]\frac{24}{8}[/tex]
= $3.00 per pound
∵ The cost of six pounds of walnuts half as much = [tex]\frac{1}{2} \times 24[/tex]
= $12.00
∴ the cost of one pound of walnuts = [tex]\frac{12}{6}[/tex]
= $2.00 per pound
Difference in the cost per pound = $3.00 - $2.00 = $1.00
Therefore, peanuts are more expensive by $1.00.
A tank that is 25 cm long, 10 cm wide, and 8 cm deep can hold how many liters of water?
Answer:
volume of tank = 2000 cm³
Step-by-step explanation:
given data
tank long = 25 cm
tank wide = 10 cm
tank deep = 8 cm
to find out
how many liters of water
solution
we get here volume of this tank that is express as
volume of tank = tank long × wide × deep .......................1
put here value and we will get
volume of tank = 25 × 10 × 8
volume of tank = 2000 cm³
The speed of a ship is given by , where d is the distance the ship travels in 3 hours. If the ship travels 48 miles in 3 hours, what is the speed of the ship? A. 12 miles per hour B. 16 miles per hour C. 45 miles per hour D. 51 miles per hour
Answer:
the answer is 16mph
Step-by-step explanation:
Answer:
16 miles per hour
Step-by-step explanation: