The model for the object's motion is [tex]h(t) = -16t^2 + 64t + 80[/tex]. It reaches its maximum height of 144 feet at 2 seconds. The object will hit the ground after 5 seconds.
To model the vertical motion of the object, we use the equation:
[tex]h(t) = -16t^2 + 64t + 80[/tex]
where:
h(t) is the height at time t64 ft/s is the initial velocity80 ft is the initial height[tex]16t^2[/tex] represents the effect of gravity (since the gravitational acceleration is approximately 32 ft/s2, and here it is halved to be per second squared)Time to Reach Maximum Height
The time to reach the maximum height can be found by using the formula:
[tex]t = \frac{v_0}{|g|} = \frac{64}{32} = 2 seconds[/tex]
Maximum Height
Plug t = 2 seconds into the height equation:
[tex]h(2) = -16(2)^2 + 64(2) + 80 = 144 feet[/tex]
Time to Hit the Ground
To find when the object hits the ground (h(t) = 0), solve:
[tex]-16t^2 + 64t + 80 = 0[/tex]
Using the quadratic formula:
[tex]t = \frac{-64\pm\sqrt{64^2-4(-16)(80)} }{2(-16)}[/tex]
Simplifies to:
t = 5 seconds (since the negative value does not make sense in this context)
The object will hit the ground after 5 seconds.
Jo lives on maple road her address has the digit 2 in the ones place and the digit 4 in the tens place what is jo address
Which is the graph of f(x) = 100(0.7)x?
PLEASE HELP!!! Hello, I've really been struggling with trying to figure these out, can someone please help me with these?
which is greater 89.001 or 89.100
If it is 5 degrees outside and the temperature will drop 17 degrees in the next 6 hours how cold will it get?
What is the volume of a frustum of a right pyramid with the area of the lower base equal to 100 square inches, the area of the upper base equal to 25 square inches, and the altitude equal to 12 inches?
A. 560 in^3
B. 700 in^3
C. 420 in^3
D. 750 in^3
Where B₁ and B₂ are the areas of the bases, the volume of the frustum is given by
... V = (1/3)(B₁ +B₂ +√(B₁B₂))h
For your dimensions, the volume is
... V = (1/3)(100 + 25 + √(100·25))·12 = (1/3)·175·12 = 700
The appropriate choice for the volume of the frustum is
... B. 700 in³
What is 8.072 rounded to the nearest hundredth
Two-thirds a number plus 4 is 7
Evaluate 37/100+3/10
A college student borrow $1,500 for 3 months to pay for a semester of school. If the interest is $30.94, find the monthly payment (Round to the nearest cent.)
Answer:
Hence, the monthly payment to the nearest cent is 510.31
Step-by-step explanation:
Consider the provided information,
A college student borrow $1,500 for 3 months to pay for a semester of school.
Let us consider the monthly payment is $x.
If he pay $x for next 3 months, then the total amount student paid in 3 month is: 3x
The interest is $30.94 for 3 months.
Student pay all the borrowed money and interest in 3 months.
That means he pay $1,500 + $30.94 in 3 months while the monthly payment was 3x.
This can be written as:
[tex]3x = 1500+30.94[/tex]
[tex]3x = 1530.94[/tex]
[tex]x = \frac{1530.94}{3}[/tex]
[tex]x = 510.31[/tex]
Hence, the monthly payment to the nearest cent is 510.31
what's the area of the Square 28in• 28in
Judy got 60 marks in test 1. She got 40 marks in test 2. What are her average marks in both tests?
What is the prime factorization of 15
Answer: 3 × 5
Step-by-step explanation: To find the prime factorization of 15, first create a factor tree with two branches.
Since 15 divided by 3 gives us 5, we know that and 5 are factors of 15. This means that we can write 3 and 5 at the bottom of our branches.
While 1 and 15 are also factors of 15, we don't use them in our factor tree. This because when finding a prime factorization, we only want factors other than 1 and the number itself.
Next, we circle any prime numbers in our factor tree. Since 3 and 5 are both prime numbers, we circle both 3 and 5. Since we have circles at the bottom of our branches, we are finished.
Therefore, the prime factorization of 15 is 3 × 5.
round 421,906 to the nearest hundred thousand and to the nearest thousand
The number 3.453 has two 3s why does each 3 have a different value
a rectangular plot of ground is 10 meters longer than it is wide. its area is 10,000 square meters
At 4:00 am the outside temperature was 28*F. By 4:00 pm that same day it rose to 38 degrees.
The temperature at 4:00 pm will be 66° F.
What are Integers?
An integer is a number with no decimal number or fractional part.
Given that;
At 4:00 am the outside temperature was 28*F. By 4:00 pm that same day it rose to 38 degrees.
Now, The temperature at 4:00 pm is calculated as;
= 28° F + 38° F
= 66° F.
Thus, The temperature at 4:00 pm will be 66° F.
Learn more about the integers visit:
https://brainly.com/question/26478372
#SPJ2
The complete question is this;
At 4:00 am, the outside temperature was 28*F. By 4:00 P.M. it rose 38 degrees. What was the temperature at 4:00 P.M. ?
a baker makes cakes and sells them at county fairs his initial cost was $45 to reserve a booth and $25 traveling expenses. He figures that it costs $1.75 to make each cake and he charges $6.50 per cake. Let x represent the number of cakes sold. Express the revenue R and Cost C as functions of x. Then find how many cakes will he need to sell before he will make a profit
Final answer:
The baker's revenue R can be expressed as R = x * 6.50, and the cost C can be expressed as C = 45 + 25 + (x * 1.75). To find the number of cakes he needs to sell before making a profit, we set the revenue equal to the cost and solve for x. The baker will need to sell at least 15 cakes before making a profit.
Explanation:
To express the revenue R as a function of x, we can use the equation R = x * 6.50. This is because the revenue is the number of cakes sold multiplied by the price per cake. So, every cake sold contributes $6.50 to the revenue.
To express the cost C as a function of x, we can use the equation C = 45 + 25 + (x * 1.75). The initial fixed costs of $45 for reserving a booth and $25 for traveling expenses are added to the variable costs of $1.75 per cake multiplied by the number of cakes sold.
To find the number of cakes he needs to sell before making a profit, we need to set the revenue equal to the cost and solve for x:
R = C => x * 6.50 = 45 + 25 + (x * 1.75)
Combining like terms, we get:
4.75x = 70
x = 70 / 4.75
x ≈ 14.74
Since you cannot sell a fraction of a cake, the baker will need to sell at least 15 cakes before making a profit.
-6+8(6x+2) < 7x+10
What is the answer to this inequality?
The answer choices are
A. x < 0
B. No solution
C. All numbers
D. x > 0
Which is a decimal expansion of 7/22?
A.
B.
C.
D.
What Is 1,270 rounded to the nearest hundred?
What is the area of a circle 3.102 cm in diameter? (note: the units will be cm2, you only need to enter the number)?
The GCF of 28x^3 and 16x^2y^2
Answer:
[tex]4x^2[/tex]
Step-by-step explanation:
We are asked to find the GCF of [tex]28x^3[/tex] and [tex]16x^2y^2[/tex].
The greatest common factor of numerical part would be GCF of 28 and 16.
Factors of 28: 1, 2, 4, 7, 14, 28.
Factors of 16: 1, 2, 4, 8, 16.
The greatest common factor of 28 and 16 is 4.
The GCF of variable part:
[tex]x^3=x\cdot x\cdot x[/tex]
[tex]x^2y^2=x\cdot x\cdot y\cdot y[/tex]
The greatest common factor of [tex]x^3[/tex] and [tex]x^2y^2[/tex] is [tex]x^2[/tex].
Upon combining the GCF of numerical part and algebraic part, we will get:[tex]4x^2[/tex]
Therefore, the greatest common factor of both expressions is [tex]4x^2[/tex].
the average person loses about 8 x 10^1 strands of hair each day. about how many strands of hair would the average person lose in 9 days?
At a store clearance, a women spent less than $200 on shirts that were labeled $15 each . How many shirts did she buy? Identify the numbers that are included in the solution set .
The cost of a 12.95 pizza was shared evenly by 5 friends. How much did each person pay?
1+3+5+7+...+1003= what is the answer?
The expression 40x2 – 65x + 50 represents the sum of the interior angles of a regular pentagon in degrees. If the interior angles of the pentagon are equal, which expression represents the measure of two angles?
Answer:
Expression representing the measure of the two angles of the given regular polygon is 16x² - 26x + 20.
Step-by-step explanation:
Given Expression of the Sum of the all interior angles of a regular polygon
40x² - 65x + 50
We need to find expression representing the measure of the two angles.
We know that regular polygons have all side and all angles equal.
Number of side or angles in regular polygon = 5
So, when we divide given expression by 5 we get expression for an angle of the regular polygon.
[tex]\frac{40x^2-65x+50}{5}=\frac{5(8x^2-13x+10)}{5}=8x^2-13x+10[/tex]
Expression for an angle of regular pentagon = 8x² - 13x + 10
Now, For 2 angles = 2( 8x² - 13x + 10 ) = 16x² - 26x + 20
Therefore, Expression representing the measure of the two angles of the given regular polygon is 16x² - 26x + 20.
Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level. What is the difference between these two elevations?
At a homeowners association meeting a board member can vote yes, vote no, or abstain a motion. There are three motions on which each board member must vote. Complete parts a through c
This question pertains to the voting options and procedures during a homeowners association meeting, covered under the broader subject of Social Studies in the context of High School education. It involves understanding quorum requirements and voting rules as per bylaws for decision-making on motions.
The question revolves around a homeowners association meeting where a board member has three options to participate in a vote: vote yes, vote no, or abstain from a motion. There are three motions for which each board member must decide how to vote. In such meetings, the rules outlined typically require a quorum to conduct business, the ability to make amendments to bylaws, and procedures for electing members, as seen in various articles of an organization's bylaws and rules of procedure. These rules ensure that the organization conducts its affairs in an orderly and democratic manner, often requiring a majority or unanimous consent for certain actions.
Meetings like these are essential, as they also involve critical decisions such as annual meetings, bylaw amendments, or the dissolution of the organization, each depending on the vote of the board members or the members of the organization. Membership eligibility and voting rights are typically determined by the board of directors or outlined within the bylaws. Furthermore, certain organizational procedures such as elections, member qualifications, and the transparency measures such as keeping a journal of proceedings of each meeting are often mandated.