A ball is thrown straight up from the top of a building that is 400 ft high with an initial velocity of 64 ft/s. The height of the object can be modeled by the equation s ( t ) = -16 t2 + 64 t + 400.
In two or more complete sentences explain how to determine the time(s) the ball is higher than the building in interval notation.
Answers
Check the picture below.
the ball is higher than the building when y = 0, or namely when s(t) = 0, any other time is above it, and hmmm when it's that?
[tex]\stackrel{s(t)}{0}~~ = ~~-16t^2+64t+400\implies 0=-16(t^2-4t-25) \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{1}t^2\stackrel{\stackrel{b}{\downarrow }}{-4}t\stackrel{\stackrel{c}{\downarrow }}{-25} \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ t= \cfrac{ - (-4) \pm \sqrt { (-4)^2 -4(1)(-25)}}{2(1)}\implies t=\cfrac{4\pm\sqrt{116}}{2}[/tex]
[tex]t=\cfrac{4\pm 2\sqrt{29}}{2}\implies t= \begin{cases} 2+\sqrt{29}~~\textit{\Large \checkmark}\\ 2-\sqrt{29} \end{cases}~\hfill \boxed{(0~~,~~2\sqrt{29})}[/tex]
notice, we can't use the 2-√29 because is a negative value and "t" is never negati ve, also notice the interval notation, we have parentheses on both sides.
Related Questions
Pete can do a job in 50 minutes while his brother Jim can do it in 1/2 the time. How long will it take them to do the job working together? (50/3 min)
Answers
It will take them 20 minutes to do the job working together.
Working time calculationGiven that Pete can do a job in 50 minutes while his brother Jim can do it in 1/2 the time, to determine how long it will take them to do the job working together, the following calculation must be performed:
1/1 + 2/1 = 3/11 / (3/1) = 1/360 min / 3 = 20 minTherefore, it will take them 20 minutes to do the job working together.
Learn more about working time calculation in https://brainly.com/question/536439
what unit of measurement would you use to weigh a elephant Oz * mm lb
Answers
Answer:
You would use lbs.
Step-by-step explanation:
mm is a unit of distance.
Oz is too small of a unit for weight.
lbs are just right!
You need to go to the library, grocery store,
and pharmacy. In how many orders can you
visit these places?
A 3
A 6
C 9
D 12
Answers
The back of Alisha's property is a creek. Alisha would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. If there is 380 feet of fencing available, what is the maximum possible area of the pasture?
Answers
9514 1404 393
Answer:
18050 square feet
Step-by-step explanation:
Let x represent the length of fence parallel to the creek. Then the remaining 380-x feet of fence is divided between the two ends of the pasture. The area will be the product ...
A = (x)(1/2)(380 -x)
The graph of this is a parabola that opens downward. It has x-intercepts at x=0 and x=380. The vertex (maximum) will be on the line of symmetry, halfway between these zeros, at x = (0 +380)/2 = 190.
Then the area is ...
A = (190 ft)(1/2)(380 -190 ft) = (190 ft²)/2 = 18,050 ft²
The maximum possible area of the pasture is 18,050 square feet.
100-point Question!!!
Arthur has decided to start saving for a new computer. His money is currently in a piggy bank at home, modeled by the function s(x) = 85. He was told that he could do the laundry for the house and his allowance would be a(x) = 10(x − 1), where x is measured in weeks. Explain to Arthur how he can create a function that combines the two and describe any simplification that can be done.
Answers
Answer:
Two or more independent functions (say f(x) and g(x)) can be combined to generate a new function (say g(x)) using any of the following approach.
h(x) = f(x) + g(x)h(x)=f(x)+g(x) h(x) = f(x) - g(x)h(x)=f(x)−g(x)
h(x) = \frac{f(x)}{g(x)}h(x)=
g(x)
f(x)
h(x) = f(g(x))h(x)=f(g(x))
And many more.
The approach or formula to use depends on the question.
In this case, the combined function is:
f(x) = 75+ 10xf(x)=75+10x
The savings function is given as
s(x) = 85s(x)=85
The allowance function is given as:
a(x) = 10(x - 1)a(x)=10(x−1)
The new function that combined his savings and his allowances is calculated as:
f(x) = s(x) + a(x)f(x)=s(x)+a(x)
Substitute values for s(x) and a(x)
f(x) = 85 + 10(x - 1)f(x)=85+10(x−1)
Open bracket
f(x) = 85 + 10x - 10f(x)=85+10x−10
Collect like terms
mark as brainiest
f(x) = 85 - 10+ 10xf(x)=85−10+10x
f(x) = 75+ 10xf(x)=75+10x
(Multiple choice question) suppose you take out a $7,200 personal unsecured loan at 12.75% APR and you are going to pay it back over 9 years. What is the total amount that you will pay back over the life of the loan
A. 7,200.00
b. 12,13.00
C. 11,807.00
Answers
Answer:
B
Step-by-step explanation:
I think its b but its 12,130 not 12,13 lol
HELP PLEASE!!!!!! + 100 POINTS
Answers
Solution:
Given:
x = 10Substitute the value of x into the expression.
[tex]5\sqrt{x - 1} + 9[/tex]
[tex]\rightarrow 5\sqrt{10 - 1} + 9[/tex]
Simplify the root:
[tex]\rightarrow5\sqrt{9} + 9[/tex]
[tex]\rightarrow(5 \times \sqrt{9}) + 9[/tex]
[tex]\rightarrow(5 \times 3) + 9[/tex]
Multiply 5 and 3:
[tex]\rightarrow15 + 9[/tex]
Add 15 and 9:
[tex]\rightarrow24[/tex]
Hellllllllllllllllllllllpp
Answers
Answer:
D
Step-by-step explanation:
No explanation anymore I just don't want to anymore lol.
100 Points
Use geometry to evaluate the integral from negative 2 to 6 of f of x, dx where f of x equals the absolute value of x for x between negative 2 and 2 inclusive, equals 2 for x greater than 2 and less than or equal to 4, and equals negative x plus 4 for x greater than 4 and less than or equal to 6.
Answers
Answer:
[tex]\int\limits^{6}_{-2} {f(x)} \, dx=6[/tex]
Step-by-step explanation:
Review the attached graph
By using geometry to evaluate the given integral, the value is equal to 6 units.
How to use geometry to evaluate an integral?In order to use a geometry to evaluate a definite integral, you should identify the portion of a graph which corresponds to the given integral.
Also, you'll mark out the geometric shapes that are formed on the graph, so as to enable you calculate their areas. Finally, you'll add the areas together.
From the graph of the integral shown in the image attached below, the geometric shapes that are formed are rectangle and triangles.
For the area of rectangle, we have:
Area of rectangle = L × B
Area of rectangle = 2 × 2
Area of rectangle = 4 units.
For the area of triangle, we have:
Area of triangle = 1/2 × b × h
Area of triangle = 1/2 × 2 × 2
Area of triangle = 2 units.
Total area = 4 + 2
Total area = 6 units.
Read more on integrals here: https://brainly.com/question/5898524
#SPJ2
Leslie sold 2 1/2 dozen sweet rolls
Answers
Which is a parallelogram? For points A B C D
Answers
Explanation:
Any parallelogram has two pairs of opposite sides that are parallel.
A rectangle is a parallelogram, but not the other way around.
Choices A and B are trapezoids with exactly one pair of parallel sides.
Help please need the answers now
Answers
Answer:
j(x) matches #3
g(x) matches #2
f(x) matches #4
h(x) matches #1
Find the value of x. enter value only
Answers
Answer:
9
Step-by-step explanation:
The product of the secant lengths BC and BD is equal to the square of the tangent length BA.
BC×BD = BA²
3×(3 +x) = 6²
3 +x = 12 . . . . . divide by 3
x = 9 . . . . . . subtract 3
_____
Additional comment
Sometimes the relationships involving secants, tangents, and chords can be difficult to remember. There is basically one rule that applies to all of these geometries:
the product of segment lengths to the circle from the point of intersection of the secants/tangents/chords is the same
A tangent can be thought of as a secant that has a length of 0 between its end points. That is, the two lengths from the point of intersection to the circle are the same.
Here is an example of this rule applied to chords:
https://brainly.com/question/27160911
PLZZZZZ HELP ME ILL MAKE YOU BRAINLIEST ANSWER PLZZZZZZ THANKYOUUU!!!!!!
Answers
Answer:
It would be neither.
Step-by-step explanation:
It definitely is not parallel since Line 1 would run into Line 2 at (4, 1). Nor could it be perpendicular because they do run into each other but do not make a 90 degree angle.
A line is drawn parallel to y = x. It has the same slope, so it’s equation has the form y = x + b. The new line passed through the point (2, 5). What is its y- intercept (b)?
Answers
Answer:
b = 3
Step-by-step explanation:
(2,5) is information! x = 2 and y = 5.
Use these values in the equation:
y = x + b
5 = 2 + b
Subtract 2.
3 = b
The equation of the line is y = x + 3.
Net A has 3 rectangles with 2 triangles on the side. Net B has 3 rectangles with 2 triangles on the sides.
Students in Mrs. Garcia’s class were practicing drawing nets. She gave them the three-dimensional figure shown. Alina drew the net labeled A and Benjamin drew the net labeled B. What statement about the students’ nets is true?
Alina drew the only correct net.
Benjamin drew the only correct net.
Both nets are correct.
Neither student’s net is correct.
Answers
Answer:
c
Step-by-step explanation:
Answer:
~c~
Step-by-step explanation:
Which of the following expresses 2.4 as a fraction in simplest form?
Answers
D. 2 4/9
[tex]\sf 2\dfrac{1}{4} \rightarrow 2.25[/tex][tex]\sf 2\dfrac{2}{5} \rightarrow 2.4[/tex][tex]\sf 2\dfrac{11}{25} \rightarrow 2.44[/tex][tex]\sf 2\dfrac{4}{9} \rightarrow 2.444444...[/tex]
Note: the symbol on top of 4 - means that the number is recurring/repeating infinitely.
Answer: (D) just did the unit test review on edge
Step-by-step explanation:
i’ll mark brainlest to whoever answers this question first! :)
Answers
A blueprint of a barn is shown.The scale is 5 inches =8 feet. Find the actual length of the wall that is labeled 20 inches.
Answers
20/5=4
8x4=32
The answer is 32 feet
Rational function
g(x) = 1 / (x-3) +2
Find x and y intercepts
Graph
Answers
Answer:
[tex]x \: intercept = ( \frac{5}{2} ,0) \\ y \: intercept = (0, \frac{5}{3} )[/tex]
Step-by-step explanation:
STEP 1: Define x and y intercepts
The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.
Step 2: We plot the graph of the given function
The graph can be seen in the graph image I sent. The x and y intercepts are also identified.
John has 12 pounds of dog food and is going to separate it into 3/4 pound portions. How many portions of dog food will he have?
HELP!
Answers
16 portions
explanation:
12 / 3/4
= 12 * 4/3
= 4*4 = 16
The verbal expression “the difference between
three times a number x and 12, increased by the quotient of 5 and the number x" is equivalent to which algebraic expression?
A. 3(x-1)+x/5
B. (3x-12)+5/x
C. 3(x-12)+5+x
D. (3x-12)+5x+x
Answers
Answer:
B. (3x-12)+5/x
Step-by-step explanation:
Difference means - or minus
Three times a number x and 12= 3x-12
Increased= + or plus
quotient= / or divide
5 and the number x= 5/x
So the answer is,
(3x-12)+5/x
I hope you understand.
Emma's family traveled 5/8 of the distance to her aunt’s house on Saturday. They traveled 1/3 of the remaining distance on Sunday. What fraction of the total distance to her aunt’s house was traveled on Sunday?
Answers
Answer:
23/24
Step-by-step explanation:
To find the total distance of Sunday and Saturday we add 5/8 + 1/3
= 5/8 + 1/3
= 5 × 3/8 × 3 + 1 × 8/3 × 8
= 15/24 + 8/24
= 15 + 8/ 24
= 23/24
root of 6x^2 -8 = -8x
Answers
Answer:
If your question is set up like this [tex]\sqrt{6x^2-8}=-8x[/tex] then your answer is No solution.
If your question is set up like this[tex]\sqrt{6x^2}-8=-8x[/tex] then your answer is [tex]x=\frac{4(8-\sqrt{6}) }{29}[/tex] or x = 0.765
Hope this helps!
How many ounces of a 18% alcohol solution and a 26% alcohol solution must be combined to obtain 34 ounces of a 22% solution?
Answers
Answer: 54 or 100 lol oozy
Step-by-step explanation: Nothing that's just the answer
Answer:
18% alcohol 17 ounces, 26% alcohol 17 ounces
Step-by-step explanation:
set some equation
18%x + 26%y = 34x22%
34= x + y
Question 13
2 pts
If a person bought a bike for $400 and sold it for $500. What is their rate of return?
0 25%
None of the Above
05%
20%
Question 14
2 pts
If you bought 1000 shares of a Vanguard Mutual Fund for $145 a share two years
Answers
Answer:
For question 13: 25%
Step-by-step explanation:
25 out of one hundred is one fourth
25 percent of 400 is one hundred
since 4 one hundreds go into 400
take one fourth and you get one hundred
500-400=100
so 25%
I dont know what the second question is asking
How did I get this wrong????
Answers
Answer:
18.98°
Step-by-step explanation:
1) p=arcsin(13/40);
2) p=arcsin0.325≈18.98°.
An iPad is marked down from $700 to $575. What is the percent markdown of the iPad?
Answers
Solution:
the percent markdown of the iPad is 17.86%
Given:
Original Price = $700
Final price = $575
The markdown is gotten by;
[tex]Markdown=original~price-final~price[/tex]
[tex]Markdown=700-575[/tex]
Markdown = $125
Thus, the percent markdown is gotten by;
[tex]percent~markdown=\frac{markdown}{original~price}~x~ 100[/tex]
percent markdown = [tex]\frac{125}{700}[/tex] × 100%
percent markdown =[tex]\frac{12500}{700}[/tex]
percent markdown = 17.857 %
percent markdown ≈ 17.86%
Therefore, the percent markdown of the iPad is 17.86%
Hope this helps!!
If you have any questions please ask.
what is 3/4X + 2 = 3/8X
Answers
Answer:
exact form: -16/3
decimal form: -5.3
mixed number form: -5 1/3
Step-by-step explanation:
solve for x by simplifying both sides of the equation, then isolating the variable.
3/4X + 2 = 3/8X
3/4X - 3/8X = - 2
(3/4 - 3/8)X = -2
((6-3)/8)X =-2
3/8X = -2
3X = (-2)(8)
3X = -16
X = -16/3
The price of a cd was decreased by 2% to £14. What was the price before the decrease?
Give your answer to the nearest penny.
Answers
Answer:
14.28
Step-by-step explanation:
2% of 14 is .28
.28 + 14 = 14.28
Hi!
Since the price was decreased by 2%, that means that 14 is 98% (100% - 2%) of the original price. So, we just have to figure out 98% of what number is 14.
98% can be written in decimal form as 0.98.
We can set up the following equation:
14 = 0.98x
Now, divide both sides by 0.98:
14/0.98 = 14.2857143
The question says to round to the nearest penny, so your answer is
14.29