Given:
[tex]h(t)=-16t^2+96t+6[/tex]Find-:
(a) Maximum second after launch will the object reach its maximum height
(b) Find the maximum height that the object reaches.
(c) Find the x-intercept and explain its meaning in the context of the problem.
(d) After how many seconds will the object be 100 feet above the ground
(e) Find the y-intercept and explain its meaning on the context of the problem
Sol:
(a)
Maximum second after launch.
For maximum value derivative should be zero.
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ h^{\prime}(t)=-(16\times2)t+96 \\ \\ \end{gathered}[/tex][tex]\begin{gathered} -32t+96=0 \\ \\ 32t=96 \\ \\ t=\frac{96}{32} \\ \\ t=3 \end{gathered}[/tex]After 3-second the object reaches maximum height.
(b)
For maximum height is at t = 3
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ h(3)=-16(3)^2+96(3)+6 \\ \\ h(3)=(-16\times9)+(96\times3)+6 \\ \\ h(3)=-144+288+6 \\ \\ =150 \end{gathered}[/tex](c) x-intercept the value of y is zero that means:
[tex]\begin{gathered} h(t)=0 \\ \\ -16t^2+96t+6=0 \\ \\ -8t^2+48t+3=0 \\ \\ t=\frac{-48\pm\sqrt{48^2-4(-8)(3)}}{2(-8)} \\ \\ t=\frac{-48\pm48.98}{-16} \\ \\ t=6;t=-0.061 \end{gathered}[/tex]The negative value of "t" is not considered so at
x-intercept is 6 and -0.061
(d) Object be 100 feet above grounded is:
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ -16t^2+96t+6=100 \\ \\ -16t^2+96t-94=0 \\ \\ -8t^2+48t-47=0 \\ \end{gathered}[/tex]So, the time is:
[tex]\begin{gathered} t=\frac{-48\pm\sqrt{48^2-4(-8)(-47)}}{2(-8)} \\ \\ t=\frac{-48\pm\sqrt{800}}{-16} \\ \\ t=\frac{-48-28.28}{-16},t=\frac{-48+28.28}{-16} \\ \\ t=4.76,t=1.23 \end{gathered}[/tex]At t= 4.76 and t =1.23
(e)
For y-intercept value of "x" is zero.
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ h(0)=-16(0)^2+96(0)+6 \\ \\ h(0)=6 \end{gathered}[/tex]So, the y-intercept is 6.
Convert:47.0 grams Cu = ? moles
In 1 grams of Cu there are 0.015736631731344 moles
So, for 47.0 gram Cu : Multiply 47.0 by 0.015736631731344 :
47.0 gram Cu = 47.0 x 0.015736631731344
47.0 gram Cu = 0.73962 mol
Answer : 0.73962 mol
6.f(x) = 2x + 3x +1g(x)=7X - 2x+7XFind h(x) = f(x) - gix)A.h(x) = -7% -5€ -5x-1B.h --- 5 -- |318
rearrange the terms and simplify
[tex]\begin{gathered} h(x)=-7x^3-7x^2+2x^2+3x+2x+1 \\ =-7x^3-5x^2+5x+1 \end{gathered}[/tex]The right option is A
3 Step Problem: Erik is building a cubby bookshelf, that is, a bookshelf divided into storage holes (cubbies) instead of shelves. He wants the height of the bookshelf to be x^2 - 2x - 3 and the width to be x^2 + 4x + 3. Each cubby hole in the bookshelf will have a height of x + 3 and width of x - 3.STEP 1 of 3: Write a rational expression to determine how many cubbies high the book shelf will be.
Step 1:
In order to determine the number of cubbies high, we just need to divide the total height x² - 2x - 3 by the height of one cubby x + 3:
x² divided by x: x
x multiplied by (x + 3): x² + 3x
x² - 2x - 3 minus x² + 3x: -5x - 3
-5x divided by x: -5
-5 multiplied by (x + 3): -5x - 15
-5x - 3 minus -5x - 15: 12
The division doesn't have remainder 0, so let's write the division as a fraction:
[tex]\text{number of cubbies}=\frac{x^2-2x-3}{x+3}[/tex]Quadrilateral BCDE is similar to quadrilateral FGHI. Find the measure of side HI. Round your answer to the nearest tenth if necessary
we have:
[tex]\frac{HI}{DE}=\frac{IF}{EB}[/tex]so
[tex]\begin{gathered} \frac{HI}{23}=\frac{59}{14} \\ 14HI=59\cdot23 \\ 14\cdot HI=1357 \\ HI=\frac{1357}{14} \\ HI=96.9 \end{gathered}[/tex]answer: HI = 96.9
which of the following would be an equivalent ratio to 2:90?
Male teachers = 2
Male students = 180/2 = 90
The ratio of male teachers to male students
2:90
2/90, simplify by 2 = 1/45
Kevala sells sodas and sundaes at his food stand. One week the number of sodas he made was 4 fewer than 5 times the number of sundaes. If he made 96 sodas, how many sundaes did he make?
hello
let sundaes be represented by x and soda by y
on this particular week, we made sodas 4 fewer than 5 times the numbers of sundaes
let's write an equation for this
[tex]y=5x-4[/tex]with this equation, we can know the numbers of sundaes he made
remember that y is representing soda and x is representing sundaes
[tex]\begin{gathered} 96=5x-4 \\ \text{solve for x} \\ \text{collect like terms} \\ 96+4=5x \\ 100=5x \\ \text{divide both sides by the coefficient of x} \\ \frac{100}{5}=\frac{5x}{5} \\ x=20 \end{gathered}[/tex]from the calculations above, Kevala made 20 sundaes and 96 soda
Allied Health - A wound was measured to be 0.8 cm in length. Whaat is the greatest possible error of this measurement?
The answer is 0.05cm
Explanation
Precision = 0.1
∴ Greatest Possible Error (GPE) = 0.1/2
GPE = 0.05cm
Hence the greatest possible error of the measurement is 0.05cm
1. Find Each Right triangles missing length. If necessary, round to thenearest tenth,5 pointsleg =8 cm, leg= 21 cm
We have a right triangle, for which we know the two legs.
We can calculate the hypotenuse H by applying the Pythagorean theorem:
[tex]\begin{gathered} H^2=L^2_1+L^2_2=8^2+21^2=64+441=505 \\ H=\sqrt[]{505}\approx22.5 \end{gathered}[/tex]The missing length (the hypotenuse) is approximately 22.5 cm.
can you please help me?
Answer : The linear function of the graph when move down 3 units is y = x - 3
The graph shift vertically because it is down 3 units
The standard equation of a linear function is
y = mx + b
Where b = intercept and m = slope
Move 3 unit down means b = -3
Hence, y = x-3
Answer is y = x - 3
A rectangular paperboard measuring 32 in long and 24 in wide has a semicircle cut out of it, as shown below.Find the area of the paperboard that remains. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.
We need to subtract the area of the semicircle that was cut out of the paperboard from its original area.
The original area of the paperboard was the area of a rectangle 32in long and 24 in wide:
[tex]32in\cdot24in=768in^{2}[/tex]And the area of the semicircle, noticing that its radius r is 24in/2, is given by:
[tex]\frac{\pi r^2}{2}=\frac{3.14\cdot(12in)^{2}}{2}=\frac{3.14\cdot144in^2}{2}=226.08in^2[/tex]Thus, the area of the paperboard that remains is:
[tex]768in^2-226.08in^2=(768-226.08)in^{2}=541.92in^{2}[/tex]Therefore, the answer is 541.92 in².
22) A game is played using one die. If the die is rolled and shows a 2, the player wins $8. If the die
shows any number other than 2, the player wins nothing. If there is a charge of $1 to play the
game, what is the game's expected value?
A) $0.33
B) $7.00
C)-$0.33
D) -$1
The game's expected value is (A) $0.33
How to determine the expected amount the player wins or lose?From the question, we have the following parameters that can be used in our computation:
Outcome of 2 = Win $8
Other outcomes = Win $0
A die has the following sample space
S = {1, 2, 3, 4, 5, 6}
Using the above sample space, the individual probabilities are:
P(Outcome of 2) = 1/6
P(Others) = 5/6
The expected value is calculated as
Expected value = Sum of the products of the probability and the amount win/lose
So, we have
Expected = 1/6 * 8 + 5/6 * 0
Evaluate the products
Expected = 1.33
The charge is $1
So, we have
Expected = 1.33 - 1
Evaluate
Expected = 0.33
Hence, the expected amount is $0.33
Read more about expected values at
brainly.com/question/15858152
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There was a survey taken to see which types of pets people prefer. Out of 11 participents, 5 said they prefer dogs, 4 said they prefer cats, and 3 said they prefer birds. What is the percentages of people that prefer dogs, cats, and birds?
To find the percentages of people that prefer dogs, cats or birds, divide the corresponding amount of people that likes each pet by the total amount of people in the survey, and then multiply that quantity by 100.
Since there are 11 participants, we should divide each quantity by 11.
Dogs:
There are 5 people who prefer dogs. The percentage is:
[tex]\frac{5}{11}\times100\text{ \%}=45.4545\ldots\text{ \%}[/tex]Cats:
There are 4 people who prefer cats. The percentage is:
[tex]\frac{4}{11}\times100\text{ \%=36.3636}\ldots\text{ \%}[/tex]Birds:
There are 3 people who prefer birds. The percentage is:
[tex]\frac{3}{11}\times100\text{ \%=27.2727}\ldots\text{ \%}[/tex]You have $500,000 saved for retirement. Your account earns 8% interest. How much will you be able to pullout each month, if you want to be able to take withdrawals for 15 years?$
The rule of the payout annuity is
[tex]P=\frac{d(1-(1+\frac{r}{n})^{-nt})}{\frac{r}{n}}[/tex]P is the initial amount
d is regular withdrawals
r is the annual rate in decimal
n is the number of periods in a year
t is the time
Since you have $500 000 saved, then
P = 500000
Since the interest is 8%, then
r = 8/100 = 0.08
Since the time is 15 years, then
t = 15
Since you want the monthly amount, then
n = 12
Substitute them in the rule to find d
[tex]\begin{gathered} 500000=\frac{d(1-(1+\frac{0.08}{12})^{-12(15)})}{\frac{0.08}{12}} \\ 500000(\frac{0.08}{12})=d(1-(\frac{151}{150})^{-180}) \\ \frac{10000}{3}=d(1-(\frac{151}{150})^{-180}) \\ \frac{\frac{10000}{3}}{(1-(\frac{151}{150})^{-180})}=d \\ 4778.260422=d \end{gathered}[/tex]Then you will be able to pull $4778.260422 each month
Triangle - Interior Angles Find the measure of the indicated angle in each triangle. 3 27 311>P 26 A ma m2Q= 1 s 스 minta mothed
Answer: We are goinf to sovle triangle Number-03:
[tex]m\angle Q=?[/tex]We know that the sum of angles in a triangle is 180 degrees, therefore we can do the following:
[tex]\begin{gathered} m\angle Q+30+31=180^{\circ} \\ \therefore\rightarrow \\ m\angle Q=180^{\circ}-61=119^{\circ} \\ \therefore\rightarrow \\ m\angle Q=119^{\circ} \end{gathered}[/tex]This is the unknown angle that we were interested in.!
1 point It takes 500 packing peanuts to fill a box that is 3 inches x 4 inches x 5 inches. How many peanuts would it take to fill a box that is 6 inches x 8 inches x 10 inches? 1,000 packing peanuts 2,000 packing peanuts 4,000 packing peanuts 8,000 packing peanuts
Well, this is a volume and ratio problem. In a box the volume is given by width times length times height, so the volume of the first box is 3*4*5=60 cubic inches.
In the second box, the volume is 6*8*10=480 cubic inches.
[tex]\frac{480}{60}=\frac{8}{1}=8[/tex]This means that in the big box you could place 8 peanuts for every peanut placed in the small box. If you need 500 peanuts to fill the small box, then for the big box:
[tex]500\cdot8=4000[/tex]So, you need
I need help to solve this I don't quite understand how to do these
Recall the definition of the sine of an angle in a right triangle:
[tex]\sin (A)=\frac{\text{Side opposite to A}}{\text{ Hypotenuse}}[/tex]In the given diagram, the length of the side opposite to the angle of 53° has a length of 10, while the length of the hypotenuse is x. Then:
[tex]\sin (53)=\frac{10}{x}[/tex]Isolate x from the equation:
[tex]x=\frac{10}{\sin (53)}[/tex]Use a calculator to find the value of the expression for x:
[tex]\begin{gathered} x=12.52135658\ldots \\ \Rightarrow x\approx12.5 \end{gathered}[/tex]Skip designs tracks for amusement park rides. For a new design, the track will be elliptical. If the ellipse is placed on a large coordinate grid with its center at (0, 0), the equation x^2/2500 + y^2/8100 = 1 models the path of the track. The units are given in yards. How long is the major axis of the track? Explain how you found the distance.show the steps
Step 1
Given:
center (0,0)
the equation given should have been:
[tex]\frac{x^2}{2500}+\frac{y^2}{8100}=1[/tex]We need to identify the larger denominator. If it is under x, the ellipse is horizontal. If it is under y, the ellipse is vertical. 8100 is the larger denominator and is under y, therefore, the ellipse is vertical
Step 2
The general equation of an ellipse is given as;
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]h and k are the center values which are both 0.
a = length of the semi-major axis
b = length of the semi-minor axis
The given equation is;
[tex]\frac{x^2}{2500}+\frac{y^2}{8100}=1[/tex]which is equivalent to;
[tex]\frac{x^2}{50^2}+\frac{y^2}{90^2}=1[/tex][tex]\begin{gathered} a^2=90^2 \\ \sqrt[]{a^2}=\sqrt[]{90^2} \\ a=90\text{ yard},\text{ the semi-major ax}is \end{gathered}[/tex]The length of the major axis will thus be; 90x2=180 yards
Answer; 180 yards
Solve forx: 3x - 5 = 2x + 6.1-111-11
To solve the equation we need to isolate the "x" variable on the left side. This is done step-by-step below:
3x - 5 = 2x + 6
3x - 2x -5 = 6
x = 6 + 5
x = 11
DEF~△VXW.244FED122WXVWhat is the similarity ratio of △DEF to △VXW?Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
We are given two triangles. We notice that each corresponding angle is equal, therefore, by Angle Angle Angle (AAA) theorem the triangles are similar. This means that each corresponding side is at the same ratio. That ratio is called the similarity ratio and it is obtained by finding the quotient between any two corresponding sides, like this:
[tex]r=\frac{DF}{VW}=\frac{DE}{VX}=\frac{FE}{WX}[/tex]Where "r" is the similarity ratio. Now, we substitute the sides:
[tex]r=\frac{4}{2}=\frac{4}{2}=\frac{2}{1}=2[/tex]Therefore, the similarity ratio is 2.
Yolanda is preparing a liquid fertilizer that she will use on her lawn. She mixes 4 tablespoons of liquid fertilizer with 6 gallons of water.Using this ratio, how many gallons of water should be mixed with each tablespoon of liquid fertilizer?
Given data:
The given amount of liquid fertilizer is f=4.
The given water is w=6 gallons.
4 tablespoons= 6 gallons of water
1 tablespoon= 1.5 gallons of water.
Thus, 1.5 gallons of water is mix with each tablespoon.
what is the slope and y-intercept of negative 3x + 5y equals -15
-3x + 5y = -15
The general form of a line using slope and y intercept is: y = mx + b
where m is the slope and b is the y intercept
So we have to write the original equation in this form:
-3x + 5y = -15
5y = 3x - 15
y = (3/5)x - 15/5
y = (3/5)x - 3
In this case, m= 3/5 and b = -3
Therefore m = 3/5
Therefore the y intercept (when x = 0) is -3
Answer:
slope is 3/5
y intercept -3
You will complete the following question on your own paper. Make sure to show ALL work including a picture you draw. He 2 A point on the ground is 50 feet from my house. The angle of elevation to the top of the house is 48º. Find the height of the house to the nearest tenth. Finis the following template: "Last Name First Name Assignment
ANSWER
The height of the house is 55.5 feet
EXPLANATION
Since this forms a right triangle, we can use the tangent of the elevation angle to the top of the house to find its height - because we know the lenght of the adjacent side and we want to know the lenght of the opposite side:
[tex]\begin{gathered} \tan 48º=\frac{h}{50} \\ h=50\tan 48º \\ h=55.53062574\approx55.5\text{ feet} \end{gathered}[/tex]The angle between 0 degrees and 60 degrees that is coterminal with the 1993 angle is degrees.Please show work neatly
Given:
[tex]1993^0[/tex]To Determine: The coterminal angle of the given angle
Solution
Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side. For example 30° , −330° and 390° are all coterminal
[tex]\begin{gathered} 1993^0-360^0=1633^0 \\ 1633^0-360^0=1273^0 \\ 1273^0-360^0=913^0 \\ 913^0-360^0=553^0 \\ 553^0-360^0=193^0 \end{gathered}[/tex]Hence, the angle that coterminal with 1993 degrees is 193⁰
Multiply4V3 * 10V12 * V6*V2Enter your answer, in simplest radical form, in the box.
Given:
[tex]4\sqrt[]{3}\cdot10\sqrt[]{12}\cdot\sqrt[]{6}\cdot\sqrt[]{2}[/tex]Simplify the expression.
[tex]\begin{gathered} 4\sqrt[]{3}\cdot10\sqrt[]{12}\cdot\sqrt[]{6}\cdot\sqrt[]{2} \\ =4\sqrt[]{3}\cdot10\sqrt[]{4\times3}\cdot\sqrt[]{3\times2}\cdot\sqrt[]{2} \\ =4\sqrt[]{3}\cdot10(\sqrt[]{2^2})\sqrt[]{3}\cdot\sqrt[]{2}\cdot\sqrt[]{3}\cdot\sqrt[]{2} \\ =4\sqrt[]{3}\cdot10(2)\sqrt[]{3}\cdot2\sqrt[]{3} \\ =(4\times20\times2)(\sqrt[]{3})^2\cdot\sqrt[]{3} \\ =480\sqrt[]{3} \end{gathered}[/tex]Answer:
[tex]4\sqrt[]{3}\cdot10\sqrt[]{12}\cdot\sqrt[]{6}\cdot\sqrt[]{2}=480\sqrt[]{3}[/tex]1 Evaluate 0.1m + 8 – 12n when m = 30 and n = 1/4.
Answer:
8
Step-by-step explanation:
0.1(30)+8-12(0.25)
3+8-3
=8
ok heres my problem,on average, a refrigerator door is opened 68 times each day.Len has 2 refrigerators in his house.based on this average,about how many times ina 1 week period are the refrigerator doors opened?
68 times / day
ok
If he open only one refrigerator per day
68 x 7 = 476
He opens the refrigerator 476 times per week
But he has 2 refrigerators
476 x 2 = 952 times
Result, Len open the doors of both refreigerators 952 times per week
Done
Do you have any question?
3.5 feet3 feet3 feet2 feet4.5 feet
The shape in the image is a trapezium. The area of a trapezium is given by:
[tex]A_{trapezium}=\text{ }\frac{1}{2}\text{ (a + b)h}[/tex]From the image, a= 3.5 feet, b= 4.5 feet and h = 2 feet.
Thus, we have:
[tex]\begin{gathered} A_{trapezium}=\text{ }\frac{1}{2}\text{ ( 3.5 + 4.5) 2} \\ A_{trapezium}=8ft^2 \end{gathered}[/tex]Hence, the area of the figure is 8 square feet
Write the quadratic equation in Vertex form with vertex (4 8) and passing through the origin.
Vertex = (4,8)
Passing through the origin = (0,0)
Vertex form:
y= a (x-h)^2+k
(h,k) is the vertex:
y= a (x-4)^2+8
Replace the (x,y ) by the origin coordinates
Solve for a
0= a (0-4)^2+8
-8 = a(-4)^2
-8 = a 16
-8/16 = a
-1/2 = a
y=-1/2 (x-4)^2+8
the table below shows the length of time a plumber takes on a job and price he charges. what does the y-intercept represent?
The data that represents the y-intercept in a table is always the output/result. In the given table, it shows the cost that the plumber charges after the given hours of work.
Thus, the y-intercept in the data is the total cost of repairs.
The answer is letter B.
Joshua is going to invest $9,000 and leave it in an account for 5 years. Assuming theinterest is compounded continuously, what interest rate, to the nearest tenth of apercent, would be required in order for Joshua to end up with $12,500?
Let r be the percent annual interest rate of the account. Since $9000 are left for 5 years, for an outcome of $12,500, then:
[tex]9000\times(1+\frac{r}{100})^5=12,500[/tex]Divide both sides by 9000:
[tex](1+\frac{r}{100})^5=\frac{12500}{9000}=\frac{25}{18}[/tex]Take the 5th root to both sides:
[tex]\begin{gathered} 1+\frac{r}{100}=\sqrt[5]{\frac{25}{18}} \\ \Rightarrow\frac{r}{100}=\sqrt[5]{\frac{25}{18}}-1 \\ \Rightarrow r=100(\sqrt[5]{\frac{25}{18}}-1) \end{gathered}[/tex]Use a calculator to find the decimal expression for r:
[tex]r=6.790716585\ldots[/tex]Therefore, to the nearest tenth:
[tex]r=6.8[/tex]This means that Joshua would need to invest his money on a 6.8% annual interest account.