24. A rocket is launched into the air. Its height in feet, after x seconds, is given by the equation The starting height of the rocket is h(x)=-16x’ +300x + 20 The maximum height is The rocket hits the ground after seconds.
Answers
Well we just need to do the analise of the function h, so for the first question we need to know what is the value of h when x=0, so if we evaluate we see that
[tex]h(0)=-16(0)^2+300(0)^{}+20^{}=20^{}[/tex]So the first answer is that the start heigth of the rocket is 20.
Now for the second we need to do the derivate and see the critical ponit to know the maximum, we are going to calculate first the derivate, so
[tex]h^{\prime}(x)=-32x^{}+300[/tex]now we need to find the critical ponits so for this, we are going to see when h'(x) = 0, this meand when the derivate is equal to zero, so h'(x) = 0 when
[tex]\begin{gathered} -32x\text{ + 300 =0} \\ 300\text{ = 32x} \\ \frac{300}{32}=x \end{gathered}[/tex]to see if this critical poni is a maximum we need to calculate the secon derivate and see that the second derivate valued in 300/32 is smaller than 0, so
[tex]h^{\doubleprime}(x)\text{ = -32}[/tex]now when x= 300/32 we have that h''(x) is -32 because the second derivate is constant, in this case h''(300/32) < 0, because of this the answer is that 300/32 is the maximum, bur 300/32 = 75/8.
Now for the third question, we need to see the roots of h, so we need to see when h is zero, so for wich values of x we have that h(x) = 0, then
[tex]-16x^2+300x+20=0^{}[/tex]we can solve this with the quadratic equation to solve this kind of equations. This equation is
so we have that
[tex]\begin{gathered} x\text{ = }\frac{-300\text{ }\pm\sqrt[]{300^2\text{ -4(-16)20}}}{2(-16)} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{90000\text{ + 1280}}}{-32} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{91280}}{-32} \end{gathered}[/tex]the answer is x = (-300 - v/ 91280)/(-32) or x = (-300 + v/ 91280)/(-32) and this is equal to x = (300 + v/ 91280)/(32) or x = (300 - v/ 91280)/(32) if you prefer. We can also write the answer in a simpler way: x = (75 + v/ 5705)/(8) or x = (75 - v/ 5705)/(8), this is
[tex]x\text{ = }\frac{75\text{ }\pm\sqrt[]{5705}}{8}[/tex]
Well we just need to do the analise of the function h, so for the first question we need to know what is the value of h when x=0, so if we evaluate we see that
[tex]h(0)=-16(0)^2+300(0)^{}+20^{}=20^{}[/tex]So the first answer is that the start heigth of the rocket is 20.
Now for the second we need to do the derivate and see the critical ponit to know the maximum, we are going to calculate first the derivate, so
[tex]h^{\prime}(x)=-32x^{}+300[/tex]now we need to find the critical ponits so for this, we are going to see when h'(x) = 0, this meand when the derivate is equal to zero, so h'(x) = 0 when
[tex]\begin{gathered} -32x\text{ + 300 =0} \\ 300\text{ = 32x} \\ \frac{300}{32}=x \end{gathered}[/tex]to see if this critical poni is a maximum we need to calculate the secon derivate and see that the second derivate valued in 300/32 is smaller than 0, so
[tex]h^{\doubleprime}(x)\text{ = -32}[/tex]now when x= 300/32 we have that h''(x) is -32 because the second derivate is constant, in this case h''(300/32) < 0, because of this the answer is that 300/32 is the maximum, bur 300/32 = 75/8.
Now for the third question, we need to see the roots of h, so we need to see when h is zero, so for wich values of x we have that h(x) = 0, then
[tex]-16x^2+300x+20=0^{}[/tex]we can solve this with the quadratic equation to solve this kind of equations. This equation is
so we have that
[tex]\begin{gathered} x\text{ = }\frac{-300\text{ }\pm\sqrt[]{300^2\text{ -4(-16)20}}}{2(-16)} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{90000\text{ + 1280}}}{-32} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{91280}}{-32} \end{gathered}[/tex]the answer is x = (-300 - v/ 91280)/(-32) or x = (-300 + v/ 91280)/(-32) and this is equal to x = (300 + v/ 91280)/(32) or x = (300 - v/ 91280)/(32) if you prefer. We can also write the answer in a simpler way: x = (75 + v/ 5705)/(8) or x = (75 - v/ 5705)/(8), this is
[tex]x\text{ = }\frac{75\text{ }\pm\sqrt[]{5705}}{8}[/tex]
Related Questions
In a school, 10% of the students have green eyes. Findthe experimental probability that in a group of 4students, at least one of them has green eyes.The problem has been simulated by generating randomnumbers. The digits 0-9 were used. Let the number "9"represent the 10% of students with green eyes. A sampleof 20 random numbers is shown.
Answers
Given that in a group of 4 students at least one has green eyes.
Also, the number 9 represents the 10% of the students with green eyes.
From the 20 random experimental numbers given, the number 9 appeared in only nine of them.
The experimental probability in percentage will be:
[tex]\frac{9}{20}\ast100\text{ = }45\text{ percent}[/tex]ANSWER;
45%
You have to multiple the whole number and the fraction if you don’t know how to do it
Answers
We need to find how much spare represents the given space for vegetables.
The total are is 24 square feet and she will use 3/4 of the space for vegetables.
Then, you need to multuply the result by 3 and then, we need to divide 24 by 4.
Therefore:
24*(3/4) =72/4 = 18
Hence, she will use 18 square feet for vegetables.
Carlos is adding insulation to a room he just finished framing in his home. The room is 16ft. by 12ft., and the ceilings are 9ft. tall. There are two windows in the room measuring 5ft. by 6ft. each. How many square feet of insulation does Carlos need?
Answers
Solution
Now
[tex]A=2(16\times12)+2(16\times9)+2(9\times12)-2(5\times6)[/tex][tex]828ft^2[/tex]square feet of insulation Carlos need is
[tex]828ft^2[/tex]It takes 2000 bees 1 year to make 7 jars of honey. How long will it take 5000 bees to make 70 jars of honey?
Answers
If the bees are working at the same rate, the number of years taken to make 70 jars is 4 years.
What is the rate of jar making by a bee?
The rate at which a bee makes a jar is calculated as follows;
rate = 2000 bees / 7 Jars
rate = 285.71 b/J
The later of rate of the bees is calculated as follows;
rate = 5000 bees / 70 jars
rate = 71.42 b/J
If the bees were to maintain the first rate, the number of years taken to make 70 jars is calculated as follows;
number of years = (285.71) / (71.42) = 4 years
Learn more about rate of work here: https://brainly.com/question/1144815
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How to put 7^3/4 in radical form
Answers
Given:
[tex]7^{\frac{3}{4}}[/tex]Resolving it to its radical form can be gotten based on the general laws of indices.
We have:
[tex]A^{\frac{x}{y}}=\sqrt[y]{A^x}[/tex]I.e. the number is raised to the power of the numerator and then we get the denominator's root of the number obtained.
Thus:
[tex]\begin{gathered} 7^{\frac{3}{4}}=\sqrt[4]{7^3}=\sqrt[4]{343} \\ \sqrt[4]{343}=343^{\frac{1}{4}}=343^{(\frac{1}{2}\times\frac{1}{2})} \\ =343^{(\frac{1}{2}\times\frac{1}{2})}=\sqrt[]{343^{\frac{1}{2}}} \end{gathered}[/tex]Now, we have our value in the square root form as:
[tex]\sqrt[]{343^{\frac{1}{2}}}=\sqrt[]{7^{\frac{3}{2}}}[/tex]what is the conjugate of the denominator of the expression 9i/-2+7i
Answers
The answer is D.
Laura, a sandwich maker, produces 80 sandwiches on average per day. How many sandwiches will she produce in pdays?Number of sandwiches =
Answers
Number of sandwiches = 80p
Explanation:Given:
Laura produces 80 sandwiches per day
To find:
The number of sandwiches that will be produced in p days
1 day = 80 sandwiches
p days = 80 × p
p days = 80p
This means that she will produce 80p number of sandwiches in p days
Carl Heinrich had lateral filing cabinets that need to be placed along one wall of a storage closet. The filing cabinets are each 2 1/2 feet wide and the wall is 15 feet long. Decide how many cabinets can be placed along the wall
Answers
In this case we have to divide the length of the wall by the width of a cabinet. Doing so, we have:
[tex]\begin{gathered} 2\frac{1}{2}=\frac{2\cdot2+1}{2}=\frac{5}{2}\text{ (Converting the mixed number to an improper fraction)} \\ \frac{15}{1}\div\frac{5}{2}=\frac{15\cdot2}{5}(\text{Dividing fractions)} \\ \frac{15\cdot2}{5}=\frac{30}{5}=6\text{ (Simplifying the result)} \\ \text{The answer is 6 cabinets.} \end{gathered}[/tex]PLEASE HELP I WILL MARK BRAINLIEST!!Which of the following equations is a linear function?A) 2x + 3y = 6B) y = x^2 + 1C) y=x^3D) x^2 + y^2 = 9
Answers
Given data:
The given sets of equations.
The polynomial in which degree of the variable is 1 is said to be linear expression.
The first option 2x+3y=6 is only linear function.
Thus, the option (A) is correct.
Carla has a music box that has a base area of 9 1/2 in² and a height of 3 1/5 inches.What is the volume of the music box?
Answers
Given in the question:
a.) Base area of music box = 9 1/2 in²
b.) Height of music box = 3 1/5 in.
Let's recall the formula for getting the volume of a rectangular prism:
[tex]\text{ Volume = Length x Width x Height or Base Area x Height}[/tex]Before we plug in the values, let's first transform the mixed numbers into improper fractions.
[tex]\text{ 9 }\frac{1}{2}\text{ = }\frac{1\text{ + (2 x 9)}}{2}\text{ = }\frac{1\text{ + 18}}{2}\text{ = }\frac{19}{2}[/tex][tex]\text{ 3 }\frac{1}{5}\text{ = }\frac{1\text{ + (3 x 5)}}{5}\text{ = }\frac{1\text{ + 15}}{5}\text{ = }\frac{16}{5}[/tex]Let's now plug in the values to get the volume of the music box.
[tex]\text{ Volume = Base Area x Height}[/tex][tex]=\text{ 9 }\frac{1}{2}\text{ x 3 }\frac{1}{5}\text{ = }\frac{19}{2}\text{ x }\frac{16}{5}\text{ = }\frac{304}{10}\text{ }[/tex][tex]\frac{304}{10}\text{ = }\frac{\frac{304}{2}}{\frac{10}{2}}=\frac{152}{5}\text{ or 30 }\frac{2}{5\text{ }}in.^3[/tex]Therefore, the volume of the music box is 30 2/5 in.^3.
What is the product of V3 and 7V30 in simplest radical form?
Answers
Determine the product of two expressions.
[tex]\begin{gathered} \sqrt[]{3}\times7\sqrt[]{30}=7\sqrt[]{30\cdot3} \\ =7\sqrt[]{3\cdot3\cdot10} \\ =7\cdot3\sqrt[]{10} \\ =21\sqrt[]{10} \end{gathered}[/tex]So answer is,
[tex]21\sqrt[]{10}[/tex]A high school counselor wants to look at the relationship between GPA and the numberof absences for students in the senior class this year. That data shows a linear patternwith the summary statistics shown below.I answered som of it I just can’t do part D, part E, part F
Answers
D.
The slope of a line means the increase in y for each unitary increase in x:
[tex]b=\frac{\Delta y}{\Delta x}[/tex]If the slope is equal to -0.1625, that means if x increases 1 unit, y will decrease by 0.1625 units.
E.
Using x = 3 in the regression equation, we have:
[tex]\begin{gathered} y=a+bx \\ y=3.71-0.16x \\ y=3.71-0.16\cdot3 \\ y=3.71-0.48 \\ y=3.23 \end{gathered}[/tex]So the estimated GPA is 3.23.
F.
If r is the value of the standard deviation, therefore r² is the variance:
[tex]\begin{gathered} r=-0.65 \\ r^2=0.4225 \end{gathered}[/tex]The variance is the average of the squared difference from each point to the mean, and it measures the average of how much each point differs from the mean.
Describe in words where the square root of 60 minus 11 would be plotted on a number line.
Answers
Answer:
it would be on 7 since 60-11=49 and the square root of 49 is 7
A cone has a height of 17 centimeters and a radius of 7 centimeters. What is its volume? Use = 3.14 and round your answer to the nearest hundredth. cubic centimeters
Answers
To find the volume of the cone, we will use the formula below:
[tex]V=\frac{1}{3}\pi r^2h[/tex]where r is the radius and h is the height
From the question,
π = 3.14
r =7
h=17
substitute the values into the formula
[tex]V=\frac{1}{3}\times3.14\times7^2\times17[/tex][tex]V\approx871.87\text{ cubic centimeters}[/tex]
What is an equation of the line that passes through the points (-3,-5) and (-5, -3)? Put your answer in fully reduced form.
Answers
Express the general equation of a line passing through two points (x1,y1) and (x2,y2).
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Put (-3,-5) for (x1,y1) and (-5,-3) for (x2,y2) implies,
[tex]\begin{gathered} y+5=\frac{-3+5}{-5+3}(x+3) \\ y+5=\frac{2}{-2}(x+3) \\ y+5=-x-3 \end{gathered}[/tex]Further simplifying gives,
[tex]y=-x-8[/tex]Therefore, the equation of the line is y=-x-8.
A resort rented 62 cabins during its first season in operation. Based on the data for a similar resort, management estimated the equation of the line of best fit for the number cabins rented as y= 4x + 62, where x is the number of seasons since the first season of operation, and y is the number of cabins rented during that season. In reality, unusually bad weather for several years beginning in the first season led to the number of rentals for each season decreasing at the rate they were expected to increase. Which is the best choice for the equation for the line of best fit for the cabin rentals?A) y = 1/4 + 62B) y = - 4x + 62C) y = - 1/4x + 62D) y = 4x - 62
Answers
In the equation y = 4x + 62, the increasing rate is 4
If the actual rate decreases at the rate they were expected to increase, then it is -4 instead of 4.
Then, the equation of the line is:
B) y = - 4x + 62
33Select the correct answer from each drop-down menu.A75°B40°AoIn the figure, line segment AB is parallel to line segment CD.СDdegreesThe measure of angle Cisdegrees, and the measure of angles Dis>254075ResetNext
Answers
Answer:
Angle C = 40 degrees
angle D = 75 degrees
Explanation:
From the information given,
Angle A = 75 degrees
Angle B = 40 degrees
AB is parallel to CD. This means that AD and BC are transversals.
Angles A and D have similar positions but they are opposite sides of the transversal. This means that they are alternate angles. Alternate angles are congruent. Thus,
angle D = 75 degrees
Angles B and C have similar positions but they are opposite sides of the transversal. This means that they are alternate angles. Alternate angles are congruent. Thus,
Angle C = 40 degrees
what is 1 5/8 + 2 1/3=
Answers
1 5/8 + 2 1/3
= 3 23/24
Explanation:1 5/8 + 2 1/3
= 1 + 2 + 5/8 + 1/3
= 3 + 23/24
= 3 23/24
The perimeter of a rectangular field is 360 m.If the width of the field is 85 m, what is its length?
Answers
In order to calculate the length of the rectangular field, you use the following formula for the calculation of the perimeter:
P = 2l + 2w
w: width = 85 m
l: length = ?
P: area = 360m
You know the value of P and w, so, you can solve for l in the formula for the perimeter of the field, just as follow:
P = 2l + 2w
2l = P - 2w
l = (P - 2w)/2
Next, you replace the values of P and w:
l = (360m - 2(85m))/2 = 95 m
Hence, the length of the rectangular field is 95m
Which recipe makes more cookies per cup of chocolate chips?
Answers
We are given the recipes of Grandma and Betty Potter box.
We are asked to find out which of them makes more cookies per cup of chocolate chips.
Let us find the unit rate for both of them and compare which is greater.
Grandma:
She uses 1 1/2 cups of chocolate chips to make 24 cookies.
The unit rate is
[tex]\frac{24}{1\frac{1}{2}}=\frac{24}{\frac{3}{2}}=24\times\frac{2}{3}=16[/tex]So the unit rate is 16 cookies per chocolate chip.
Betty Potter box:
60 cookies are made using 3 chocolate chips.
80 cookies are made using 4 chocolate chips.
200 cookies are made using 10 chocolate chips.
The unit rate is
[tex]\begin{gathered} \frac{60}{3}=20 \\ \frac{80}{4}=20 \\ \frac{200}{10}=20 \end{gathered}[/tex]So the unit rate is 20 cookies per chocolate chip.
As you can see, the recipe of Better Potter box makes more cookies per cup of chocolate chip.
do an addition in binary (inverse code) on following numbers:
00011101
+ 111111101
please, help asap thank u
Answers
The first complement of the binary addition is 00011111.
What is a binary addition?
The binary addition operation works similarly to the base 10 decimal system, except that it is a base 2 system. The binary system consists of only two digits, 1 and 0.
Given that, the addition of the given number
00011101 + 11111101
In the binary addition,
0+1 = 1
1+0 = 1
1+1 = 0
00011101 + 11111101 = 11100000
Then inverse code means first complement of the answer.
In the first complement, 0 is the inverse of 1 and 1 is inverse of 0.
11100000 = 00011111
Hence, The first complement of the binary addition is 00011111.
To learn more about binary addition from the given link:
https://brainly.com/question/17195235
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Which expression is equivalent to 8 - (-5) ?O 8+50 -8 +(-5)O 8+-5O -5 +8
Answers
Answer:
The first option is correct
[tex]8+5[/tex]Explanation:
[tex]\begin{gathered} 8--5 \\ \\ 8+5 \\ \end{gathered}[/tex]Two negatives makes a positive.
find the slope and y intercept, then write out the linear equation (y=mx+b) below
Answers
Answer:
y = 2x + 3
Step-by-step explanation:
You can find the slope on the graph by looking at the points. From one point to the next you go Up2Over1.
Up2Over1 is the slope and in actual algebra it is 2/1, which is just 2.
The slope is 2. Fill in 2 in place of m in
y = mx + b
y = 2x + b
Next the y-intercept which is the b, can also be seen on the graph. The y-intercept is where the graph crosses the y-axis. The line crosses the y-axis at 3. Fill in 3 in place of the b.
y = 2x + 3
I’m struggling on this math question and could use some help on it
Answers
Let's determine the values of f(-4) and g(6).
For f(-4),
[tex]\text{ f\lparen x\rparen= -2x}^3\text{ - 5}[/tex][tex]\text{ f\lparen-4\rparen= -2\lparen-4\rparen}^3-5\text{ = -2\lparen-64\rparen- 5}[/tex][tex]\text{ f\lparen-4\rparen = 128 - 5}[/tex][tex]\text{ f\lparen-4\rparen = 123}[/tex]Therefore, f(-4) = 123
For g(6),
[tex]\text{ g\lparen x\rparen = -3x - 3}[/tex][tex]\text{ g\lparen6\rparen = -3\lparen6\rparen - 3 = -18 - 3}[/tex][tex]\text{ g\lparen6\rparen = -21}[/tex]Therefore, g(6) = -21
? QuestionWhat is the equation of the quadratic function represented by this table?х5678910f(x)-4585-4-19HolaType the correct answer in each box. Use numerals instead of words.f(x) =(x -12 +
Answers
To determine the equation of the quadratic equation, which is a parabola, we substitute the coordinates of the vertex of the parabola (h,k) into the general equation.
[tex]y=a(x-h)^2+k[/tex]From the given, notice that the only value of f(x) that does not repeat is 8. This means that the vertex is at (7,8).
[tex](h,k)=(7,8)[/tex]Thus, we only need to obtain the value of a.
Substitute the coordinate of a point (x,y) into the equation and the vertex as well. In this case, let us use the first given point, (5,-4).
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ (5,-4)\rightarrow-4=a(5-7)^2+8 \end{gathered}[/tex]Simplify the obtained equation.
[tex]\begin{gathered} (5,-4) \\ -4=a\mleft(5-7\mright)^2+8 \\ -4=a\mleft(-2\mright)^2+8 \\ -4=a(4)+8 \\ -4-8=4a \\ -12=4a \\ a=\frac{-12}{4} \\ a=-3 \end{gathered}[/tex]Now that we have the value of a, substitute the coordinates of the obtained vertex and the value of a into the equation of the quadratic equation.
[tex]\begin{gathered} y=a(x-h)^2+k \\ y=-3(x-7)^2+8 \end{gathered}[/tex]To check, the graph of the given function is as follows:
Therefore, the equation of the quadratic equation is y=-3(x-7)²+8.
When a projectile is launched at an initial height of H feet above the ground at an angle of theta with the horizontal and initial velocity is Vo feet per second. the path of the projectile...
Answers
Given,
The initial height of H feet.
The initial velocity of the object is Vo.
The equation of the path of projectile is,
[tex]y=h+x\text{ tan }\theta-\frac{x^2}{2V_0\cos ^2\theta}_{}\text{ }[/tex]This is the expression of the projectle path.
Hence, the path of the projectile object is y = h + xtan(theta) - x²/2V₀²cos²(theta)
61 less than twice vidy's score
Answers
We are given the following word problem
"61 less than twice Vidy's score"
Let us translate the word problem into an algebraic expression
Let v represents Vidy's score
twice Vidy's score means 2 times v
61 less than means to subtract 61 from 2 times v
So, the algebraic expression becomes
[tex]2v-61[/tex]in the graph below line k,y=-x makes a 45 degree angle with the x and y axescomplete the following
Answers
step 1
The equation of line k is y=-x
The rule of the reflection across the line y=-x is equal to
(x,y) -------> (-y,-x)
so
we have the point (2,5)
Apply the rule
(2,5) -----> (-5,-2)
step 2
Reflection across the x axis
The rule of the reflection across the x axis is
(x,y) ------> (x,-y)
so
Apply the rule to the point (-5,-2)
(-5,-2) ------> (-5,2)
therefore
the answer is
(-5,2)I’ve been stuck for a while and it logged me out:(
Answers
Solution
A polynomial is a function in the form of ; where n is non- negative integers which is known as the degree of polynomial. from this definition, it is clear that only option (2) √2 x -1 , is polynomial. because coefficient of variables ; √2, -1 are real number and also power of variable is non-negative integer.
I have selected the options , the ones I have ticked are polynomials, while the one cancelled are none polynomials:
find the value of the 30th percentile of the following set of data
Answers
The given data is:
[tex]18,9,7,5,11,7,17,20,19,2,17,12,5,1,13,12,11,15,16,20[/tex]Rearrange the data in ascending order:
[tex]1,2,5,5,7,7,9,11,11,12,12,13,15,16,17,17,18,19,20,20[/tex]