Answers
Answer:
[tex]y-x=-10[/tex]
Step-by-step explanation:
In any trapezoid, the sum of all angles is 360°. Additionally, the sum of both angles on the same side of the trapezoid is 180°. Therefore, we know that:
[tex](7x+40)+(68-6y)=180[/tex]
[tex](17y+73)+(121-4x)=180[/tex]
To solve for [tex]x[/tex] and [tex]y[/tex], we must set up a system of equations and solve by substitution, elimination, or graphing.
To start, simplify the first formula, then isolate the [tex]x[/tex] variable:
[tex](7x+40)+(68-6y)=180[/tex]
[tex]7x-6y+68+40=180[/tex]
[tex]7x-6y+108=180[/tex]
[tex]7x-6y=72[/tex]
[tex]7x=72+6y[/tex]
[tex]x=\frac{72+6y}{7}=\frac{72}{7}+\frac{6}{7}y[/tex]
Next, simplify the second formula, then substitute the value above for [tex]x[/tex]:
[tex](17y+73)+(121-4x)=180[/tex]
[tex]-4x+17y+121+73=180[/tex]
[tex]-4x+17y+194=180[/tex]
[tex]-4(\frac{72}{7}+\frac{6}{7}y)+17y+194=180[/tex] (substituted for [tex]x[/tex] here)
[tex]-\frac{288}{7}-\frac{24}{7}y+17y+194=180[/tex]
[tex]-\frac{288}{7}-\frac{24}{7}y+\frac{119}{7}y+\frac{1358}{7}=\frac{1260}{7}[/tex]
[tex]-288-24y+119y+1358=1260[/tex]
[tex]95y+1070=1260[/tex]
[tex]95y=190[/tex]
[tex]y=2[/tex]
Finally, substitute 2 for [tex]y[/tex] in the first formula as simplified:
[tex]7x=72+6y[/tex]
[tex]7x=72+6(2)[/tex]
[tex]7x=72+12[/tex]
[tex]7x=84[/tex]
[tex]x=12[/tex]
Therefore:
[tex]x=12[/tex] and [tex]y=2[/tex]
And the expression [tex]y-x[/tex] equals:
[tex]y-x=2-12=-10[/tex]
Related Questions
Find the measure of each angle indicated.
Answers
Answer:
Step-by-step explanation:
11: 180-133= 47 degrees
12: 72 degrees
13: 15x+5+(-1+7x)=180
15x+5-1+7x=180
22x+4=180
22x=176
X=8
14: 180-45= 135
14x-5=135
14x=140
x=10
Hopes this helps please mark brainliest
A water tank contains 55 gallons of water when Baxter begins to drain it. Water drains from the tank at a rate of 2 gallons per minute. Write a linear equation to model this situation.
i'm confused
Answers
The linear equation to model the situation of water when Baxter begins to drain it is 55 + 2x = y.
Describe the term linear equation?A linear equation is indeed an algebraic equation with only a constant and the first-order (linear) term of the form y=mx+b, in which m is the slope and b is just the y-intercept. The above is sometimes referred to as a "linear equation of two variables," in which y and x are the variables.The initial amount is 55 gallons and will not change.
The amount of water in the tank is increasing by 2 gallons per minute.
The minutes are the independent variable, which we can represent with the x.
The amount just at end of the minutes is the dependent variable, which we can represent with the y.
The linear equation;
55 + 2x = y
Thus, the linear equation to model the situation of water when Baxter begins to drain it is 55 + 2x = y.
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A student was asked to find the length of the unknown leg of the right triangle. He incorrectly said that the length of the unknown leg of the right triangle is about 6.2 cm. Find the length of the unknown leg of the right triangle.The length of the unknown leg of the triangle is ______cm. (Round to one decimal place as needed.)What mistake might the student have made? A. He added the two given valuesB. He subtracted the two given values C. He did not square the length of the given leg D. He did not square the length of the hypotenuse
Answers
6 cm, C. He did not square the length of the given leg
Explanation
to solve this we need to use the Pythagorean theorem
T.P states for all rigth triangles:
[tex]a^2+b^2=c^2[/tex]then
Step 1
let
a=2.3
b=b
c=6.4
replace
[tex]\begin{gathered} 2.3^2+b^2=6.4^2 \\ \text{now, we n}eed\text{ isolate b} \\ 5.29+b^2=40.96 \\ \text{subtract 5.29 in both sides} \\ 5.29+b^2-5.29=40.96-5.29 \\ b^2=35.67 \\ \text{square root in both sides} \\ \sqrt[]{b^2}=\sqrt[]{35.67} \\ b=5.97 \\ \text{rounded} \\ b=6 \end{gathered}[/tex]Step 2
What mistake might the student have made?
check
A)He added the two given values
[tex]2.3+6.4=8.7[/tex]B) He subtracted the two given values
[tex]6.4-2.3=4.1[/tex]C)He did not square the length of the given leg
[tex]\begin{gathered} 2.3^{}+b^2=6.4^2 \\ b^2=6.4^2-2.3 \\ b^2=38.66 \\ b=\sqrt[]{38.66} \\ b=6.21 \\ \text{rounded} \\ b=6.2 \end{gathered}[/tex]D. He did not square the length of the hypotenuse
[tex]\begin{gathered} 2.3^2+b^2^{}=6.4 \\ b^2=6.4-2.3^2 \\ b^2=1.11 \\ b=\sqrt[]{1.11} \\ b=1.05 \end{gathered}[/tex]so, the answer is C
I hope this helps you
What is the solution to this equation? 6+7 (b−1) = 5+b
Responses:
A. b = 0
B. b = 1
C. b = 2
D. b = 5
(K12 question math 5.04)
Answers
The solution of the given equation is 1. Therefore, option B is the correct answer.
The given equation is 6+7(b-1) = 5+b.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation can be solved as follows:
Now, 6+7b-7 = 5+b
⇒ 7b-1=5+b
⇒ 7b-b=5+1
⇒ 6b=6
⇒ b=1
The solution of the given equation is 1. Therefore, option B is the correct answer.
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Write a piecewise function for the graph.
Answers
For the given graph , piecewise function for the given graph is as follow:
f(x) = 1 , if x < -2
2x , if -2 < x ≤ 0
(- x / 2) + 2 if x > 0
As given in the question,
Given is the graph of the function f( x )
Now to find the piecewise function for the given graph is as follow:
For x < -2 it is given that f ( x) = 1
Now consider two points for -2 < x ≤ 0
( x₁ , y₁ ) = ( 0 , 0 )
( x₂ , y₂ ) = ( -2 , -4 )
Equation of f(x) is given by :
( y - 0 )/ ( x -0 ) = ( -4 - 0)/ (-2 - 0 )
⇒ y = 2x
Now consider two points for x > 0
( x₁ , y₁ ) = ( 0 , 2 )
( x₂ , y₂ ) = ( 2 , 1 )
Equation of f(x) is given by :
( y - 2 )/ ( x -0 ) = ( 1 - 2)/ ( 2 - 0 )
⇒ y - 2 = -x / 2
⇒ y = ( -x / 2 ) + 2
Therefore, for the given graph , piecewise function for the given graph is as follow:
f(x) = 1 , if x < -2
2x , if -2 < x ≤ 0
(- x / 2) + 2 if x > 0
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Help me!!
2. pts) Set up a proportion and soive for
side TV (y):
Answers
The required measure of side y = 8
Given : Triangle TUV and triangle XWV are similar
Thus [tex]\frac{UV}{VW} = \frac{6}{21}[/tex]
this is further equal to [tex]\frac{2}{7}[/tex]
Thus the ratio UV : VW = 2 : 7
this implies that the ratio TV : VX should also be equal to the ratio of UV : VW = 2 : 7 because of cpst or also called corresponding parts of similar triangles.
Given UV : VW = 2 : 7
thus TV : VX = [tex]\frac{y}{28 }[/tex] which on equation will give y as 8
because [tex]\frac{8}{28}[/tex] when divided by 4 will give us the required ratio that is 2 : 7
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Which theorem, term, or corollary is represented by the picture?
Answers
The triangle is an Corollary 1 to the isosceles triangle theorem.
Given that,
In the picture we have a triangle,
We have to find which triangle is it.
From the triangle,
The 2 sides are equal and the 2 angles are also equal.
So, The triangle is an Corollary 1 to the isosceles triangle theorem.
According to the isosceles triangle theorem, if two triangle sides are congruent, then the angles across from those sides are likewise congruent.
An isosceles triangle is one with two sides that are the same size and a third side that is a different size.
Therefore, The triangle is an Corollary 1 to the isosceles triangle theorem.
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hello, I need help asap on this following problem. I don’t know how to approach and don’t want to get it wrong.
Answers
The slope-intercept form of a line equation is given by:
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y-intercept. From the problem, we identify:
[tex]m=-0.6[/tex]To find b, we use the fact that when x = 20, y = 13:
[tex]\begin{gathered} 13=(-0.6)20+b \\ 13=-12+b \\ \\ \Rightarrow b=25 \end{gathered}[/tex]Finally, for x = 16 (the corresponding y is the height of the candle after 16 hours):
[tex]\begin{gathered} y=-0.6(16)+25=-9.6+25 \\ \\ \therefore y=15.4\text{ cm} \end{gathered}[/tex]Suppose that you are designing an aluminum can which will hold a volume of 200pi cm^3 of soup. Find the value of the radius that minimizes the amount of aluminum used, and justify that this gives a local minimum. Include units.
Answers
The value of the radius that minimizes the amount of Aluminium is 4.64 cm and it gives the local minimum of the function
How to determine the value of the radius that minimizes the amount of Aluminium?From the question, the volume of the aluminium is given as
Volume = 200pi cm^3
Rewrite this volume properly using the correct symbols and units
So, we have the following representation
Volume = 200π cm³
Solving further, we make use of the volume of a cylinder (i.e. a can)
The volume of a sphere is represented as
V = πr²h
Substitute Volume = 200π cm³ in
πr²h = 200π
Make h the subject in the above equation
This gives
h = 200π/πr²
Cancel the common factors
h = 200/r²
The surface area of a can is
A = 2πr(h + r)
So, we have
A = 2πr(200/r² + r)
This gives
A = 400π/r + 2πr²
Differentiate the function
This gives
A' = -400π/r² + 4πr
Set the differentiated function to 0
-400π/r² + 4πr = 0
So, we have
-400π/r² = -4πr
Cross multiply
-400π = -4πr³
Divide through by -4π
r³ = 100
Take the cube roots
r = 4.64
Hence, the radius that given minimum material is 4.64 cm
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NEED HELP FAST FOR GEOMETRY 10TH PLEASEEEEEE
Answers
Answer:
The answer is the first option
Step-by-step explanation:
Tan is opposite over adjacent
so its 24/10
simplify
12/5
hope this helped
Lamar is 4 times as old his brother Malcolm. In 2 years; Lamar will be 3 times as old as Malcolm is than. How old will Lamar be in 2 years?
Answers
In 2years time, Lamar will be 18years old by application of an algebraic expression x for the unknown value.
What is algebraAlgebra is the branch of mathematics that helps to represent problems or unknown values in the form of mathematical expressions.
Algebraically, let us represent the age of Malcolm with the unknown value x
then the age of Lamar will be 4x
In 2years time;
Malcolm's age = x + 2
Lamar's age = 3(x + 2) {3times as old as Malcolm}
Also
Lamar's age = 4x + 2 {Lamar's age plus 2years}
So
4x + 2 = 3(x + 2)
open bracket by expansion
4x + 2 = 3x + 6
collect like terms
4x - 3x = 6 - 2
x = 4
Hence, substituting the known value of x in the algebraic expressions of x for Malcolm's age and 4x for Lamar's age, we have 4years and 16years respectively. And in 2years time Lamar will be 18years
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The revenue equation for a certain brand of toothpaste is y = 2.2x, where x is the number of tubes of toothpaste sold andy is the total income for selling x tubes. The cost equation is y = 0.6x + 2000, where x is the number of tubes of toothpastemanufactured and y is the cost of producing x tubes. The following set of axes shows the graph of the cost and revenueequations. For what x-values will the company make a profit?
Answers
step 1
equate the revenue and the cost
so'
2.2x=0.6x+2000
solve for x
2.2x-0.6x=2000
1.6x=2000
x=1,250
step 2
the company will make a profit when the revenue is greater than the cost
therefore
the value of x must be greater than 1,250
x> 1,250 tubes of toothpaste
Note: For x=1,250 ----> the revenue is equal to the cost (Profit 0)
Determine whether each statement is true or false: The reason that trig ratios work is because all right triangles are congruent [ Select ] You can find sine, cosine, and tangent from all angles in a right triangle, including th angle (Select] The sine of one acute angle is the cosine of the other acute angle in any right triang [ Select] Tangent is the only trig ratio that can have a value larger than 1 [ Select]
Answers
Use a calculator to find the value of each trigonometric function evaluated at their corresponding angles, up to 3 decimal places:
[tex]\begin{gathered} \cos (58)=0.530 \\ \cos (88)=0.035 \\ \tan (50)=1.192 \\ \tan (20)=0.364 \end{gathered}[/tex]Days after posting, x 1 2 3 4 5 6
Unique daily views, y 5 8 13 20 29 40
A video with information about preparing for the following school year was posted on a school’s website. The number of unique daily views, y , of the video x days after it was posted is shown in the table. Which of the following statements identifies the most appropriate type of function for modeling the data in the table and provides a reason to support its appropriateness?
Answers
The graph rises parabolically. The rise in the value is not perfectly parabolic, but the increase can be structured as parabolic.
What is the general equation of a parabola?The general equation of a parabola is given by a quadratic equation as-
y = ax² + bx + c. It has a degree of [2] and has two possible roots.
We have the following table -
Days after posting [x] → 1 2 3 4 5 6
Unique daily views [y] → 5 8 13 20 29 40
Refer to the graph attached. It can be seen that, the graph is a parabola. Although the rise in the value is not perfectly parabolic, but the increase can be structured as parabolic. Mathematically, the equation of the parabola can be written as -
y = ax²
The parabola is wide open {not close to y - axis}, this signifies that the value of [a] is in decimals. If we make a estimate, it would be almost [a] = 1/88 for the mentioned data.
Therefore, the graph rises parabolically. The rise in the value is not perfectly parabolic, but the increase can be structured as parabolic.
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4. A mail carrier earns time and a half for any overtime hours. If her
regular wages are $9.80 per hour, what is her overtime hourly rate ?
Answers
Answer:
$14.70
Step-by-step explanation:
If she get paid the time and a half you would first divide $9.80 by 2 which is $4.90. Now that you have the half price you add the original time to it. $9.80+$4.90= 14.70 so that’s the answer
Jina needs to memorize words on a vocabulary list for Latin class. She has memorized 12 of the words, which is three-fourths of the list. How many words are on the list?
Answers
12 words is 3/4 or 75% of the list
How many words are=
Find 100- 75=25%
25%= 1/4 = 3/4÷3
Then divide 75%/3= 12/3= 4
Now add 12words + 4 words = 16 words
Then answer is, there are 16 words
Lin drew a triangle and a dilation of the triangle with scale factor 1/2:What is the center of the dilation? Explain how you know.Which triangle is the original and which triangle is the dilation? Explain how you know.
Answers
Answer:
• Point A
,• Triangle ABC
,• Triangle ADE
Explanation:
From the diagram
The center of dilation is point A.
We know this because the center of dilation is a fixed point in the plane about which all points are expanded or contracted.
Point A does not change in the two triangles.
The original triangle is triangle ABC.
We know this because it is the larger of the two triangles. A scale factor of 1/2 will reduce the size of the original image.
The dilation is triangle ADE.
It is believed that the best angle to fly a kite is 45°. If you fly a kite at this angle and let out 190 feet of string, approximately how high above the ground will the kite be?
Answers
write interval notation x>2 or -x >6
Answers
To answer this question, we need to have into account the following:
1. In the context of interval notation, the word "or" can be represented by the symbol "U".
2. We need to rearrange the inequality -x > 6 in a way that we have positive x.
We can proceed as follows:
Case x>2[tex]x>2\Rightarrow(2,\infty)[/tex]We can express the inequality in this way because it expresses all of the values greater than 2, and these values tend to the positive infinity. We have parenthesis here since the values are not equal to 2 (only greater than 2).
Case -x > 6If we multiply both sides of the inequality by -1, we need to reverse the direction of the inequality as follows:
[tex]\begin{gathered} -1(-x>6)=-1(-x)<-1(6) \\ x<-6 \end{gathered}[/tex]Now, we have all of the values less than -6, not equal, and because of this, we have to use parenthesis:
[tex]x<-6=(-\infty,-6)[/tex]Therefore, we can say that:
[tex]\begin{gathered} x>2\text{ or -x>6} \\ \end{gathered}[/tex]Can be expressed in interval notation as:
[tex](-\infty,-6)\cup(2,\infty)[/tex]In summary, the answer to this question is:
[tex](-\infty,-6)\cup(2,\infty)[/tex]Select all the numbers that are equivalent.
4.836 × 106 and 4,836,000,000
5.812 × 10-7 and 0.0000005812
5.46 × 1011 and 546,000,000,000
4.836 × 10 and 4,836,000
) 5.812 × 10-7 and 58,120,000
Answers
The Equivalent numbers are
5.812 × 10⁻⁷ and 0.0000005812
5.46 × 10¹¹ and 546,000,000,000
What is the meaning exponent of 10?
A power of 10 is the sum of all the tens that the exponent indicates. As a result, a power of 10 is represented in long form as the number 1 followed by n zeros, where n is the exponent and is bigger than 0; for instance, 10⁶ is represented as 1,000,000.
Given numbers are:
4.836 × 10⁶ and 4,836,000,000
5.812 × 10⁻⁷ and 0.0000005812
5.46 × 10¹¹ and 546,000,000,000
The equivalent form of 4.836 × 10⁶ is
4.836 × 1000000 = 4,836,000
The equivalent form of 5.812 × 10⁻⁷ is
5.812 × 10⁻⁷ = 5.812/ 10000000 = 0.0000005812.
The equivalent form of 5.46 × 10¹¹ is
5.46 × 10¹¹ = 5.46 × 100000000000 = 546,000,000,000
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Test: PRACTICE TEST for Final Exam (RE...This question: 2 point(s) possibleAnn and Tom want to establish a fund for their grandson's college education. What lump sum must they deposit at a 10% annual interest rate, compounded annually. In order to have $20,000 in the fund at the end of 10 years?They should deposits(Round up to the nearest cent)
Answers
Answer
They should deposit $7710.99
Explanation
Using compound interest formula,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
A = Amount = $20,000
P = Principal = ?
r = Interesr rate = 10% = 0.1
n = 1
t = 10
[tex]\begin{gathered} \Rightarrow20000=P(1+0.1)^{1\times10} \\ 20000=P(1.1)^{10} \\ 20000=P(2.5937) \\ \text{Divide both sides by 2.5937} \\ \frac{P\mleft(2.5937\mright)}{2.5937}=\frac{20000}{2.5937} \\ P=7710.9920 \\ \text{To the nearest cent, the answer is} \\ P=7710.99 \end{gathered}[/tex]1) Eliminate one of the variable terms on one side of each multi-step equation: Multi-Step Equation 7a-6=7+ 2a 11 - 3b = 3b + 4 -2b-5=6 - 5b Equivalent Two-Step Equation
Answers
Answer:
Step-by-step explanation:lol
Raj completed his homework in 5/6 hour. His older brother took 1 1/2 times as long as Raj did to
complete his homework.
How long did it take Raj's older brother to complete his homework?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answers
The time that it took Raj's older brother to complete his homework was 1 ¹ / ₄ hours
How to find the time taken to complete the homework?The time that it would take for Raj to complete the homework is 5/6 hours. His older brother would do it in 1 1/2 times as long.
The first thing to do is to convert this to an improper fraction:
= 1 1/2
= (2 x 1 + 1) / 2
= 3 / 2
The time it would take Raj's brother is therefore:
= Time it took Raj x Multiple
= 3 / 2 x 5 / 6
= 15 / 12
= 1 .25
1.25 in mixed fractions is:
= 1 ¹ / ₄ hours
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here is the 4rth one to do
Answers
The correct option is; Yes, all the three expressions are equivalent to each other.
What is meany by the term exponent?A number's exponent signifies how many times a number has been multiplied by itself. For instance, 2×2×2×2 can be written as 2⁴, because 2 is multiplied on its own four times. In this case, 2 is referred to as the "base," and 4 is referred to as the "exponent" as well as "power." In general, xⁿ denotes that x has been multiplied by itself n times.For the given question;
The three expressions are given as;
a: 20(1.1ˣ) ...1
b: 20(1.1⁻¹)⁻¹ˣ
Simplifying as;
= 20(1.1⁻¹⁽⁻¹ˣ⁾)
= 20(1.1ˣ) ....2
c: 20(1.1¹/⁵)⁵ˣ
Simplifying.
= 20(1.1¹/⁵⁽⁵ˣ⁾)
= 20(1.1ˣ) ....3
So, a = b = c
Thus, all three expressions are equivalent to each other.
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Multiply (x-4)².
Please help me
Answers
⇒ x-4 is the term in this case there for the term (x-4) is squared meaning the term has to multiply itself twice.
[tex]=(x-4)(x-4)\\=x(x-4)-4(x-4)\\=x^{2} -4x-4x+16\\=x^{2} -8x+16[/tex]
If you are still struggling on how to multiply out DM ASAP.
15-5 Similar Figures and ProportionsNLesson Quiz: Part 11. Identify the correspondingsides in the pair of triangles,and use ratios to determine 14 cmwhether the triangles aresimilar.12 cm4 cm7 cmR56 cmPOLook at Slide 19.Identify the corresponding sides in the pair of triangles, and use ratios to determine whetherthe triangles are similar.(50 Points)SimilarNotSimilar
Answers
In order to identify if the triangles are similar, you first take into account the rect angle of the triangles. Form there you can notice that side ON in the bigger triangle, is similar to the side as RQ in the little one.
So, you calulate the proportion between sides ON and RQ, just as follow:
[tex]\frac{ON}{RQ}=\frac{8cm}{4\operatorname{cm}}=2[/tex]Then, the proportion of those sides is 2. This proportion must be the same for the other similar sides of both traingles, in order to conclude that the triangle are similar.
[tex]\frac{PN}{QS}=\frac{14\operatorname{cm}}{7\operatorname{cm}}=2[/tex][tex]\frac{PO}{RS}=\frac{12\operatorname{cm}}{6\operatorname{cm}}=2[/tex]Hence, the triangles are similar
If the simple interest on a $5,000 for 8 years is $2,000, then what is the interest rate?
Answers
Given data:
The principal is
[tex]P=\text{ \$5,000}[/tex]The time is
[tex]t=8[/tex]The interest is
[tex]=\text{ \$2,000}[/tex]Concept:
The formula to calculate interest rate (R) is given below as
[tex]\begin{gathered} I=\frac{P\times R\times T}{100} \\ 100I=P\times R\times T \\ divide\text{ both sides by PT} \\ R=\frac{100I}{PT} \end{gathered}[/tex]By substituting the values in the formula above, we will have
[tex]\begin{gathered} R=\frac{100I}{PT} \\ R=\frac{100\times2000}{5000\times8} \\ R=\frac{200000}{40000} \\ R=5 \end{gathered}[/tex]Hence,
The final answer is 5%
Write an equation for a circle in standard
form with a center at (-6, 5) and passes
through the point (-11, 3).
Answers
Answer:
is a way to express the definition of a circle on the coordinate plane. The formula is ( x − h) 2 + ( y − k) 2 = r 2. h and k are the x and y coordinates of the center of the circle. ( x − 9) 2 + ( y − 6) 2
Step-by-step explanation:
Hope it helped the answer is up there☝
solve the system by the addition methodx + 2y = 35× +5y = 5
Answers
x=-1, y =2 S { -1,2}
1) Solving that linear system
x + 2y = 3 x -5 To eliminate x
5× +5y = 5
-5x -10y = -15
5x +5y = 5
---------------------
-5y = -10
y =2
1.2 Plugging into the I equation:
x +2(2)= 3
x +4=3
x=-1
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The point of maxima of any function can be known by equating its derivative to zero. The rocket will take 1.5 sec to reach the maximum height and the maximum height is 27 feet.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as g'(x) = (g(x + h) - g(x)) /(x + h - x).
Its geometric aspect is the slope of the function at a given point.
Given that,
Initial height of the launching pad is 4 feet,
Initial velocity of rocket is 48 feet/sec,
Height of the rocket as a function of time, h(t) = -16t² + 48t + 3
In order to find the time for maximum height equate h'(t) = 0 as follows,
-32t + 48 = 0
⇒ t = 48 / 32
⇒ t = 3 / 2
⇒ t = 1.5
To find the maximum height find h(t) for t = 1.5 as follows,
h(1.5) = -16 × 1.5² + 48 × 1.5 + 3
= -36 + 60 + 3
= -36 + 63
= 27
Hence, the time taken by the rocket to reach the maximum height is 1.5 sec and the maximum height reached is 27 feet.
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