a) The time taken by the rocket to reach the maximum height is 2.75 seconds.
b) The maximum height of the rocket will be 127 feet.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
Given that:-
A toy rocket is shot vertically into the air from a launching pad 6 feet above the ground with an initial velocity of 88 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=−16t²+88t+6.a) The time taken by the rocket will be calculated as:-
We have a function h(t)=−16t²+88t+6. Now by taking the derivative of the function with respect to time and equating it to zero we will get the maximum time in which the rocket will reach the maximum height.
h(t) = -16t² + 88t + 6
h'(t) = 0
-32t + 88 = 0
32t = 88
t = 88 / 32 = 2.75 seconds
So the maximum time is 2.75 seconds.
b) Maximum height will be calculated as:-
Put the value of maximum time in the function h(t) = -16t² + 88t + 6 we will get the maximum height.
h(t) = -16t² + 88t + 6
h(2.75) = -16(2.75)² + ( 88 x 2.75 ) + 6
h(2.75) = 127 feet
Therefore the time taken by the rocket to reach the maximum height is 2.75 seconds and the maximum height of the rocket will be 127 feet.
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Which statement is true about the polynomial
5s6t2 + 6st9 – 8s6t2 – 6t7 after it has been fully simplified?
It has 3 terms and a degree of 9.
It has 3 terms and a degree of 10.
It has 4 terms and a degree of 9.
It has 4 terms and a degree of 10.
The polynomial 6st⁹ – 3s⁶t² – 6t⁷ has 3 terms and the degree of the polynomial is 10. Then the correct option is B.
What is polynomial?A polynomial expression is an algebraic expression with variables and coefficients.
The polynomial is given below.
5s⁶t² + 6st⁹ – 8s⁶t² – 6t⁷
Then polynomial can be arranged as
⇒ 6st⁹ + 5s⁶t² – 8s⁶t² – 6t⁷
⇒ 6st⁹ – 3s⁶t² – 6t⁷
The polynomial 6st⁹ – 3s⁶t² – 6t⁷ has 3 terms and the degree of the polynomial is 10.
Then the correct option is B.
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Given that a = 10 cm and b = 13 cm, work out the height of the triangle.
The Pythagorean theorem is also known as the Pythagoras' theorem. The height of the triangle is 12cm.
What is Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
Given a=10cm and b=13cm, therefore, the height of the triangle can be found using the Pythagoras theorem, therefore,
AB² = AD² + BD²
13² = AD² + 5²
169 = AD² + 25
AD = 12cm
Hence, the height of the triangle is 12cm.
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Could someone Help it’s a new topic
Answer:
So to do this you need a protactor and measure it with it, then add the total
Step-by-step explanation:
Simplify the quotient 3-¹ ÷34
Answer:
[tex]\frac{1}{102}[/tex]
Step-by-step explanation:
1) Negative Power Rule: [tex]x}^{-a}=\frac{1}{{x}^{a}}[/tex].
[tex]\frac{1}{3}\div 34[/tex]
2) Use this rule: [tex]a\div \frac{b}{c}=a\times \frac{c}{b}[/tex].
[tex]\frac{1}{3}\times \frac{1}{34}[/tex]
3) Use this rule: [tex]\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}[/tex].
[tex]\frac{1\times 1}{3\times 34}[/tex]
4) Simplify [tex]1\times 1[/tex] to [tex]1[/tex].
[tex]\frac{1}{3\times 34}[/tex]
5) Simplify [tex]3\times 34[/tex] to [tex]102[/tex] .
[tex]\frac{1}{102}[/tex]
Maya runs 4.5
miles more than Remy every week. Maya runs 18.35
miles per week. Which equation can be used to find the distance Remy runs every week, x?
Answer:
Remy runs 13.75 Miles Per Week
Step-by-step explanation:
X=18.35 - 4.5
*100 points* A circle has a diameter with endpoints (-7, -1) and (-5, -9).
What is the equation of the circle?
Diameter
√(-7+5)²+(-1+9)²√2²+8²√4+64√682√17Radius
2√17/2√17unitsNow
Centre
(h,k)
(-7-5/2,-1-9/2)(-12/2,-10/2)(-6,-5)Equation
(x-h)²+(y-k)²=r²(x+6)²+(y+5)²=(√17)²(x+6)²+(y+5)²=17Option A
Answer:
Step-by-step explanation:
Consider the end points (-7,-1) and (-5,-9)
The center is the mid point between these two points.
The value of center is,
(h,k) = ((-7-5)/2, (-1-9)/2)
(h,k) = (-12/2,-10/2)
(h,k) = (-6, -5)
If the center (h,k) = (-6, -5) and radius is r then the equation of the circle is,
Equation of Circle,
((x-h)^2)+((y-k)^2) = r^2
((x+6)^2)+(y+5)^2 = r^2
Hence, the answer is ((x+6)^2)+(y+5)^2 = r^2.
PLEASE 100 POINTS AMD BRAINLIEST IF YOU ANSWER ALL
Pls help. Answer the question in the picture. I will give 5 stars, a thanks, and brainliest!
*20 points*
Answer:
1/5x + 2
Step-by-step explanation:
hope this helps
A rectangle has a height of m+8m+8m, plus, 8 and a width of
2m^3+m^2+3m2m 3 +m 2 +3m2, m, cubed, plus, m, squared, plus, 3, m. Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
Answer:
it is 18
Step-by-step explanation:
A geologist in South America discovers a bird skeleton that contains 43% of its original amount of C-14. K value
of C-14 is 0.0001
Find the age of the bird skeleton to the nearest year.
The age of the bird skeleton is 6539.
What is Exponent Function?An exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
Here, N =[tex]N_{0}.e^{-0.0001t}[/tex]
= 52% N₀
[tex]e^{-0.0001t}[/tex] = 0.52
-0.0001 t = ln 0.52
t = -10000 ln 0.52
t = 6539
Thus, the age of the bird skeleton is 6539.
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Answer:
Step-by-step explanation:
Each of the s swimmers on the relay team swam an equal number of the 8 laps in a race. Write an expression that shows how many laps each swimmer swam.
The number of laps that Swimmer A swam was 50 laps.
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
Let we suppose that:
Swimmer A swam x laps
Swimmer B swam y laps.
Then, according to the given data, we have:
x + y = 175 laps
y = 25 + 2x
(25 more than twice of laps of A is the number of laps of B).
Thus, we get a system of two equations:
x + 25 + 2x = 175
3x + 25 = 175
3x = 175 - 25 = 150
x = 50
As x is the number of laps Swimmer A swam, thus, the number of laps that Swimmer A swam was 50 laps.
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Write the standard equation of the circle with center (-4,-4) and radius 6.8
Answer: [tex](x+4)^{2}+(y+4)^{2}=46.24[/tex]
Step-by-step explanation:
[tex](x+4)^{2}+(y+4)^{2}=6.8^{2} \\(x+4)^{2}+(y+4)^{2}=46.24[/tex]
According to the graph of the rational function y equals 2 over the quantity x squared minus 1 end quantity which of the following statements is/are true?
The function is odd.
The function is decreasing for all values in the domain.
There is a horizontal asymptote along the x-axis.
The given function y = 2(x² - 1) is decreasing for all values in the domain and it has a horizontal asymptote along the x-axis so options (B) and (C) will be correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The nature of the relationship between the variables that makes up a function, such as y = sinx and y = x +6, defines the function.
Given the function,
y = 2(x² - 1)
If we increase the value of x to positive then the denominator x² - 1 will go to increase and thus y will decrease.
If we increase the value of x in negative then denominator x² - 1 will go to increase and thus y will decrease.
Therefore it is decreasing for all values in the domain.
Now,
Lim at x tends to ∞ of function is 2/∞ = 0 so y = 0 means there is a horizontal asymptote along the x-axis.
Hence "The given function y = 2(x² - 1) is decreasing for all values in the domain and it has a horizontal asymptote along the x-axis".
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what is the area of triangle ABC
Answer:
enter traverse Does the middle traverse indeed bisect the triangle?
Angles In the triangle ABC, the ratio of angles is: a:b = 4: 5. ...
Triangle P2 Can a triangle have two right angles?
Diagonal Can be a diagonal of diamond twice longer than it side?
Similarity coefficient The triangles ABC and A "B" C "are similar to the similarity coefficient 2. ...
That how u find the area
It wont always be easy, but always try to do what ' s right!
In a world of worriers, be the warrior!
When nothing goes right, go left.
Answer;
The area of a triangle is the region enclosed between the sides of the triangle. Area of ΔABC = 1/2 × Base × Height. Let us know the basics of the area of a triangle. If ABC is an equilateral triangle, Area of ΔABC = (√3/4)a2 where a is the length of a side of the equilateral triangle.
In ΔIJK, the measure of ∠K=90°, KJ = 11, IK = 60, and JI = 61. What is the value of the cosine of ∠J to the nearest hundredth?
The sine of ∠I is represented by the ratio 63:65
First, let's draw the triangle (see the picture below.)
We need to use it here.
What are trigonometric ratios?-sin = opposite/hypotenuse
-cos = adjacent/hypotenuse
-tan = opposite/adjacent.
Assuming that ∠I is Ф,
we can see that its opposite side is equal to 63 and the hypotenuse is 65. Therefore,
[tex]sin(I)=\frac{63}{65} \\\\sinI=75^0[/tex]
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Answer:
0.18
Step-by-step explanation:
It’s right bc I got it correct with that answer
Select all of the true statements below.
• Circles always contain arcs.
• Line segments always contain lines.
• Lines always contain line segments.
• Angles always form perpendicular lines.
Answer:
Circles always contain arcs.Lines always contain line segments.HELP PLEASE Can someone at lest help me with the 2nd question a) b) and c) PLEASE AND THANKYOU
Answer:
a
Step-by-step explanation:
I say you need to get mays age to even get lilacs age
how to solve 52 divided by 4!
A rocket is launched from the ground at an initial velocity of 39.2 meters per second. Which equation can be used to model the height of the rocket after t seconds?
s(t) = –4.9t2 + 39.2
s(t) = –4.9t2 + 39.2t
s(t) = –4.9t2 + 39.2t + 39.2
s(t) = –4.9t2 + 39.2t – 39.2
The quadratic equation that models the height of the rocket after t seconds is:
s(t) = -4.9t² + 39.2t.
What is the quadratic function for a projectile's height?Considering the height in meters, the equation is given by:
s(t) = -4.9t² + v(0)t + h(0)
In which:
v(0) is the initial velocity, in m/s.h(0) is the initial height, in m.In this problem, we have that v(0) = 39.2, h(0) = 0, hence the equation is:
s(t) = -4.9t² + 39.2t.
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Answer: B
Step-by-step explanation: on Edge (*^*)
What is c value in the equation
Log 57.9/c=0.293
If a log has no base written, you should generally (in algebra classes) assume that the base is 10
we raise 10 to the power log 57.9/c = 57.9/c
and 10 to the power 0.293 = 1.9633602768
so 57.9/c = 1.96
c = 57.9 /1.96 = 29.5
Identify the fractions labeled with the letters a and b on the scale below
In the given fraction, we have the value of 1 divided in four portions and we just have to identify which portion does A and B fall into
FractionThis can be defined as a part of portion of a complete value.
In the first part, the portion A is representing 1 out of 5 parts. So, the fraction of A is
[tex]A = \frac{1}{5}[/tex]
In the second fraction B, we can say that B is representing 3 out of 5 parts.
[tex]B = \frac{3}{5}[/tex]
From the above, the value of A and B are
A = 1/5B = 3/5Learn more on fractions here;
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Find the slope rise/run
Answer:
m = -1/3
Step-by-step explanation:
Find two points in order to calculate slope:
(0, 2) (3, 1)Slope (m) =
ΔY /ΔX= -1/ 3= -0.33333333333333
( ΔX = 3 – 0 = 3ΔY = 1 – 2 = -1 )Slope intercept:
y = -0.33333333333333x + 2
Answer:
Slope = - 1/3
Step-by-step explanation:
Choose the point on the right and move upwards. How many times did you move upwards until you were at the same level as the point on the left? You moved once, which means your rise is 1.
Now from the point where you are at now, move right or left depending on where the point is. In this case, it's on the left which means our run will be negative. Now move left until you reach that point on the left. How many times did you move left? You moved three times, which means your run is 3.
Rise/Run = -1/3
Slope = Rise/Run
Slope: - 1/3
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The radius of a circle is 9 inches. What is the circle's circumference?
Use 3.14 for
Answer:
56.52
Step-by-step explanation:
The formula for circumference is C=2πr
So, C=2(3.14)(9)
C=56.52 answer
(-2p+7) (4p - 3) please help
Answer:
Step-by-step explanation:
-8p^2 + 6p + 28p - 21
-8p^2 + 34p - 21
Answer:
-8p² + 34p - 21
Step-by-step explanation:
(-2p + 7)(4p-3)
= -2p*4p -2p*-3 + 7*4p + 7*-3
= -8p² + 6p + 28p - 21
= -8p² + 34p - 21
Simplify the expression.
3.2a + 3.5b – 2.1a
Answer:
1.1a+3.5b
Step-by-step explanation:
Determine whether each triangle with sides of given length is a right triangle. justify your answer
7 yd, 5 yd, 9 yd
10 ft, 24ft, 26 ft
The triangles with the side lengths 10 ft, 24ft, 26 ft, is a right triangle while a triangle with side lengths of 7 yd, 5 yd, 9 yd is NOT based on the Pythagorean theorem.
What is a Right Triangle?A triangle is said to be a triangle based on the Pythagorean theorem, if the square of the longest side equals the sum of the squares of the other smaller sides of the triangle.
9² = 7² + 5²
81 = 74 (NOT TRUE), therefore, the triangle with the side lengths 7 yd, 5 yd, 9 yd, is not a right triangle.
26² = 10² + 24²
676 = 676 (TRUE), therefore, the triangle with the side lengths 10 ft, 24ft, 26 ft, is a right triangle.
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Scan the n the questions
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63
Answer:
what man we can barley see
Step-by-step explanation:
Solve, using the substitution method.
x = 10
y = 2x – 6
(10, 14)
(10, 4)
(10, –4)
(10, –1)
Answer:
10/14
Step-by-step explanation:
substitute x in equation 2
y= 2(10) -6
y= 20 - 6
y= 14
substitute y in equation 2
14 = 2x - 6
-2x= -6-14
-2x= -20
divide both sides by -2
-20/-2
x= 10
y= 14, x= 10
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14. Write the converse of each statement and then determine whether or not the converse is true.
Part A
Converse = "If corresponding angles are equal, then two lines are parallel"Result = TrueExplanation:
Refer to the converse of the corresponding angles theorem. The original version is stated as part A, and the converse is marked in bold above.
Conditional statements are of the form "if this, then that". Symbolically we can use the template "If P, then Q". The P and Q are placeholders for logical statements.
The converse of "if P, then Q" is "If Q, then P". We swap the positions of P and Q. Do not negate either piece.
========================================================
Part B
Converse = "If angle C is 70 degrees, then the sum of angles A and B is 110 degrees"Result = TrueExplanation:
Recall that for any triangle, the three interior or inside angles always add to 180 degrees. In short: A+B+C = 180. If C = 70, then A+B = 180-C leads to A+B = 180-70 and A+B = 110. This process can be reversed.
========================================================
Part C
Converse = "If two lines are not parallel, then alternate interior angles k and s are not equal"Result = TrueExplanation:
For more information, check out the converse of the alternate interior angles theorem. The regular version of the theorem is "If two lines are parallel, then the alternate interior angles are congruent".
The converse of this theorem flips things to say: "If alternate interior angles are congruent, then the lines are parallel".
========================================================
Part D
Converse = "If John loses his money, then he throws coins in the fountain"Result = FalseExplanation:
Throwing coins in a fountain is one way to lose money, but there are other ways. He could drop a coin somewhere, or leave the coin somewhere he forgot.
In other words, just because he lost his money does not mean he threw a coin in the fountain.
express as a mixed fraction 5¼×6
I need method
And answer should be 31½
Answer:
express as a mixed fraction 5¼×6
I need method
And answer should be 31½