The height of an object off the ground, h (in feet) t seconds after it is launched into the air is given by
h(t) = −16t2 + 128t, 0 ≤ t ≤ 8.
Find the average rate of change of h over the interval
[4, 8].
The height of an object off the ground h after t seconds is [tex]h(t)=-16t^2+128t[/tex] and the rate of change of h is 192.
Given data:
The average rate of change of a function over an interval [a,b] is given by the formula:
[tex]R=\frac{f(b)-f(a)}{b-a}[/tex]
Now, the function [tex]h(t)=-16t^2+128t[/tex] represents the height of an object off the ground at time t seconds. We are asked to find the average rate of change of h over the interval [4,8].
So, the value of a = 4 and b = 8.
[tex]h(8)=-16(8)^2+128(8)[/tex]
[tex]h(4)=-16(4)^2+128(4)[/tex]
On simplifying the equation:
[tex]R=\frac{h(8)-h(4)}{8-4}[/tex]
[tex]R=\frac{768}{4}[/tex]
[tex]R=192[/tex]
Hence, the average rate of change of h over the interval is 192 feet per second.
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The average rate of change of h over the interval [4,8] is -64 feet per second. This is found by substituting the values of a = 4 and b = 8 into the equation h(t) = -16t² + 128t and into the formula for average rate of change.
Explanation:To find the average rate of change of h over the interval [4, 8], we use the formula for the average rate of change: (h(b) - h(a)) / (b - a). Here, a = 4 and b = 8.
First, calculate h(a) and h(b) using the given equation h(t) = -16t² + 128t:
h(4) = -16*(4)² + 128*(4) = -256 + 512 = 256.h(8) = -16*(8)² + 128*(8) = -1024 + 1024 = 0.Substitute h(a) and h(b) into the formula to get:
(0 - 256) / (8 - 4) =-256/4 = -64.
So, the average rate of change of h over the interval [4, 8] is -64 feet per second.
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Could someone explain linear functions to me? I dont get them at all. Thanks!
Answer:
Step-by-step explanation:
Linear functions are whose graph is a straight line. They contain a slope and a constant also known as the y intercept.
Example: y = 3x + 2
The slope is 3 and the y intercept is 2.
The length of a rectangle is the sum of the width and 1. The area of the rectangle is 20 units. What is the width, in units, of the rectangle?
Width of the rectangle is 4 units
Step-by-step explanation:
Step 1: Let the width of the rectangle be x. Then the length = x + 1. Find dimensions if area = 20 sq. unitsArea of the rectangle = length × width
⇒ 20 = x (x + 1)
⇒ 20 = x² + x
⇒ x² + x - 20 = 0
⇒ x² + 5x - 4x - 20 = 0 (Using Product Sum rule to factorize)
⇒ x(x + 5) - 4(x + 5) = 0
⇒ (x + 5)(x - 4) = 0
⇒ x = -5, 4 (negative value is neglected)
x = 4
Final answer:
The solution reveals that the width of the rectangle is 4 units.
Explanation:
The student is asking to find the width of the rectangle when the length is given as the sum of the width and 1 unit, and the area of the rectangle is 20 square units.
To solve this, we can set up an equation using the area formula for a rectangle, A = length * width, where the area (A) is 20 square units.
Let's denote the width as w units.
Then the length can be expressed as w + 1 units. Substituting these expressions into the area formula gives us:
20 = w * (w + 1)
Expanding the right side, we get:
20 = w² + w
This is a quadratic equation, which we can solve by setting it equal to zero:
w² + w - 20 = 0
Factoring the quadratic equation, we find:
(w + 5)(w - 4) = 0
Therefore, w could be -5 or +4. Since a width cannot be negative, the only reasonable solution is w = 4 units.
Thus, the width of the rectangle is 4 units.
Can somebody help me ASAP !!!!!
Step-by-step explanation:
√17= 4.12
Therefore, we need to find an irrational no. between 4.1 and 4.12
So, the correct option is a
4.1001000100001000001....
90 in terms of pi please help
90 in terms of pi is [tex]\frac{\pi}{2}[/tex] .
Step-by-step explanation:
We know that ,
Degrees are a unit of angle measure. A full circle is divided into 360 degrees. For example, a right angle is 90 degrees. A degree has the symbol ° and so ninety degrees would written 90°. Another unit of angle measure is the radian.The radian is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees.We have to convert 90 in terms of pi i.e. degree to radians:
⇒ [tex](90)\frac{\pi }{180}[/tex]
⇒ [tex]\frac{90 }{180}(\pi)[/tex]
⇒ [tex]\frac{1 }{2}(\pi)[/tex]
⇒ [tex]\frac{\pi}{2}[/tex]
Therefore, 90 in terms of pi is [tex]\frac{\pi}{2}[/tex] .
Find the range f(x) =-2x-5 for the domain (-2,-1,1,2).
Answer:
{ - 9, - 7, - 3, - 1 }
Step-by-step explanation:
To obtain the range substitute the values of x from the domain into f(x)
f(- 2) = - 2(- 2) - 5 = 4 - 5 = - 1
f(- 1) = - 2(- 1) - 5 = 2 - 5 = - 3
f(1) = - 2(1) - 5 = - 2 - 5 = - 7
f(2) = - 2(2) - 5 = - 4 - 5 = - 9
range is { - 9, - 7, - 3, - 1 }
The table represents an exponential function
ative rate of change of the function?
1/3
2/3
2
9
An envelope is 5 inches tall and 11 inches wide. What is its perimeter?
Answer:
32 inches
Step-by-step explanation:
5 + 5 + 11 + 11 = 32 inches
Can you help me on this math problem pleaseee?
Answer:
a. - 1 3/4
b. 6
Step-by-step explanation:
For each, plug in the given number to the corresponding variable:
a. When x = -2. Plug in -2 for x in the given expression:
2^(-2) - 2
Simplify. Note that when a negative sign is located in the power sign, you would do the normal power, and then put the number over 1.
2^(-2) = 1/(2 x 2) = 1/4
Simplify:
1/4 - 2 = - 1 3/4
- 1 3/4, or -7/4 is your answer.
b. When x = 3. Plug in 3 for x in the given expression:
2^(3) - 2
Simplify. First solve the power, then subtract:
2^3 = 2 * 2 * 2 = 4 * 2 = 8
8 - 2 = 6
6 is your answer.
~
Answer:
a. - 1 3/4
b. 6
The circumference of a circle is 157 centimeters. What is the area of the circle in terms
of t?
A
7.570 cm?
B
157 cm
C
D
56.251 cm
2257 cm
The radius of the circle is approximately 7.5 cm, and the corresponding area is approximately 56.25π cm², as calculated using the formulas for circumference and area. Here option C is correct.
1: Find the radius using the circumference formula
We know the circumference C = 157 cm.
We also know the formula for circumference of a circle: C = 2πr, where r is the radius.
Rearranging the formula to solve for r, we get: r = C / (2π).
Substituting C with 157, we get: r = 157 / (2π) ≈ 7.5 cm.
2: Calculate the area using the area formula
Now that we know the radius, we can use the formula for the area of a circle: A = πr², where A is the area.
Substituting r with 7.5, we get: A = π * (7.5)² ≈ 56.25π cm².
Therefore, the area of the circle is 56.25π cm². Here option C is correct.
Complete question:
The circumference of a circle is 157 centimeters. What is the area of the circle in terms of t?
A - 7.570 cm?
B - 157 cm
C - 56.251 cm
D - 2257 cm
find the mean,median,and mode of the data: 0,100,25,25,25.Which outlier,0, 100, affects the data more?
Mean: 175/5 = 35.
Median: 0, 25, 25, 25, 100 - 25 is in the middle.
Mode: 25, it appears the most.
The outlier 100 affects the data, because the number 100 still farthest from the main cluster. (Sorry if this is wrong)
In a fraction, this is the number under the fraction bar.
EWE
YUIU Problems DV
A florist has 9 tulips and 18 carnations. If the florist wants to create identical bouquets
without any leftover flowers, what is the greatest number of bouquets the florist can make?
Answer:
9
Step-by-step explanation:
GCF of 9 and 18 is 9. I hope it helps. Srry of the last mishap and i hope you accept my apology.
Me. Sanchez bought some books at a book sale, including 15 paperback books. 75% of all the books he bought were paperbacks
The total number of books based on the given percentage will be 20 including 15 paperback books.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
Suppose Mr. Sanchez bought a total of x number of books.
75% of x = (75/100)x
This is the paperback thus,
(75/100)x = 15
x = 1500/75 = 20
Thus, the number of total books = 20 including 15 paperback books.
Hence "The total number of books based on the given percentage will be 20 including 15 paperback books".
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fill in the blanks
a ---÷48=-1
Ans is -48.
Hope this will help u..
3 is what percent of 5
Answer:
we can write
3 as a percent of 5 as
as is = to sign
percent is 100
and of is multiplication sign that gives us
3=x/100×5
x=(3×100)/5
x=300/5
x=60
so 3 is 60% of 5
Answer:
The answers would be 60%
Step-by-step explanation:
Rachel joggled along a trail that was 1/4 of a mile Long she jogged along the trail eight times how many miles did Rachel jog in all
Answer:
2
Step-by-step explanation:
1/4 times 8 = 2
Answer: She jogged 2 miles
Step-by-step explanation: 1\4 x 8 which will give you 8\4, then you simplify it and you get 2.
Factor –3y – 18 and choose the correct option.
A -3(y + 6)
B 3(y+6)
C
(y – 6)
3 (y – 6)
Please help!?
Solution:
Given that we have to factor -3y - 18
Use the distributive property,
a(b + c) = ab + bc
From given,
-3y - 18
Factor out the greatest common factor of 3 and 18
The factors of 3 are: 1, 3
The factors of 18 are: 1, 2, 3, 6, 9, 18
Then the greatest common factor is 3
Factot out 3 from given expression
-3y - 18 = 3( - y - 6)
Or else we can rewrite as,
-3y - 18 = -3(y + 6)
Thus the given expression is factored
Prime factorization
98
2 x 7 x 7 or in exponential form, 2 x 7². 98 turns into 2 times 49, then 49 turns into 7 times 7.
The prime factorization of 98 is equal to 2 x 7².
The prime factorization of 98 involves breaking it down into prime numbers that multiply together to give the original number, 98.
The process for finding the prime factors of 98 is as follows:
Start with the smallest prime number, 2.
Since 98 is an even number, it is divisible by 2. So, divide 98 by 2 to get 49.
Now, 49 is not divisible by 2, so we try the next prime number, which is 3.
Since 49 is not divisible by 3 either, we move to the next prime number, 5, and so on until we reach 7, which does divide 49.
Divide 49 by 7 to get 7. So, 49 is 7 multiplied by 7, both of which are prime numbers.
Putting it all together, the prime factorization of 98 is 2 × 7 × 7 or 2 × 7².
If a car travels 150km for 1hour and 30 minutes how long in hours will it take the car to travel 260km
Time taken by the car to cover 260 km is 2.6 hrs
Step-by-step explanation:
Step 1: Find the speed of the car given distance covered = 150 km and time = 1.5 hrs.Speed = Distance/Time = 150/1.5 = 100 km/hr
Step 2: Find the time taken by the car to cover 260 km.Time = Distance/Speed = 260/100 = 2.6 hrs
Which is the rate of change for the interval between 2 and 6 on the x-axis?
–3
-one-third
one-third
3
Answer:
3
Step-by-step explanation:
I think you misses attaching the photo, so please have a look at my photo for your better understanding.
We know the formula for rate of change of the parabola line:
[tex]\frac{f(b)- f(a)}{b-a}[/tex]
Given here:
a= 2 => f(a) = 2
b=6 => f(b) = 2
Substitute all the values into the function, we have:
[tex]\frac{14-2}{6-2} = 3[/tex]
So the rate of change is 3
Answer:
D.) 3
Step-by-step explanation:
Got it right on the assignment
4(4)
4(5)
4(6)
4(7)
4(8)
4(9)
4(10)
Answer:
4(4)= 16
4(5)= 20
4(6)=24
4(7)= 28
4(8)= 32
4(9)= 36
4(10)= 40
Step-by-step explanation:
i need help understanding!
In 4 hours, you hike 10 miles.
Which unit rate describes your speed on the hike?
CLEAR CHECK
5 miles per hour
410 mile per hour
2.5 miles per hour
10 miles per hour
What is the value of X?
The two given angles are vertical angles and equal each other:
3x + 50 = 6x -10
Now solve for x:
Subtract 3x from both sides:
50 = 3x -10
Add 10 to both sides:
60 = 3x
Divide both sides by 3
X = 20
What is the following quotient 6-3(^3+6)/^379
Answer:
Quotient given:
\frac{6-3 \sqrt[3]{6} }{ \sqrt[3]{9} }
Answer:
2 \sqrt[3]{3} - \sqrt[3]{18}
Explanation:
1) Rationalize by multiplying numerator and denominator by \sqrt[3]{9}
2)
\frac{6-3 \sqrt[3]{6} }{ \sqrt[3]{9} } \frac{\sqrt[3]{9}}{\sqrt[3]{9}}
3) Due the operations
\frac{6 \sqrt[3]{3}-3 \sqrt[3]{6.3}}{ \sqrt[3]{27} }
\frac{6 \sqrt[3]{3}-3 \sqrt[3]{6.3}}{ 3 }=2 \sqrt[3]{3} - \sqrt[3]{18}
Step-by-step explanation:
Which distance measures 5 units?
Answer:
the only thing i can think of is a 5K so kilometers
Step-by-step explanation:
more context in the question? all distance measures 5 units
Answer:
can you give options please
Step-by-step explanation:
I want to buy a combination of Dr.pepper and sprite. dr pepper cost 2.98 each and sprite is on sell for 1.99 each. I need at least 8 total and i can spend more than 20 dollars
High School
There are quite a few possible combinations that are minimum 8 sodas, and under $20.
1. 4 Dr. Peppers and 4 Sprites. $2.98 times 4 = $11.92. $1.99 times 4 = $7.96. $7.96 + $11.92 = $19.88.
2. 3 Dr. Peppers and 5 Sprites. $2.98 times 3 = $8.94. $1.99 times 5 = $9.95. $9.95 + $8.94 = $18.89.
3. 2 Dr. Peppers and 6 Sprites. $2.98 times 2 = $5.96. $1.99 times 6 = $11.94. $11.94 + $5.96 = $17.90.
4. 2 Dr. Peppers and 7 Sprites. $2.98 times 2 = $5.96. $1.99 times 7 = $13.93. $5.96 + $13.93 = $19.89.
5. 1 Dr. Pepper and 7 Sprites. $2.98 times 1 = $2.98. $1.99 times 7 = $13.93. $2.98 + $13.93 = $16.91.
6. 1 Dr. Pepper and 8 Sprites. $2.98 times 1 = $2.98. $1.99 times 8 = $15.92. $15.92 + $2.98 = $18.90.
I hope this helps!
What is the slope of the line passing through the points (2,5) and (-1,-4)? Show
all your work.
Answer:the slope is 3/9
Step-by-step explanation:use the y intercept form
Answer:
3
Step-by-step explanation:
Slope = change in y/change in x
That’s y2 - y1 /x2 - x1
Given
x1 = 2
y1 = 5
x2 = -1
y2 = -4
Slope = -4 - 5 /-1 - 2
= -9/-3
= 3
what is the inverse of cube root x/3 +1
Answer:
[tex] {f}^{ - 1} (x) = 3 {x}^{2} - 3[/tex]
Step-by-step explanation:
We want to find the inverse of
[tex] y = \sqrt[3]{ \frac{x}{3} + 1} [/tex]
We interchange x and y to get:
[tex]x= \sqrt[3]{ \frac{y}{3} + 1} [/tex]
We solve for y;
[tex] {x}^{2} = \frac{y}{3} + 1[/tex]
Multiply through by 3
[tex]3 {x}^{2} = y + 3[/tex]
Subtract 1 from both sides:
[tex]y = 3 {x}^{2} - 3[/tex]
Therefore the inverse is
[tex] {f}^{ - 1} (x) = 3 {x}^{2} - 3[/tex]