The exact average speed when x = 56 seconds is approximately 30.86 mph.
To use linear approximation to approximate a person's average speed if they travel one mile in 56 seconds, we'll first find the derivative of the function [tex]\( s(x) = \frac{3600}{60 + x} \)[/tex] with respect to x.
[tex]\[ s'(x) = -\frac{3600}{(60 + x)^2} \][/tex]
Now, we'll evaluate the derivative at x = 0 to find the slope of the tangent line at that point, which will be our linear approximation.
[tex]\[ s'(0) = -\frac{3600}{(60 + 0)^2} = -\frac{3600}{3600} = -1 \][/tex]
So, the slope of the tangent line at x = 0 is -1.
Now, using the point-slope form of the equation of a line, we'll find the equation of the tangent line at x = 0:
y - s(0) = s'(0)(x - 0)
[tex]\[ y - s(0) = -1 \cdot x \][/tex]
y = -x + s(0)
We know that s(0) is the exact speed at x = 0, so we'll substitute x = 0 into the original function to find it:
[tex]\[ s(0) = \frac{3600}{60 + 0} = 60 \text{ mph} \][/tex]
So, the equation of the tangent line is:
y = -x + 60
Now, to approximate the average speed when x = 56, we'll substitute x = 56 into the equation of the tangent line:
y = -56 + 60 = 4
So, the approximate average speed when x = 56 seconds is 4 mph.
To find the exact speed, we'll substitute x = 56 into the original function s(x):
[tex]\[ s(56) = \frac{3600}{60 + 56} = \frac{3600}{116} \approx 30.86 \text{ mph} \][/tex]
So, the exact average speed when x = 56 seconds is approximately 30.86 mph.
For problems 2-3: data were collected on the contents of 1-kilogram sugar packets of brands 1 and 2. assume contents are normally distributed. let and be the true average and standard deviation of contents for brand ( = 1, 2). data summaries are given below. data summary brand 1: = 16, ̅ = 1.053, = 0.058 brand 2: = 16, ̅ = 1.071, = 0.062 2. we would like to determine if there is evidence that brand 1 has a lower average content that brand 2. what hypothesis test will we conduct?
a. : − = 0 versus : − ≠ 0
b. : − = 0 versus : − > 0
c. : − < 0 versus : − = 0
d. : − = 0 versus : − < 0 3. what is the value of the test statistic for testing : = ?
a. 0.9355
b. 0.8751
c. −0.018
d. −0.848
It is estimated that there are 10^20 grains of sand on a beach in Florida in April. The beach is heavily eroded by tourists over the peak summer holiday season. Approximately one hundredth of the beach is removed as a result of this erosion. How many grains of sand are removed from the beach?
Answer:
c
Step-by-step explanation:
Mr.Chaves spent $199.99 for a new smart phone $39.99 on a carrying case, and $59.99 on accesiories. The expression l-199.99l+l39.99l+l59.99l represents the total amount that Mr.Chaves spent. How much did he spend all together.
First answer will get brainiliest
G write the equation in spherical coordinates. (a) 7z2 = 8x2 + 8y2
Answer:
[tex]\displaystyle 7 \cos^2 \phi - 8 \sin^2 \phi = 0[/tex]
General Formulas and Concepts:
Multivariable Calculus
Spherical Coordinate Conversions:
[tex]\displaystyle r = \rho \sin \phi[/tex][tex]\displaystyle x = \rho \sin \phi \cos \theta[/tex][tex]\displaystyle z = \rho \cos \phi[/tex][tex]\displaystyle y = \rho \sin \phi \sin \theta[/tex][tex]\displaystyle \rho = \sqrt{x^2 + y^2 + z^2}[/tex]Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle 7z^2 = 8x^2 + 8y^2[/tex]
Step 2: Convert
[Equation] Substitute in Spherical Coordinate Conversions:∴ we have found the given equation in terms of spherical coordinates.
---
Learn more about spherical coordinates: https://brainly.com/question/9557773
Learn more about multivariable calculus: https://brainly.com/question/4746216
---
Topic: Multivariable Calculus
Unit: Triple Integrals Applications
Which equations have a greater unit rate than the rate represented in the table?
Choose more than one
x y
-----
3 2
6 4
9 6
A. y=5/7x
B. y=3/5x
C. y=1/3x
D. y=7/9x
E. y= 7/11x
(a) y=5/7x and (d) y=7/9x have a greater unit rate than the rate represented in the table.
What is slope intercept form?y=mx+c is the slope intercept form where m is the slope and c is y intercept.
The given table is
x 3 6 9
y 2 4 6
The formula to calculate slope is m =y₂-y₁/x₂-x₁
(3,2 ) and (6, 4) are two points.
x₁=3, y₁=2 , x₂=6 and y₂=4
m=4-2/6-3
m=2/3.
Now let us check the equation with greatest slope
(a) y=5/7x
5/7 > 2/3
(b) y=3/5x
3/5 < 2/3
(c) y=1/3x
1/3 < 2/3
(d) y=7/9x
7/9 > 2/3
(e) y= 7/11x
7/11< 2/3
Hence (a) y=5/7x and (d) y=7/9x have a greater unit rate than the rate represented in the table.
To learn more on slope intercept form click:
https://brainly.com/question/3605446
#SPJ5
A package of breadcrumbs to feed the ducks at the duck pond costs $0.25. How many packages of bread crumbs could be bought with $23.50
Is m=0.75d-2 proportional?
Answer:
No, the equation m=0.75d-2 does not represent proportional relationship.
Step-by-step explanation:
The given equation is
[tex]m=0.75d-2[/tex]
We need to check whether the given equation represents proportional relationship or not.
If variable y is proportional to variable x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is the constant of proportionality.
At x=0 the value of y is 0. It means, if a linear equation represents proportional relationship then it must be passes though the origin.
Substitute d=0 in the given equation.
[tex]m=0.75(0)-2[/tex]
[tex]m=-2[/tex]
The line passes through the point (0,-2).
Since the line does not pass through the origin, therefore it does not represent proportional relationship.
Can someone help me with this question?
State the Pythagorean Theorem and tell how you can use it to solve problems
What is the average rate of change of f(x) = −2x + 1 from x = −5 to x = 1?
Answer:-2
Step-by-step explanation:
What is the 4th term of the sequence?
a1 = 8 and an = 6 + an – 1
a4 =
f (x) = x5 − 8x4 + 21x3 − 12x2 − 22x + 20 Three roots of this polynomial function are −1, 1, and 3 + i. Which of the following describes the number and nature of all the roots of this function?
f (x) has two real roots and one imaginary root.
f (x) has three real roots.
f (x) has five real roots.
f (x) has three real roots and two imaginary roots.
Answer:
It's D on edge.
The f(x) has three real roots and two imaginary roots option (D) is correct.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a polynomial:
f(x) = x⁵ − 8x⁴ + 21x³ − 12x² − 22x + 20
The three roots of this polynomial function are −1, 1, and 3 + i.
We can write the function in a factored form:
f(x) = (x - 1)(x⁴ - 7x³ + 14x² +2x - 20)
Again factoring the above polynomial:
f(x) = (x - 1)(x + 1)(x - 2)(x² -6x + 10)
The roots of the polynomial are
x - 1 = 0
x = 1
x + 1 = 0
x = -1
x - 2 = 0
x = 2
x² - 6x + 10 = 0
The above quadratic equation has two complex roots.
x = 3 + i
x = 3 - i
Thus, the f(x) has three real roots and two imaginary roots option (D) is correct.
Learn more about Polynomial here:
brainly.com/question/17822016
#SPJ6
whats the awnser is it 600
3600/300 = 12
4800/400 = 12
the common ratio is 12 so divide pounds of milk by 12 to get pounds pf ice cream
6000 / 12 = 500
Answer is B
For integer values of a and b, b^a = 8. The ratio of a to b is equivalent to the ratio of c to d, where c and d are integers. What is the value of c when d = 10?
To find the value of c when d = 10, we first need to determine the values of a and b. Given that b^a = 8, we know that 8 is the result of raising b to the power of a.
Since the question states that a and b are integers, there are a limited number of possibilities to consider. Let's examine the possible combinations of a and b that satisfy this equation: [tex]1^3 = 1 2^3 = 8 3^2 = 9[/tex](which is not 8) [tex]4^2 = 16[/tex] (which is not 8) [tex]5^1 = 5 6^1 = 6 7^1 = 7 8^1 = 8[/tex]From these calculations, we find that the only combination that satisfies the equation is a = 3 and b = 2. Now, let's consider the ratio of a to b and the ratio of c to d.
The ratio of a to b is a/b = 3/2. The question states that the ratio of a to b is equivalent to the ratio of c to d, which means: a/b = c/d Given that d = 10, we can substitute the value into the equation: [tex]3/2 = c/10[/tex] Next, we can cross-multiply to solve for c: [tex]3 * 10 = 2 * c 30 = 2[/tex] c Dividing both sides by 2, we get: c = 15 Therefore, when d = 10, the value of c is 15. In conclusion, when d = 10, the value of c is 15 based on the given equation and calculations.
To know more about cross-multiply visit:
https://brainly.com/question/28308012
#SPJ2
Payout Annuities:
1. You want to be able to withdraw $30,000 from your account each year for 15 years after you retire.
You expect to retire in 30 years.
If your account earns 5% interest, how much will you need to deposit each year until retirement to achieve your retirement goals?
To achieve your retirement goals of withdrawing $30,000 per year for 15 years, you will need to deposit approximately $121,200 each year until retirement.
Explanation:To determine how much you need to deposit each year until retirement, you can use the formula for the present value of an annuity. The formula is:
PV = PMT x ((1 - (1 + r)^-n) / r)
Where:
In this case, the annuity payment amount is $30,000, the interest rate is 5%, and the number of periods is 15 years. Plugging these values into the formula:
PV = $30,000 x ((1 - (1 + 0.05)^-15) / 0.05)
Simplifying the equation:
PV = $30,000 x ((1 - 1.798) / 0.05)
PV = $30,000 x (0.202 / 0.05)
PV = $30,000 x 4.04
PV = $121,200
Therefore, you will need to deposit approximately $121,200 each year until retirement to achieve your retirement goals.
____ provides a greater degree of security by implementing port-based authentication. ieee 802.3ad ieee 802.11n ieee 802.1x ieee 802.1z
A disc jockey must allow time for 24 minutes of commercials every hour, along with 4 minutes for news, 3 minutes for weather, and 2 minutes for public-service announcements. If each record lasts and average of 3 minutes, how many records per hour can the DJ play?
A water tank holds 24000 gallons. How many hours will it take for 2/3 of the water to be used if the water is used at an average rate of 650 gallons a day?
A 7 pound bag of grass seed covers 2,000 square feet. How many pounds would be needed to cover 35,000 square feet? Round your answer to the nearest pound.
35000 / 2000 = 17.5
17.5 * 7 = 122.5 pounds round to 123 pounds are needed
What does −2/3(12c−9)+14c simplify to?
Answer:
The simplified form of the provided expression is [tex]6c+6[/tex] or [tex]6(c+1)[/tex]
Step-by-step explanation:
Consider the provided expression.
[tex]\frac{-2}{3}(12c-9)+14c[/tex]
Use the distributive property:
[tex]a(b+c)=ab+ac[/tex]
By using the above property we can simplify it as shown:
[tex]\frac{-2}{3}\times 12c-\frac{-2}{3}\times 9+14c[/tex]
[tex]-2\times 4c+2\times 3+14c[/tex]
[tex]-8c+6+14c[/tex]
Add or subtract the like terms.
[tex]6c+6[/tex] or [tex]6(c+1)[/tex]
Thus, the simplified form of the provided expression is [tex]6c+6[/tex] or [tex]6(c+1)[/tex]
The simplest form of expression by applying distributive property would be, 6 (c + 1)
Given that,
The expression is,
[tex]\dfrac{- 2}{3} (12c - 9) + 14c[/tex]
Now, used the concept of distributive property to simplify the expression,
[tex]\dfrac{- 2}{3} (12c - 9) + 14c[/tex]
Apply distributive property,
[tex][\dfrac{- 2}{3} \times 12c - (\dfrac{- 2}{3} )\times 9] + 14c[/tex]
[tex][- 2 \times 4c + 2 \times 3] + 14c[/tex]
[tex][- 8c + 6] + 14c[/tex]
Combine like terms,
[tex]- 8c + 14c + 6[/tex]
[tex]6c + 6[/tex]
Take 6 as a common term,
[tex]6 (c + 1)[/tex]
So, the solution of expression 6 (c + 1).
To learn more about the equation visit:
brainly.com/question/28871326
#SPJ6
What percent of 43.75 is 70
Name all sets of numbers to which each real number belongs
A real number can belong to several sets of numbers, including the integers, rationals, irrationals, and reals. Integers are the set of whole numbers and their negatives, rationals can be expressed as a fraction of two integers, irrationals cannot be expressed as a fraction, and reals represent all possible numbers on the number line.
Explanation:A real number can belong to several sets of numbers, including the integers, rationals, irrationals, and reals.
Integers are the set of whole numbers and their negatives, including zero. They don't include fractions or decimals.
Rationals are the set of numbers that can be expressed as a fraction of two integers, like 3/4 or -5/2.
Irrationals are the set of numbers that cannot be expressed as a fraction, like √2 or π.
Reals represent all possible numbers on the number line, including integers, rationals, and irrationals.
Learn more about Sets of Numbers here:https://brainly.com/question/13045235
#SPJ2
1/4 + -2/3 (SIMPLIFY)
Answer:
[tex]\large\boxed{\dfrac{1}{4}+-\dfrac{2}{3}=-\dfrac{5}{12}}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{4}+\left(-\dfrac{2}{3}\right)=\dfrac{1}{4}-\dfrac{2}{3}\\\\\text{You must find the common denominator.}\\\\\text{List of multiples of 3:}\ 0,\ 3,\ 6,\ 9,\ \boxed{12},\ 15,\ ...\\\text{List of multiples of 4:}\ 0,\ 4,\ 8,\ \boxed{12},\ 16,\ ...\\\\\text{The common denominator is}\ \boxeed{12}.\\\\3\cdot4=12\\\\\dfrac{1}{4}=\dfrac{1\cdot3}{4\cdot3}=\dfrac{3}{12}\\\\\dfrac{2}{3}=\dfrac{2\cdot4}{3\cdot4}=\dfrac{8}{12}\\\\\\\dfrac{1}{4}-\dfrac{2}{3}=\dfrac{3}{12}-\dfrac{8}{12}=\dfrac{3-8}{12}=-\dfrac{5}{12}[/tex]
explain...................
The mass of a radioactive element at time x is given by the equation below, where c is the original mass and h is the half-life of the element. The half-life of a substance is 4.9 years. How long will it take for 36 grams to decay to 10 grams? (Round your answer to one decimal place.)
M(x)=c(.5^x/h)
the quotient of a number and three is equal to negative eight
Divide m2n2/p3 by mp/n2 .
Answer:
The answer is 'm'.
Step-by-step explanation:
Here, the given expression,
[tex]\frac{\frac{m^2n^2}{p^3}}{\frac{mp}{n^2}}[/tex]
[tex]=\frac{m^2n^2\times n^2}{p^3\times mp}[/tex]
[tex]=\frac{m^2n^{2+2}}{p^{3+1}m}[/tex] ( [tex]a^m.a^n=a^{m+n}[/tex] )
[tex]=\frac{m^2p^4}{p^4m}[/tex]
[tex]=m^2p^4p^{-4}m^{-1}[/tex] ( [tex]a^{m}=\frac{1}{a^{-m}}[/tex] )
[tex]=m^{2-1}p^{4-4}[/tex]
[tex]=m^1p^0[/tex]
[tex]=m[/tex]
Help me asap!!! :) please
Mark you a brainly!
30 /10 = 3
so multiply 9 by 3
9*3 = 27
9/10 = 27/30
a = 27
The complex number z = –1 + 3i can be expressed in trigonometric form as:
the senior is having a car wash to raise money. They can wash about 35 cars in 5 hours. if they are washing the same number of cars each hour, how many cars do they wash in 1 hour
Hello!
your answer is 75 • $6 - $35
next time add the answers too for these questions that's why the other guy didn't give you the right answer
The veterinarian weighed Oliver’s new puppy, Boaz, on a defective scale. He weighed 46 pounds. However, Boaz weighs exactly 44.5 pounds. What is the percent of error in measurement of the defective scale to the nearest tenth?