The amount of rainfall is an illustration of inverse functions, and rates.
The function is given as: R = f(t)
(a) Interpret f(6) = 4.8
This means that:
The amount of rainfall at 6 seconds is 4.8 cm
(b) Interpret f'(6) = 0.5
f'(6) represents the rate of the function
So, this means that:
The rate at which rain falls at 6 seconds is 0.5 cm per second
(c) Interpret f^-1(5) = 14
f^-1(6) represents the inverse function
So, this means that:
The time at which 5 cm of rain falls, is 14 seconds
(d) Interpret f^-1'(5) = 1.5
f^-1'(5) represents the rate of the inverse function
So, this means that:
The rate of time when 5 cm of rain falls is 1.5 seconds per cm
Read more about functions, inverse and rates at:
https://brainly.com/question/15634149
2/3x + 7 = -1/5x + 3
if there is any doubt leave a comment
Find the domain of the function.
f(x) = -5x + 3
Enter a problem...
Calculus Examples
Popular Problems Calculus Find the Domain and Range f(x)=5x-3
f
(
x
)
=
5
x
−
3
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
(
−
∞
,
∞
)
Set-Builder Notation:
{
x
|
x
∈
R
}
The range is the set of all valid
y
values. Use the graph to find the range.
Interval Notation:
(
−
∞
,
∞
)
Set-Builder Notation:
{
y
|
y
∈
R
}
Determine the domain and range.
Domain:
(
−
∞
,
∞
)
,
{
x
|
x
∈
R
}
Range:
(
−
∞
,
∞
)
,
{
y
|
y
∈
R
}
Suppose `h\left(t\right)=-5t^{2}+10t+3`is an expression giving the height of a diver above the water (in meters), t seconds after the diver leaves the springboard.
a. How high above the water is the springboard? Explain how you know.
Answer:
Step-by-step explanation:
a) The height of the springboard above the water should be h(0) : Read, the height at t = 0
h(0) = -5(0) + 10(0) + 3
h(0) = 0 + 0 + 3
h(0) = 3
a) 3 meters
b) The time it takes the diver to hit water should be, the positive 0 solution for t. Remember, in a quadratic equation, there are two values for t where a parabola crosses the horizontal axis, which in this case would be t. Just by looking at the function, h(t) = -5t2 + 10t + 3 , one should be able to see that it cannot be factored easily, so it requires the Quadratic Formula to find the zeros ; x = -b ±√(b2-4ac) / 2a
Substitute t for x, and use the coefficients for a, b, c:
t = (-10 ± √((102 - 4(-5)(3)))/2(-5)
t = (-10 ±√(100 + 60))/-10
t = (-10 ±√160)/-10) ; Now factor the 160 to simplify:
t = (-10 ±√(10*16))/-10
t = (-10 ±4√10)/-10 ; Factor out leading coefficient of -2 from the numerator:
t = -2(5 ± 2√10)/-10
t = (5 ± 2√10)/5
Using a calculator to find the zeros, and disregarding the negative zero (because t starts at 0):
t ≈ 2.265
b) approx. 2.265 seconds for diver to hit water.
c) To find this, set the function equal to 3 to find what other value for t would be equal to 3 (we know one is 0).
-5tt + 10t + 3 = 3
-5t2 + 10t = 0 ; factor out t
t(-5t + 10) = 0
We know t = 0:
We also know that -5t + 10 = 0
-5t = -10
t = 2
c) 2 seconds. This is the time that diver would equal height of t=0 which is where he started, and where he equals the height of the springboard.
d and e) The peak of the dive (parabola), is determined using the formula h = -b/2a (Derived from the Quadratic Formula) to find the y value (in this case, the h value, answering e) and then using that result in the function to find the x value (in this case, the t value answering d) of the point where the parabola (dive path) reaches a maximum(height), or minimum(in upward opening parabolas).
h = -10/2(-5)
h = -10/-10
h = 1
h(1) = -5(1)2 + 10(1) + 3
h(1) = -5 + 10 + 3
h(1) = 8
d) At t = 1 second, diver will have reached peak of dive.
e) At t = 1 second, diver will have reached a maximum height of 8 meters.
)) Fill in the missing number.
()) 70% of
=
56
Answer: x=80
Step-by-step explanation: multiplying both sides by 100 and dividing both sides by 70 then we have x=56 x 100/70 then your answer is x=80. If you're using a calculator, simply enter 56x100 divided by 70 which will give you the answerLet that be x
70% of x=567/10 × x=56x=56×10/7x=8(10)x=80A boy dressed in a robot costume weighs a total of 50 7/8 lb. If the costume itself weighs 3 1/2 lb, how much does the boy weigh?
The weight of the boy in the robot costume is 351/8 lb or 43 7/8 lb.
To find the weight of the boy, we need to subtract the weight of the costume from the total weight of the boy in the costume.
Total weight of boy and costume = 50 7/8 lb
Weight of costume = 3 1/2 lb
To find the weight of the boy, we can subtract the weight of the costume from the total weight:
Weight of boy = Total weight - Weight of costume
Convert both the total weight and the weight of the costume to improper fractions:
Total weight = 50 + 7/8 = 400/8 + 7/8 = 407/8 lb
Weight of costume = 3 + 1/2 = 6/2 + 1/2 = 7/2 lb
Now, subtract:
Weight of boy = (407/8) lb - (7/2) lb
To perform subtraction, we need to have a common denominator, which is 8 in this case:
Weight of boy = (407/8) lb - (56/8) lb
Now, subtract the fractions:
Weight of boy = (407 - 56)/8 lb
Weight of boy = 351/8 lb
To learn more about fraction click on,
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#SPJ2
what is the probability of a person randomly selecting an apple pie, eating it, then selecting another apple pie
Answer:
if its me then i will bye the store. but the answer is 50%
Step-by-step explanation:
a car travels 55 miles per hour for 2 hours. How far did it travel in 1 1/2 hours
Answer:
82.5 miles in 1 1/2 hours
Step-by-step explanation:
Using the information the question gives us we can find the appropriate answer to this question by dividing the miles per hour by two, and then add that number to the additional miles per hour.
55 miles = one hour
2 hours = 110 miles
1 1/2 hours = 55 ÷ 2 = 27.5
55 + 27.5 = 82.5 miles
82.5 miles
Hope this helps
what is the radius and diameter of the following circle ? 5.1 cm ?
2yx= 4 is it a linear function?
Answer:
No, it is not a linear function, rather a rational function
Step-by-step explanation:
Because the term on the left-hand side contains both x and y, then neither variable varies directly with the other, hence, it's a rational function:
2yx=4
yx=2
y=2/x
Mr. Hinkle baked a pie for Thanksgiving. He cut the pie into 6 piece. He and 2 of his friends each at one slice. What percent of the pie did they eat? *
30%
60%
50%
20%
Answer:
30%
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
three sevenths of num is 12.find
the number
Answer:
x = 28Solution:
3/7x = 12
3/7x ÷ 3/7 = 12 ÷ 3/7 ( divide 3/7 in both sides )
x = 12 ÷ 3/7 (divide)
x = 84/3 (simply divide 84 and 3)
x = 28
_______________________
(solution for dividing the fraction and the whole number 12 and 3/7, for those who don't know how to divide fractions and whole numbers...)
12/1 ÷ 3/7
12/1 ÷ 7/3 (reciprocal method)
12/1 × 7/3 (change operation to multiplication)
12/1 × 7/3 = 84/3 (multiply)
84/3 ⇒ 28 (simplify)
Rachel's income for July is $3300. She spent $1000 for rent, $150 on student loans, $100 for a new
tablet, and $450 on groceries. How much of her monthly income is left?
Answer: 1300
Step-by-step explanation:
3300-1000=2000
2000-450=1550
1550-150=1400
1400-100=1300
The student government snack shop sold 64 snacks this week. 8 of the snacks sold were fruit cups. What percentage of all snacks sold were fruit cups?
Rewrite the equation as a division equation.
Answer:
8/64 = 0.125 = 12.5%
Step-by-step explanation:
8/64 = 0.125 = 12.5%
Hey everyone! Can you help me out with this(for those wondering, these are test corrections, I plan to do half today and half tomorrow)
State whether the following relation is a function.
Answer:
no its not since some dots are above each other and fail the vertical line test
Hope This Helps!!!
Answer:
no the x value repeat
Step-by-step explanation:
PLEASE HELP ME
It snowed 2/3 of a foot in January and 1/2 of a foot in February. How much more did it snow in January than in February?
Answer:
Step-by-step explanation:
2/3 - 1/2 ?=?
4/6 - 3/6 = 1/6 ft more
please help me calculation completing square?
x²+2x-24=0?
Answer:
x = 4, -6
Step-by-step explanation:
x = 4, -6
Please take a look at the picture
Answer:
D) The number that is 5 to the right of -6 on the number line
Hope this helps :)
Expand the function.
f(x) = (2x + 3)4
Answer:
y = 8x + 12
Step-by-step explanation:
y = (2x + 3)4
Distribute the 4 to the 2x and 3
y = 8x + 12
^ Expanded form
solve pls brainliest
Answer:
Mixed number: 8.72=8 72/100
Improper fraction: 8.72= 872/100
Step-by-step explanation:
8 is in the ones place, 7 is in the tenths place, and 2 is in the hundreths place, which makes 8.72. In fractions, that would be 8 wholes, and 72/100, which is 8 72/100. After that, you can turn it into an improper fraction by doing 8x100, which is 800, then you add 72, which is 872. That makes 872 the numerator, and 100 the denominator, which makes 872/100.
Btw (I didn't simplify, as the problem states against it!)
figure b is a scaled copy of figure a
Step-by-step explanation:
figure B is a scaled copy of figure B
by scale factor : 1/2
cosθ(tanθ + cotθ) =
• cscθ
• secθ
• cos^2θ
• 1
Answer:
ayo i think is ufo trying to communicate hey alien we come in peace
Step-by-step explanation:
[tex]\cos \theta(\tan \theta + \cot \theta)\\\\=\cos \theta \tan \theta + \cos \theta \cot \theta \\\\=\cos \theta \left (\dfrac{\sin \theta}{\cos \theta} \right)+ \cos \theta \left(\dfrac{\cos \theta}{\sin \theta} \right)\\\\\\=\sin \theta + \dfrac{\cos^2 \theta}{\sin \theta}\\\\=\dfrac{\sin^2 \theta + \cos^2 \theta}{\sin \theta}\\\\=\dfrac 1{\sin \theta}\\\\=\csc \theta[/tex]
What is 11% of 96 students
Answer:
8.7
Step-by-step explanation:
8.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.7
What are the solutions to the quadratic function. f(x) = x^2+4x-12
Answer:
2, -6
Step-by-step explanation:
x^2 + 4x - 12
A = 1
B = 4
C = -12
i used the "X" method to solve for the solutions. i think it's easier than using the quadratic formula but it doesn't always work
for the "X" method you have to multiply your A value and your C value together so 1 x (-12) = -12. that is going to be the top part of the X
the bottom part of the x will be your B value which is 4
we have to find multiples of -12 that will also add to 4
so -2 and 6 multiply to -12 but also add to 4 so we know these numbers will work
i added added two drawings to show how i found the solutions using the "X" method and the quadratic formula
Find the accumulated value of an investment of $2000 at 8% compounded continuously for 4 years
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &4 \end{cases} \\\\\\ A=2000e^{0.08\cdot 4}\implies A=2000e^{0.32}\implies \boxed{A\approx 2754.26}[/tex]
Help help help help help help
Answer:
70.2
Step-by-step explanation:
28.08 / 0.4 = 70.2
5/7 times 7/8 in simple form
Answer:
609
Step-by-stepStep-by-step explanation:
nope
What is the minimum of the sinusoidal function?
Enter your answer in the box.
Answer:
The minimum is 1
Step-by-step explanation:
1 is the lowest point of the function so that's your answer (:
The minimum of the sinusoidal function is 1.
FunctionThe function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
TrigonometryTrigonometry deals with the relationship between the sides and angles of a right-angle triangle.
Right angle triangleIt is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
Given
y = 2sin(x + ∅) + 3 is a function
To findThe minimum of the sinusoidal function.
How to find the minimum of the sinusoidal function?y = 2sin(x + ∅) + 3 is a function is given
For the minimum value of sin(x + ∅) = -1, then
y = 2(-1) + 3
y = -2 + 3
y = 1
Thus the minimum of the sinusoidal function is 1.
More about the function link is given below.
https://brainly.com/question/5245372
x-10/3=5x+2/2 I need help with he next step please
Answer:
x2 the left side and x3 the right side of the equation
Answer:
X = -2
First you cross multiply, and then you expand to get 15x+6
after that its basic algebra with adding/subtracting from each side, simplifying, and then divide both sides by -13.
What's the negative reciprocal of 5? Question 12 options: A) 1∕5 B) –5 C) –1∕5 D) 5
Answer:
[tex]\huge\boxed{C)\ -\dfrac{1}{5}}[/tex]
Step-by-step explanation:
The reciprocal of 5: [tex]\dfrac{1}{5}[/tex]
The negative reciprocal of 5: [tex]-\dfrac{1}{5}[/tex]
Toby and Emily went to the grocery store to buy food for breakfast for the week. They needed 8 bananas, 2 loaves of bread, 1 bottle of OJ, 1 gallon of milk and a dozen eggs. Each banana was .25, each loaf of bread was 2.55, a bottle of OJ was $2.45 and dozen eggs were $3.15. How much money in total did Toby & Emily spend?
Answer:
$12.70
Step-by-step explanation:
8 x .25 = 2
2 x 2.55 = 5.10
1 x 2.45 = 2.45
1 x 3.15 = 3.15
__________
2 + 5.10 + 2.45 + 3.15 = 12.70 = $12.70
Answer:
they spent $15.85 in all.
Step-by-step explanation:
2.00 banana 5.10 bread 2.45 oj and 3.15 egg, add it all.
