Engineers are draining a water reservoir until its depth is only 10 feet. The depth decreases exponentially as
shown in the graph below. The engineers measure the depth after 1 hour to be 64 feet and after 4 hours to be
28 feet. Develop an exponential equation in y=a(6)" to predict the depth as a function of hours draining.
Round a to the nearest integer and b to the nearest hundredth. Then, graph the horizontal line y = 10 and
find its intersection to determine the time, to the nearest tenth of an hour, when the reservoir will reach a
depth of 10 feet.
The draining of the reservoir follows an exponential function
The reservoir will reach a depth of 10 feet at 7.6 hour
The given parameters are:
[tex]\mathbf{(x,y) = (1,64)(4,28)}[/tex]
An exponential equation is represented as:
[tex]\mathbf{y = ab^x}[/tex]
Substitute [tex]\mathbf{(x,y) = (1,64)(4,28)}[/tex] in [tex]\mathbf{y = ab^x}[/tex]
[tex]\mathbf{64 = ab^1}[/tex]
[tex]\mathbf{64 = ab}[/tex]
[tex]\mathbf{28 = ab^4}[/tex]
Divide [tex]\mathbf{64 = ab}[/tex] and [tex]\mathbf{28 = ab^4}[/tex]
[tex]\mathbf{\frac{ab^4}{ab} = \frac{28}{64}}[/tex]
[tex]\mathbf{b^3 = 0.4375}[/tex]
Take cube roots
[tex]\mathbf{b= 0.76}[/tex]
Substitute [tex]\mathbf{b= 0.76}[/tex] in [tex]\mathbf{64 = ab}[/tex]
[tex]\mathbf{64 = 0.76a}[/tex]
Solve for a
[tex]\mathbf{a = 84}[/tex]
So, the equation is:
[tex]\mathbf{y = 84(0.76)^x}[/tex]
See attachment for the graphs of [tex]\mathbf{y = 84(0.76)^x}[/tex] and y = 10
The point of intersection is: x = 7.6
Hence, the reservoir will reach a depth of 10 feet at 7.6 hour
Read more about exponential functions at:
https://brainly.com/question/15352175
NEED ANSWER ASAP!!!!!!!!
Find the slope from the following points:
(-4,2) (1,8)
-3/6
5/6
6/-3
6/5
15.7 x 102 = ___
1.57
15.7
157
1,570
[tex]15.7 \times 102 = 157[/tex]
Identify an equation in point-slope form for the line parallel to y = 1x-7 that
passes through (-3,-2).
Answer:
y +2 = 1 (x +3)
Step-by-step explanation:
y = 1x - 7
Slope: 1
Point: (-3, -2)
A decimal that contains digits that continue forever in a pattern is called a (n) decimal
Its a repeating decimal
2+3×5(-4)÷5
how does it work
Solve the equation
3x²-17x+10=0
Answer:
(3x-2) (x-5)
Step-by-step explanation:
30 = -15 X -2
-17 = -15 + -12
3x2 - 15x - 2x +10
factorise
3x(x-5) - 2(x-5)
(3x-2) (x-5)
The functions f(x) and g(x) are shown on the graph. fx) = x² What is g(x)? 10- y (f(x) 5 X >> 10 10 5 5 -5-+ g(x) -10 O A. g(x) = (-x)2 - 2 O B. g(x) = -x2 - 2 --- O c. g(x) = -x2 + 2 O D. g(x) = (- x)2 + 2
Answer:
C
Step-by-step explanation:
i hoped i did something
The value of g(x) will be -x² + 2 so option (C) will be correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
Given,
f(x) = x²
g(x) = shifts graph downward by 2 units and reflected down.
Now,
The value of f(x) for positive x will be positive
But the value of g(x) for positive x is negative and 2 units shifted downward.
So it should be -x² - 2.
Hence"The value of g(x) will be -x² + 2 so option (C) will be correct".
For more about the function,
brainly.com/question/23712366
#SPJ5
14. What is 7/4 as a mixed number?
A. 1 3/4
B. 1 7/4
c. 1 1/4
D. 3/4
Answer:
A
Step-by-step explanation:
7/4 means you have one whole 1 and 3 left over
Answer:
A
Step-by-step explanation:
7/4 as a mixed number can be written as 1 3/4.
Which equations represent linear functions?
•8x – 3y = 2
•y = |x – 41-7
•y + 8 = 5(x-4)
• y=-7
•y = 6
•y=-4x* - 6
Answer:
1,3,4,5 (2 and four I can't make out what the notations are)
Step-by-step explanation:
Any equation that has a constant slope is a linear equation.
1 has a slope of 8/3
3 has a slope of 5
4 and 5 have a slope of 0
2 looks to be some form of absolute value equation and therefore is in the shape of a V and not a straight line.
6 looks to be an equation with an exponent as part of a term and will have a gradually decreasing slope (decreasing because of the negative 4)
pls hurry!! i need this asap
Answer:
Look at image
Step-by-step explanation:
Look at image
Look at image
somebody
help me!!!
god will bless you
Answer:
2
Step-by-step explanation:
Help please and thank you
Answer:
a
Step-by-step explanation:
a triangle has 180 degrees in total
so adding the angles altogether we get 180
set the equation up like this
6x + 3 + 75 + 60 = 180
and then combine like terms
6x + 138 = 180
then subtract
6x = 42
and then finally divide
x = 7
Answer:
A) 7
Step-by-step explanation:
180-60=120
120-75= 45
45-3=42
42/6= 7
A) 7
Which is the net for this triangular prism?
1
Answer:
The first one
Step-by-step explanation:
I think, because if you fold it, it will form the shape.
5/3n-17=3n-25solve the equation
Answer:
n= 6
Step-by-step explanation:
Solve for n by simplifying both sides of the equation, then isolating the variable.
The table shows information about all students doing GCSE's at a school.
Year 10 Year 11 Total
Girls 60 110 170
Boys 140 80 220
Total 200 190 390
What fraction of the boys are in Year 11?
Give your answer in its simplest form
what is the importance of derivative classification?
Answer:
Classifying information helps to protect our national security
#Brainly lovers
The importance of derivative classification lies in its role in safeguarding sensitive information and ensuring national security. Derivative classification involves the process of determining the level of classification of information that is derived from a primary source.
what is the importance of derivative classification?Derivative classification is an essential aspect of information security and classification systems. It involves assigning the appropriate level of classification to information that is derived from a primary classified source. This process ensures that the derived information is protected and handled with the same level of care as its source material.
The importance of derivative classification lies in several key factors. Firstly, it helps prevent unauthorized disclosure of sensitive information. By classifying derived information, access to it can be controlled, limiting its availability to individuals with appropriate security clearances. This restriction ensures that only authorized personnel can access and handle the information, reducing the risk of it falling into the wrong hands.
Derivative classification promotes information sharing within authorized channels. When information is properly classified, it can be shared securely among individuals or organizations that have the necessary clearances. This controlled sharing allows for effective collaboration and coordination among different entities while maintaining the confidentiality of the information.
Read more about derivative classification here: https://brainly.com/question/18383880
#SPJ6
express the question below as function of angle less than 45°
[tex]cot330 [/tex]
step by step plzzz
At the basketball game, Leo scored points in 30% of his attempts. Which of the following statements is true?
A- Leo scored points in more than 1/3 of his attempts.
B- Leo scored points in 1/4 of his attempts.
C- Leo scored points in 3/10 of his attempts,
D- Leo scored points in less than 1/6 of his attempts.
THIS IS FOR A TEST, PLEASE HELP
Answer:
2/3
Step-by-step explanation:
irdk
brainliest for answers
Answer:
B
Step-by-step explanation:
if this is correct can i get brainliest and i hope this helps (:
What is the mean of a set of data?
The mean set of the data is the average, you find it by adding all the numbers up then dividing it by the amount of numbers added.
Which expressions are equivalent to this expression?
4x + 4
Select each correct answer.
2(2x+2)
4(x+4)
x + 3x + 4
2x + 1 + 2x + 3
Answer:
4(x+4)
Step-by-step explanation:
Answer:
2 ( 2x + 2 )
Step-by-step explanation:
4x = 2x * 2
4 = 2 * 2
4x + 4
= 2x * 2 + 2 * 2
= 2 ( 2x + 2 )
What is the slope of the line?
Answer:
The slope of this line is 2.
Step-by-step explanation:
The slope of a line can be calculated using the formula (y1 - y2) / (x1 - x2).
We take two points from the line. I took the points (0, -3) and (2, 1).
Now we plug in the coordinates into the formula. (-3 - 1) / (0 - 2).
This simplifies to -4 / -2 which is equal to 2.
One fifth of the earths atmosphere is oxygen. What fraction is not oxygen?
Answer:4/5ths hope this helped hunny boo!✨
Giving brainliest to correct answer
1/4 + 1/3 + 11/12 6/15 + 3/10 + 3/5
4/5 + 3/15 - 2/3 4 2/5 + 5 2/6
Step-by-step explanation:
0 = 0 = 0 = 0 = 0 = 0 = 0 < 3/
15
< 1/
4
< 3/
10
< 1/
3
< 6/
15
< 3/
5
< 4/
5
< 11/
12
< 4 2/
5
< 5 2/
6
0 is equal to 0 is equal to 0 is equal to 0 is equal to 0 is equal to 0 is equal to 0 is less than 3/
15
is less than 1/
4
is less than 3/
10
is less than 1/
3
is less than 6/
15
is less than 3/
5
is less than 4/
5
is less than 11/
12
is less than 4 2/
5
is less than 5 2/
6
0/
60
= 0/
60
= 0/
60
= 0/
60
= 0/
60
= 0/
60
= 0/
60
< 12/
60
< 15/
60
< 18/
60
< 20/
60
< 24/
60
< 36/
60
< 48/
60
< 55/
60
< 264/
60
< 320/
60
Step-by-step explanation:
[tex]6 \frac{2}{5} [/tex]
What triangle congruence theorem could be used to prove that these triangles are congruent?
Answer:
side angle side theorem
Step-by-step explanation:
Richard has 650 kilograms of candy bag then Ming has 137 kilograms. What is the total mass is the candy bag?
Answer:
787 kg
Step-by-step explanation:
what are the factor of 25
A.2,4,6,8,10
B.5,10,15,20,25
C.1,5,5
D.3,6,9
Cann someone please help??
option 1 is correct [5root2]
Answer:
It can be simplified to 5√2
Step-by-step explanation:
If lines l and m are parallel find the value of X
