In the context of a function representing temperature over time, the derivative f'(x) indicates the rate of change of the temperature with respect to time.
If a function f(x) represents the temperature in degrees as a function of time in minutes, the function f'(x) represents the rate of change of temperature with respect to time. This implies that if you have the temperature reading from a thermometer at different times, f'(x) tells you how quickly the temperature is rising or falling at any given moment. The concept of the derivative as the rate of change applies to many types of functions beyond just temperature over time.
2. Dan poured 5 cups of water into a rectangular container measuring 8 inches by 6 inches by 7 centimeters.
[1 cup = 14.44 cubic inches; 1 inch = 2.54 cm]
Part A: What is the maximum volume of water that the rectangular container can hold? Show your work. (3 points)
Part B: How many cubic inches of water was poured into the container? (3 points)
Virginia beach is about 20 miles wide and 28 miles long. if one inch of rain falls there during a daily rain shower, how many cubic feet of rain fell? (convert all units to feet first)
One less than twice a number is greater than 7 and less than 13. Write a compound inequality to represent this and solve to find the solution set.
A stuntwoman jumps from a building 73ft high and lands on an air bag that is 9ft tall. Her height above ground h in feet can be modeled by h (t) = 73 – 16 t^2, where t is the time in seconds.
a. How many seconds will the stuntwoman fall before touching the air bag? (Hint: Find the time t when the stuntwoman’s height above ground is 9 ft.)
When maggie applies the brakes of her car, the car slows uniformly from 15.0 m/s to 0 m/s in 2.50 s. how many meters before a stop sign must she apply her brakes in order to stop at the sign?
Use the distributive property to simplify the expression. 8(3x + 4)
Answer:
24x + 32
Step-by-step explanation:
Answer:
24x+32
Step-by-step explanation:
trust
complete the next three terms in the pattern below
The sum of three numbers is 62. The second number is equal to the first number diminished by 4. The third number is four times the first. What are the numbers?
Which three expressions could be used to represent the numbers?
1st number = x
2nd number = x-4
3rd number = 4x
now you have x + x-4 +4x = 62
combine like terms
6x-4 = 62
add 4 to each side
6x = 66
divide both sides by 6
x = 66/6 = 11
1st number = 11
2nd number = 11-4 = 7
3rd number = 4*11 = 44
11+7+44 = 62
N the ideal normal curve, 95% of the population falls within _____ standard deviation(s) of the mean. a. one b. two c. three d. four
Simplify 3^5/3^2.
I do have a basic understanding but I need help on this.
Anyone wanna help teach me how to do any of this or just give me the answers if you don't wanna teach me
just replace the value in the appropriate equation:
a) says f(-2)
so use the f equation above it and replace x with -2
f(x) = 3x-5 becomes f(-2) = 3x-5 =
3(-2)-5 = -6-5 = -11
for b use the equation for h and replace x with -5
so x^2 - 6 = -5^2 - 6 = -31
for c use the equation for g and replace x with (a+b)
-7x+3 =
-7(a+b)+3 = -7a-7b+3
Tucker drove at a speed of 45 miles per hour. This means that Tucker traveled _______ feet per second.
Answer:
the answer is 66 feet per second.
How many times does 15000 go in to 3000000?
To determine how many times 15000 goes into 3000000, divide 3000000 by 15000. The answer is 200.
To find out how many times 15000 goes into 3000000, we need to perform a simple division.
We divide 3000000 by 15000:
3000000 ÷ 15000 = 200
Thus, 15000 goes into 3000000- 200 times.
What is the quotient of (7^-1/7^-2)?
Answer:
7^1 = 7
Step-by-step explanation:
we need to find quotient of [tex]\frac{7^-1}{7^-2}[/tex]
The exponents are in division
When the base of exponents are same and exponents are in division then we subtract the exponents
We apply the property [tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
[tex]\frac{7^-1}{7^-2}=7^{-1-(-2)}=7^{-1+2}=7^1=7[/tex]
what's the equation of the line parallel to the equation 2x+6y=-4 and that passes through the point (3, -3) .
Prove the diagonals of the square with vertices P (0,4), Q (4,4), R (0,0) and S (4,0) are perpendicular bisectors of each other.
Step 1: calculate the slope of the diagonals.
The slope of diagonal PS is ____
The slope of diagonal QR is ____
Step 2: calculate the midpoint of the diagonals
The midpoint of PS is ___
Midpoint of QR is ___
The diagonals are perpendicular because the product of their slope is -1, and their midpoint is same (2,2). Hence, it is proved that the diagonals of the given square are perpendicular bisectors of each other.
Given information:
The square with vertices P (0,4), Q (4,4), R (0,0) and S (4,0).
It is required to prove that the diagonals of the given square are perpendicular bisectors.
First, calculate the slope of the diagonals.
The slope of diagonal PS will be,
[tex]m = \dfrac{0-4}{4-0}\\m = -1[/tex]
So, the slope of diagonal PS is -1.
The slope of diagonal QR will be,
[tex]m' = \dfrac{0-4}{0-4}\\m' = 1[/tex]
So, the slope of diagonal QR is 1.
From the slope of the diagonals, the diagonals are perpendicular because the product of slope is -1.
Now, it is required to find the mid-point of the diagonals.
The midpoint of PS will be,
[tex](x,y)=(\dfrac{0+4}{2},\dfrac{4+0}{2})=(2,2)[/tex]
Midpoint of QR will be,
[tex](x,y)=(\dfrac{4+0}{2},\dfrac{4+0}{2})=(2,2)[/tex]
So, the midpoint of both the diagonals is also same.
Therefore, it can be said that the diagonals are perpendicular because the product of their slope is -1, and their midpoint is same (2,2). Hence, it is proved that the diagonals of the given square are perpendicular bisectors of each other.
For more details, refer to the link:
https://brainly.com/question/3417399
Answer:
-1, 1, (2,2), (2,2), and perpendicular and share the same midpoint
Step-by-step explanation:
is this right? putting that into scientific notation
4.6 x 10 ^8 = 460,000,000
you are correct
The function c = 2.50(n – 2) + 4.50 represents the cost c in dollars of printing n invitations. Which of the following is not true?
A/Each invitation costs $4.50 to print.
B/The cost depends on the number of invitations printed.
C/For each additional invitation, it costs an extra $2.50 to print.
D/One cannot print just one invitation.
The equation c = 2.50(n - 2) + 4.50 represents the cost of printing n invitations, with $4.50 being a fixed cost and $2.50 as the additional cost per invitation after the first two. Thus, the statement that A. each invitation costs $4.50 to print is not true.
The function in question, c = 2.50(n – 2) + 4.50, represents the total cost c of printing n invitations. To determine which of the provided statements is not true, we can analyze the components of the equation:
4.50 is a fixed cost, indicating a base charge that is applied regardless of the number of invitations printed.The term 2.50(n – 2) shows that each additional invitation, beyond the first two, incurs a variable cost of $2.50.Analyzing the provided options:
Each invitation costs $4.50 to print. This statement is false, as the $4.50 in the equation is a fixed cost and not reflective of the individual cost per invitation.The cost depends on the number of invitations printed. This is true as the cost increases with each additional invitation after the first two.For each additional invitation, it costs an extra $2.50 to print. This is true given the variable cost component of the equation.One cannot print just one invitation. There is nothing in the equation that inherently prevents printing one invitation, so this statement is true.Therefore, the answer to the student's question is option A: Each invitation costs $4.50 to print is not true.
In 1 1/2 h, a lawnmower uses 2 1/16 gal of fuel. How many gallons of fuel did the lawnmower use each hour?
Answer:
[tex]\frac{11}{8}[/tex] [tex]\text{gallons}[/tex]
Step-by-step explanation:
Given: In [tex]1\frac{1}{2}[/tex] hour, a lawnmower uses [tex]2\frac{1}{16}[/tex] gallon of fuel.
To Find: How many gallons of fuel did the lawnmower use each hour.
Solution:
Number of hour lawnmower used [tex]=1\frac{1}{2}[/tex] [tex]\text{hour}[/tex]
[tex]\frac{3}{2}[/tex] [tex]\text{hour}[/tex]
Fuel consumed by lawnmower [tex]=2\frac{1}{16}[/tex] [tex]\text{gallon}[/tex]
[tex]\frac{33}{16}[/tex] [tex]\text{gallon}[/tex]
Fuel used by lawnmower each hour [tex]=\frac{\text{Total fuel used}}{\text{Total time taken}}[/tex]
[tex]=\frac{\frac{33}{16}}{\frac{3}{2}}[/tex]
[tex]=\frac{11}{8}[/tex] [tex]\text{gallon}[/tex]
Hence the fuel consumed by lawnmower each hour is [tex]=\frac{11}{8}[/tex] [tex]\text{gallon}[/tex]
The mesaure of an angles supplement is 28 more than 3 times the measure of the angle. find the measure o the angle and its suplment
What is the perimeter of a rectangular garden with a width of 24 feet and a diagonal of 40 feet?
Simplify the following expression 5^2-4/5+2
To simplify the expression 5^2-4/5+2, we first simplify the exponent, divide 4 by 5, and add the results together to get 129/5 or 25.8.
Explanation:To simplify the expression 5^2-4/5+2, we need to follow the order of operations which is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).
Using PEMDAS, we first simplify the exponent, so 5^2 = 5 x 5 = 25.
Next, we divide 4 by 5 to get 4/5.
Finally, we add 25 and 4/5 which can be written as 25 + 4/5. To add these two fractions, we need a common denominator which is 5. Converting 25 into a fraction with a denominator of 5 gives us 125/5. Adding 125/5 and 4/5 gives a result of 129/5. Therefore, the simplified expression is 129/5 or 25.8.
An angle is a right angle if and only if the measure of the angle is 90°. True or false?
If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability that all 4 cards are diamonds
Determine the x- and y-intercepts of the graph of y=−12x−4 . Then plot the intercepts to graph the equation.
Answer:
X-Intercept: [tex]\frac{4}{-12}[/tex]
Y-Intercept: -4
Step-by-step explanation:
Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.
The X and Y intercepts show at what points the function values cross the X and Y axis. We can solve for the X-intercept by substituting the value of y for 0 and then solving for x. Like so...
[tex]0=-12x-4[/tex] .... add 4 on both sides
[tex]4=-12x[/tex] ... divide both sides by -12
[tex]\frac{4}{-12}[/tex] = -x
Now we can see that the X-Intercept is [tex]\frac{4}{-12}[/tex] . Now we substitute 0 for x and solve for the Y-intercept.
[tex]y=-12(0)-4[/tex]
[tex]y= -4[/tex]
Finally we can see that the Y-intercept is -4
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Which expression is equal to 2√ -32 ? 8i√2 −8√2 8√2i −8i√2
the first one is the answer
Final answer:
The expression 2√ -32 is equal to 8i√2
Explanation:
To find an expression equal to 2√ -32, we need to recall that the square root of a negative number involves an imaginary unit i. The square root of -1 is defined as i. Thus, we can rewrite the expression as:
2√ -32 = 2√(-1 × 32) = 2√(-1)√(32) = 2i√(16 × 2) = 2i × 4√2 = 8i√2.
which is found by using the property that the square root of -1 is the imaginary unit i.
This demonstrates that the correct expression equivalent to the original one is 8i√2.
What is the period of y = 3cot(4x - 3pi)
Answer:
.25
Step-by-step explanation:
PLATO
The answer is y=25.
What's the period formula?Every whole oscillation, known as the length, is steady. The method for the duration T of a pendulum is T = 2π square root of√L/g, where L is the period of the pendulum and g is the acceleration because of gravity.
What are period and frequency?Frequency refers to how often something occurs. period refers back to the time it takes something to take place. Frequency is a rate amount. The period is a time amount. Frequency is the cycles/second.
Learn more about the Period here: https://brainly.com/question/558692
#SPJ2
Find the quotient of 10/5
Standard deduction on federal income tax return for head of the household is $8350. hilda, a single mom of two, paid $6780 in state income tax and $1230 in mortgage interest last year. how should she file her taxes?
The answer is Claiming standard deduction
Answer:
Hilda can file her taxes by claiming standard deduction.
Step-by-step explanation:
Standard deduction is that amount of someone's income, for which tax is not to be paid, thus reducing the tax bill amount. The amount of the standard deduction is based on one's filing status, age, disability, dependency etc.
Here in this scenario, Hilda can claim standard deductions.
anyone good at trigonometry please help
to find the vertical height
multiply the tangent of the angle by the horizontal distance
so tan(12) x 5 = 1.0628
rounded to nearest hundredth = 1.06 miles