Answers
\(\large\huge\green{\sf{Answer:-}}\)
\( \red {\mathbb{ \underline { \tt By \: using \: Pythagoras \: theorm}}}\)
\(h {}^{2} = p {}^{2} + b {}^{2} \\ x {}^{2} = (7 {}^{2} + 6 {}^{2} )ft {}^{2} \\ x {}^{2} = (49 +3 6)ft {}^{2} \\ x {}^{2} = 85 ft\\ x = \sqrt{85 } ft \\ \)
Answer:
\(\huge\boxed{\sf H = 9.2\ ft}\)
Step-by-step explanation:
Since the triangle is a right-angled triangle, we can apply Pythagoras Theorem on this triangle.
Pythagoras Theorem:
\((Hypotenuse)^2= (Base)^2+(Perpendicular)^2\)
Given:
Base = 6 ft
Perpendicular = 7 ft
Required:
Hypotenuse = x ft
Solution:
Put the givens in the above formula of the Pythagoras Theorem:
(x)² = (6)² + (7)²
(x)² = 36 + 49
(x)² = 85
Taking sqrt on both sides
x = 9.2 ft
\(\rule[225]{225}{2}\)
Hope this helped!
~AH1807Related Questions
Given the function f(x)=-x^2+x+3, determine the average rate of change of the function over the interval 0≤x≤7
Answers
The average rate of change of the function over the interval 0≤x≤7 is -6.857.
The average rate of change of a function over an interval is the slope of the line connecting the two points on the function at the endpoints of the interval. We can find this slope using the formula:
average rate of change = (f(x2) - f(x1)) / (x2 - x1)
In this case, our interval is 0≤x≤7, so x1 = 0 and x2 = 7. We can plug these values into the function to find f(x1) and f(x2):
f(x1) = f(0) = -(0)^2 + (0) + 3 = 3
f(x2) = f(7) = -(7)^2 + (7) + 3 = -45
Now we can plug these values into the formula for the average rate of change:
average rate of change = (f(x2) - f(x1)) / (x2 - x1)
average rate of change = (-45 - 3) / (7 - 0)
average rate of change = -48 / 7
average rate of change = -6.857
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i will make you brainly
PLEASE HELP
please kindly awnser 1 and 2 questions
these are all wrong awnsers a. Identify the student’s mistake with the given question.
b. Explain why the answer is incorrect, then demonstrate and explain the correct way to
answer the question.
Answers
Jeans are on sale with a 65% off. The jeans originally cost $72. What is the sales price?
Answers
As the sales price is 65% off you find the 65% of the original cost and then substract it from the original cost:
\(\begin{gathered} 72\cdot0.65=46.8 \\ \\ 72-46.8=25.2 \end{gathered}\)Then, the sales price is $25.2A random sample of n = 4 scores is obtained from a normal population with m = 30 and s = 8. what is the probability that the sample mean will be smaller than m = 22?
Answers
the probability that the sample mean will be smaller than m = 22 is 0.02275.
For the given question,
A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.
Here sample size, n = 4
mean, μ = 30
standard deviation, σ = 8
The probability that the sample mean will be smaller than m = 22 is
z = \(\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }\)
⇒ z =\(\frac{22-30}{\frac{8}{\sqrt{4} } }\)
⇒ z = \(\frac{22-30}{\frac{8}{2} }\)
⇒ z = \(-\frac{8}{4}\)
⇒ z = -2
Refer the Z table for p value,
Thus for P(z < -2) is 0.02275.
Hence we can conclude that the probability that the sample mean will be smaller than m = 22 is 0.02275.
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Write the polnt-slope form of the equation of the line passing through the points (-5, 6) and (0, 1).
y- 6 = 1(x + 5)
y+6= -1(x - 5)
y- 6 = -1(x + 5)
y+ 6 = 1(x - 5)
Answers
Answer:
y - 6 = -1 (x+5)
Step-by-step explanation:
1) First, find the slope of the line. Use the slope formula \(m = \frac{y_2-y_1}{x_2-x_1} \\\). Substitute the x and y values of (-5,6) and (0,1) into the formula and simplify like so:
\(m = \frac{(1)-(6)}{(0)-(-5)} \\m = \frac{1-6}{0+5} \\m = \frac{-5}{5} \\m = -1\)
So, the slope of the line is -1.
2) Now we have enough information to write the equation of the line in point-slope form. Use the point-slope formula \(y-y_1 = m (x-x_1)\) and substitute real values for the \(m\), \(x_1\), and \(y_1\).
Since \(m\) represents the slope of the line, substitute -1 in its place. Since \(x_1\) and \(y_1\) represent the x and y values of a point the line intersects, substitute the x and y values of (-5, 6) in those places as well. This gives the following equation and answer:
\(y-6 = -1(x+5)\)
Todd has a job mowing lawns for a landscaping company. In addition to getting a $30 bonus for each day he is called to work, he gets paid by the hour. If Todd earns $38.50 for working one hour, how much does Todd earn per hour? Round your answer to the hundredths place.
Todd earns $ per hour.
Answers
Answer: Todd earns 8.50 per hour
Step-by-step explanation: If todd earned $38.50 and he gets 30 extra a day 30 minus 30.50 is 8.50 and since he only worked for an hour he only got $8.50 which is what he makes per hour
Suppose the voltage in an electrical circuit varies with time according to the formula V(t) = 40 sin(t) for t in the interval [0,].
The numerical value of the mean voltage in the circuit is
Answers
The numerical value of the mean voltage is 25.47 V
To find the numerical value of the mean voltage, V of V(t) = 40 sin(t), we integrate V(t) with respect to t over the interval [0.π]
So,
\(V = \frac{1}{\pi } \int\limits^\pi _0 {V(t)} \, dt \\V = \frac{1}{\pi } \int\limits^\pi _0 {40sint} \, dt \\V = \frac{1}{\pi } [-40cost]_{0}{\pi } \\V = \frac{1}{\pi } -[40cos\pi - 40cos0]\\\\V = \frac{1}{\pi } (-[40 X (-1) - 40 X 1})\\V = -\frac{1}{\pi } [-40 - 40]\\V = \frac{80}{\pi } \\V = 25.465 V\)
V ≅ 25.47 V
So, the numerical value of the mean voltage is 25.47 V
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 Janet Henderson is a secretary. She works Monday to Friday every week. If she worked a
total of 44.5 hours this week, and her regular pay is $11.46 per hour. What is Janet's
overtime pay?
Answers
Answer: Janet's overtime pay is: " $ 17. 19 per hour ."
→ and specifically: " $ 77.36 " ;
→ [for the 4.5 hours of overtime pay worked Within the total 44.5 hours Janet worked within the particular Monday to Friday workweek as given within this particular Brainly question/].
__________
Step-by-step explanation:
__________
Note: Let us assume that up to and including "40 hours within a workweek" is paid as a "base rate of regular pay"—and that any hours worked over "40 hours" count as "overtime hours.."
Furthermore: Let us assume that "overtime pay" is paid at the rate of "time and a half". This means that any and all hours worked over 40 hours are "overtime hours"—and that these "overtime hours" are paid at the rate at "1.5 times" the rate of the regular hourly rate.
__________
Note: A secretary is typically a job that is paid by the "hour"; as opposed to certain management positions (which are paid by "salary").
→ So, we shall assume that the secretary, "Janet Henderson", is a "hourly worker"—who is "non-exempt" from being paid "overtime."
→ So, first, given: Janet Henderson worked Monday through Friday for a total of "44.5 hours."
Note: This amount: "44.5 hours" ; is over "40 hours."
{i.e. " [44.5 hours] > [40 hours] ".}.
Note: Any and all hours Janet earned in excess of 40 hours are considered : "overtime hours."
Now: Let us calculate the number of "overtime hours":
→ We subtract: "40"; from the actual amount of hours Janet worked [which is "44.5 hours"] ;
→ " (44.5 − 40) hours " ;
= " 4.5 hours " (of overtime worked).
Now, we are given that Janet's regular pay is: " $ 11.46 per hour."
→ To solve: Find the value of: " (1.5) * ($ 11.46) " ;
Method 1) Use a calculator: to get: " 17. 19 " .
→ The answer is: " $ 17.19 per hour."
Method 2)
→ " 11.46 + [(1/2)* 11.46] " ;
= "11.46 + (11.46 /2)" ;
Note: Let us start by calculating: "(11.46 / 2)" ; that is: "(11.46 ÷ 2)" .
Method A) Note: " 11.46 ÷ 2 = 5.73 " ; → {Using a calculator.}.
Method B)
Using long division; to get: "5.73 " ; as follows:
5.73
2⟌ 11.46
- 10
1.46
- 1.4
0.06
- 0.06
0.00 .
Now: We can write the expression:
→ " 11.46 + [(1/2)* 11.46] " ; as:
→ " 11.46 + 5.73 " ; & then calculate (add the values);
to get" 11.46 + 5.73 = " 17. 19 "
So; Janet's overtime pay is $17.19 per hour.
Other:
To find the specific, exact dollar amount of overtime pay earned for the "4.5 hours" of overtime worked in the particular Monday to Friday workweek as given within the actual question:
→ We multiply this amount—"17.19 dollars"— by the number of overtime hours that Janet worked—"4.5 hours"—as follows:
→ " \(\frac{17.19 dollars}{hr} *\frac{4.5 hr}{1}\) " ;
→ The units of "hr" ["hour(s)"] cancel out to: "1 ";
→ {since: ["hr/ hr " = 1 .] } ;
And we have:
→ " (17.19 dollars * 4.5) = _? dollars " ; Solve for: {the "_?_" value.}:
Using a caculator: We get:
→ 77.355 dollars; ⇒ write as: $77.355 ; round to: " $ 77.36 " .
________
Hope this is helpful to you!
Best wishes to you in your academic pursuits!
________
The final velocity of an object moving in one dimension is given by the formula v = u + at, where u is the initial velocity, a is the acceleration, and t is the time. Solve this equation for t.
To solve for t, first
both sides of the equation.
Answers
Given problem;
We are to make t, the subject of the expression v = u + at.
The equation is one of the equations of motion.
Usually, v is the final velocity, u is the initial velocity, a is the acceleration and t is the time taken.
To make "t" the subject of the expression; follow these steps;
v = u + at
Subtract "u" from both sides;v (-u) = u (-u) + at
2. the expression is now;
v - u = at
3. now multiply both sides by \(\frac{1}{a}\) to isolate "t";
\(\frac{1}{a}\)(v - u) = at x \(\frac{1}{a}\)
t = \(\frac{v - u}{a}\)
Answer:
First part (is subtract U from)
Step-by-step explanation:
Took the exam
There are 4 gallons of water in a tank. If a water bottle holds ¼ of a gallon of water, how many water bottles can be filled using all of the water in the tank?
Answers
Answer: 3
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
4 * 1/
4
= 4 · 1/
1 · 4
= 4/
4
= 1 · 4/
1 · 4
= 1
Kara is sending a gift to her grandmother. The gift is wrapped in a cube-shaped box with side lengths of 6 inches. She wants to use the shipping box that is closest to the size of her gift. The table shows the cube-shaped shipping boxes that the post office has available for her to use.
Which shipping box should Kara use?
A. Box A
B.Box B
C.Box C
D.Box D
Answers
Answer:
C. Box c
Step-by-step explanation:
Took this assignment the other day
Hope this helped
Answer:
C
Step-by-step explanation:
box c
Write some examples of interval variables
Answers
An interval variable is a type of quantitative variable, where the difference between two values of the variable is meaningful and the values can be ordered.
Examples of interval variables include temperature (in Celsius or Fahrenheit), time (in seconds, minutes, hours, etc.), and dates. You can calculate the difference in temperature between two points, the length of time between two events, or the number of days between two dates. For example, let's say that the temperature outside is 25°C at noon and 29°C at 4 pm. The interval variable is the temperature, and the difference between the two temperatures is 4°C (29°C - 25°C = 4°C). Another example is the length of time between two events. Let's say that Event A began at 1 pm and Event B began at 2 pm. The interval variable is the length of time between the two events and the difference between the two times is 1 hour (2 pm - 1 pm = 1 hour). Finally, let's say that Date A is January 1, 2020 and Date B is January 10, 2020. The interval variable is the number of days between the two dates, and the difference between the two dates is 9 days (January 10,)An interval variable is a type of quantitative variable, where the difference between two values of the variable is meaningful and the values can be ordered.
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Declaring variables - Declare two integer variables x and y, - Assign them any values. - Print addition/subtraction/multiplication and division of these two variables on to the screen
Submission Task (- Grade 1%) Follow the same steps asin Exercise 2, but change the step 2 to ask the user for input forthese values by using Scanner class.
Answers
Two integer variables x and y, prompts the user to enter values for them using the Scanner class, and performs addition, subtraction, multiplication, and division operations on those variables:
import java.util.Scanner;
public class VariableOperations {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
System.out.print("Enter the value for x: ");
int x = scanner.nextInt();
System.out.print("Enter the value for y: ");
int y = scanner.nextInt();
// Addition
int addition = x + y;
System.out.println("Addition: " + addition);
// Subtraction
int subtraction = x - y;
System.out.println("Subtraction: " + subtraction);
// Multiplication
int multiplication = x * y;
System.out.println("Multiplication: " + multiplication);
// Division
if (y != 0) {
double division = (double) x / y;
System.out.println("Division: " + division);
} else {
System.out.println("Cannot divide by zero.");
}
}
}
This code prompts the user to enter values for x and y, performs the four basic arithmetic operations, and displays the results on the screen.
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Expedition Everest, a major thrill ride at Walt Disney World, often has a demand of over 3,000 riders an hour causing long waiting times for guests wishing to ride. The attraction averages 1,800 riders an hour. The roller coaster has a design capacity of 2,050 riders an hour and an effective capacity of 1,900 riders an hour.
a. What is the efficiency of Expedition Everest?
b. What is the utilization of Expedition Everest?
c. Is the operation overcapacity or undercapacity?
Answers
a. The efficiency of Expedition Everest is approximately 87.8%.
b. The utilization of Expedition Everest is approximately 94.7%.
c. The demand is greater than the effective capacity, the operation is considered overcapacity. This means that the ride cannot accommodate all the riders who wish to ride, resulting in long waiting times for guests.
To calculate the efficiency and utilization of Expedition Everest, we need to compare the actual number of riders with the design capacity and effective capacity.
Given:
Demand = 3,000 riders/hour
Average riders = 1,800 riders/hour
Design capacity = 2,050 riders/hour
Effective capacity = 1,900 riders/hour
a. Efficiency:
Efficiency is calculated as the average riders divided by the design capacity, multiplied by 100%.
Efficiency = (Average riders / Design capacity) * 100%
= (1,800 / 2,050) * 100%
≈ 87.8%
Therefore, the efficiency of Expedition Everest is approximately 87.8%.
b. Utilization:
Utilization is calculated as the average riders divided by the effective capacity, multiplied by 100%.
Utilization = (Average riders / Effective capacity) * 100%
= (1,800 / 1,900) * 100%
≈ 94.7%
Therefore, the utilization of Expedition Everest is approximately 94.7%.
c. Capacity Analysis:
To determine if the operation is overcapacity or undercapacity, we compare the demand with the effective capacity.
Demand > Effective capacity
3,000 > 1,900
Since the demand is greater than the effective capacity, the operation is considered overcapacity. This means that the ride cannot accommodate all the riders who wish to ride, resulting in long waiting times for guests.
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Tony bought a $25 hornets t-shirt and used a coupon for a 25% discount. Keith bought an identical t-shirt at a different store for $19.95. which statement is true?
A.Tony paid $2.55 less than keith paid.
B.Tony paid $1.20 less than keith paid.
C.Keith paid $2.55 less than tony paid.
D.Keith paid $1.20 less than tony paid.
Answers
Answer: Tony paid $1.20 less than Keith paid.
Step-by-step explanation: Easy math, try asking your teacher for help. It takes time.
determine whether the following graph represents a function
1. one to one function
2. Not a function
3. Function, but not one to one
Answers
Answer:
3. function, but not one to one
Step-by-step explanation:
If you do a vertical line test anywhere you draw a vertical line will only hit in one spot
If you do a horizontal line test to check If the line is one to one it hits in multiple spots therefore the line that is graphed is a function but not one to one
Emma invested $630 in an account in the year 1997, and the value has been growing exponentially at a constant rate. The value of the account reached $840 in the year 2002. Determine the value of the account, to the nearest dollar, in the year 2005.
Answers
Answer:
$966
Step-by-step explanation:
Given that $630 was invested in 1997
At a constant rate the value grew to $840 in 2002.
This implies that $210 was gotten in 5years:
$(840-630)=$210
and 2002-1997= 5years
therefore, to determine the value of the account in 2005: 2005-1997=8years
$210=5years
$x=8years
CROSS MULTIPLY
5x= 210×8
5x=1680
x=$336
Value of account in 2005 will be: $630+$336=$966
Therefore $966 was made in the next 8years(2005).
HELPPPP!!!!!!!!! SIMPLIFY THE EXPRESSION!!!!!!!!!!!
(9ab^-5)^-2
Answers
Step-by-step explanation:
The lengths of the sides of a triangle are consecutive integers. If the perimeter of the triangle is 111, find the lengths of the sides.
Answers
Answer:
we know
perimeter of triangle = sum of all sides
here lengths of sides are consecutive integers so
length of three sides = x, (x+1) and (x+2)
now
Perimeter = 111
or, x + (x+1) + (x+2) = 111
or 3x + 3 = 111
or 3x = 108
x = 36
x = 36
(x+1) = 36 + 1 = 37
(x+2)= 36 + 2 = 38
Can anyone help me and show proof of how I got the answer
Answers
The y intercept is the point at which the line/curve cuts the y axis
The curve cuts the y axis at point (0 , 22) so the y intercept is therefore
(0 , 22)
1. Solve for the unknown in each triangle. Round each answer to the nearest tenth.
Answers
The values of the missing sides are;
a. x = 35. 6 degrees
b. x = 15
c. x = 22. 7 ft
d. x = 31. 7 degrees
How to determine the valuesTo determine the values, we have;
a. Using the tangent identity;
tan x = 5/7
Divide the values
tan x = 0. 7143
x = 35. 6 degrees
b. Using the Pythagorean theorem
x² = 9² + 12²
find the square
x² = 225
x = 15
c. Using the sine identity
sin 29= 11/x
cross multiply the values
x = 11/0. 4848
x = 22. 7 ft
d. sin x = 3.1/5.9
sin x = 0. 5254
x = 31. 7 degrees
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About 1/10 of the bones in your body are in your skull. Your hands have about 1/4 of the bones in your body . Write and solve an equation to find the fraction of the bones in your body that are in your hands or skull.
Answers
Answer:
Step-by-step explanation:
so to get the answer, we just add the number of bones in your hands and bones in your skull1/4 (bones in hands) + 1/10 (bones in skull)we can only add fractions that have the same denominator (bottom number in a fraction) so we change the numbers to have a common denominator:5/20 + 2/20 = 7/20so 7/20 of your bones are in your hands or skull
What is the answer to this geometry question?
Answers
Answer:
88cm^3
Step-by-step explanation:
The volume of a pyramid is the base times height divided by 3. First, we can find the area of the base. We have a right triangle with a base of 8 and a height of 6. The area of a triangle is the base times height divided by 2. This gives us:
8 * 6 ÷ 2 = 24cm^2
We can see that 11cm is the height as it is perpendicular to the base. We can set up an expression from the formula mentioned at the beginning:
11 * 24 ÷ 3 = 88cm^3
If sec θ =25/24, find cot θ.
A. cot θ =10/7 B. cot θ = 24/7
C. cot θ =23/25 D. cot θ = 25/23
Answers
Answer:
24/7
Step-by-step explanation:
cos(theta)=24/25
so draw right triangle
you get the length of each side be
7 24 25
(you must draw a picture)
then the answer would be 24/7
Which of the points a(8, 0, 6), b(9, 6, 2), and c(2, 9, 3) is closest to the yz-plane? which point lies in the xz-plane?
Answers
The point closest to -
the yz-plane is c(2, 9, 3).the xz-plane is a(8, 0, 6).What is a plane in 3-D?A plane is a two-dimensional flat surface that can extend indefinitely. A plane would be the two-dimensional equivalent of a point with zero dimensions, a line with one dimension, and three-dimensional space.
The equation is written on a three-dimensional plane is;ax+by+cz+d=0,
where minimum one number out of a, b, and c must be non-zero.
In 3D coordinate space, a plane is defined by a point and a vector perpendicular to the plane.Now, as per the question;
A point (x, y, zdistance )'s from the yz plane is equal to |x|.
As a result, for small |x|, the point would be closest to the yz plane.
C does have the smallest among A, B, and C that is |x| = 2.
Thus, c point is closest to yz-plane.
If the point is in the xz-plane, after which y equals 0.
Only A has a y value of zero.
As a result, A is in the xz-plane.
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c) After this tax is collected you can assume that these funds are gone and that no goods or services are purchased with them, and no government employees are paid with this tax revenue. Determine the impact the tax has on the steady state levels of capital per worker \& consumption per worker. Sketch a diagram showing the impact of this shock. Explain what impact the shock has on the level and growth rate of the standard of living (as measured by output per worker) in steady state. ( 8 points)
d) Suppose instead, after the tax is collected, the government is able to use these funds to create and implement plans that cause the growth rate of labour augmenting technological change to rise to 3% per year. Determine the impact the tax has on the steady state levels of capital per effective worker, output per effective worker \& consumption per effective worker. Sketch a diagram showing the impact of this shock. Explain what impact the shock has on the level and growth rate of the standard of living (as measured by output per worker) in steady state. ( 10 points)
Answers
The shock in part (c) leads to a decrease in capital per worker and consumption per worker, potentially affecting the standard of living. In contrast, the shock in part (d) leads to an increase in output per effective worker, which can positively impact the standard of living.
(c) When the tax funds are assumed to be gone without any goods or services purchased or government employees paid, it implies that the tax revenue is completely removed from the economy. In this case, the impact on the steady state levels of capital per worker and consumption per worker would depend on the specific economic model and assumptions.
Generally, the removal of tax revenue would lead to a reduction in both capital per worker and consumption per worker. The exact magnitude of the impact would depend on various factors, such as the marginal propensity to consume and the saving behavior of individuals. In steady state, the reduction in capital per worker could lead to lower productivity and potentially lower output per worker, affecting the standard of living.
To sketch a diagram showing the impact of this shock, you would typically have the levels of capital per worker and consumption per worker on the y-axis and time or steady state on the x-axis. The diagram would show a downward shift in both the capital per worker and consumption per worker curves, indicating a decrease due to the removal of tax revenue.
(d) When the tax funds are used by the government to implement plans that increase the growth rate of labor-augmenting technological change to 3% per year, it implies that the tax revenue is directed towards productivity-enhancing investments or policies. In this case, the impact on the steady state levels of capital per effective worker, output per effective worker, and consumption per effective worker can be analyzed.
The increase in the growth rate of labor-augmenting technological change would lead to higher productivity and potentially higher output per effective worker in steady state. This increase in output per effective worker could also translate into higher consumption per effective worker, depending on the saving and consumption behavior.
To sketch a diagram showing the impact of this shock, you would typically have the levels of capital per effective worker, output per effective worker, and consumption per effective worker on the y-axis and time or steady state on the x-axis. The diagram would show an upward shift in the output per effective worker curve, indicating an increase due to the improved technological change.
Overall, the shock in part (c) leads to a decrease in capital per worker and consumption per worker, potentially affecting the standard of living. In contrast, the shock in part (d) leads to an increase in output per effective worker, which can positively impact the standard of living.
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On Wednesday, a local hamburger shop sold a combined total of 339 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold?
Answers
Answer:
113
Step-by-step explanation:
c/b(cheeseburger)-2x
h/b(hamburgers)-x
2x+x=339
3x=339(divide both sides by 3)
x=113
Using the Distributive Property to Solve
Solve to find the value for x in the linear equation: 36-4x + 5) = 12
1. Use the distributive property:
3(-4x) + 3(5) = 12
-12x + 15 = 12
-12x + 15 - 15 = 12 - 15
-12x = -1
Use the subtraction property of equality:
Division property of equality
Y
Intro
Done
Answers
Answer:
-4x=-29 or 4x-29
step-by-step explanation
This is Section 4.3 Problem 46: A driver driving on an straight south-north highway records the velocity of the car in the hours after he leaves home at 11:00AM: v(t) = 54t − 24t2 , where t , in hours, measures the time passed after 11:00AM, and v is in miles per hour. Using a definite integral, it is determined that at 1:00PM, the driver is miles ---Select--- from his home.
Answers
Using the definite integral, it is determined that the driver is 108 miles from his home at 1:00 PM.
We need to find the distance travelled by the driver between 11:00 AM and 1:00 PM.
The velocity of the driver is given by v(t) = 54t − 24t^2.
We can find the distance travelled by finding the definite integral of v(t) with respect to t, between 0 and 2 (since the driver leaves at 11:00 AM and we need to find the distance travelled by 1:00 PM, which is 2 hours later).
\(\int\limits^0_2\)v(t) dt = \(\int\limits^0_2\)(54t − 24t²) dt
= [27t² - 8t³] between 0 and 2
= [27(2)² - 8(2)³] - [27(0)² - 8(0)³]
= 108 - 0
= 108 miles
Therefore, the driver is 108 miles away from his home at 1:00 PM.
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What would be the angle measures for ∠X, ∠Y and ∠Z? Type your answers in the blanks below.
PLEASE HELPP i might faill!!! C:
Answers
X=30
Y=60
Z=90
Answer:
X=30 Y=60 Z=90
Step-by-step explanation:
When you dilate the triangle the angles don’t change and they are similar triangles so you just follow the order QRS the X would have the same angle as the Q, Y would have the same angle as R and Z would have the same angle as S.