The speed limit on a highway is 70 miles per hour. About how fast is this in miles per minute?
A fireman, 57.6 m away from a burning building, directs a stream of water from a fire hose at an angle of 35.2° above the horizontal. if the initial speed of the stream is 42.7 m/s, at what height will the stream of water strike the building?
First calculate the time it takes to reach the building using the x-component of the velocity.
t = 57.6 m / (42.7 m/s * cos35.2) = 1.65 s
Then we calculate the height y using the y-component of the velocity:
y = (42.7 m/s * sin35.2) * 1.65 s – 0.5 (9.81 m/s^2) (1.65 s)^2
y = 11.26 m
Final answer:
Using principles of projectile motion and given the initial speed, angle of projection, and horizontal distance, the stream of water from the fire hose will strike the building at a height of approximately 20.3 meters.
Explanation:
To determine at what height the stream of water will strike the building, we need to apply the principles of projectile motion. We are given the initial speed of the water stream (42.7 m/s), the angle of projection (35.2 degrees), and the horizontal distance from the fireman to the building (57.6 meters).
First, we separate the initial velocity into horizontal (ux) and vertical (uy) components:
ux = u * cos(θ) = 42.7 m/s * cos(35.2°) = 42.7 m/s * 0.8192 ≈ 35.0 m/s
uy = u * sin(θ) = 42.7 m/s * sin(35.2°) = 42.7 m/s * 0.5759 ≈ 24.6 m/s
Next, we use the formula for the horizontal motion to find the time (t) it takes for the water to reach the building:
x = ux* t => 57.6 m = 35.0 m/s * t => t ≈ 1.65 s
Finally, we can calculate the vertical distance (y) using the time and the vertical component of the velocity:
y = uy*t - (1/2) * g * t2 = 24.6 m/s * 1.65 s - (0.5 * 9.81 m/s2 * (1.65 s)2) ≈ 20.3 m
Therefore, the stream of water will strike the building at a height of approximately 20.3 meters above the ground.
What is the place value of the2 in 324 and 0.324
Compute, in centimeters and in meters, the height of a basketball player who is 6 ft 6 in. tall.
Answer:
Height in cm =198.12 cm
Height in m =1.9812 m
Step-by-step explanation:
To make this conversion we have to get the conversion rate from feet and inches to centimeters.
Each feet is 30.48 cm. And each inch is 2.54 cm This is the rate of conversion.
So, to get the height of the basketball player we have to multiply the height in feet and inches by the rate.
6 ft x 30.48 cm= 182.88 cm
6 in x 2.54 cm= 15.24 cm
Adding both, height in cm =198.12 cm
Rate of conversion cm to m= 100 cm are a meter
We divide the height in cm by 100 to get the height in m
Height in m =1.9812 m
What is the domain of f(x) = 3x?
Answer:
C. All real numbers.
Step-by-step explanation:
We have been given a function [tex]f(x)=3^x[/tex]. We are asked to find the domain of our given function.
We know that domain of a function is all values of x for which a function is real and defined.
We know that the domain of an exponential function is all real values of x that is [tex](-\infty,\infty)[/tex].
Since our given function is an exponential function, therefore, domain of our given function is all real numbers.
The domain of a function is the set of input values the function can take.
The domain of f(x) = 3x is (c) all real numbers
The function is given as:
[tex]f(x)=3x[/tex]
The above function is not restricted to any input value.
This means that, x can assume any real number as its value, and the function will still be defined.
Hence, the domain of f(x) = 3x is (c) all real numbers
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An apartment has 918 square feet of carpeting. How much is this in square meters? Use the following conversion: 1 square meter is 10.8 square feet.
The area of the apartment in square meters will be 85 square meters.
Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
Given that an apartment has 918 square feet of carpeting. The area of the apartment in square meters will be calculated as:-
As we know that 1 square meter is equal to 10.8 square feet.
10.8 square feet = 1 square meter
918 square feet = 918÷10.8
918 square feet = 85 square meters
Therefore, the apartment will have an area of 85 square meters.
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What is 0.81 as a fraction when the 81 is repeating?
Circle D is shown with the measures of the minor arcs. Which segments are congruent? EH and EF GH and FE FG and EH EF and GF
Answer:
The answer is D or "EF and GF"
Step-by-step explanation:
Priscilla has 56 stickers in her collection. Write the prime factorization of 56
Answer:
Prime factorization: 56 = 2 x 2 x 2 x 7.
Step-by-step explanation:
Given : 56
To find : Write the prime factorization.
Solution : We have given number 56.
Prime factorization : Factors of 56 as prime number
56 = 56 = 1 x 56, 2 x 28, 4 x 14, or 7 x 8.
Prime factorization: 56 = 2 x 2 x 2 x 7
Therefore, Prime factorization: 56 = 2 x 2 x 2 x 7.
find the reciprocal 8
If y= -6 when x= -24 what is the value of x when y= -7
Make s the subject of the formula t to the power of 2
= 2p+as
How do you solve for this show steps for it
Which is the graph of f(x) = 100(0.7)x?
Answer:
a
Step-by-step explanation:
A single six-sided die is rolled. find the probability of rolling a number less than 3
Can someone PLEASE help me with this? ^^^ (25 points)
what adds to be the bottom number but also multiplies to the top
A class of 144 students voted for a class president. Three fourths of the students voted for you. Of the students who voted for you, 5/9 are female. How many female students voted for you?
Dr. Hong prescribed 0.019 liter more medicine than Dr. Tannenbaum. Dr. Evans prescribed 0.02 less than Dr. Hong. Who prescribed the most medicine. Who prescribed the least
Who prescribed the
most medicine?
It would be Dr. Hong. This is because Dr. Hong has prescribed more than Dr.Tannenbaum and Dr.Evans.
Who prescribed the least?
It would be Dr.Evans. Because he has prescribed 0.02
less than Dr.Hong and 0.01 less than Dr.Tannenbaum.
Dr. Hong prescribed most medicine and Dr. Evan prescribed less medicine among all other doctors.
Further explanation:
Given:
Dr. Hong prescribed 0.019 liter more medicine than Dr. Tannenbaum.
Dr. Evans prescribed 0.02 liter less than Dr. Hong.
Calculation:
Consider Dr. Tannenbaum prescribed x liter medicine.
It is given that the Dr. Hong prescribed 0.019 liter more than the Dr. Tannenbaum.
Therefore Dr. Hong prescribed [tex]x+0.019{\text{liter}}[/tex] medicine.
It is also given that the Dr. Evans prescribed 0.02 liter less than Dr. Hong.
Therefore, Dr. Evans prescribed [tex]\left({x+0.019-0.02}\right){\text{liter}}[/tex] medicine.
So the Dr. Evans prescribed exactly [tex]\left({x-0.001}\right){\text{liter}}[/tex].
Therefore the medicine prescribed by Dr. Hong is [tex]\left({x+0.019}\right){\text{liter}}\\[/tex].
The medicine prescribed by Dr. Tannenbaum is x liters.
The medicine prescribed by Dr. Evans is [tex]\left({x-0.001}\right){\text{liter}}[/tex].
Arrange all doctors in ascending order with their prescribed medicine.
Dr. Hong > Dr. Tannenbaum > Dr. Evans
So it is obtained from the above expression that the Dr. Evans prescribed less medicine and Dr. Hong prescribed most medicine than other doctor.
Thus, Dr. Hong prescribed most medicine and Dr. Evans prescribed less medicine among all other doctors.
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Algebraic expression
Keywords:
Dr. Hong, Dr. Tannenbaum, Dr. Evans, medicine, Doctor, prescribed, less, more, liter.
please help me what is 1462 ÷ 58 as a mixed number then put it in simplest form
evaluate -x+y+6 for x=-3 and y=-1
area of rectangular window is 360 square centimeters if the length of the window is bigger than the width of the window by 4 centimeters what are the dimensions
Determine the number(s), x, between 0 and 2π where the line tangent to the function f(x)=2sin(x)+2cos(x) is horizontal.
Determine whether the equation defines y as a function of x. y equals = 8 Over x Does the equation define y as a function of x?
Yes, the equation defines y as a function of x.
Yes, the equation defines y as a function of x.
A function is a relation where each input x corresponds to exactly one output y. In this equation, y is defined as 8 over x. For any given value of x, the equation will give us a unique value for y. For example, if we plug in x = 2, y = 8/2 = 4. If we plug in x = 4, y = 8/4 = 2.
Thus, this equation defines y as a function of x.
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7x2 + 7y2 − 28x + 42y − 35 = 0. in standard form
Answer:
[tex](x-2)^2+(y+3)^2=18[/tex]
Step-by-step explanation:
This is a circle. It already is in standard form, so maybe you mean work form? I'll go with that, since there's nowhere else to go!
Let's group the x terms together and the y terms together and move the constant to the other side of the equals sign first.
[tex]7x^2-28x+7y^2+42y=35[/tex]
In the world of conics, this is a circle because the leading coefficients on the x-squared term and y-squared term are the same, namely 7.
But if we are going to get this into its graphing form, or work form, we need that 7 to be a 1. We are going to complete the square on both the x terms and the y terms. First we factor out the 7 from both x and y:
[tex]7(x^2-4x)+7(y^2+6y)=35[/tex]
The rules for completing the square are as follows:
Take half the linear term, square it, and add it to both sides, keeping in mind the 7 you factored out as a multiplier.
Our linear term in the first set of parenthesis is 4 (from the -4x). Half of 4 is 2, and 2 squared is 4. We add a 4 into the parenthesis, but multiplying in the 7 has us actually adding in a 28.
Our linear term in the second set of parenthesis is a (from 6y). Half of 6 is 3, and 3 squared is 9. We add a 9 into the parenthesis, but multiplying in the 7 has us actually adding in a 63. Now here is what we have done thus far:
[tex]7(x^2-4x+4)+7(y^2+6y+9)=35+28+63[/tex]
We have, in the process of completing the square, created 2 perfect square binomials on the left. That's why we do this...to get those perfect square binomials. Stating those on the left and adding on the right breaks down our equation into work form. Well, almost.
[tex]7(x-2)^2+7(y+3)^2=126[/tex]
Actual work form has us divide both sides by 7 to get the final answer of
[tex](x-2)^2+(y+3)^2=18[/tex]
And there you are!
Emily brought $35 to the fair. at the fair, she spent $16 on ride tickets and she also bought lunch. she had $7 when she left the fair. how much did emily spend on lunch?
A. 23 + x =35
x=12
B. 16 + x =35
x = 19
C. x - 23 = 35
x = 58
D. x + 9 = 35
x= 26
Answer:
the answer is A
Step-by-step explanation:
first you have to add 16+7 which is 23, then subtract 23 from 35 and you get 12, she spent 12 dollars on lunch.
Given the functions, f(x)=x^3+2 and g(x)=x-9, perform the indicated operation. When applicable, state the domain restriction. (f/g)(x)
Final answer:
To divide f(x) by g(x), we get [tex](f/g)(x) = (x^3 + 2) / (x - 9)[/tex] with a domain restriction where x cannot equal 9 because division by zero is undefined.
Explanation:
To perform the indicated operation (f/g)(x), we divide the function f(x) by the function g(x). Given[tex]f(x)=x^3+2[/tex] and g(x)=x-9, we have:
[tex](f/g)(x) = (x^3 + 2) / (x - 9).[/tex]
There is a domain restriction for the function g(x) because we cannot divide by zero. Therefore, the value that makes g(x) = 0 must be excluded from the domain of (f/g)(x). In this case, the domain restriction is x ≠ 9, as 9 would make the denominator zero.
A rectangle's width is one-fifth it's length, and it's perimeter is 180m. Find the dimensions of the rectangle. The length is M and the width is m
The dimension of the rectangle will be 15 meters (width) and 75 meters (length).
What is the perimeter of the rectangle?The sum of all the sides of the rectangle will be known as the perimeter of the rectangle. Let L be the length and W be the width of the rectangle.
Then the perimeter of the rectangle will be
Perimeter of the rectangle = 2(L + W) units
The length is M and the width is m. A rectangle's width is one-fifth its length, and its perimeter is 180 metes. Then the equation will be
m = (1/5)M
m = M/5
M = 5m
Then the perimeter of the rectangle will be
P = 2(m + M)
180 = 2(m + 5m)
90 = 6m
m = 15 meters
Then the length of the rectangle will be
M = 5m
M = 15 x 5
M = 75 meters
The dimension of the rectangle will be 15 meters (width) and 75 meters (length).
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Harlen has a wooden board that is 2 and one-fourth feet long. He needs to cut the board into one half-foot piece. How many can one half-foot piece of the board Harlen cut? These are the answer choices
Answer Options with 4 options
A.
1 and one eighth
B.
1 and one fourth
C.
3 and one half
D.
4 and one half
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a 25-foot wire is to be cut so that the longer piece is one foot longer than 5 times the shorter peice . find the length of each peice
short piece = x
long piece = 5x +1
x +5x +1 = 25
6x = 24
x = 24/6 = 4
short piece = 4 feet
long piece = 21 feet