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.
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.
At 4:00 am the outside temperature was 28*F. By 4:00 pm that same day it rose to 38 degrees.
The temperature at 4:00 pm will be 66° F.
What are Integers?
An integer is a number with no decimal number or fractional part.
Given that;
At 4:00 am the outside temperature was 28*F. By 4:00 pm that same day it rose to 38 degrees.
Now, The temperature at 4:00 pm is calculated as;
= 28° F + 38° F
= 66° F.
Thus, The temperature at 4:00 pm will be 66° F.
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The complete question is this;
At 4:00 am, the outside temperature was 28*F. By 4:00 P.M. it rose 38 degrees. What was the temperature at 4:00 P.M. ?
If y= -6 when x= -24 what is the value of x when y= -7
please help me what is 1462 ÷ 58 as a mixed number then put it in simplest form
Make s the subject of the formula t to the power of 2
= 2p+as
Which is the graph of f(x) = 100(0.7)x?
Answer:
a
Step-by-step explanation:
a baker makes cakes and sells them at county fairs his initial cost was $45 to reserve a booth and $25 traveling expenses. He figures that it costs $1.75 to make each cake and he charges $6.50 per cake. Let x represent the number of cakes sold. Express the revenue R and Cost C as functions of x. Then find how many cakes will he need to sell before he will make a profit
Final answer:
The baker's revenue R can be expressed as R = x * 6.50, and the cost C can be expressed as C = 45 + 25 + (x * 1.75). To find the number of cakes he needs to sell before making a profit, we set the revenue equal to the cost and solve for x. The baker will need to sell at least 15 cakes before making a profit.
Explanation:
To express the revenue R as a function of x, we can use the equation R = x * 6.50. This is because the revenue is the number of cakes sold multiplied by the price per cake. So, every cake sold contributes $6.50 to the revenue.
To express the cost C as a function of x, we can use the equation C = 45 + 25 + (x * 1.75). The initial fixed costs of $45 for reserving a booth and $25 for traveling expenses are added to the variable costs of $1.75 per cake multiplied by the number of cakes sold.
To find the number of cakes he needs to sell before making a profit, we need to set the revenue equal to the cost and solve for x:
R = C => x * 6.50 = 45 + 25 + (x * 1.75)
Combining like terms, we get:
4.75x = 70
x = 70 / 4.75
x ≈ 14.74
Since you cannot sell a fraction of a cake, the baker will need to sell at least 15 cakes before making a profit.
A college student borrow $1,500 for 3 months to pay for a semester of school. If the interest is $30.94, find the monthly payment (Round to the nearest cent.)
Answer:
Hence, the monthly payment to the nearest cent is 510.31
Step-by-step explanation:
Consider the provided information,
A college student borrow $1,500 for 3 months to pay for a semester of school.
Let us consider the monthly payment is $x.
If he pay $x for next 3 months, then the total amount student paid in 3 month is: 3x
The interest is $30.94 for 3 months.
Student pay all the borrowed money and interest in 3 months.
That means he pay $1,500 + $30.94 in 3 months while the monthly payment was 3x.
This can be written as:
[tex]3x = 1500+30.94[/tex]
[tex]3x = 1530.94[/tex]
[tex]x = \frac{1530.94}{3}[/tex]
[tex]x = 510.31[/tex]
Hence, the monthly payment to the nearest cent is 510.31
in slope intercept form, what is the equation of the line passing through the points (3,17) and (7, 25)
A. y=-2x+23
B. y=2x+11
C. y=-3x+26
D. y=2x-11
Answer:
B
Step-by-step explanation:
To write the equation of the line, use the slope formula to find the slope. Then substitute the slope and a point into the point slope form. Simplify using the distributive property to write in slope intercept form.
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{25 - 17}{7-3} = \frac{8}{4} = 2[/tex]
Using the point slope form of a line equation, substitute m = 2 and the point (3,17).
[tex]y - y_1 = m(x-x_1)\\y -17 = 2(x - 3)\\y - 17 = 2x - 6 \\ y = 2x - 6 + 17 \\ y = 2x + 11 [/tex]
evaluate -x+y+6 for x=-3 and y=-1
The number 3.453 has two 3s why does each 3 have a different value
evaluate the expression of 8+(-1)+(-3)
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.
Can someone PLEASE help me with this? ^^^ (25 points)
Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level. What is the difference between these two elevations?
A union charges monthly dues of $6.00 plus $0.15 for each hour worked during the month.A union member's due for march were $33.00.How many hours did the union member work during the month of march?
What Is 1,270 rounded to the nearest hundred?
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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What is the volume of a frustum of a right pyramid with the area of the lower base equal to 100 square inches, the area of the upper base equal to 25 square inches, and the altitude equal to 12 inches?
A. 560 in^3
B. 700 in^3
C. 420 in^3
D. 750 in^3
Where B₁ and B₂ are the areas of the bases, the volume of the frustum is given by
... V = (1/3)(B₁ +B₂ +√(B₁B₂))h
For your dimensions, the volume is
... V = (1/3)(100 + 25 + √(100·25))·12 = (1/3)·175·12 = 700
The appropriate choice for the volume of the frustum is
... B. 700 in³
find two consecutive integers such that the larger is nine more than twice the smaller
Two consecutive integers are - 7 and - 8.
Here,
We have to find the two consecutive integers.
What are Integers?
An integer is a number which includes negative and positive numbers, including zero.
Now,
Let the smaller number is x.
Then, the larger is nine more than twice the smaller.
So, Larger number = 2x + 9
Since, The difference of two consecutive number are always 1.
So,
2x + 9 - x = 1
x + 9 = 1
x = -8
Therefore, The larger number = 2x + 9 = 2*-8 + 9 = -16 + 9 = -7
Hence,
Two consecutive integers are - 7 and - 8.
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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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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
Which answer is a reasonable estimate to the following problem? 94 · 689
60,000
70,000
600,000
700,000
The reasonable estimate for multiplying 94 by 689 is found by rounding the numbers to the nearest convenient figures, which gives an estimated result of 70,000.
Explanation:To estimate the product of 94 and 689, you can round each number to its nearest simple form and then multiply. Round 94 to 100 because it is close to that multiple of ten. Round 689 to 700, as it is close to this hundred mark. When you multiply 100 by 700, you get 70,000.
This process of rounding to the nearest convenient number simplifies the multiplication and gives us an answer that is easy to calculate and understand. Hence, by rounding the numbers before multiplying, the reasonable estimate for the problem 94 · 689 is 70,000.
Final answer:
By rounding the numbers and multiplying, a reasonable estimate for the product of 94 and 689 is 70,000.
Explanation:
To estimate the product of 94 · 689, we can round the numbers to the nearest ten or hundred and then multiply. For estimation purposes, we can approximate 94 to 100 (since it's closer to 100 than 90) and 689 to 700 (since it's closer to 700 than 600).
Multiplying these rounded figures: 100 × 700 equals 70,000. Therefore, 70,000 is a reasonable estimate for the product of 94 and 689.
What is the area of a circle 3.102 cm in diameter? (note: the units will be cm2, you only need to enter the number)?
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
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.
Two-thirds a number plus 4 is 7
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
the product of two numbers is 14. One of the numbers is d. What expression represents the other number