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.
please help 13(3+2x)−1=10
Simplify the expression 16 − x2 as much as possible after substituting 4 sin θ for x. (assume 0° < θ < 90°.)
The value of the expression [tex]16 - x^{2}[/tex] is 16 cos^2θ
Here,
The expression is [tex]16 - x^{2}[/tex]
We have to find the value of expression after substitute 4 sinθ for x.
What is substitution method?
Substitution method is algebraic method to solve the linear equations.
Now,
The expression is [tex]16 - x^{2}[/tex]
By putting x = 4 sinθ in above equation, we get;
[tex]16 - x^{2}[/tex] = 16 - ( 4 sinθ)^2
= 16 - 16 sin^2θ
= 16 ( 1 - sin^2θ )
= 16 cos^2θ
Since, 1 - sin^2θ = cos^2θ
Hence, The value of the expression [tex]16 - x^{2}[/tex] is 16 cos^2θ
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To simplify the expression 16 - x² after substituting 4 sin θ for x, you end up with 16 cos² θ, using the Pythagorean trigonometric identity.
Explanation:To simplify the expression 16 - x² after substituting 4 sin θ for x, where 0° < θ < 90°, we follow these steps:
Substitute 4 sin θ into the expression for x.Simplify the resulting expression.The substitution gives us 16 - (4 sin θ)².
To further simplify:
Calculate the square of 4 sin θ, which is 16 sin² θ.Subtract 16 sin² θ from 16, giving us 16 - 16 sin² θ.Factor out the common factor of 16, resulting in 16(1 - sin² θ).Recognize that (1 - sin² θ) is equal to cos² θ due to the Pythagorean identity.Finally, the simplified expression is 16 cos² θ.An urn contains 8 red balls, 8 white balls, and 8 blue balls, and a sample of 5 balls is drawn at random without replacement. Compute the probility that all of the balls in the sample are the same color.
50 POINTS!!! DO NOT ANSWER JUST FOR THE POINTS!!! IF YOU DO, IF YOU DO ALL OF YOUR EARNED POINTS WILL BE TAKEN~~~~~~~~~~~~~~~
Find this a bit complicated. Please explain and show work with steps.
Suppose f(x)=–x²–4x+4. Compute the following:
A. f(–5)+f(5)=
B. f(–5)–f(5)=
A. f(-5) = -(-5)^2-4(-5)+4 = -1
f(5) = -(5)^2-4(5)+4 = -41
-1 + -41 = -42
B. -1 - -41 = 40
Specify 3 fractions with different denominators that have an LCD of 24
The denominator of a fraction is 1 more than the numerator. If both the numerator and denominator are decreased by 3, the resulting fraction is equal to 4/5. Find the fraction
Solve for q 8r-5q=3
In a certain grocery store, strawberries cost $5.92 per pound ( 5.92 dollars/lb ). what is the cost per ounce? express your answer numerically to the hundredths place.
Convert 1.2x10^(-2) into standard form
n standard form, we express it without using scientific notation, so [tex]1.2\times10^{-2}[/tex] becomes 0.012.
We have,
In scientific notation, a number is expressed as the product of a coefficient between 1 and 10 and a power of 10.
Given [tex]1.2\times10^{-2}[/tex],
We can rewrite it by moving the decimal point two places to the left to obtain 0.012.
The coefficient 0.012 is between 0.01 and 0.1, which is equivalent to 1/100 or 1 divided by 10 raised to the power of 2.
Thus, we can write it as 1.2 multiplied by 10 raised to the power of -2.
Thus,
In standard form, we express it without using scientific notation, so [tex]1.2\times10^{-2}[/tex] becomes 0.012.
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The temperature in Minneapolis changed from -7°F at 6 AM to 7°F at noon. how much did the temperature increase?
Write 3.16 as a mixed number in lowest terms
which is 625 written as a power of 5 (exponets) A. 4*5 B.3*5 C.5*3 D.5*4
Select the expression that has a quitiont greater than 1. Explain your reasoning.
4 2/3 divided by 5 1/4= 3 1/8 divided by 2 2/5=
1 6/7 divided by 2 1/3= 5 3/4 divided by 7 3/8=
Final answer:
To find the expression with a quotient greater than 1, we convert the mixed numbers into improper fractions and perform the division for each expression. The expression that gives a quotient greater than 1 is 5 3/4 divided by 7 3/8.
Explanation:
To find the expression that has a quotient greater than 1, we need to divide the given fractions. Let's examine each expression:
4 2/3 divided by 5 1/4: To divide mixed numbers, we convert them into improper fractions and then perform the division. In this case, the quotient is less than 1.
3 1/8 divided by 2 2/5: Similar to the first expression, we convert the mixed numbers into improper fractions and divide. The quotient is also less than 1.
1 6/7 divided by 2 1/3: Again, convert the mixed numbers into improper fractions and perform the division. The quotient is less than 1.
5 3/4 divided by 7 3/8: Convert the mixed numbers into improper fractions and divide. The quotient is greater than 1, so this is the expression we're looking for.
Therefore, the expression with a quotient greater than 1 is 5 3/4 divided by 7 3/8.
Fine the missing coordinate of the ordered pair
A soccer ball is kicked into the air from the ground. If the ball reaches a maximum height of 25 ft and spends a total of 2.5 s in the air, which equation models the height of the ball correctly? Assume that acceleration due to gravity is –16 ft/s2.
A principal of $1,000 is invested in an account paying an annual interest rate of 4% using the formula A=P(1+r/n) ^nt
find the amount in the account after 2 years if the account is compounded annually
Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are . If point D divides in the ratio 4 : 5, the coordinates of point D are
Answer:
I just had to do this problem and,
B is (10, -4) and D is (58/9, -2)
Step-by-step explanation:
Solve for A. R = x(A + B) A = (R - B)/x A = (B - Rx)/x A = (R - Bx)/x
In the given equation of the provided problem, the solution for A is A = [tex]\frac{R - xB}{x}[/tex].
Mathematically, an equation is a statement that asserts the equivalency of two expressions. It consists of two hands, the left-hand side( LHS) and the right-hand side( RHS), separated by an equal sign( =). The LHS and RHS can be numbers, variables, constants, or further complex fine expressions.
To solve for A in each of the given equations, we'll isolate the variable A on one side of the equation. Let's go through each equation:
R = x(A + B)
To solve for A, we'll start by expanding the expression on the right side:
R = xA + xB
R - xB = xA
Divide both sides of the equation by x to solve for A:
A = [tex]\frac{R - xB}{x}[/tex].
Therefore, the solution for A is A = [tex]\frac{R - xB}{x}[/tex].
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For a school assembly, students sit in chairs that are arranged in 53 rows. There are 12 chairs in each row. About how many students can be seated?
Solve for x: 1/4(4x+15)=24
The motorcycle engine on a kawasaki ninja 1000 has a displacement of 1043 cubic-centimeters (cm3). in order to calculate its engine displacement in cubic-inches (in3) what unit conversion factor would you use to multiply the given displacement
[tex]\boxed{\boxed{ \ 0.061 \frac{inch^3}{cm^3}\ }}[/tex]
Further explanationWe will calculate the unit conversion factor used to convert its engine displacement from cubic-centimeters to cubic-inches.
The relationships between inch and cm are as follows:
[tex]\boxed{ \ 1 \ inch = 2.54 \ cm\ }[/tex]
Inches and cm represent units of length.
Made into fractions, 1 inch as the denominator and 2.54 cm as the numerator.
[tex]\boxed{ \ \frac{1 \ inch}{2.54 \ cm} \ }[/tex]
As a unit conversion factor of volume, the numerator and the denominator in cubic.
[tex]\boxed{ \ \frac{(1 \ inch)^3}{(2.54 \ cm)^3} \ }[/tex]
[tex]\boxed{ \ \frac{1 \ inch^3}{16.387 \ cm^3} \ }[/tex]
Thus, we get the unit conversion factor
[tex]\boxed{\boxed{ \ 0.061 \frac{inch^3}{cm^3}\ }}[/tex]
Let's use this unit conversion factor to calculate its engine displacement in new units.
[tex]\boxed{= 1,043 \ cm^3 \times 0.061 \ \frac{inch^3}{cm^3}}[/tex]
Note for cm³ units that have been crossed out.
The conversion result is [tex] \ \boxed{ \ 63.623 \ inch^3\ }[/tex]
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What's S divided by 8=2 ?.....Answer needed ASAP.
Find the probability of randomly selecting 4 good quarts of milk in succession from a cooler containing 20 quarts of which 5 have spoiled
The question asked is related to probability, which is a topic in Mathematics. After calculating the probability of selecting a good quart of milk four times in a row (considering that the quantity decreases each time a good quart is selected), the probability equates approximately to 0.3 or 30%.
Explanation:The given question is a statistical problem related to probability and involves the concept of independent events. In this case, each quart of milk being good or spoiled is an independent event, meaning the outcome of one event doesn't affect the other.
In the cooler, there are 20 quarts of milk in total, 15 of which are good (20 - 5 spoilt quarts equals 15 good ones). Hence, the probability of selecting a good quart of milk at first is 15/20, or 0.75.
After removing one good quart, there are now 14 good quarts out of 19. Hence, the probability of drawing a second good quart is 14/19. We can calculate the probabilities for the third and fourth quarts in the same way, resulting in 13/18 and 12/17 respectively.
Since these are independent events, the probability of all these events happening is the product of their individual probabilities. Therefore, the answer is 0.75* (14/19)* (13/18)* (12/17), which is approximately 0.3 or 30%.
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Solve the system using the elimination method.
2x + 2y + 5z =−1
2x − y + z =2
2x + 4y − 3z =14
What x,y, and z?
Find the true balance:
Check register balance:$463.80
Bank statement balance: $592.53
Outstanding checks: $49.80 and $86.93
Service charge: $8.00
A. $592.53
B. $584.53
C. $327.07
D. $455.80
Answer:
D. $455.80
Step-by-step explanation:
True Balance = Bank Statement - Outstanding Checks
= $592.53 - ($49.80 + $86.93)
= $455.80
Find the numerator of the equivalent fraction with denominator 12 :
1/2
The numerator of the equivalent fraction with denominator 12 for 1/2 is 6. This comes from multiplying both the numerator and denominator of 1/2 by the same number (6).
Explanation:To find the numerator of the equivalent fraction with denominator 12 for 1/2, we simply multiply both parts of the fraction by the same number such that the denominator becomes 12. We know that 2 * 6 equals 12, so we multiply the numerator 1 by 6 as well, which gives us the numerator 6.
Therefore, the fraction 1/2 is equivalent to 6/12.
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1/3 (9x+3)=3x+1 what does x equal
Find the area of the rectangle?! Please :)
Problem Page A science fair poster is a rectangle 48 inches long and 24 inches wide. What is the area of the poster in square feet?
48/12 = 4 feet
24/2 = 2 feet
4 *2 = 8 square feet
Answer:
8 feet squared
which undefined using the undefined terms point más line?
A angle
B circle
C parallel lines
D ray