Answer:
a. 22.3°
b. 2940.16 ft/s
Step-by-step explanation:
Here is the complete question
A projectile fired into the first quadrant from the origin of a coordinate system will pass through the point (x, y) at the relationship cot theta = 2x/2y + gt^2 where theta is the angle of elevation of the launcher and g is the acceleration due to gravity (32.2 feet/second^2). An artillery man is firing at an enemy barker located 2275 feet up the side of a hill that is 6325 feet away. He fires a round, and exactly 2.84 seconds later he scores a direct hit.
a. What angle of elevation did he use? theta = degree (Do not round until the final answer. Then round to one decimal place as needed.)
b. f the angle of elevation is also given by sec theta = v_0 t/x, where v_0 is the velocity of the weapon, find the muzzle velocity of the artillery piece he used. v_0 = feet/second (Round to two decimal places as needed.)
Solution
(a) What angle of elevation did he use?
Given that cosθ = 2x/(2y + gt²) where x = horizontal distance of projectile = 6175 feet away,y = vertical distance of projectile = 2450 feet up, g = acceleration due to gravity = 32 ft/s² and t = time of hit = 2.27 s
So, cosθ = 2x/(2y + gt²)
cotθ = 2 × 6175 ft/(2 × 2450 ft + 32 ft/s² × (2.27 s)²)
cotθ = 12350 ft/(4900 ft + 32 ft/s² × 5.1529 s²)
cotθ = 12350 ft/(4900 ft + 164.8928 ft)
cotθ = 12350 ft/(5064.8928 ft)
1/tanθ = 2.4384
tanθ = 1/2.4384
tanθ = 0.4101
θ = tan⁻¹(0.4101)
θ = 22.3°
(b) If the angle of elevation is also given by sec θ = υ0t/x. where υ0 is the muzzle velocity of the weapon, find the muzzle velocity of the artillery piece he used.
Making u0 subject of the formula, we have
u0 = xsecθ/t
u0 = x/tcosθ
since x = 6175ft, t = 2.27 s and θ = 22.3°, then
u0 = x/tcosθ
u0 = 6175 ft/(2.27 s × cos22.3°)
u0 = 6175 ft/(2.27 s × 0.9252)
u0 = 6175 ft/(2.1 s)
u0 = 2940.16 ft/s
solve the equation: 1/2n - 3 = 5
Answer:
n=16
Step-by-step explanation:
Let's solve your equation step-by-step.
1/ 2 n−3=5
Step 1: Add 3 to both sides.
1/ 2 n−3+3=5+3
1/ 2 n=8
Step 2: Multiply both sides by 2.
2*( 1/ 2 n)=(2)*(8)
n=16
Answer:
n=16
Answer:
n=16
Step-by-step explanation:
First you have to do 3+-3 to cross it out
then you have to add 3 to 5
lastly divide 8 and 1/2
Then you get your answer.
Challenge A bag contains pennies, nickels dimes, and quarters. There are 50 coins in all of the
coins 18% are pennies and 40% are dimes. There are 2 more nickels than pennies. How much
money does the bag contain
The bag contains S
Answer:
The bag contains $5.14
Step-by-step explanation:
18% of 50 = (.18)(50) = 9 pennies
40% of 50 = (.40)(50) = 20 dimes
2 more nickels than pennies = 9 + 2 = 11 nickels
40 coins so far, so 50 - 40 = 10 quarters
Total value:
9 x ($0.01) = $0.09 for pennies
20 x ($0.10) = $2.00 for dimes
11 x ($0.05) = $0.55 for nickels
10 x ($0.25) = $2.50 for quarters
Grand total value = $5.14
HELP
What is the equation of the trend line in the scatter plot ?
Answer:
its decreasing
Step-by-step explanation:
the graph will always be read from left to right.
69 to the power of 2
Answer:
4761
Step-by-step explanation:
69 times 69 since it is to the power of 2.
Answer:
4761
Step-by-step explanation:
[tex]69 *69=4761[/tex]
please give brainliest I need to feed my children
A new car is purchased for $30,000 and over time its value depreciates by one half
every 5 years. What is the value of the car 11 years after it was purchased, to the
nearest hundred dollars?
Answer:
Step-by-step explanation:
6600
The car is about $6529.12 eleven years after it was bought.
What is an exponent?The formula below can be used to determine a car's value after a particular number of years if its value depreciates by half every five years:
[tex]\rm P=P_{\circ} \left ( \dfrac{1}{2} \right)^{x/5}[/tex]
Here, x is how long ago the car was bought.
With x = 11 and a starting value of $30,000, this calculation yields:
[tex]\rm P=$30,000 \times \left ( \dfrac{1}{2} \right)^{11/5}\\[/tex]
Simplify the equation, then we have
P = $30,000 x 0.2176
P = $6529.12
The car is about $6529.12 eleven years after it was bought.
More about the exponent link is given below.
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find the area, seventh grade math problem please help
Answer:
78 ft²
Step-by-step explanation:
[tex]A=\frac{a+b}{2} h[/tex]
[tex]A=\frac{11+15}{2}6[/tex]
78
Line m is mapped onto line n by a dilation centered at the origin with a scale factor of 2. The equation of line m is 3x−2y=63x-2y=63x−2y=6 . Find the equation for line n showing all work for full credit.
9514 1404 393
Answer:
3x -2y = 12
Step-by-step explanation:
The constant in the standard form equation for a line is proportional to the distance of the line from the origin. Dilation by a factor of 2 moves the line to twice its original distance from the origin. The equation of the new line will have the constant 2×6 = 12:
3x -2y = 12
_____
Additional comment
The actual distance of line ax+by=c from the origin is ...
d = |c|/√(a²+b²)
The distance from any point in the plane to the line is ...
d = |ax +by -c|/√(a²+b²)
The previous equation is for the special case of (x, y) = (0, 0), the distance from the origin.
WILL MARK BRAINLIEST!!!!!
In A ABC, AB= 6 cm, AC= 15 cm, and mZA= 48°
What is the area of A ABC?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
cm?
Answer:
33.44 cm²
Step-by-step explanation:
sorry if incorrect
simplify 1/a+b + 1/a-b + 2b/a^2-b^2
Answer:
−a^2 b^2 + 2a + 2b
_________________
a^2
Step-by-step explanation:
Please mark as brainliest if answer is right
Have a great day, be safe and healthy
Thank u
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Segments AB and CD coincide.
Vinay concluded: "Segments AB and CD have no angles with the same measurement, so they are not congruent."
What error did Vinay make in his conclusion?
Choose 1 answer:
A. These segments are mapped onto each other, so they are congruent
B. The segments are not congruent, because no transformations were used
C. There is no error. This is a correct conclusion
Answer:
A
Step-by-step explanation:
The correct reason should be These segments are mapped onto each other, so they are congruent.
What is Congruency.In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
We have the statements as
Segments AB and CD coincide
Now, Vinay concluded: "Segments AB and CD have no angles with the same measurement, so they are not congruent."
As per Vinay the lines would never able to coincide if they are not congruent.
So, the correct reason should be These segments are mapped onto each other, so they are congruent.
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Solve this exercise using the fact that the sum of the measures of the three angles of a triangle is 180.
In a triangle, the measures of the three angles are x, x+5, and x-35. What is the measure of each angle?
Answer:
X=70
Step-by-step explanation:
70 + 75 + 35 =180
x + x+5 + x-35
give your answer as a mixed number
will someone show me how
to work out questions like this in the pictures step but step
Answer:
The value of given expression is 13 / 3
Step-by-step explanation:
Given expression in the form of improper fraction;
17/3 - [tex]1\frac{1}{3}[/tex]
Find;
The value of given expression
Computation:
⇒ 17/3 - [tex]1\frac{1}{3}[/tex]
Step 1 ;
Change mixed fraction into simple fraction
⇒ 17/3 - 4/3
Step 2 ;
By taking LCM of denominators;
⇒ [17 - 4] / 3
Step 3 ;
Subtract 17 from 3
⇒ [13] / 3
The value of given expression is 13 / 3
Determine the slope of the line that passes through the points (-4,-2) and (3,1).
Answer:
Step-by-step explanation:
Stephanie, so many people ask questions about this type of problem, I think the teachers don't know how to explain these at all. Ask your teacher if I can have some of their salary :) I have to explain this to that many people.. :0
given"
point P1 (-4,-2) in the form (x1,y1)
point P2(3,1) in the form (x2,y2)
slope = m
formula for slope is:
m = (y2-y1) / (x2-x1)
m = (1-(-2) ) / (3 - (-4))
m = (1+2) / (3+4)
m = 3 /7
That's your slope, ask if you need more explanation, I'm really curious about why this type of problem causes so many questions :/
f (x)
2x2+72-15
3x2 +13x –10
Horizontal Asymptote- type your answer..
Answer:
2×2+72-15
=4+72-15
=76-15
=61
3×2+13×-10
=6-130
=-124
WILL
GIVE
BRAINLIST ANSWER
..
.
.
.
.
Click on the picture for the graph!
Remember to label!
Hope this helps! Have a great day!
Only answer if you’re sure, will give Brainly :) thank you
A mechanical engineer is creating a new composite carbon fiber material made from two different materials. The strength of the carbon fiber material depends on how much pressure it can withstand, and it follows a standard normal distribution. The new carbon fiber material will be slated for research and development purposes if it can withstand more than 2.45 standard deviations above the mean of pressure compared to the individual materials. Fiber material that withstand less than 2.45 standard deviations above the mean of pressure when compared to the individual materials are not of research interest. What is the probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials
Answer:
0.9929 = 99.29% probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
What is the probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials?
2.45 standard deviations above the mean is Z = 2.45, so this probability is the p-value of Z = 2.45.
Looking at the z-table, Z = 2.45 has a p-value of 0.9929.
0.9929 = 99.29% probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials
Simplify: -4r + s - 2r - 3s
Answer:
-6r - 2s
Step-by-step explanation:
Combining Like Terms like this
-4r + s-2r - 3 s <<<
-6r + s - 3 s
= -6r - 2s <<<
Answer:
-6r - 2s
Step-by-step explanation:
Find the volume of a sphere with a diameter of 6.2 in.
Answer: its 23 meters
Step-by-step explanation:
The volume of a sphere with a diameter of 6.2 in is 39.72π
What is the volume of the sphere?The volume of a sphere is defined as the total amount of capacity applied in a sphere that can be calculated using the volume formula for the sphere which is V = (4/3)πr3.
The radius of the sphere is;
[tex]\rm Radius =\dfrac{Diameter}{2}\\\\Radius=\dfrac{6.2}{2}\\\\Radius=3.1[/tex]
The volume of the sphere is;
[tex]\rm Volume =\dfrac{4}{3}\pi r^3\\\\Volume =\dfrac{4}{3}\pi (3.1)^3\\\\Volume = 39.72\pi[/tex]
Hence, the volume of a sphere with a diameter of 6.2 in is 39.72π.
Learn more about sphere here;
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A sum of money is divided amongst Farah, Shaiyara and Zahin in the ratio 10: 7: 5. If
Shaiyara gets $20 more than Zahin, find the total sum of money shared and the amount
Farah gets.
Answers:
Total amount of money = 220 dollarsAmount Farah gets = 100 dollars==========================================================
Explanation:
F = amount Farah getsS = amount Shaiyara getsZ = amount Zahin getsThe money is divided in the ratio 10:7:5
This means that
F = 10xS = 7xZ = 5xfor some positive real number x.
Since Shaiyara gets $20 more than Zahin, we can say,
S = Z+20
Let's plug in S = 7x and Z = 5x and solve for x
S = Z+20
7x = 5x+20
7x-5x = 20
2x = 20
x = 20/2
x = 10
Therefore,
F = 10x = 10*10 = 100S = 7x = 7*10 = 70Z = 5x = 5*10 = 50The ratio F:S:Z becomes 100:70:50 which reduces fully to 10:7:5 after dividing all three parts by the GCF 10.
The total sum of money shared is 100+70+50 = 220 dollars and Farah gets $100 of that total.
Jack places the bottom of a ladder 9 feet from the wall. It is a huge 41 foot long ladder so he asks his sister Katie to help him. How far up the wall does the ladder reach?
Answer:
40 feet
Step-by-step explanation:
Use the Pythagorean Theorem
a² + b² = c²
a² + 9² = 41²
a² + 81 = 1681
Subtract 81 from both sides
a² = 1600
Take the square root of both sides
a = 40
Find the surface area of the cube.
5.5 yd
5.5 yd
5.5 yd
The surface area is
square yards.
HELPPPPPP
Answer:181.5
Step-by-step explanation:
5.5*5.5*6
multiply by six because there are six side
Vance invests S15,000 in an account that pays 3 1/4% simple interest for 72 months. Assuming Vance doesn't
make any other deposits or withdrawals, how much will be in his account after 72 months?
Answer:
$15487.5
Step-by-step explanation:
Using the formula for calculating the amount as;
Amount = Principal + Interest
Principal = $15,000
Get the interest
Interest = PRT/100
Interest = 15000*13/4 * 3/100 (72months = 3years)
Interest = 195000/400
Interest = $487.5
Amount = 15000 + 487.5
Amount= $15487.5
Hence he will have $15487.5 in his account after 72months
What is the answer to 4 1/3 - 1 1/5
Answer:
3 2/15 or approximately 3.13
Step-by-step explanation:
4 1/3 - 1 1/5
=13/3 - 6/5
= 47/15
=3 2/15 or approximately 3.13
Mr. Ortiz's car drives 12 miles in 20 minutes. Use a model to find out how many miles his car drives in 1 HOUR.
Answer:
36 miles
Step-by-step explanation:
Since there are 60 minutes in a hour, you can see that 20 minutes is a third of that time. To find the answer, you multiply the values by 3 to equal on hour. 20x3 = 60 and 12x3 = 36, meaning he drove 36 miles in a hour.
j need help w number 4 algebra to have to show all work
Answer:
[tex]\sqrt[3]{\frac{-729}{216} } = \sqrt[3]{\frac{9*9*9*}{6*6*6} } = (\frac{9^3}{6^3})^{\frac{1}{3} } = \frac{9}{6} = \frac{3}{2}[/tex]
option a
x ( x + 4 ) − 3 = 4 ( x + 19.5 )
Answer:
9
Step-by-step explanation:
HELLO CAN SOMEONE PLEASE HELP
Answer:
1, 4
Step-by-step explanation:
X increases up by one
Y multiplies 4 from the previous
Which of the following are solutions to the equation below?
Check all that apply.
4x2 - 81 = 0
A butterfly flew 743 cm, Then the butterfly flew another 567 cm end to go to a daisy.
How many meters did the butterfly travel?
Answer:
it 567+743
hope it works