Answer:
10³ = l
Step-by-step explanation:
A projectile fired into the first quadrant from the origin of a coordinate system will pass through the point (x, y) at time t according to the relationship,
cos theta 2x/2y + gt2
where theta = the angle of elevation of the launcher and g = the acceleration due to gravity An artilleryman is firing at an enemy bunker located 2450 feet up the side of a hill that is 6175 feet away. He fires a round, and exactly 2.27 seconds later he scores a direct hit.
(a) What angle of elevation did he use?
(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.
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
The three-dimensional figure below is a cylinder with a hole in the shape of a rectangle prism going through the center of it. The radius is 10 feet. Find the volume of the solid and cubic feet. Use 3.14 for pi.
Answer:
4488ft^3
Step-by-step explanation:
Given data
Dimension of the hole
Length= 5ft
Width= 3ft
Height= 15ft
Volume of Hole=L*W*H
Volume of Hole= 5*3*15
Volume of Hole= 225ft^2
Volume of cylinder
Radius= 10ft
Height = 15ft
Volume of cylinder= πr^2h
Volume of cylinder= 3.142*10^2*15
Volume of cylinder= 3.142*100*15
Volume of cylinder= 4713ft^3
Hence the volume of the shape is
Volume of shape= Volume of cylinder- Volume of hole
Volume of shape= 4713- 225
Volume of shape= 4488ft^3
The right triangle on the right is a scaled copy of the right triangle on the left. Identify
the scale factor. Express your answer in simplest form
Answer:
scale factor = [tex]\frac{34}{39}[/tex]
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original.
scale factor = [tex]\frac{34}{39}[/tex]
Please help me ASAP I need this answer quick!!!
Answer:
The Rule of 72 is a simplified formula that calculates how long it'll take for an investment to double in value, based on its rate of return. The Rule of 72 applies to compounded interest rates and is reasonably accurate for interest rates that fall in the range of 6% and 10%.
How many solutions does the equation 6z − 3z − 7 = −2 + 3 have?
Two
None
Infinitely many
One
There could only be one aolition
choose two tables that represent a function
Answer:
I think the answer it b and a
1/5? jaslyyyyyyyyyyyyyyyyyyyy??
Answer:
2/7
hope this helps
have a good day :)
Step-by-step explanation:
Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run?
A 2-column table with 4 rows. Column 1 is labeled Situation with entries increasing, difference, finding part of a total, sharing, or grouping. Column 2 is labeled Operation with entries +, minus, times, divided by.
Select all that apply.
You know the difference in the distances the boys ran, so this is a subtraction problem.
You are finding the total distance the boys ran, so this is an additional problem.
Dean ran part of the distance Sam ran, so this is a multiplication problem.
The correct equation is s + 2.3 = 6.8.
The correct equation is s – 2.3 = 6.8.
The correct equation is 2.3s = 6.8.
HELP MEEEEEEEEEEEEEE
Answer:
Sam ran 8.1 km
6.8 + 2.3= 8.1
Answer:
A. You know the difference in the distances the boys ran, so this is a subtraction problem.
E. The correct equation is s – 2.3 = 6.8.
The answers are a and e
Please please please help!!!
Victor earned $60, which was more than three times Joyce's earnings. What was the greatest whole-dollar amount Joyce could have earned? Write an inequality and solve.
Answer:
j < 20
19
Step-by-step explanation:
60 > 3j
Divide both sides by 3
20 > j
Flip
j < 20
greatest whole-dollar amount Joyce could have earned?
19
An angle measures 10° more than the measure of its complementary angle. What is the
measure of each angle?
Answer:
50 and 40
Step-by-step explanation:
Complimentary angles must add up to equal 90 degrees. Therefore, you must find two numbers that add to 90 and have a difference of 10. Try different number values until this is true. One must be 50 and the other 40 degrees.
pleaseehehhehe bellopppp
Answer:
A is right
Step-by-step explanation:
The Stem-and-Leaf plot and the Box-and-Whisker Plot here display the number of shoes sold daily in a 12-day sale. What is the median number of this data set?
A. 80
B. 89
C. 84
D. 86
What is the data set?
Post it in the comments... PLZ
Two parallel lines cut by a transversal are shown.
What is the measure of Xº?
Answer:
X° is A=D116°
Step-by-step explanation:
Hope you helpThe area of a circle is pi square centimeters. What is the diameter? Please help!!!!
Answer:
Radius of the circle = 1 centimeter.
Step-by-step explanation:
Expression that represents the area of a circle,
Area = πr²
Here, r = Radius of the circle
Area of the circle given = π square centimeters
πr² = π
r² = 1
r = 1
Therefore, radius of the circle is 1 centimeter.
Kayla was cutting right triangles from wood to use for an art project. Two of the right triangles she cut are shown below
Answer:
The answer is "[tex]28^{\circ}[/tex]"
Step-by-step explanation:
Please find the complete question in the file.
The angle F measure is identical to the angle C measure.
The adjacent BC and the hypotenuse AC have been developed. That would be used cosine.
[tex]\cos C = \frac{15}{17}\\\\C =\ cos^{-1}\frac{15}{17} = 28.07\approx 28^{\circ}[/tex]
PLZZ HELP I WILL GIVE A !)) POINTS Danny attempts the feat of jumping his motorcycle through the Flaming Hoop Jump of Awesome. In order for Daredevil Danny to pass through the hoop, he will need a safe path to travel. Let’s explore the parabolic trajectory that he will need for a safe journey.Step 4: Calculate the equation for the flaming hoop jump.
Using the same method for the practice jump, write the standard form of the equation that will get Daredevil Danny safely through the Flaming Hoop Jump of Awesome!
Determine the values of a, b, and c. Show your work. (10 points)
Using your values of a, b, and c, did Daredevil Danny successfully pass through the Flaming Hoop Jump of Awesome? If not, describe what happened. Then, go back to critique your work and revise it. Write about your revision. (5 points)
Once you have determined the correct values of a, b, and c, verify algebraically that Daredevil Danny will successfully pass through the Flaming Hoop Jump of Awesome. (5 points
Answer:
par t a:
plug in the root (4,0) to find a
0=a(4-24)^2+50
subtract 50 from both sides
-50=a(4-24)^2
4-24
=-20
-20^2=400
back to the equation
-50=a(400)
-50=400a
-50/400=-0.125
a = -0.125
part b:
-0.125(x-24)^2+50
-0.125(x-24)(x-24)+50
-0.125(x^2-24x-24x+576)+50
-0.125(x^2-48x+576)+50
-0.125x^2+6x-75+50
-0.125x^2+6x-22
a=-0.125
b=6
c=-22
part c: yes he went through
part d:
plug in vertex (4,0) and (44,0)
if x is 4 and y is 0
0=-0.125(4)^2+6(4)-22
0=-2+24-22
0=-2+2
0=0
if x=44 and y=0
0=-0.125(44)^2+6(44)-22
0=-242+264-22
0=-242+242
0=0
Step-by-step explanation:
MRK ME BRAINLIEST PLZZZZZZZZZZZZZ
How can you tell if a number can be divided by 2?
Answer:
If in the ones place of a number contains digits like 0,2,4,6 or 8 then we can say that the number is divisible by 2.
Olivia's team played 8 games of basketball. During those 8 games her team's score was: 70, 67, 79, 66, 64, 80, 64 and 75. Find the median.
Round to the nearest TENTH.
Answer:
70
Step-by-step explanation:
First put it to least to greatest- 64, 64, 66, 67, 70, 75, 80
Then find the median which is the number in the middle
Round it so it gives us are answer of 70
If the radius is 3.5in, then the diameter is
Answer:
the diameter is 7
What is the exponent for 4.4.4.4=?
Answer:
the answer is four to the the power of four
Step-by-step explanation:
how, well because the main number there is four and the the amount is four so there's your answer
The exponent for 4.4.4.4 = 4^4
What is exponent?An exponent of a number is the number of times the number is multiplied to itself. For example, 10 is multiplied for n times by itself can be expressed as 10^n.For any number x raised to the power n can be expressed as x^n = x.x.x....x (n times) = x^nIn x^n, x is called base and n is called exponent otherwise index or power of x.In short,Exponentation is the shortest method for repeated multiplication.It is given that 4.4.4.4
Here 4 is multiplied repeatedly by the number itself. So we use exponentation.
Base is 4 and exponent is 4
Therefore, the exponent for 4.4.4.4 is 4^4
Learn more about exponent here:
https://brainly.com/question/11975096
#SPJ2
questionon on picture
Answer:
yes this option is correct
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
HELP I NEED TO DO THIS NOW NO LINKS THEY WOULD BE REPORTED JUST TELL ME WHAT I NEED TO PUT
Tiffany quiz grades on 1st 4 quizzes are 72,87,83,90
Answer:
90
Step-by-step explanation:
72 is the least and 90 is the greatest
87 is the second most greatest and 83 is the third most.
Therefore the answer is 90
A large corporation sent out four groups of people to conduct observational studies on the average wait time at four different restaurants in its restaurant group. The restaurants have approximately the same ratings in terms of quality and popularity.
In their reports to the company board, each of the four groups described different methods used to conduct their studies, as shown in the table. Which group’s method will give the most accurate, unbiased results?
Answer:
It's midwest
Step-by-step explanation:
Midwest's groups will give the most accurate, unbiased results, and the correct option is B.
To solve this question, we analyze each sample, and find which of them will give the most accurate results.
Northeast: Only 3 hours a day, which can either have a very low or very high wait time, not being a correct representation, so there are bias factors.West Coast: One full day, which also can be a day with a lot of demand, leading to high wait time, or a day with low demand leading do low demand time, so there are also bias factors.South: Phone survey is not very accurate, people may not remember, for example.Midwest: Consider lots of periods over the course of the week, thus surveying both periods of low and of high demand, to get a good estimate for the average time, not having bias factors.Thus, the Midwest's groups will give the most accurate, unbiased results, and the correct option is B.
A similar example is given here: https://brainly.com/question/16609573
A circus acrobat is shot out of a cannon with an initial upward speed of 50 . The equation for the acrobat's pathway can be modeled by the equation h = - 16t ^ 2 + 50t + 4 .
a.Find the maximum height of the acrobat.
b.How long will it take to reach the ground?
Answer:
Step-by-step explanation:
h = - 16t ^ 2 + 50t + 4
maximum height take the first derivative of h (calculus if you are taking it)
h' = -32t + 50 set this equal to zero
0 = -32t +50
t = 50/32
t = 1.5625 now plug t = 1.5625 into the height equation
h = - 16(1.5625) ^ 2 + 50(1.5623) + 4
h = 43.0625 ft
you can also find the maximum height by graphing the function and locating the peak value (much easier)
how long to reach the ground h = zero
0 = - 16(t) ^ 2 + 50(t) + 4
use the quadratic equation to solve this or graph the function h(t) and find the roots (much easier) and you will find that
t = -0.078 and 3.203 seconds
obviously the negative root makes no sense unless he time travelled so
t = 3.203 seconds
What is the value of X HELP PLEASE
Answer:
x = 25
Step-by-step explanation:
In the image shown you have correctly identified the angles as vertical. Vertical angles are equal. This means that the angle "4x - 25" is the same as the angle "75". we can write this as:
4x - 25 = 75
Add 25 to both sides
4x = 100
This means that 4 x's will make one hundred. If you divide 100 by four you get four equal parts that make 100. Divide both sides by 4.
x = 25
The corporate board of directors is hiring a consultant to do a deep analysis of one randomly selected XYZ manufacturing site. Given that 7 of the 14 XYZ sites have had 95% or higher widget production success rate in the last month, what is the probability that a successful site will be selected
Answer:
Hence, the probability of a successful site is :
[tex]P(\text{succes sites})=\frac{8}{9}=89\%[/tex]
Step-by-step explanation:
Given :
[tex]7[/tex] of the [tex]14,XYZ[/tex] sites have had [tex]95\%[/tex] or higher widget production success rate in the last month
To find :
The probability that a successful site will be selected.
We can select either of [tex]8[/tex] sites out of [tex]9[/tex].
These [tex]8[/tex] sites can be selected in [tex]8[/tex] ways.
Total sites[tex]=9[/tex]
Therefore, the probability of a successful site is :
[tex]P(\text{succes sites})=\frac{8}{9}=89\%[/tex]
what are the slope and y-intercept of the line described by y = 2x +6?
Slope is m= ________
Y-interept is (0, ________)
Answer:
Slope is m= 2
Y-interept is (0, 6)
Step-by-step explanation:
y = 2x +6
Equating it with
y = mx + b
We find
m = 2
b = 6
Therefore,
Slope is m= 2
Y-interept is (0, 6)
Answer:
slope is m=2
y intercept is (0,6)
Step-by-step explanation: