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
2 5/6 times 8 as a mixed number.
Answer:
lets make it an improper fraction:
17/6 x 8/1(consider 8 over 1) = 22 2/3
Simplify first though
17 x 8 divide by 2 = 4
_____
6 divide by 2 = 3 (8 and 6 are divisible by 2)
Your new simplified multiplication:
17 x 4
_____ then you can do your multiplication across.
3
What does the term 9b represent
A,B,C,D
Answer:
(B) The cost to rent a bike
Answer: the cost to rent a bike
Step-by-step explanation:
what property is occurring in the following example? 11.5 + (- 11.5) = 0
A- Commutative
B- Associative
C- Addictive Inverse
D- Distributive Property
PLEASE I NEED ANSWERS!!
Answer: A property occurring in the example 11.5 + (-11.5) = 0, is additive inverse.
Step-by-step explanation:
A property where sum of any number and its inverse is equal to zero is called additive inverse property.
For example, 11.5 + (-11.5) = 0
Here, 11.5 is the number and its inverse is (-11.5). The sum of both these is equal to zero. Hence, it shows a property of additive inverse.
Thus, we can conclude that property occurring in the example 11.5 + (-11.5) = 0, is additive inverse.
The spinner has 8 congruent sections. What is the probability of
spinning a number divisible by 3 two times in a row?
Answer:
1/16 or 0.0625
Step-by-step explanation:
There are two numbers on the chart that are divisible by 3.
So the odds of spinning and getting one of those on the first try would be 2/8 or 1/4.
The odds are then multiplied by the chance of spinning it again on the second try, which would still be 1/4.
To get: 1/16
If tan θ=1/4 and cos θ≤0, find the exact value of sin x
If you can answer this soon that would be great.
Answer:
Step-by-step explanation:
Tan(theta) = Sin(theta) / cos(theta)
1/4 = sin(theta) / sqrt(1 - sin^2(theta) ) Cross multiply
sqrt(1 - sin^2(theta)) = 4*sin^2(theta) Square both sides.
1 - sin^2(theta) = 16 * sin^4 (theta) Transfer the left side to the right side.
0 = 16 sin^4(theta) + sin^2(theta) - 1
Use the quadratic formula to find a value for sin^2(theta)
a = 16
b = 1
c = - 1
I'll leave solving the quadratic to you.
There are two answers
sin^2(theta)= .22069
The other root is - 0.28 which you cannot use.
Sin(theta) = +/- 0.4698
Cos(theta) is < 0 in quads 2 and 3
So sin(theta) is positive in quad 2
and sin(theta) is minus in quad 3
Work out the mean for the data set below: 5, 6 Give your answer as a decimal.
Answer:
5.5
Step-by-step explanation:
5 + 6 =
11 / 2 =
5.5
In one game there are 85 spins.
How many of these spins are expected to be 'Go forward 2 squares'?
I dont know the question sory
compute the value of the discriminant and give the number of real solutions of the quadratic equation
mag aral ng mabuti para may alm
Step-by-step explanation:
yan ang answer
Someone please help me, this test determines if I pass or not.
Answer:
Your answer is C :)
Which expression is shown on the number line?
Answer: i think its e
Step-by-step explanation:......
Answer:
no.A 5/3÷×1/3 is the answer
I need help like right now. Im brain dead
Answer:
y-intercept: [tex](0,-\frac{5}{2} )[/tex]
x-intercept: [tex](-2,0)[/tex]
Step-by-step explanation:
Hi there!
Important things to note:
the y-intercept occurs when x=0the x-intercept occurs when y=01) Find the y-intercept
[tex]-5x-4y=10[/tex]
Substitute x with 0
[tex]-5(0)-4y=10\\0-4y=10\\-4y=10[/tex]
Divide both sides by -4
[tex]\frac{-4y}{-4} =\frac{10}{-4} \\y=-\frac{5}{2}[/tex]
Therefore, the y-intercept is [tex]-\frac{5}{2}[/tex]. When written in (x,y) form, x will always be 0 while y is the y-intercept:
[tex](0,-\frac{5}{2} )[/tex]
2) Find the x-intercept
[tex]-5x-4y=10[/tex]
Substitute y with 0
[tex]-5x-4(0)=10\\-5x-0=10\\-5x=10[/tex]
Divide both sides by -5
[tex]-5x=10\\\frac{-5x}{-5}= \frac{10}{-5} \\x=-2[/tex]
Therefore, the x-intercept is -2. When written in (x,y) form, x will always be the x-intercept while y is always 0:
[tex](-2,0)[/tex]
I hope this helps!
Please, show some work
I can not see the photo
9514 1404 393
Answer:
A. x -4y
Step-by-step explanation:
The first expression factors as ...
= 2x(x -4y)
The second expression factors as ...
= 3x^2(x -4y)
Factors that are common between these factorizations are ...
x, (x -4y)
Of these, the one on your list of choices is ...
x -4y
you buy rice at $0.71 a pound a batch requires 4 pounds or rice how much is one batch
Answer:
$2.84 for one batch
Step-by-step explanation:
$0.71 x 4 = $2.84
Answer:
$2.84 for one batch
Step-by-step explanation:
I know this how you ask? $0.71 x 4 = $2.84
The polynomial f(x) is written in factored form:
f(x) = (x - 6)(x + 5)(x - 9)
What are the zeros of the polynomial function?
O x = 6, x = -5, X = 9
O x = 6, X = 5, X = 9
Ox= -6, X = 5, x = -9
Ox= -6, X = 6, X = -5, x= 5, X = -9, x = 9
15points please help
Answer:The zeros are 6, -5, 9
Step-by-step explanation:
The zeros of the polynomial function are x = 6, x = -5, and x = 9. The correct option is A.
What are polynomials?In mathematics, a polynomial is an expression that solely uses the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables. It is made up of coefficients and indeterminates.
The zeros of the polynomial function are the values of x that make f(x) equal to zero.
The polynomial f(x) is written in factored form as:
f(x) = (x - 6)(x + 5)(x - 9)
The zeros of the polynomial are the values of x that make any of the factors equal to zero. Therefore, the zeros are:
x - 6 = 0, which gives x = 6
x + 5 = 0, which gives x = -5
x - 9 = 0, which gives x = 9
Thus, the zeros of the polynomial function are x = 6, x = -5, and x = 9.
To know more about polynomials follow
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When Houa was born her parents started a college fund for her. They initially put $3500 in the account. They saved in additional $550 per year. How much we have in
the account after 10 years?
Answer: 9000
Step-by-step explanation:
3500+5500=9000
5500=10years x 550/year
Addition can be defined as the process of adding two numbers such that the result is the combined value of the two numbers. The balance that the account will have after 10 years is $9,000.
What is Addition?Addition can be defined as the process of adding two numbers such that the result is the combined value of the two numbers.
When Houa was born her parents started a college fund for her. They initially put $3500 in the account. They saved an additional $550 per year.
Therefore, the balance of the account after 10 years is,
Balance after 10 years = $3500 + $550(Number of years)
= $3500 + $550(10)
= $9,000
Hence, the balance that the account will have after 10 years is $9,000.
Learn more about Addition:
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In the Formula SA=1/2PL+B
What does "L" Mean.
A. the height of the prism
B. the slanted height of the prism
C. the slanted height of the pyramid
D. the height of the pyramid
Please help
Answer:
L = the slanted height of the pyramid
Step-by-step explanation:
The surface area of a pyramid is given by :
[tex]SA=\dfrac{1}{2}PL+B[/tex]
Where
P is perimeter of base of pyramid
L is the slant height of the pyramid
B is the area of base.
So, the correct option is (c) "the slanted height of the pyramid".
Who’s can help me with this, it is to hard
Answer:
x = 10
MB = 16
CM = 16
CB = 32
Step-by-step explanation:
Since it's the mispoint
2x - 4 = x + 6
Subtract x from both sides
x - 4 = 6
Add 4 to both sides
x = 10
MB = 2x - 4
MB = 20 - 4
MB = 16
CM = x + 6
CM = 16
CB = 16 + 16
CB = 32
A salesperson at a furniture store earns a 3% commission on all sales. How much commission does the salesperson earn on a $1400 sale? A) $21 B) $42 C) $420 D) $1,420
Answer:
B
Step-by-step explanation:
What is the slope of line a?
Given:
The graph of a line a.
To find:
The slope of the line a.
Solution:
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the given graph it is clear that the line a passes through the points (-1,1) and (0,-2). So, the slope of the line a is:
[tex]m=\dfrac{-2-1}{0-(-1)}[/tex]
[tex]m=\dfrac{-3}{1}[/tex]
[tex]m=-3[/tex]
The slope of the line a is -3. Therefore, the correct option is C.
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
What is equivalent to 3^-5
Answer:
The answer is the choose: (D)
[tex] {3}^{ - 5} = \frac{1}{ {3}^{5} } [/tex]
Write an inequality for the graph
What does 5-10n equal ?
Jessica is making cookies. Each batch requires 1/4 cups of sugar. If she has 3 cups of sugar, how many batches can she make total?
10. If 1000 cm = 1 l, find the capacity of the following water tank in litre
a) 1 = 200 cm, b = 150 cm, h = 100 cm
[tex] \large \boxed{volume = l \times b \times h}[/tex]
[tex]200 \times 150 \times 100[/tex][tex]3000000 \: \: cm {}^{3} [/tex]Through the statement above we have,
[tex] \small\mathrm{1000 \: cm³ = 1 \: \: }l[/tex][tex]\small\mathrm{1 \: cm {}^{3} = \dfrac{1}{1000} \: }l[/tex][tex] \small\mathrm{3000000 \: cm {}^{3} = 3000000 \times \dfrac{1}{1000} \: }l[/tex][tex] \small\mathrm{3000000 \: cm {}^{3} = 3000000 \times \dfrac{1}{1000} \: }l[/tex][tex]\small\mathrm{ 3000 \: \: litres}[/tex]_____________________________
[tex]\mathrm{ \#TeeNForeveR}[/tex]
Which statements are true? Select all that apply.
Answer:
A,B, D
Step-by-step explanation: I just took that test and i got it right
Suppose that A, B, C, D, and E are matrices with the following sizes:
A B C D E
(4x 1) (4 x 1) (1 x 2) (2 x 1) (1 x 4)
Determine whether the matrix expression E (3B + A) is defined. Matrix is defined Enter the size of the resulting matrix (enter 'NA in each box if undefined).
E (3B + A) is a 3 X 3.
Answer:
The expression E (3B + A) is defined. The size of the resulting matrix is (1 x 1).
Step-by-step explanation:
Let's consider the following operations between matrices.
E (3B + A)
B is a matrix of (4 x 1), that is, it has 4 rows and 1 column. Let F = 3B. This is the product of a scalar by a matrix, which results in a matrix of the same size as the original. Then, F is a matrix of (4 x 1).
Now, let's consider the sum F + A, which we well call G. We can sum F and A because they are of the same size and we will get G, a matrix of the same size, (4 x 1).
Finally, we have the product E . G. We can multiply 2 matrices of sizes (m x k) and (k x n), that is, the number of columns of the first matrix must be equal to the number of rows of the second matrix, and the resulting matrix has a size (m x n). This is the case because E is (1 x 4) and G is (4 x 1), and the resulting matrix will be (1 x 1).
The lowest part of the Caspian Sea has an elevation of 28 meters below sea level. Enter the integer that represents the elevation of the lowest part of the Caspian Sea, in meters
Answer:
-28 meters
Step-by-step explanation:
Sea level is represented as 0 meters typically, so for something that is 28 meters below sea level, you would represent that as -28 meters.
At the city Museum child admission is $6.40 in adult admission is $9.70 on Sunday 149 tickets were sold for a total sales of $1145 how many adult tickets were sold that day
Answer:
Adult=58
Step-by-step explanation:
c=child, a=adult
6.4c+9.7a=1145 equation 1
c+a=149 equation 2
a=149-c modified equation 2 to isolate a
6.4c+9.7(149-c)=1145 substitute value of a from equation 1 into equation 2
6.4c+1445.3-9.7c=1145
-3.3c=-300.3
c=91
solve for a
c+a=149
91+a=149
a=58
Check answer:
6.4c+9.7a=1145
6.4(91)+9.7(58)=1145
582.40+562.60=1145
1145=1145
Suppose that documentation lists the average sales price of a single-family home in the metropolitan Dallas/Ft. Worth/Irving, Texas, area as $213,200. The average home price in Orlando, Florida, is listed as $198,000. The mean of a random sample of 43 homes in the Texas metroplex was $217,800 with a population standard deviation of $30,300. In the Orlando, Florida, area a sample of 35 homes had a mean price of $204,700 with a population standard deviation of $33,800. At the 0.05 level of significance, can it be concluded that the mean price in Dallas exceeds the mean price in Orlando
Answer:
"0.0373" seems to be the appropriate solution.
Step-by-step explanation:
The given values are:
n₁ = 43
n₂ = 35
[tex]\bar{x_1}=217800[/tex]
[tex]\bar{x_2}=204700[/tex]
[tex]\sigma_1=30300[/tex]
[tex]\sigma_2=33800[/tex]
Now,
The test statistic will be:
⇒ [tex]Z=\frac{\bar{x_1}-\bar{x_2}}\sqrt{\frac{\sigma_1^2}{n_1} +\frac{\sigma_2^2}{n_2} }[/tex]
On substituting the given values in the above formula, we get
⇒ [tex]=\frac{217800-204400}{\sqrt{\frac{(30300)^2}{43} +\frac{(33800)^2}{35} } }[/tex]
⇒ [tex]=\frac{217800-204400}{\sqrt{\frac{918090000}{43} +\frac{1142440000}{35} } }[/tex]
⇒ [tex]=\frac{13400}{7347.93}[/tex]
⇒ [tex]=1.7828[/tex]
then,
P-value will be:
= [tex]P(Z>1.7828)[/tex]
= [tex]0.0373[/tex]