The profit function in dollars, is given by P(x)= -0.02x² + 44x - 1750, where x is the number of wireless headphones sold. (a) How many headphones must be sold in order to maximize profit? (b) What is the maximum profit?
To determine the number of headphones that must be sold to maximize profit and the maximum profit, we can analyze the profit function P(x) = -0.02x² + 44x - 1750. The number of headphones sold to maximize profit is 1100, and the maximum profit is $17,050.
(a) To find the number of headphones that maximize profit, we need to identify the x-value at which the profit function reaches its maximum. The maximum point occurs at the vertex of the quadratic function. The x-coordinate of the vertex can be found using the formula x = -b / (2a), wherea and b are the coefficients of the quadratic function. In this case, a = -0.02 and b = 44. Plugging these values into the formula, we find x = -44 / (2 * -0.02) = 1100. Therefore, 1100 headphones must be sold to maximize profit.
(b) To calculate the maximum profit, we substitute the value of x = 1100 into the profit function P(x). P(1100) = -0.02(1100)² + 44(1100) - 1750 = -24200 + 48400 - 1750 = 17050. Hence, the maximum profit is $17,050.
In conclusion, in order to maximize profit, 1100 headphones must be sold, resulting in a maximum profit of $17,050.
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help pleaseee, no links!
Determine L {f(t)} for f (t) = sin (V24) + te- T sin (T) dr. S Ts +1 Fully explain your reasoning to receive full credit. Is it possible for F(s) = 1 + 1 to be the Laplace transform of some function f (t)?
The Laplace transform of [tex][f(t) = \sin{\sqrt{24}} + te^{-t}\sin{t} \implies L{f(t)} = \frac{\sqrt{24}}{s^2 + 24} + \frac{1}{(s + 1)^2 + 1}][/tex] . However, F(s) = 1 + 1 cannot be the Laplace transform of any valid function f(t) because it does not satisfy the properties and rules of Laplace transforms.
To determine the Laplace transform of the function [tex]\[f(t) = \sin{\sqrt{24}} + te^{-t}\sin{t}\][/tex], we need to apply the properties and formulas of Laplace transforms.
1. Laplace Transform of sin(√24):
The Laplace transform of sin(at) is given by [tex]\[F(s) = \frac{a}{s^2 + a^2}\][/tex]. In this case, a = √24.
So, the Laplace transform of [tex]\[\sin{\sqrt{24}} \implies F(s) = \frac{\sqrt{24}}{s^2 + 24}\][/tex].
2. Laplace Transform of [tex]\[te^{-t}\sin{t}\][/tex]:
To find the Laplace transform of this term, we can use the product rule and the Laplace transform of each component.
The Laplace transform of t is given by [tex]\[F(s) = \frac{1}{s^2}\][/tex], and the Laplace transform of e^(-t)sin(t) can be found using the table of Laplace transforms.
Using the table, the Laplace transform of [tex]\begin{equation}\mathcal{L}(e^{-t}\sin(t)) = \frac{1}{(s + 1)^2 + 1}[/tex].
3. Adding the Laplace transforms:
Since the Laplace transform is a linear operator, we can add the individual Laplace transforms of [tex]sin(\sqrt{24})[/tex] and [tex]te^{-t}\sin(t)[/tex] to obtain the Laplace transform of the whole function f(t).
Therefore, [tex]L\{f(t)\} = \frac{\sqrt{24}}{s^2 + 24} + \frac{1}{(s + 1)^2} + 1[/tex]
Now, to address the second part of the question:
Is it possible for F(s) = 1 + 1 to be the Laplace transform of some function f(t)?
No, it is not possible for F(s) = 1 + 1 to be the Laplace transform of a valid function f(t). The Laplace transform is a mathematical operation that converts a function of time (f(t)) into a function of the complex variable s (F(s)). The Laplace transform must follow specific properties and rules, and it is not possible for F(s) = 1 + 1 to satisfy these properties and correspond to a valid function f(t).
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The Laplace transform of
L {f(t)} for f (t) = sin (V24) + te- T sin (T) => Lf(t) = √24/s²+24 + 1/(s+1)²+1 .
However, F(s) = 1 + 1 cannot be the Laplace transform of any valid function f(t) because it does not satisfy the properties and rules of Laplace transforms.
Here, we have,
To determine the Laplace transform of the function
f (t) = sin (V24) + te- T sin (T) , we need to apply the properties and formulas of Laplace transforms.
1. Laplace Transform of sin(√24):
The Laplace transform of sin(at) is given by F(s)= a/s²+a².
In this case, a = √24.
So, the Laplace transform of sin(√24) => F(s)= √24/s²+24 .
2. Laplace Transform of te- T sin (T):
To find the Laplace transform of this term, we can use the product rule and the Laplace transform of each component.
The Laplace transform of t is given by F(s)=1/s², and the Laplace transform of e^(-t)sin(t) can be found using the table of Laplace transforms.
Using the table, the Laplace transform of L(e^(-t)sin(t)) = 1/(s+1)²+1.
3. Adding the Laplace transforms:
Since the Laplace transform is a linear operator, we can add the individual Laplace transforms ofsin(√24) and e^(-t)sin(t) to obtain the Laplace transform of the whole function f(t).
Therefore,
Lf(t) = √24/s²+24 + 1/(s+1)²+1
Now, to address the second part of the question:
Is it possible for F(s) = 1 + 1 to be the Laplace transform of some function f(t)?
No, it is not possible for F(s) = 1 + 1 to be the Laplace transform of a valid function f(t). The Laplace transform is a mathematical operation that converts a function of time (f(t)) into a function of the complex variable s (F(s)). The Laplace transform must follow specific properties and rules, and it is not possible for F(s) = 1 + 1 to satisfy these properties and correspond to a valid function f(t).
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A country has 40 parks that alllow camping and 107 parks that have playground. Of those, 32 parks both allow camping and have playgrounds. The country has a total of 252 parks. What is the probability of randomly selecting a park that neither allows camping nor has a playground? Write your answer as a fraction.
Answer:
Let’s use the formula for the probability of the complement of an event: P(A') = 1 - P(A), where A is the event and A' is the complement of the event. In this case, the event A is selecting a park that either allows camping or has a playground. The complement of this event, A', is selecting a park that neither allows camping nor has a playground. We can use the formula for the probability of the union of two events to find P(A): P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where A and B are two events and A ∩ B is the intersection of the two events. Let’s let event C represent selecting a park that allows camping and event P represent selecting a park that has a playground. Then, we have: P(C ∪ P) = P(C) + P(P) - P(C ∩ P) The probability of each event is equal to the number of parks with that characteristic divided by the total number of parks. We are given that there are 40 parks that allow camping, 107 parks that have playgrounds, and 32 parks that both allow camping and have playgrounds. The country has a total of 252 parks. So we have: P(C) = 40/252 P(P) = 107/252 P(C ∩ P) = 32/252 Substituting these values into our formula for P(C ∪ P), we get: P(C ∪ P) = (40/252) + (107/252) - (32/252) = (40 + 107 - 32)/252 = 115/252 Now we can use our formula for the probability of the complement of an event to find P(A'): P(A') = 1 - P(A) = 1 - P(C ∪ P) = 1 - (115/252) = (252/252) - (115/252) = (252 - 115)/252 = **137/252** So the probability of randomly selecting a park that neither allows camping nor has a playground is 137/252.
Step-by-step explanation:
Answer:
Ermm, hey Vivi, give me a sec
Step-by-step explanation:
To find the probability of randomly selecting a park that neither allows camping nor has a playground, we need to determine the number of parks that fit this criteria and divide it by the total number of parks.
Let's denote:
A = Number of parks that allow camping (40)
B = Number of parks that have a playground (107)
C = Number of parks that both allow camping and have a playground (32)
T = Total number of parks (252)
To find the number of parks that neither allow camping nor have a playground, we can use the principle of inclusion-exclusion:
Number of parks that neither allow camping nor have a playground = T - (A + B - C)
Substituting the given values, we have:
Number of parks that neither allow camping nor have a playground = 252 - (40 + 107 - 32)
= 252 - 147
= 105
Therefore, there are 105 parks that neither allow camping nor have a playground.
To calculate the probability, we divide this number by the total number of parks:
Probability = Number of parks that neither allow camping nor have a playground / Total number of parks
= 105 / 252
The probability of randomly selecting a park that neither allows camping nor has a playground is 105/252.
What is the equation, in slope-intercept form, of the line that contains the points (3, -4) and (5, -6)? A. y = -x - 1 B. y = -x + 1 C. y = x - 1 D. y = x + 1
Answer:
Hi! The answer to your question is A. [tex]y=-x-1[/tex]
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☁Brainliest is greatly appreciated!☁
Hope this helps!!
- Brooklynn Deka
Answer:
a
Step-by-step explanation:
Quadrilateral ABCD is reflected across line m to create quadrilateral A'B'C'D',
What is the length of segment
Answer:
41
Step-by-step explanation:
Its correct ^^
Viking Voyager specializes in the design and production of replica Viking boats. On January 1, 2021, the company issues $2,900,000 of 9% bonds, due in 20 years, with interest payable semiannually on June 30 and December 31 each year.
Required:
1. If the market interest rate is 9%, the bonds will issue at $2,900,000. Record the bond issue on January 1, 2021, and the first two semiannual interest payments on June 30, 2021, and December 31, 2021. (If no entry is required for a particular transaction/event, select "No Journal Entry Required" in the first account field.)
2. If the market interest rate is 10%, the bonds will issue at $2,651,193. Record the bond issue on January 1, 2021, and the first two semiannual interest payments on June 30, 2021, and December 31, 2021. (If no entry is required for a particular transaction/event, select "No Journal Entry Required" in the first account field. Round your answers to the nearest dollar amount.)
3. If the market interest rate is 8%, the bonds will issue at $3,186,995. Record the bond issue on January 1, 2021, and the first two semiannual interest payments on June 30, 2021, and December 31, 2021. (If no entry is required for a particular transaction/event, select "No Journal Entry Required" in the first account field. Round your answers to the nearest dollar amount.)
The bond issue and interest payments are recorded differently based on the market interest rate.
How to find the bond issue and interest payments recorded based on the market interest rate?The recording of bond issue and interest payments depends on the market interest rate. When the market interest rate is equal to the stated rate of 9%, the bonds will issue at their face value of $2,900,000.
On January 1, 2021, the company would debit Cash for $2,900,000 and credit Bonds Payable for $2,900,000 to record the bond issue.
The interest payments on June 30, 2021, and December 31, 2021, would be recorded by debiting Interest Expense for $130,500 ([$2,900,000 * 9%]/2) and crediting Cash for $130,500.
However, when the market interest rate is 10% or 8%, the bonds will issue at a discount or premium, respectively. If the market interest rate is 10%, the bonds will issue at $2,651,193 (rounded).
In this case, the bond issue on January 1, 2021, would be recorded by debiting Cash for $2,651,193 and crediting Discount on Bonds Payable for $248,807 ($2,900,000 - $2,651,193).
The interest payments on June 30, 2021, and December 31, 2021, would be recorded as mentioned earlier.
Conversely, if the market interest rate is 8%, the bonds will issue at $3,186,995 (rounded).
The bond issue on January 1, 2021, would be recorded by debiting Cash for $3,186,995 and crediting Premium on Bonds Payable for $286,995 ($3,186,995 - $2,900,000).
The interest payments on June 30, 2021, and December 31, 2021, would be recorded accordingly.
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Let * be an operation defined on the real numbers R by x*y = x +y - ry. Please answer the following questions and explain your answers. (a) Is * closed on the real numbers? (b) Is * commutative? (c) Is * associative? (d) Does * have an identity element? If so, does every integer have an inverse? (e) Is (R, *) a group?
(a) No, the operation * is not closed on the real numbers.
To determine closure, we need to check if for any two real numbers x and y, xy is also a real number. However, if we choose r to be any real number other than 1, the result of xy will involve a term (-ry) that may not be a real number, breaking closure.
(b) No, the operation * is not commutative.
Commutativity requires that xy = yx for all real numbers x and y. However, in this case, xy = x + y - ry, while yx = y + x - rx. Since ry and rx are not generally equal, the operation is not commutative.
(c) No, the operation * is not associative.
Associativity requires that (xy)z = x(yz) for all real numbers x, y, and z. However, if we substitute the definition of * into both sides of the equation, we get different expressions that are generally not equal. Therefore, the operation * is not associative.
(d) Yes, the operation * has an identity element.
The identity element e is a real number such that for any real number x, xe = ex = x. In this case, choosing e = 0 satisfies the identity condition, as x0 = x + 0 - r0 = x. However, not every real number has an inverse since there are values of x for which xy = e has no solution, violating the requirement for every element to have an inverse.
(e) No, (R, *) is not a group.
A group requires closure, associativity, an identity element, and every element having an inverse. Since the operation * fails to satisfy closure and does not have inverses for all real numbers, it cannot form a group.
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PLEASE HELP FAST WILL GIVE BRAINLIEST
Answer:
QT=8 VQ=17 this is what i came up with because i myself have ur question and i don't know what it is?
Someone help me out plzz
Answer:
with what? You forget to attach the problem lol
Step-by-step explanation:
Answer: What is the question you need help with??
Step-by-step explanation:
A researcher wanted to determine the number of televisions in households. He conducts a survey of 40 randomly selected households and obtains the data in the accompanying table. Complete parts (a) through (h) below. 囲 (a) Are these data discrete or continuous? Explain O A. The given data are discrete because they can take on any real value. Click the icon to view the table of television counts. Table of television counts B. ° C. O D. The given data are discrete because they can only have whole number values. The given data are continuous because they can take on any real value. The given data are continuous because they can only have whole number values. 0 3 2 211 1 3P 3 21 3 21 3 2 2 1 1 3 1 11 2
The correct statement regarding the variable in this problem is given as follows:
D. The given data are discrete because they can only have whole number values.
What are continuous and discrete variables?Continuous variables: Can assume decimal values.Discrete variables: Assume only countable values, such as 0, 1, 2, 3, …In the context of this problem, the variable is the number of televisions, which must be a whole number, such as 0, 1, 2, ..., 10, ..., hence option D is the correct option for this problem.
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Which choice does not represent a set of endpoints that create a horizontal line segment? A (1, 13) and (14, 13) B (-10, 0) and (-10, 1) C (3, -20) and (-11, -20) D (16, 2) and (-2, 2)
Answer:
Step-by-step explanation:
horizontal line segment: B (-10, 0) and (-10, 1)
HELP HELP PLS I NEED TO DO THIS BY TONIGHT PLS HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Question:What percent of the time did Trent spend at least 80 minutes on homework?
Answer:
25%
Step-by-step explanation:
Why is convenience sampling biased? a. It takes too long to obtain b. none of the above c. The sample does not represent the population d. is too easy
Answer:
A
Step-by-step explanation:
Answer:
A)
Step-by-step explanation:
Let the inverse demand function for the vaccine of the monopolist BoTex be given by:pq=360-2q (p: Price in € ;
q: Quantity in millions of units). The cost function is given by 1000 +q2.
a) Calculate the profit-maximizing quantity of BoTex.
b) Calculate the monopoly price.
c) Calculate the profit.
The profit-maximizing quantity of Bo Tex is 90 million units.
The monopoly price is 180 million euros.
The profit of Bo Tex is 8400 million euros.
a) Calculation of profit-maximizing quantity of BoTex:
In order to calculate the profit-maximizing quantity of Bo Tex, we have to differentiate the total profit function with respect to q and equate the result to zero.
Total profit (Π) = Total revenue (TR) – Total cost (TC)TR = p.
q = (360 - 2q)q = 360q - 2q2TC = 1000 + q2Π = TR - TC
Differentiating Π w.r.t. q: {d \Pi}{dq} = 360 - 4q
Equating it to zero, we get:
360 - 4q = 0q = 90 million units
Therefore, the profit-maximizing quantity of Bo Tex is 90 million units.
b) Calculation of monopoly price:
To calculate the monopoly price, we need to substitute the quantity obtained in part (a) into the inverse demand function:
pq = 360 - 2q = 360 - 2(90) = 180 million euro
Therefore, the monopoly price is 180 million euros.
c) Calculation of profit:
We have to substitute the value of quantity (90 million units) and price (180 million euros) into the total revenue and total cost functions.
Total revenue (TR) = p.q = 180 × 90 = 16,200 million euro
Total cost (TC) = 1000 + q2 = 1000 + 902 = 8200 million euro
Profit (Π) = TR - TC = 16,200 - 8200 = 8400 million euro
Therefore, the profit of Bo Tex is 8400 million euros.
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Help is much needed pls. I can only put 15 points.
Answer:
9.2
Step-by-step explanation:
first i added 5 + 3 = 8
then i did 1 1/5 + 8=9 1/5
2. (6 points) Use Bisection method to find solution accurate to within 10-5 for the following problems: x2 + 2x – 3 = 0, for – 2 < x < 2, X – 2-4 = 0, for 0 < x < 1. Show the number of iteration
Using the Bisection method, we need to find solutions accurate to within [tex]10^{-5}[/tex] for the equations [tex]x^{2}[/tex]+ 2x - 3 = 0 in the range -2 < x < 2 and x - [tex]2^{-4}[/tex] = 0 in the range 0 < x < 1.
For the equation [tex]x^{2}[/tex] + 2x - 3 = 0:
We start with an initial interval [-2, 2] and evaluate the function at the midpoint of the interval. If the function value is close to 0, we consider it as the solution. Otherwise, we narrow down the interval by dividing it in half and selecting the subinterval where the function changes sign. This process is repeated until the desired accuracy is achieved (within [tex]10^{-5}[/tex]). The number of iterations required will be recorded.
For the equation x - [tex]2^{-4}[/tex]= 0:
We follow the same steps as above but with the initial interval [0, 1]. Again, we iterate until the desired accuracy is reached and keep track of the number of iterations.
By applying the Bisection method and counting the number of iterations for each equation, we can find solutions accurate to within 10^-5 for both equations and determine the required number of iterations for each case.
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f(1) = -6
f(2) = -4
f(n) = f(n − 2) + f(n − 1)
f(3) =
Answer:
-10
Step-by-step explanation:
f(n)= f(n-2)+f(n-1)
• Put n = 3
=> f(3) = f(3-2) + f(3-2)
=> f(3) = f(1) + f(2)
=> f(3) = -6 + -4
=> f(3) = -10
Answer:
it in a file here
Step-by-step explanation:
xycba.com/file
Maria is decorating her school's cafeteria for the end- of- year dance. The dimensions of the room are labelled below. What is the smallest length of streamer that will go around the entire perimeter of the room? Round your answer to the nearest foot.
Answer:
59 feets
Step-by-step explanation:
The length of bottom base = (8 + 2 + 2) = 12
Circumference of semicircle : 2πr/2 ; r = 4/2 = 2
Circumference of semicircle = π * 2 = 6.28
Length of streamer that will go around the entire perimeter :
From the figure attached :
Circumference of semicircle = 6.28
6.28 + 6 + 2(down) + 2(right) + 8(down) + 2(left) + 2(up) + 2(left) + 2(down) + 8(left) + 10
6.28 + 6 + 2 + 2 + 8 + 2 + 2 + 2 + 2 + 8 + 10 = 50.28 feets = 50 ft (nearest whole number)
what is the solution of x equals 2 + sqrt x - 2
a.) x=2
b.)x=3
c.)x=2 or x=3
d.) no solution
Answer:
x = 2 or x = 3
Step-by-step explanation:
x = 2 + sqrt(x - 2)
x - 2 = sqrt(x - 2) You could divide both sides by sqrt(x - 2)
sqrt(x - 2) = 1 Square both sides
x - 2 = 1 Add 2 to both sides
x = 3
There is a second way.
x - 2 = sqrt(x - 2) Square
x^2 - 4x + 4 = x - 2 Transfer x - 2 to the left
x^2 - 5x + 6 = 0 Factor
(x - 2)(x-3) = 0 Find the roots.
x - 2 = 0
x = 2
x - 3 = 0
x = 3
We have to check both results.
x = 2 + sqrt(x - 2)
2 = 2 + sqrt(2 -2)
2 = 2 + 0
2 = 2 This seems to work.
x = 2 + sqrt(x - 2)
3 = 2 + sqrt(3 - 2)
3 = 2 + sqrt(1)
3 = 2 + 1
3 = 3 And this works.
Find the lengths of the curves in y = tan x, -7/3 = x < 0
The length of the curve y = tan x, -7/3 ≤ x < 0 is approximately 4.481 units.
To calculate the length of the curve, we can use the arc length formula. For a function y = f(x) on the interval [a, b], the arc length is given by the integral:
L = ∫[a,b] √(1 + (f'(x))²) dx,
where f'(x) represents the derivative of f(x) with respect to x.
In this case, the function is y = tan x and the interval is -7/3 ≤ x < 0. To find the derivative, we differentiate y = tan x with respect to x, which gives:
y' = sec² x.
Now we can substitute these values into the arc length formula:
L = ∫[-7/3,0] √(1 + (sec² x)²) dx.
Simplifying the expression under the square root gives:
L = ∫[-7/3,0] √(1 + tan⁴ x) dx.
To evaluate this integral, we can make a substitution. Let u = tan x. Then du = sec² x dx. Using this substitution, the integral becomes:
L = ∫[tan(-7/3),tan(0)] √(1 + u⁴) du.
Now we need to find the limits of integration. Since -7/3 ≤ x < 0, we can evaluate the tangent function at these values to get:
L = ∫[tan(-7/3),0] √(1 + u⁴) du.
Finally, we can use numerical methods or a calculator to evaluate this integral. The result is approximately 4.481 units.
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How many edges does the complete bipartite graph K_(4, 9) have? Your answer
The number of edges in the complete bipartite graph is 36
How to determine the number of edges in the complete bipartite graphFrom the question, we have the following parameters that can be used in our computation:
K = (4, 9)
The above means that
The vertices in the sets of the bipartite graph are
Set 1 = 4
Set 2 = 9
The number of edges in the complete bipartite graph is then calculated as
Vertices = Set 1 * Set 2
So, we have
Vertices = 4 * 9
Evaluate
Vertices = 36
Hence, there are 36 edges in the bipartite graph
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Determine the are length on a circle of radius 7 and an included angle of 4.5 radians.
Answer:
The arc length of a circle is 31.5.
Step-by-step explanation:
The arc length can be found as follows:
[tex] arc = r\theta [/tex]
Where:
arc: is the length of the arc of the circle
r: is the radius = 7
θ: is the angle = 4.5 rad
[tex] arc = r\theta = 7*4.5 = 31.5 [/tex]
Therefore, the arc length of a circle is 31.5.
I hope it helps you!
Alright here is a repost
Answer:
50 degrees
Step-by-step explanation:
180-130=50
Answer:
The answer was already given(50°), but I can explain it further.
Step-by-step explanation:
These are supplementary angles, two angles that, together, make 180 degrees.
We know the angle of one of them, 130°, and in order to find the other one, x, we have to subtract what the entire this equals, 180°:
180° - 130° = x
50° = x
x = 50°
I hope this helped you, even if this was two hours ago.
Which golf ball went higher, and how many feet? (Desmos!) - Just added the answer choices!
Answer:
Max height: 64 feet, and the socond one was higher.
Step-by-step explanation:
The max height is the y value of the vertex, because that’s when the graph peaks.
we can already very clearly see the vertex on the graph, so we don’t need to calculate it.
the max height of the second golf ball is 64 feet.
Now let’s look at the max height on the first golf ball.
we get the equation
h=-16t squared + 48t
to find the vertex of this, we can use the formula -b/2a
-48/-32 = 1.5
1.5 is the t value of this vertex.
to find the h value, we plug it in.
h = -16 (1.5) squared + 48(1.5)
h =2.25 times -16 + 72
h = -36 +72
h = 36
the first one is 36 max height, and the second is 64. The second one is bigger.
PLS HELP ME ASAP PLS PLS PSL
Answer:
25
Step-by-step explanation:
Find the length of side x in simplest radical form with a rational denominator
Answer:
x = 6
Step-by-step explanation:
We solve that above question using the trigonometric function of Tangent
Tan theta = Opposite/Adjacent
Theta = 45°
Opposite = 6
Adjacent = x
tan 45° = 6/x
tan 45 in rational form = 1
1 = 6/x
Cross Multiply
x = 6
Solve the triangle using the law of cosines
edg2021
How to write the equation for ¨The quotient of x and three increased by 12 is 20. What is x?
Answer:
x/3 + 12 = 20
Step-by-step explanation:
what is the measure of ∠x?
Answer:
83°
Step-by-step explanation:
WZ is a straight line. Angles at a straight line add up to 180°.
180 - 97 =83°