Could you please elaborate? Is there an equation?
Answer: What do you need to know?
Step-by-step explanation:
please can someone answer this.
Answer:
• x = -4, x = 0, x = 1
Step-by-step explanation:
x is a factor of all terms, so x=0 is a zero. (Eliminates choices 1 and 5.)
The sum of coefficients is 0, so x=1 is a zero. (Eliminates choices 3 and 4.)
Reversing the sign of the odd-degree terms gives signs of -++, so there is one sign change, hence one negative real root (by Descartes' rule of signs). This confirms choice 2 as the answer.
___
Of course, your graphing calculator can answer this almost as quickly.
Find the value of x in the triangle above
Answer:
62 degrees
Step-by-step explanation:
degrees in a triangle: 180
this triangle is isosceles, so remaining 2 angles must be congruent
2x+56=180
2x=124
x=62
Which of the following is a zero for the function f(x) = (x + 3)(x − 7)(x + 5)? x = −7 x = −3 x = 3 x = 5
Answer:
x = −3
Step-by-step explanation:
A zero of a function is a value that makes one of the factors be zero.
To make x+3 = 0, x = -3.
To make x-7 = 0, x = 7.
To make x+5 = 0, x = -5.
Of these values that make the factors zero, only x = -3 is on your choices list.
Answer: The correct option is
(B) x = - 3.
Step-by-step explanation: We are given to select the correct zero of the following polynomial function :
[tex]f(x)=(x+3)(x-7)(x+5)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
The zeroes of the function f(x) are given by
[tex]f(x)=0\\\\\Rightarrow (x+3)(x-7)(x+5)=0\\\\\Rightarrow x+3=0,~~x-7=0,~~x+5=0\\\\\Rightarrow x=-3,7,-5.[/tex]
Therefore, the zeroes of the given function are
x = -3, x = 7 and x = -5.
Thus, the correct option is
(B) x = -3.
Find the circumference of a circle:
Whose radius is 3 ½ in. (22/7)
Whose diameter is 3.6 (3.14)
Answer:
1. 22 in
2. 11.304 units
Step-by-step explanation:
Formulas for the circumference are
C = 2πr
C = πd
___
1. Put the given numbers in the appropriate formula:
C = 2·(22/7)·(7/2 in) = 22 in
__
2. Put the given numbers in the appropriate formula:
C = 3.14·3.6 = 11.304 . . . units
50 POINTS
Which of the following can be determined from the table above?
A.
Events B and C are independent.
B.
Events D and A are independent.
C.
Events C and A are independent.
D.
Events E and B are independent.
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
P(A) = 0.5
P(B) = 0.5
P(C) = 0.15
P(D) = 0.7
P(E) = 0.15
We need to find the independent events.
When we consider,
P(A∩D) = P(Event A and Event D) = 0.35
and
P(A) × P(D) = 0.7 × 0.5 = 0.35
We get that
P(A∩D)= P(A) × P(D) = 0.35
All other options are not satisfying the conditions of "Independent events".
Hence, Option 'B' is correct.
Answer:
option b would be the correct answer
Step-by-step explanation:
A box contains 8 red balls, 5 brown balls, 4 purple balls, and 3 green balls. What is the probability that a purple ball will be selected from the box after a red ball is taken out and not replaced?
Write the probability as a percent. Round to nearest tenth of a percent as needed.
Answer:
21.1 percent
Step-by-step explanation:
Total balls after -1 red ball=7+5+4+3=19
Prob of purple ball= purple ball/total balls
= 4/19
=0.2105...
percentage:21.1%
The probability of selecting a red ball and then a purple one without replacement from a box containing 8 red, 5 brown, 4 purple, and 3 green balls is approximately 8.4%.
Explanation:In probability, there are two events of interest here: selecting a red ball and then selecting a purple ball. Since the total number of balls changes after picking the red ball, these are dependent events. The probability of the first event (selecting a red ball) is 8 out of 20 (total balls). Then, with a red ball removed and not replaced, the probability of the second event (selecting a purple ball) is 4 out of 19. To find the overall probability, we multiply the probabilities of these two events.
To convert the probability to a percentage, multiply the result by 100. By doing this, the probability rounds to approximately 8.4%.
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the researchers have also determined that the current rate of the rise in water level is twice the 1880 to 2009 rate. assuming that this new rate began in 2009, you can use the function g(x) = 3.2(x - 2009) + 206, which models the total rise in water level in mm since 1880 for any year x, beginning in 2009.
1. what is the domain of g(x)?
2. write a simplified function, g(x)
3. according to the model, what will be the total rise in water level by 2025?
4. when will the total rise in water level be equal to about half a meter?
please help and thank you!!
Answer:
x ≥ 20093.2x -6222.8257.2 mmyear 2100Step-by-step explanation:
1. The problem statement tells you the function applies for year values (x) 2009 and later. The domain is real numbers greater than or equal to 2009.
__
2. We can use the distributive property to eliminate parentheses:
3.2(x -2009) +206 = 3.2x -6428.8 +206
= 3.2x -6222.8
__
3. Put 2025 in the equation and do the arithmetic
g(2025) = 3.2·2025 -6222.8 = 257.2 . . . . mm
__
4. Put this value of level rise in the equation and solve for x.
g(x) = 3.2x -6222.8
500 = 3.2x -6222.8 . . put 500 mm where g(x) is in the equation
6722.8 = 3.2x . . . . . . . add 6222.8
x = 6722.8/3.2 = 2100.875
The water rise will be equal to about half a meter late in the year 2100.
[tex]4(x - 8) {}^{3} - 18 = 846[/tex]
need help solving it
Answer:
x=14
Step-by-step explanation:
4(x - 8)³ - 18 = 846
4(x - 8)³ = 864
(x - 8)³ =216
∛(x - 8)³ =∛216
x-8 = 6
x= 6+8
x=14
Answer:
x=14
Step-by-step explanation:
look this solution :
Answer this question please; number 5... show all work thank you
Answer:
rate of the plane in still air is 33 miles per hour and the rate of the wind is 11 miles per hour
Step-by-step explanation:
We will make a table of the trip there and back using the formula distance = rate x time
d = r x t
there
back
The distance there and back is 264 miles, so we can split that in half and put each half under d:
d = r x t
there 132
back 132
It tells us that the trip there is with the wind and the trip back is against the wind:
d = r x t
there 132 = (r + w)
back 132 = (r - w)
Finally, the trip there took 3 hours and the trip back took 6:
d = r * t
there 132 = (r + w) * 3
back 132 = (r - w) * 6
There's the table. Using the distance formula we have 2 equations that result from that info:
132 = 3(r + w) and 132 = 6(r - w)
We are looking to solve for both r and w. We have 2 equations with 2 unknowns, so we will solve the first equation for r, sub that value for r into the second equation to solve for w:
132 = 3r + 3w and
132 - 3w = 3r so
44 - w = r. Subbing that into the second equation:
132 = 6(44 - w) - 6w and
132 = 264 - 6w - 6w and
-132 = -12w so
w = 11
Subbing w in to solve for r:
132 = 3r + 3(11) and
132 = 3r + 33 so
99 = 3r and
r = 33
A spinner has five equal sections that are numbered 1-5. In which distributions does the variable X have a binomial distribution? Select each correct answer.
A.) When the spinner is spun multiple times, X is the number of spins until it lands on 5.
B.) When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.
C.) When the spinner is spun three times, X is the sum of the numbers the spinner lands on.
D.) When the spinner is spun five times, X is the number of times the spinner lands on 1.
Answer: The answer is C
Step-by-step explanation: If you think about it the spinner only spun 3 times and when that happens them you sum up X
(C) When the spinner is spun three times, X is the sum of the numbers the spinner lands on.
Binomial Distribution:The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability [tex]q=1p[/tex]). This distribution is used in probability theory and statistics. A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results. For a single trial, or [tex]n=1[/tex], the binomial distribution is a Bernoulli distribution. The popular binomial test of statistical significance is based on the binomial distribution.Therefore, the correct option is (C) When the spinner is spun three times, X is the sum of the numbers the spinner lands on.
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Which of these is a key feature of an experimental study? A. The treatment in the experiment should be simple enough for each individual in the experimental group to understand. B. The treatment in the experiment must vary for each individual in the experimental group. C. The treatment in the experiment must be applied to each of the individuals in the experimental group. D. The treatment in the experiment should be short so that each individual is tested quickly.
Answer:
I believe it is "E"
Step-by-step explanation:
E-series can eat my memes
Kill me please I'm Swedish ree
Answer: The key feature in the experimental study is C. The treatment in the experiment must be applied to each of the individuals in the experimental group. This is because it is made sure that the variables and conditions in different correspondents are applied so that actual results may be concluded.
Step-by-step explanation:
Consider the following function. f(x) = 9 − x2/3 Find f(−27) and f(27). f(−27) = f(27) = Find all values c in (−27, 27) such that f '(c) = 0. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) c = Based off of this information, what conclusions can be made about Rolle's Theorem? This contradicts Rolle's Theorem, since f is differentiable, f(−27) = f(27), and f '(c) = 0 exists, but c is not in (−27, 27). This does not contradict Rolle's Theorem, since f '(0) = 0, and 0 is in the interval (−27, 27). This contradicts Rolle's Theorem, since f(−27) = f(27), there should exist a number c in (−27, 27) such that f '(c) = 0. This does not contradict Rolle's Theorem, since f '(0) does not exist, and so f is not differentiable on (−27, 27). Nothing can be concluded.
I guess the function is [tex]f(x)=9-x^{2/3}[/tex]. Then [tex]f(-27)=0[/tex] and [tex]f(27)=0[/tex].
The derivative is [tex]f'(x)=-\dfrac23 x^{-1/3}[/tex], but there is no [tex]c[/tex] such that
[tex]-\dfrac23c^{-1/3}=0[/tex]
This doesn't contradict Rolle's theorem because [tex]f'(0)[/tex] does not exists. In other words, [tex]f[/tex] is not differentiable on (-27, 27), so the conditions of Rolle's theorem are not met. (Looks like that would be the last option, or the second to last option if the last one is "Nothing can be concluded")
The function f(x) = 9 - x²/3 is even, and its derivative f'(c) equals to zero at c=0, which lies within the interval (-27, 27). Therefore, it does not contradict Rolle's theorem.
Explanation:The function in question is f(x) = 9 - x²/3. When we substitute x with -27 and 27, we get f(-27) = 9 - ((-27)²/3) = -243 and f(27) = 9 - (27²/3) = -243. This confirms that the function is even as f(-27) = f(27).
To find the critical values, we'll take the derivative of the function, which gives us f'(x) = -2x/3. We set f '(c) = 0, solving for c, and determine c = 0. Rolle's Theorem states that if a function is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one c in the interval (a, b) such that f '(c) = 0. With f(-27) = f(27) and the derivative proving to be zero at c=0 (which is inside the interval (-27,27)) this does not contradict Rolle's theorem.
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Derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.
1. Divide all terms in the equation by a.
2. Subtract the constant (the term without an x) from both sides.
3. Add a constant (in terms of a and b) that will complete the square.
4. Take the square root of both sides of the equation.
5. Solve for x.
Answer:
The result is the well-known quadratic formula: x = (-b±√(b²-4ac))/(2a)
Step-by-step explanation:
Start with the standard form quadratic equation:
ax² +bx +c = 0
1. Divide by a
x² +(b/a)x +(c/a) = 0
2. Subtract the constant
x² +(b/a)x = -(c/a)
3. Complete the square
x² +(b/a)x + (b/(2a))² = (b/(2a))²-(c/a)
(x +b/(2a))² = (b²-4ac)/(2a)²
4. Take the square root
x +b/(2a) = ±√(b²-4ac)/(2a)
5. Subtract the constant on the left to get x by itself
x = (-b±√(b²-4ac))/(2a)
Final answer:
The quadratic formula, which provides the solution to the standard quadratic equation ax² + bx + c = 0, is derived through a series of algebraic manipulations, including dividing by a, completing the square, taking the square root, and solving for x.
Explanation:
Derivation of the Quadratic Formula
The objective is to derive the quadratic formula from the standard quadratic equation (ax² + bx + c = 0). Following the given steps:
Divide all terms by a: x² + (b/a)x + (c/a) = 0.Subtract c/a from both sides to isolate the x terms: x² + (b/a)x = -c/a.Add the square of half the coefficient of x to both sides to complete the square: (b/2a)². Now the equation is x² + (b/a)x + (b/2a)² = (b/2a)² - c/a.Take the square root of both sides: x + (b/2a) = ±√(b² - 4ac)/2a.Solving for x leads to the quadratic formula: x = (-b ± √(b²- 4ac))/(2a).which fraction is closer to 0 than 1
Answer:
5/12
Step-by-step explanation:
Since 1/2 is the same distance from zero and one, we can use it to judge whether a fraction is closer to 0 or 1.
Since 5/8 is greater than 4/8 which is 1/2, it is closer to 1.
Since 8/10 is greater than 5/10 which is 1/2, it is closer to 1.
Since 5/12 is less than 6/12 which is 1/2, it is closer to 0.
So our answer is C. 5/12
The value close 0 than 1 is 0.41667.
FractionA fraction is a part of a whole number. for example, [tex]\bold{\dfrac{1}{4}}[/tex] represent a quarter of a number. Similarly, when we solve the fraction meaning [tex]\bold{\dfrac{1}{4}}[/tex] in the decimal form we divide the numerator, therefore, 1 in this case with the denominator as 4 in this case. the value thereafter we get is known as the decimal form of a fraction.
for example, = 0.25.
DecimalAlso, to convert a decimal to a fraction we simply divide the number by a multiple of 10. the number will be depending upon the number of numbers are after the decimal.
for example, 0.25 will be written as [tex]\bold{\dfrac{25}{100}}[/tex] while 0.5 will be written as [tex]\bold{\dfrac{5}{10}}[/tex].
Now, solving the question,
Bring every fraction to decimal form,
[tex]\bold{\dfrac{5}{8}= 0.625}[/tex]
[tex]\bold{\dfrac{8}{10} = 0.8}[/tex]
[tex]\bold{\dfrac{5}{12} = 0.41\overline6}[/tex]
[tex]\bold{\dfrac{7}{14} = 0.5}[/tex]
Hence, the value close 0 than 1 is 0.41667.
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which fraction is equivalent to 1 use the number line to help answer the question
10/10 it simplifies to 1
Answer: 10/10
Step-by-step explanation:
10 divided by 10 is 1.
Which is most likely to have a mass of 3 grams? A. an apple B. a backpack C. a paper clip D. a cat
Answer:
C. a paper clip
Step-by-step explanation:
An apple generally weighs more than 3 grams, and can go even into oz.
Depending on the type of material the backpack is made of, and also how big it is, the mass can vary, however, it is safe to say the backpack will be more than 3 grams.
A cat definitely weighs more than 3 grams. Any born cat that weighs only 3 grams will not survive.
~
For this case we have the following options:
An apple, it is known that the apple will never weigh 3 grams.
A backpack will not have that weight either.
A cat would never weigh 3 grams or be newborn.
To have an object of 3 grams, the object must be very light.
A paperclip is very likely to weigh 3 grams because it is a very small and extremely light object.
Answer:
Option C
Given: m KP =2m IP , m IVK =120° Find: m∠KJL.
Will give 99 points!!!
Answer:
KJL = 40 degrees
Step-by-step explanation:
KJL = 1/2*( arc KP - arc IP)
arc IPK=360-120=240
KP=2(IP)
Kp=2x, IP = x
3x=240, x=80
KP=160
IP=80
KJL=(160-80) / 2 = 40 degrees
Answer:
40°
Step-by-step explanation:
write a polynomial function in standard form with the given roots: -4i
Answer:
[tex]f(x)=x^2+16[/tex]
Step-by-step explanation:
By the conjugate rule, if -4i is a root, then so is +4i. So we have 2 roots, thus, we have a second degree polynomial (namely, a quadratic). If
x = -4i, then
x + 4i is a root.
If
x = 4i, then
x - 4i is a root.
Having (x - 4i)(x + 4i) as roots, we can now FOIL them together to get a polynomial of least degree.
FOILing gives us
[tex]x^2+4ix-4ix-16i^2[/tex]
Notice that the +4ix and the -4ix cancel each other out, leaving you with
[tex]x^2-16i^2[/tex]
Since
[tex]i^2=-1[/tex]
we can make the substitution:
[tex]x^2-16(-1)[/tex]
which simplifies to
[tex]x^2+16[/tex]
In function notation form:
[tex]f(x)=x^2+16[/tex]
Final answer:
The polynomial function in standard form with the root -4i is f(x) = x² + 16. We derive this by realizing that the conjugate, 4i, is also a root and multiplying the factors (x + 4i)(x - 4i), simplifying to the quadratic polynomial.
Explanation:
To write a polynomial function with the given root -4i, we must take into consideration that complex roots come in conjugate pairs for polynomials with real coefficients. Hence, if -4i is a root, then its conjugate 4i must also be a root. The factors of the polynomial corresponding to these roots are (x + 4i) and (x - 4i).
We can find the polynomial by multiplying these two factors:
(x + 4i)(x - 4i)
Applying the difference of squares, we get:
x² - (4i)²
x² - (-16)
x² + 16
The polynomial function in standard form with the given root -4i is:
f(x) = x² + 16
What is the degree of x?
Subtract the smaller angle from the larger angle and divide by 2.
66 -14 = 52
52/2 = 26
x = 26
The graph of the function y = cos(2x) is shown below.
Answer:D pie
Step-by-step explanation:
You get 2pie/2 cancel out you get pie
The period of y=cos(2x) is π, so the frequency is 1/π.
The key features of the graph are:
Amplitude: The amplitude of the graph is 1, which means the function oscillates between −1and 1.
Period: The period of the graph is π, which means the function completes one cycle every πunits on the x -axis. This is because the frequency of the function is 2, which means it completes two cycles for every 2π units on the x -axis.
Midline: The midline of the graph is y=0. This is because the function is neither shifted up nor down.
Extrema: The graph has maxima at x=2kπ for any integer k, and minima at x=2(2k+1)πfor any integer k.
The graph of the function y=cos(2x). The frequency of a trigonometric function is the reciprocal of its period. The period of y=cos(2x) is π, so the frequency is 1/π.
Solve the equation on the interval
Answer:
The solutions of the equations are π/3 , 2π/3 , 4π/3 , 5π/3
Step-by-step explanation:
* Lets revise the four quadrant before solving the equation
# First quadrant the measure of all angles is between 0 and π/2
the measure of any angle is α
∴ All the angles are acute
∴ All the trigonometry functions of α are positive
# Second quadrant the measure of all angles is between π/2 and π
the measure of any angle is π - α
∴ All the angles are obtuse
∴ The value of sin(π - α) only is positive ⇒ sin(π - α) = sinα
# Third quadrant the measure of all angles is between π and 3π/2
the measure of any angle is π + α
∴ All the angles are reflex
∴ The value of tan(π + α) only is positive ⇒ tan(π + α) = tanα
# Fourth quadrant the measure of all angles is between 3π/2 and 2π
the measure of any angle is 2π - α
∴ All the angles are reflex
∴ The value of cos(2π - α) only is positive ⇒ cos(2π - α) = cosα
* Now lets solve the equation
∵ 4 sin²Ф - 3 = 0 ⇒ the domain is 0 ≤ Ф ≤ 2π
- Add 3 for both sides
∴ 4 sin²Ф = 3 ⇒ divide the both sides by 4
∴ sin²Ф = 3/4 ⇒ take square root for both sides
∴ √(sin²Ф) = √(3/4)
∴ sinФ = √3/2 OR sinФ = -√3/2
- When the value of sinФ is positive
∴ The angle Ф is on the first or second quadrant
- When the value of sinФ is negative
∴ The angle Ф is on the third or fourth quadrant
- We have four values of Ф because 0 ≤ Ф ≤ 2π
- Lets find the measure of the acute angle α
∵ sinα = √3/2
∴ α = sin^-1(√3/2) = π/3
- If Ф is on the first quadrant
∴ Ф = α = π/3
- If Ф is on the second quadrant
∴ Ф = π - α = π - π/3 = 2π/3
- If Ф is on the third quadrant
∴ Ф = π + α = π + π/3 = 4π/3
- If Ф is on the fourth quadrant
∴ Ф = 2π - α = 2π - π/3 = 5π/3
* The solutions of the equations are π/3 , 2π/3 , 4π/3 , 5π/3
How do I find the diagonal length?
B. 16 Inches The original length was 12 inches but since you are cutting across the cheese it will be longer. Since you are cutting across that means the width of the cheese will come into the equation as well.
Just add 12 and 4.
Check the picture below.
What is the solution with steps?
2cosx=-sin^2x
Try this option, the answer is marked with red colour.
A software designer is mapping the streets for a new racing game. All of the streets are depicted as either perpendicular or parallel lines. The equation of the lane passing through A and B is -7x + 3y = -21.5. What is the equation of the central street PQ?
A.
-3x + 4y = 3
B.
-1.5x − 3.5y = -31.5
C.
2x + y = 20
D.
-2.25x + y = -9.75
This is a PLATO math question, will give 15 pts to the best answer
Answer:
B. -1.5x − 3.5y = -31.5
Step-by-step explanation:
You forgot to provide the reference image which is essential to answer the question, but I managed to find it... and attach it to my answer.
In the given equation for AB, if we place the y term on the left and x term on the right, we see the slope of that line is 7/3 (y = (7x - 21.5)/3 ==> 7/3x).
We see on the image that the line PQ is perpendicular to AB. That means that its slope is -3/7.
If we quickly check the slopes of each of the possible answers...
A. -3x + 4y = 3 ----> 4y = 3x - 3 ==> y = (3x-3)/4 => slope = 3/4
Not what we're looking for.
B. -1.5x - 3.5y = -31.5 ==> 3.5y = -1.5x + 31 ===> y = (-1.5x +31)/3.5
that gives us a slope of -1.5/3.5... We can simplify it... -3(0.5)/7(0.5) = -3/7
Exactly as predicted.
Since we have the point P (7,6), we can enter it in the equation to verify:
-1.5x - 3.5y = -31.5
-1.5 (7) - 3.5 (6) = -10.5 - 21 = -31.5 --- Verified
C. 2x + y = 20 ==> y = 20 - 2x ===> slope is -2, not what we want.
D. -2.25x + y = -9.75 ==> y = 2.25x - 9.75 ==> slop is 2.25 cannot be it.
Answer: B. -1.5x − 3.5y = -31.5
Step-by-step explanation:
If 4a+8b+4c=1
What is 16a+16c+32b?
Answer:
4
Step-by-step explanation:
[tex] 16a+32b+16c= 4*(4a+8b+4c)[/tex]
Answer:
If 4a+8b+4c=1, then 16a+16c+32b = 4
Step-by-step explanation:
To answer the question, a rule of three can be raised:
4a + 8b + 4c --------------- 1
16a + 16c + 32b --------- X
X = (16a + 16c + 32b) ÷ (4a + 8b + 4c)
This is equivalent to the division of the two polynomials, 16a + 16c + 32b by 4a + 8b + 4c.
Before dividing we organize the first polynomial,
16a + 16c + 32b = 16a + 32b + 16c
Dividing the two polynimials, we have
16a + 32b + 16c | 4a + 8b + 4c
-16a - 32b - 16c 4
= 0 =
The exact quotient is 4, since the residue is 0
Hope this hepls!
How many times as bigger is it? Picture shown above
2 * 10^2
Divide the first numbers, which are 6 and 3, to get 2. Then, subtract the powers of the exponents, which are 5 and 3, to get 2.
Someone help me understand how to do this
Answer:
6.7 cm
Step-by-step explanation:
To make use of the Law of Sines for finding b, you need to know the missing angle B. Since the sum of the angles of a triangle is 180°, you can find angle B as ...
B = 180° -82° -55° = 43°
Now, you put the numbers you know into the formula given and solve for b.
sin(A)/a = sin(B)/b
sin(55°)/(8 cm) = sin(43°)/b
Cross multiplying gives ...
b·sin(55°) = (8 cm)·sin(43°)
and dividing by the coefficient of b gives you ...
b = (8 cm)·sin(43°)/sin(55°) ≈ 6.7 cm
Answer:
6.7 cm
Step-by-step explanation:
An object is launched from a launching pad 144 ft. above the ground at a velocity of 128ft/sec. what is the maximum height reached by the rocket?
Answer:
18) a. h(x) = -16x² + vx + h(0) ⇒ h(x) = -16x² + 128x + 144
b. The maximum height = 400 feet
c. Attached graph
19) The rocket will reach the maximum height after 4 seconds
20) The rocket hits the ground after 9 seconds
Step-by-step explanation:
* Lets study the rule of motion for an object with constant acceleration
# The distance S = ut ± 1/2 at², where u is the initial velocity, t is the time
and a is the acceleration of gravity
# The vertical distances h in x second is h(x) - h(0), where h(0)
is the initial height of the object above the ground
∵ h(x) = vx + 1/2 ax², where h is the vrtical distance, v is the initial
velocity, a is the acceleration of gravity (32 feet/second²) and x
is the time
18)a.
∵ The value of a = -32 ft/sec² ⇒ negative because the direction
of the motion
is upward
∴ h(x) - h(0) = vx - (1/2)(32)(x²) ⇒ (1/2)(32) = 16
∴ h(x) = vx - 16x² + h(0)
∴ h(x) = -16x² + vx + h(0) ⇒ proved
* Find the height of the object after x seconds from the ground
∵ h(0) = 144 and v = 128 ft/sec
∴ h(x) = -16x² + 128x + 144
b.
* At the maximum height h'(x) = 0
∵ h'(x) = -32x + 128
∴ -32x + 128 = 0 ⇒ subtract 128 from both sides
∴ -32x = -128 ⇒ ÷ -32
∴ x = 4 seconds
- The time for the maximum height = 4 seconds
- Substitute this value of x in the equation of h(x)
∴ The maximum height = -16(4)² + 128(4) + 144 = 400 feet
c. Attached graph
19)
- The object will reach the maximum height after 4 seconds
20)
- When the rocket hits the ground h(x) = 0
∵ h(x) = -16x² + 128x + 144
∴ 0 = -16x² + 128x + 144 ⇒ divide the two sides by -16
∴ x² - 8x - 9 = 0 ⇒ use the factorization to find the value of x
∵ x² - 8x - 9 = 0
∴ (x - 9)( x + 1) = 0
∴ x - 9 = 0 OR x + 1 = 0
∴ x = 9 OR x = -1
- We will rejected -1 because there is no -ve value for the time
* The time for the object to hit the ground is 9 seconds
Amanda bought $500 bond with a 6% coupon that matures in 20 years. What are amanda's total annual earnings for this bond?
A.) $30.00
B.) $6.00
C.) $50.00
D.) $60.00
Answer:
it is $30.00
Step-by-step explanation:
The difference of two numbers is 15, and their quotient is 6. what are the two numbers
the two numbers are 18 and 3