Answers
Step-by-step explanation:
(4²-x²)³/²
or,(4+X) (4-X)
Substitute [tex]x = 4 \sin(y)[/tex], so that [tex]dx = 4\cos(y)\,dy[/tex]. Part of the integrand reduces to
[tex]16 - x^2 = 16 - (4\sin(y))^2 = 16 - 16 \sin^2(y) = 16 (1 - \sin^2(y)) = 16 \cos^2(y)[/tex]
Note that we want this substitution to be reversible, so we tacitly assume [tex]-\frac\pi2\le y\le \frac\pi2[/tex]. Then [tex]\cos(y)\ge0[/tex], and
[tex](16-x^2)^{3/2} = 16^{3/2} \left(\cos^2(y)\right)^{3/2} = 64 |\cos(y)|^3 = 64 \cos^3(y)[/tex]
(since [tex]\sqrt{x^2} = |x|[/tex] for all real [tex]x[/tex])
So, the integral we want transforms to
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 64 \int \cos^3(y) \times 4\cos(y) \, dy = 256 \int \cos^4(y) \, dy[/tex]
Expand the integrand using the identity
[tex]\cos^2(x) = \dfrac{1+\cos(2x)}2[/tex]
to write
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 256 \int \left(\frac{1 + \cos(2y)}2\right)^2 \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \cos^2(2y)) \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \frac{1 + \cos(4y)}2\right) \, dy \\\\ = 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy[/tex]
Now integrate to get
[tex]\displaystyle 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy = 32 \left(3y + 2 \sin(2y) + \frac14 \sin(4y)\right) + C \\\\ = 96 y + 64 \sin(2y) + 8 \sin(4y) + C[/tex]
Recall the double angle identity,
[tex]\sin(2y) = 2 \sin(y) \cos(y)[/tex]
[tex]\implies \sin(4y) = 2 \sin(2y) \cos(2y) = 4 \sin(y) \cos(y) (\cos^2(y) - \sin^2(y))[/tex]
By the Pythagorean identity,
[tex]\cos(y) = \sqrt{1 - \sin^2(y)} = \sqrt{1 - \dfrac{x^2}{16}} = \dfrac{\sqrt{16-x^2}}4[/tex]
Finally, put the result back in terms of [tex]x[/tex].
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 128 \frac x4 \frac{\sqrt{16-x^2}}4 + 32 \frac x4 \frac{\sqrt{16-x^2}}4 \left(\frac{16-x^2}{16} - \frac{x^2}{16}\right) + C \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 8 x \sqrt{16 - x^2} + \frac14 x \sqrt{16 - x^2} (8 - x^2) + C \\\\ = \boxed{96 \sin^{-1}\left(\frac x4\right) + \frac14 x \sqrt{16 - x^2} \left(40 - x^2\right) + C}[/tex]
Related Questions
Write an expression in factored form for the polynomial of least possible degree graphed below.
Answers
The expression in factored form for the polynomial of least possible degree graphed will be y(x) = (x + 3)(x + 2 )(x - 1 )(x - 3 )
How to factor the polynomial?From the graph, the zeros of the polynomial of given graph are:
x = -3
x = -2
x = 1
x = 3
Equate the above equations to zero
x + 3 = 0
x + 2 = 0
x - 1 = 0
x - 3 = 0
Multiply the equations
(x + 3)(x + 2 )(x - 1 )(x - 3 ) = 0
Express as a function gives;
y = (x + 3)(x + 2 )(x - 1 )(x - 3 )
Hence, the factored form of the polynomial will be y = (x + 3)(x + 2 )(x - 1 )(x - 3 )
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in 1979 the Wincom river was 33 feet below the bridge. Because of silt build-up in the river bottom, the
river was only 12 feet below the bridge by 1986. Write an equation for the distance of the river from the
bridge, d, with t = 0 representing 1979. If the silt build-up continues at the same rate, what year will the
river reach the bridge?
Answers
Answer: d = 40 - 5/2t; 1995
Hope it helps :)
()
8
What is 11 - 2³
Answers
Answer:
[tex]11 - 2 {}^{3} [/tex]
[tex]11 - 8[/tex]
[tex]3[/tex]
You toss a coin and roll a number cube. The table shows the sample space,
where H means heads, T means tails, and the numbers represent the number
cube roll.
H
T
1
H1
T1
2
H2
T2
3
H3
T3
4
H4
T4
5
H5
T5
6
H6
T6
What is the probability of tossing heads and rolling a number less than 3?
Answers
Probability helps us to know the chances of an event occurring. The probability of tossing heads and rolling a number less than 3 is 1/6.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The number of cases where coins land on heads and a number less than 3 are rolled is 2, which are H1 and H2.
The probability of tossing heads and rolling a number less than 3 is,
Probability = (Outcomes where coins land on heads and a number less than 3 are rolled)/(Total number of cases)
Probability = 2/12 = 1/6
Hence, the probability of tossing heads and rolling a number less than 3 is 1/6.
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John is 5 years younger than David. Four years later David will be twice as old as John. Find their present age.
Answers
David will be 10 and John will be 9
An equation is shown below:
6(3x − 7) = 2
Which of the following correctly shows the beginning steps to solve this equation?
Step 1: 9x − 1 = 2
Step 2: 9x = 3
Step 1: 9x − 7 = 2
Step 2: 9x = 9
Step 1: 18x − 7 = 2
Step 2: 18x = 9
Step 1: 18x − 42 = 2
Step 2: 18x = 44
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex] \texttt{Step 1: 18x − 42 = 2} [/tex][tex] \texttt{Step 2: 18x = 44 } [/tex]____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 6(3x - 7) = 2[/tex]
Step 1 -
[tex]\qquad \tt \rightarrow \: 18x - 42 = 2[/tex]
[ distributive property ]
Step 2 -
[tex]\qquad \tt \rightarrow \: 18x = 2 + 42[/tex]
[tex]\qquad \tt \rightarrow \: 18x = 44[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
d) Step 1: 18x - 42 = 2
Step 2: 18x = 44
Step-by-step explanation:
Given equation,
→ 6(3x - 7) = 2
Now the value of x will be,
→ 6(3x - 7) = 2
→ 6(3x) - 6(7) = 2
→ 18x - 42 = 2
→ 18x = 2 + 42
→ 18x = 44
→ x = 44/18
→ [ x = 22/9 ]
Hence, value of x is 22/9.
Part A: Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form
Answers
The expression that represents this inequality must relate both temperatures, then it would look like this: -40°F < x < 140°F.
How to write this situation with an inequality?To express this situation in an inequality we must include the temperature values. Additionally, we must include the greater than (>) or less than (<) symbols to relate the values.
According to the above, the expression would look like this:
-40°F < x < 140°FNote: This question is incomplete because some information is missing. Here is the information:
A truck driver is driving from Nome, Alaska to Death Valley, California. Because he is traveling between locations with extreme temperatures, he needs to check the weather continuously to make sure the gas in his truck remains in liquid form. The gas he uses freezes at −40° F and evaporates at 140° F.
Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form.
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A researcher conducts an between-subjects study examining the
effectiveness of a memory enhancement program at an assisted living
facility for elderly adults. One group of residents is selected to
participate in the program, and a second group of participants serves as
a control group. After 6 weeks, the researcher reports a combined score
measuring memory for each individual. The data are:
Control
Exercise
n = 10
M = 12
SS = 120.5
n=15
M= 15.5
SS = 190.0
a) Does the exercise program have a significant effect? Use a two
tailed test with an alpha level of .05
b) Compute Cohen's d to measure the size of the treatment effect
Answers
H0: µ1 = µ2; The exercise program do not have significant effect on physical fitness, H1: µ1 =/ µ2; the exercise program had a significant effect on physical fitness and the Estimated Cohen's d is 0.82.
HypothesisA. Significant effect
H0: µ1 = µ2
Based on the above hypothesis the exercise program does not have significant effect on physical fitness
H1: µ1 =/ µ2
Based on the above hypothesis the exercise program had a significant effect on physical fitness
Pooled variance: sp2 = (190 + 120.5/(15-1) + (10-1)
Pooled variance: sp2 = 310.5/23
Pooled variance: sp2 =13.5
Estimated standard error ( sM1-M2):
sM1-M2 =√13.5/15 +13.5/10
sM1-M2 =√2.25
sM1-M2 = 1.5
Tailed test (t)
t = (15.5 - 12)/1.5
t=3.5/1.5
t= 2.33
B. Estimated Cohen's d:
Estimated Cohen's d = 3/√13.5
Estimated Cohen's d = 3/3.67
Estimated Cohen's d= 0.817
Estimated Cohen's d= 0.82 (Approximately); this is a large effect.
Conclusion demonstrating how the outcome of the hypothesis test would tend to appear in a research report is: (Reject H0). Because the group exercise program tend to have a significant effect on the physical fitness of elderly adults, t = 2.33, p <.05, d = 0.82.
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Dan Barker, the chief engineer, told Ms. Silva that the company is currently making 150 units of Model Diamond per batch and 245 units of Model Gold per batch. He suggests doubling the batch sizes to cut the number of setups in half, thereby reducing the setup cost by 50 percent. Compute the cost per unit for each product if Ms. Silva adopts his suggestion.
Answers
The cost per unit for each product is given as:
x ≈ 0.0067; and
y ≈ 0.0041. See explanation below.
What is the cost per unit for each product?Given that the current production:
Model Diamond (Md) - 150 UnitsModel Gold (Mg) - 245 UnitsCurrent cost of production is given as:
Current Total Cost = 150y + 245x where;
if doubling the batch sizes will reduce the cost per unit by 50% then the new cost equation will be:
Thus, New Total Cost of production = (150 x 2) (y/2) + (245 x 2) (x/2)
= (300)(y/2) + (490) (x/2)
Since we are looking for the cost per unit of each product:
f(x) = 300 * (x/2)..........Unit cost of Model Gold
If we make x subject of the formula, then we arrive at:
1/300 = x/2
x = (1/300) * 2
x = 0.00666666666
x ≈ 0.0067
f(x) = 490* (x/2)
If we make y subject of the formula, then we arrive at:
i/490 = y/2
y = (1/490) * 2
y = 0.00408163265306122448979591836735
y ≈ 0.0041
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Which of the following is most likely the next step in the series?
⠀⠀
Answers
The next step in the series is choice D.
Answer:
D
Step-by-step explanation:
if we define the diagrams in terms of their rows and columns, then
1st : 2 by 1
2nd : 3 by 2
3rd : 4 by 3
note that the rows and columns both increase by 1
then the next likely diagram is
5 by 4 , that is diagram D
What is the area of the triangle?
24 square units
32 square units
48 square units
96 square units
Answers
Answer:
24 square units
Step-by-step explanation:
1) the area can be calculated using the formula:
A=0.5*a*h, where a- base, h-height;
2) if a=8, h=6, then the required area is:
A=0.5*8*6=24 [units²].
Answer: 24 square units
Step-by-step explanation:
The base: 8
The height: 6
The area: 8 x 6 / 2 = 24
/ stands for divided by
Solve for n in the inequality 3|n − 1] > 9. (If this is an "and" inequality, give your answer as a single compound inequality. If this is an "or" inequality, separate your answers using a comma.) Solve for n in the inequality 3 | n − 1 ] > 9. ( If this is an " and " inequality , give your answer as a single compound inequality . If this is an " or " inequality , separate your answers using a comma . )
Answers
Answer:
3,n-1>9
3>n2+9
3>n11 is ans
Because the two distributions displayed below have similar shapes, they have
the same standard deviation.
A. True
B. False
Answers
Answer:
False, distributions having the same mean and standard deviation can have very different shape of distribution.
HELP PLS 100 POINTS PLS BRAINLY IF CAN
find the domain y=[tex]\frac{2-3x}{12-|x-12|}[/tex]
Answers
Step-by-step explanation:
hope you can understand
a drone traveling horizontally at 120m s over a flat ground at an elevation of 4500 meters must drop an emergency package on a target on the ground the trajectory of the package is given by x 120t y 4.9t 2 4500
Answers
The packet should be dropped 3636.55 horizontal meters before the target in order to hit the target
What is a Trajectory ?Trajectory is the path followed by a moving object when it is falling under gravitational force.
x = 90 t
y = -4.9 t²2 + 4500
t ≥ 0
y = 0
-4.9t² + 4500 = 0
4.9t²2 = 4500
[tex]\rm t = \sqrt {\dfrac{4500}{4.9}}[/tex]
t = 30.30 seconds
substituting the value to determine the horizontal distance
x = 120 * 30.30
x = 3636.55 meters
Therefore the packet should be dropped 3636.55 horizontal meters before the target in order to hit the target
The complete question is
a drone traveling horizontally at 120m s over a flat ground at an elevation of 4500 meters must drop an emergency package on a target on the ground the trajectory of the package is given by x 120t y 4.9t 2 4500 where the origin is the point on the ground directly beneath the drone at the moment of release. How many horizontal meters before the target should the package be released in order to hit the target? Round to the nearest meter.
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A Cepheid star is a type of variable star, which means that its brightness is not constant.
The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by
M = − 2.78 (log P) − 1.35,
where M is the absolute magnitude, or brightness, of the star, and P is the number of days required for the star to complete one cycle.
Use a calculator to solve each problem. Round your answers to the nearest hundredth.
What is the absolute magnitude of a star that has a period of 62 days?
Answers
A function assigns the values. The absolute magnitude of a star that has a period of 62 days is -6.3328.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by
M = − 2.78 (log P) − 1.35,
Given the absolute magnitude of a star that has a period of 62 days is,
M = − 2.78 (log 62) − 1.35
M = -6.3328
Hence, the absolute magnitude of a star that has a period of 62 days is -6.3328.
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What is the product of the reciprocal of 6 and the reciprocal of 7?
Answers
Answer:
The answer is 1/42 as you take reciprocal of 6=(1/6) and reciprocal of 7=(1/7) and multiply.
Answer:
[tex]\boxed {\frac{1}{42}}[/tex]
Step-by-step explanation:
Reciprocal of 6 : 1/6
Reciprocal of 7 : 1/7
Their product :
1/6 × 1/71/42Hello, I would like help with his question. Please do as quickly as you can, Thank you.
Answers
Answer:
Step-by-step explanation:The answer is 45
You have all the other side measures besides for the bottom one. To get that length do 18 - 5, giving you 13. Once you add all the sides including the missing one that we just calculated you get 58.
You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. How many randomly selected air passengers must you survey? Assume that you want to be 90% confident that the sample percentage is within 1.5 percentage points of the true population percentage. Complete parts (a) and (b) below. Assume that nothing is known about the percentage of passengers who prefer aisle seats.
Answers
Using the z-distribution, it is found that 3,007 passengers must be surveyed.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
In this problem, we desired a margin of error of M = 0.015, with no prior estimate, hence [tex]\pi = 0.5[/tex], then we solve for n to find the minimum sample size.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.015 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.015\sqrt{n} = 1.645(0.5)[/tex]
[tex]\sqrt{n} = \frac{1.645(0.5)}{0.015}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645(0.5)}{0.015}\right)^2[/tex]
n = 3007.
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square root of 0.98 simplified
Answers
Answer:
0.98994949366117
√0.98 = 0.98994949366117
Step 1:
Divide the number (0.98) by 2 to get the first guess for the square root.
First guess = 0.98/2 = 0.49.
Step 2:
Divide 0.98 by the previous result. d = 0.98/0.49 = 2.
Average this value (d) with that of step 1: (2 + 0.49)/2 = 1.245 (new guess).
Error = new guess - previous value = 0.49 - 1.245 = 0.755.
0.755 > 0.01. As error > accuracy, we repeat this step again.
Step 3:
Divide 0.98 by the previous result. d = 0.98/1.245 = 0.7871485944.
Average this value (d) with that of step 2: (0.7871485944 + 1.245)/2 = 1.0160742972 (new guess).
Error = new guess - previous value = 1.245 - 1.0160742972 = 0.2289257028.
0.2289257028 > 0.01. As error > accuracy, we repeat this step again.
Step 4:
Divide 0.98 by the previous result. d = 0.98/1.0160742972 = 0.9644963982.
Average this value (d) with that of step 3: (0.9644963982 + 1.0160742972)/2 = 0.9902853477 (new guess).
Error = new guess - previous value = 1.0160742972 - 0.9902853477 = 0.0257889495.
0.0257889495 > 0.01. As error > accuracy, we repeat this step again.
Step 5:
Divide 0.98 by the previous result. d = 0.98/0.9902853477 = 0.9896137535.
Average this value (d) with that of step 4: (0.9896137535 + 0.9902853477)/2 = 0.9899495506 (new guess).
Error = new guess - previous value = 0.9902853477 - 0.9899495506 = 0.0003357971.
0.0003357971 <= 0.01. As error <= accuracy, we stop the iterations and use 0.9899495506 as the square root.
So, we can say that the square root of 0.98 is 0.989 with an error smaller than 0.01 (in fact the error is 0.0003357971). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(0.98)' is 0.9899494936611666.
Note: There are other ways to calculate square roots. This is only one of them.
To round it to the tenths, it's 1
To round to the hundredths, it's.99
Thousandth is.990
Genesis throws a ball up in the air. The graph below shows the height of the ball hh in meters after tt seconds. Find the interval for which the ball’s height is decreasing.
help please
Answers
We conclude that the interval in which the function decreases is (1.5, 3]
In which interval is the ball's height decreasing?
The ball is decreasing when the graph, reading from left to right, is going downwards.
Particularly, in this parabola that opens downwards, the graph will decrease after the vertex.
And we can see that the vertex is at x = 1.5
And we also see that the graph of the function ends at x = 3.
Then we conclude that the interval in which the function decreases is (1.5, 3]
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A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 8 inches.
Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning. For example, the point (0, 8) would represent a height of 8 inches after 0 hours. Explain how you obtained the ordered pairs. (5 points)
Part B: Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A. (2 points)
Part C: If the rate at which the candle burned was 0.4 inches per hour instead of 0.5 inches per hour, would the relation be a function? Explain your answer using input and output values. (3 points)
Answers
The ordered pairs are (0,8), (1, 7.5), (2, 7), (3,6.5), (4, 6) and (5, 5.5)
How to determine the ordered pairs?The given parameters are:
Initial height, h = 8 inches
Rate = 0.5 inches per hour
The height of the candle at x hour is:
y = Initial - rate * x
This gives
y = 8 - 0.5x
Set x = 0 to 5
y = 8 - 0.5(0) = 8
y = 8 - 0.5(1) = 7.5
y = 8 - 0.5(2) = 7
y = 8 - 0.5(3) = 6.5
y = 8 - 0.5(4) = 6
y = 8 - 0.5(5) = 5.5
So, the ordered pairs are (0,8), (1, 7.5), (2, 7), (3,6.5), (4, 6) and (5, 5.5)
Is the relation a function?In (a), we have:
y = 8 - 0.5x
The above is a linear relation.
All linear relations are functions
Hence, the relation is a function.
Would a new relation be a function?
We have
Initial height, h = 8 inches
New rate = 0.4 inches per hour
The height of the candle at x hour is:
y = Initial - rate * x
This gives
y = 8 - 0.4x
The above is a linear relation.
All linear relations are functions
Hence, the new relation is also a function.
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You are creating a table that you want to use to measure the temperature inside the arena. You have made a few mistakes.
Highlight the errors in the table below.
Answers
Answer + Step-by-step explanation:
When Evil Kenevil was a kid, he decided to attempt to jump a distance of 30 yards using ramps that extended 9 yards high for take off and landing with his motorcycle.
As the figure below illustrates, at zero yards from the take off ramp, he was 9 yards high. At 8 yards from the ramp, he was 17 yards high, and at 18 yards from the ramp, he was 18 yards high.
Since there are no rockets or wings affecting Evil’s flight, he should closely follow a parabolic path that can be modeled by a quadratic equation:
y=ax^2+bx+c, where y is the height of Evil’s bike, and x is the horizontal distance he has traveled.
1.) Using the three data points (x, y) that we know Evil passed through and the general quadratic equation, create three corresponding equations:
Equation 1: (5 pts.)
Equation 2: (5 pts.)
Equation 3: (5 pts.)
2.) Solve your system of equations from above for a, b, and c.
a = (10 pts.)
b = (10 pts.)
c = (10 pts.)
3.) Using your values of a, b, and c, what is the quadratic equation that models Evil’s jump?
Quadratic Equation: (10 pts.)
4.) What is the maximum height for Evil during this jump? (15 pts.)
5.) What is Evil’s height when he gets to the landing ramp? Is this a successful stunt? (15 pts.)
6.) Evil was at a height of 17 yards when he was 8 yards out. Where else was he at a height of 17 yards?
Answers
6ac+bd-3bc-2ad help
Answers
Answer:
(2a-b)(3c-d)
Two vertical angles are complementary. Statement is always, sometimes, or never true. Explain your reasoning
Answers
Answer:
depends upon the degree of the angle
Step-by-step explanation:
vertically opposite angles are always equal like
80 = 80 sum is equal to 160 degrees not equal to 90
45 = 45 , sums equal to 90 degrees ,equal to 90
30 = 30 sum is equal to 60 degrees, not equal to 90
so we can say it depends what is the no of degrees if it is 45 only we can say the vertically opposite angles are complementary angle
Sarah and her friends split a bag of candy evenly. They each ate 13 pieces of candy and there are 2 pieces leftover. How many pieces of candy were originally in the bag?
Answers
Answer:
54
Step-by-step explanation:
⇒ 1 + 3 = 4
⇒ 4 * 13 = 52
⇒ 52 + 2 = 54 (Basic Operation)
For which value of x is the expression y
=
a. 1
b. -1
C. 5
d. -5
3x-3
x-5
- undefined?
Answers
1
Step-by-step explanation:
when we put 1 in the equation the nominator becomes zero and it becomes undefined
Hii!
___________________________________________________________
[tex]\stackrel\star\rightsquigarrow\circ\boldsymbol{\underbrace{Answer:}}}\circ\leftharpoonup[/tex]
The value of x should be 5! ^^
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation:}}}\circ\leftharpoonup[/tex]
[tex]\boxed{\\\begin{minipage}{7cm} For\,an\,expression \\ \boldsymbol{to\,be\,und efined,} \\ \,its\,denominator\,should\,be\,zero \end{minipage}}}[/tex]
Remember this! ^^
Now let's consider this:
Which value of x will make the denominator equal to 0?
Is it 1? If we stick 1 in, we will not obtain 0.
[tex]\twoheadrightarrow\sf y=\cfrac{3\cdot1-3}{1-5}[/tex]
[tex]\bullet[/tex] Simplify this
[tex]\twoheadrightarrow\sf y=\cfrac{3-3}{-4}[/tex]
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We will obtain 0 in the numerator, but not in the denominator; if the numerator is 0, then the fraction, or fractional expression, is 0.
Let's try 5. 5-5 is equal to 0, so this sounds promising! ^^
[tex]\twoheadrightarrow\sf y=\cfrac{3\cdot5-3}{5-5}[/tex]
[tex]\bullet[/tex] Look what we obtain when we simplify
Don't we obtain 15-3/0?
Like I said above, if an expression has 0 as its denominator, it's undefined.
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Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}[/tex]
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If 6x = 54, then x = ___. (Only input whole number)
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6x = 54}\\\\\large\textbf{DIVIDE 6 to BOTH SIDES}\\\\\mathsf{\dfrac{6x}{6} = \dfrac{54}{6}}\\\\\textbf{SIMPLIFY IT!}\\\\\mathsf{x = 9}\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 9}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]What are the domain and range of the function f of x equals the quantity of x squared minus 3 x minus 28, all over x plus 4?
Answers
2