Do you use integration by parts to solve this problem? If so, how? I can't seem to figure out the right answer
Answers
The integral of [tex]\int\limits^e_1 {x^{1/2}lnx } \, dx[/tex] is (2/3)[tex]e^{3/2}[/tex] - (4/9).
To find the integral of [tex]\int\limits^e_1 {x^{1/2}lnx } \, dx[/tex] , we can use integration by parts. Let u = ln x and dv = [tex]x^{1/2}[/tex] dx. Then du/dx = 1/x and v = (2/3) [tex]x^{3/2}[/tex] .
Using the formula for integration by parts, we have:
∫[tex]x^{1/2}[/tex]lnx dx = uv - ∫v du/dx dx
= ln x * (2/3) [tex]x^{3/2}[/tex] - ∫(2/3) [tex]x^{3/2}[/tex] * (1/x) dx
= ln x * (2/3) [tex]x^{3/2}[/tex] - (2/3) ∫ [tex]x^{1/2}[/tex] dx
= ln x * (2/3) [tex]x^{3/2}[/tex] - (4/9) [tex]x^{3/2}[/tex] + C
where C is the constant of integration.
To evaluate the definite integral from 1 to e, we substitute e for x in the expression above and subtract the result when x = 1:
[tex]\int\limits^e_1 {x^{1/2}lnx } \, dx[/tex] = [(2/3) [tex]e^{3/2}[/tex] ln e - (4/9) [tex]e^{3/2}[/tex] ] - [(2/3)[tex]1^{3/2}[/tex]ln 1 - (4/9)[tex]1^{3/2}[/tex]]
= (2/3) [tex]e^{3/2}[/tex] - (4/9)
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Related Questions
The height y(in feet) of a ball thrown by a child isy=−114x2+2x+3
where x is the horizontal distance in feet from the point at which the ball is thrown.
(a) How high is the ball when it leaves the child's hand? (Hint: Find y
when x=0)
Your answer is y=____
(b) What is the maximum height of the ball? _____
(c) How far from the child does the ball strike the ground?_____
Answers
y = -114(0)^2 + 2(0) + 3
y = 3
So the ball is 3 feet high when it leaves the child's hand.
(b) The maximum height of the ball occurs at the vertex of the parabola. We can find the x-coordinate of the vertex using the formula:
x = -b/2a
where a = -114 and b = 2. Substituting these values, we get:
x = -2/(2*(-114)) = 0.0088
We can find the maximum height by substituting this value of x into the equation:
y = -114(0.0088)^2 + 2(0.0088) + 3
y ≈ 3.036
So the maximum height of the ball is approximately 3.036 feet.
(c) To find how far from the child the ball strikes the ground, we need to find the value of x when y = 0. We can solve the equation for x:
-114x^2 + 2x + 3 = 0
Using the quadratic formula, we get:
x = (-2 ± sqrt(2^2 - 4*(-114)*3))/(2*(-114))
x = (-2 ± sqrt(9252))/(-228)
We can ignore the negative root since the ball is moving in the positive x-direction. Simplifying the expression for the positive root, we get:
x = (-2 + sqrt(9252))/(-228) ≈ 0.232
So the ball strikes the ground approximately 0.232 feet away from the child.
12,59,294,1469,7344 what is the pattern rule
Answers
Both equations give the correct terms, so we can conclude that the pattern rule is: [tex]an^2 - 131n + 80[/tex] , where [tex]a=63[/tex] .
What is the consecutive terms?To find the pattern rule for the given sequence 12, 59, 294, 1469, 7344, we need to observe the differences between consecutive terms. Let's find the differences between each pair of terms:
[tex]59 - 12 = 47[/tex]
[tex]294 - 59 = 235[/tex]
[tex]1469 - 294 = 1175[/tex]
[tex]7344 - 1469 = 5875[/tex]
The differences are not constant, so we need to find the differences between these differences:
[tex]235 - 47 = 188[/tex]
[tex]1175 - 235 = 940[/tex]
[tex]5875 - 1175 = 4700[/tex]
Now, the second differences are constant (equal to 940), which suggests that the pattern rule is a quadratic equation. Let's assume the pattern rule is of the form:
[tex]an^2 + bn + c[/tex]
where n is the term number (starting with n=1 for the first term).
To find the coefficients a, b, and c, we can use the first three terms of the sequence. Let's substitute n=1,2,3 into the equation and equate it to the corresponding terms:
[tex]a + b + c = 12 (for n=1)[/tex]
[tex]4a + 2b + c = 59 (for n=2)[/tex]
[tex]9a + 3b + c = 294 (for n=3)[/tex]
We can solve these equations simultaneously to get the values of a, b, and c:
[tex]a = 63[/tex]
[tex]b = -131[/tex]
[tex]c = 80[/tex]
Therefore, the pattern rule for the sequence is:
[tex]an^2 - 131n + 80[/tex]
where a=63.
To check if this pattern rule works for the other terms of the sequence, we can substitute n=4 and n=5:
[tex]a(4^2) - 131(4) + 80 = 1469[/tex]
[tex]a(5^2) - 131(5) + 80 = 7344[/tex]
Therefore, Both equations give the correct terms, so we can conclude that the pattern rule is:
[tex]an^2 - 131n + 80, where a=63.[/tex]
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Pre calculus trigonometry
Answers
The result of the division of the two complex numbers is equal to z₁ / z₂ = (8 / 9) · [cos (π / 10 - π / 12) + i sin (π / 10 - π / 12)].
How to find the division of two complex numbers
In this problem we find two complex numbers in rectangular form, whose division must be found. This can done by easily by means of complex numbers in polar form and definition of division:
Complex number (rectangular form)
z = r · (cos θ + i sin θ)
Complex number (polar form)
[tex]z = r\cdot e^{i\cdot \theta}[/tex]
Where:
r - Normθ - DirectionDivision between two complex numbers in polar form:
[tex]\frac {z_{1}}{z_{2}} = \left(\frac{r_{1}}{r_{2}}\right)\cdot e^{i\cdot (\theta_{1}-\theta_{2})}[/tex]
This number is equivalent to the following expression in rectangular form:
z₁ / z₂ = (r₁ / r₂) · [cos (θ₁ - θ₂) + i sin (θ₁ - θ₂)]
If we know that r₁ = 8, r₂ = 9, θ₁ = π / 10 and θ₂ = π / 12, then the division of the two complex numbers is:
z₁ / z₂ = (8 / 9) · [cos (π / 10 - π / 12) + i sin (π / 10 - π / 12)]
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The amount of money in a saving account increases bu D. 2% every month
Write a function for the amount of money in the accounts, after t months with an initial deposit of tr $ 100
By what' factor does the amount in the account increases ever meant every year?
Answers
The exponential function giving the balance of the account after t months is:
[tex]y = 100(1.02)^t[/tex]
The yearly growth factor is given as follows:
26.82%.
How to define an exponential function?An exponential function has the definition presented as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The parameter values for this problem are given as follows:
a = 100 -> initial deposit.b = 1.02 -> increase of 2% every month -> 1 + 0.02 = 1.02.Hence the function is:
[tex]y = 100(1.02)^t[/tex]
The yearly growth factor can be obtained as follows:
[tex](1.02)^{12} = 1.2682[/tex]
Increase of 26.82% each year, which is composed by 12 months.
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Please help me who knows how to do this
Answers
Step 1: X^2+3x-4x-12
Step 2: (X^2+3x)+(-4x-12)
Step 3: X(x+3)-4(x+3)
Answer: (x-4)(x+3)
Find relative extrema (x, y) of a function h(x) = x^3 + 3x^2 − 2 using
(a) the first derivative test
(b) the second derivative test
Which test is easiest?
Answers
a) Based on the first derivative test, h(x) has a relative minimum at x = -2 and a relative maximum at x = 0.
b) For x = -2: h''(-2) = 6(-2) + 6 = -6 < 0, so h(x) has a relative maximum at x = -2.
For x = 0: h''(0) = 6(0) + 6 = 6 > 0, so h(x) has a relative minimum at x = 0.
What is the calculus?Calculus is a branch of mathematics that deals with the study of rates of change, accumulation, and the properties and behavior of functions.
(a) First derivative test:
The first derivative test involves finding the critical points of the function, where the first derivative is equal to zero or undefined, and then checking the sign of the first derivative in the intervals between the critical points to determine whether the function has relative extrema at those points.
Find the first derivative of h(x):
h'(x) = 3x² + 6x
Set h'(x) = 0 and solve for x to find the critical points:
3x² + 6x = 0
x(x + 2) = 0
x = 0 or x = -2
Test the intervals between the critical points using the sign of the first derivative:
For x < -2: Choose x = -3, h'(-3) = 27 + (-18) = 9 > 0, so h(x) is increasing.
For -2 < x < 0: Choose x = -1, h'(-1) = 3 - 6 = -3 < 0, so h(x) is decreasing.
For x > 0: Choose x = 1, h'(1) = 3 + 6 = 9 > 0, so h(x) is increasing.
Based on the first derivative test, h(x) has a relative minimum at x = -2 and a relative maximum at x = 0.
(b) Second derivative test:
The second derivative test involves finding the critical points of the function using the first derivative, and then checking the sign of the second derivative at those points to determine whether the function has relative extrema at those points.
Find the second derivative of h(x):
h''(x) = 6x + 6
Evaluate the second derivative at the critical points found in step 2 of the first derivative test:
For x = -2: h''(-2) = 6(-2) + 6 = -6 < 0, so h(x) has a relative maximum at x = -2.
For x = 0: h''(0) = 6(0) + 6 = 6 > 0, so h(x) has a relative minimum at x = 0.
Hence, the ease of a test may vary for different individuals and their familiarity with calculus concepts.
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The formula v= √√2gh gives the velocity v, in feet per second, of an object after it falls h feet accelerated by gravity g, in feet
per second squared. If g is approximately 32 feet per second squared, find how far an object has fallen if its velocity is 96 feet
per second.
Answers
We can rearrange the formula to solve for h:
v = √√2gh
Squaring both sides: v^2 = 2gh
Dividing both sides by 2g: h = v^2 / 2g
Substituting v = 96 ft/s and g = 32 ft/s^2, we get:
h = (96 ft/s)^2 / (2 × 32 ft/s^2)
h = 288 ft
Therefore, the object has fallen 288 feet.
Seven days a year, Tiger Stadium becomes the fifth largest city in the state of Louisiana. Over 92,000 fans pack the stadium to watch the Tigers play. After the game, if the fans leave at a rate of 10% per minute, how long will it take before the stadium is half empty?
1. Find the data using at least 10 numbers in the x column.
2. Create a scatter plot. Label the graph and show increments.
3. Write an exponential equation.
4. Interpret the meaning of the "a" and "b" in your function y=ab^x including the units.
5. Find out how long it will take before the stadium is half empty and all the way empty.
Answers
y = 92000(0.9)^x
where y is the number of fans remaining in the stadium after x minutes.
Using this formula, we can plug in x values from 0 to 30 (or more) to generate a table of values:
| x | y |
|------|---------|
| 0 | 92000 |
| 1 | 82800 |
| 2 | 74520 |
| 3 | 67068 |
| 4 | 60361 |
| 5 | 54325 |
| 6 | 48892 |
| 7 | 43903 |
| 8 | 39313 |
| 9 | 35082 |
| 10 | 31174 |
2. Here is a scatter plot based on the above data:
The x-axis represents the time in minutes, and the y-axis represents the number of fans remaining in the stadium.
3. The exponential equation that best fits the data is:
y = 92000(0.9)^x
where y is the number of fans remaining in the stadium after x minutes.
4. In the equation y = ab^x, a represents the initial value or starting point, and b represents the rate of change or growth factor. In this case, a = 92000 represents the initial number of fans in the stadium, and b = 0.9 represents the rate at which the number of fans decreases per minute. The units of a are fans, and the units of b are fans per minute.
5. To find out how long it will take before the stadium is half empty, we need to solve the equation y = 0.5a for x:
0.5a = 92000(0.9)^x
0.5(92000) = 92000(0.9)^x
0.5 = 0.9^x
Taking the logarithm of both sides, we get:
log(0.5) = x log(0.9)
x = log(0.5) / log(0.9)
x ≈ 7.72 minutes
Therefore, it will take approximately 7.72 minutes for the stadium to be half empty.
To find out how long it will take for the stadium to be completely empty, we need to solve the equation y = 0 for x:
0 = 92000(0.9)^x
Taking the logarithm of both sides, we get:
log(0) = x log(0.9)
This equation has no real solution, which means that the stadium will never be completely empty (in theory). However, in practice, the number of fans will eventually become small enough that it can be considered empty for all practical purposes.
3d *5d*2=?
Please what is 3d times 5d times 2
Answers
Answer:
[tex]30d^2[/tex]
Step-by-step explanation:
Help please!!!!
Whoever answers right gets brainliest!
Answers
Answer:
25
Step-by-step explanation:
To solve this problem you have to use this formula [tex](\frac{b}{2})^{2}[/tex] it. So in this case b is the term next to the x term. This number is 10. So all we have to do is insert it into the formula. This would give us:
[tex]=(\frac{10}{2})^{2}\\\\=(5)^{2}\\\\= 25[/tex]
The constant term is 25.
Could I get Brainilest, please? I'm trying to get to the expert level
Anna baked 4 batches of cookies with c cookies in each batch she then ate 8 cookies there were 72 cookies left after Anna ate her cookies
Answers
The expression for the number of cookies Anna has left is [tex]3c - 8[/tex].
What does an expression means?An expression refers to statement that have minimum of two numbers or variables or both and an operator connecting them.
The total number of cookies Anna baked is:
= 3 batches * c cookies/batch
= 3c cookies
After eating 8 cookies, Anna has left:
= 3c cookies - 8 cookies
So, the expression for the number of cookies Anna has left is [tex]3c - 8[/tex].
Full question "Anna baked 3 batches of cookies with c cookies in each batch she then ate 8 cookies. How many cookies does anna have left write your answer as an expression.
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Can someone help me I dont understand this :(
Answers
Check the picture below.
At the time of her grandson's birth, a grandmother deposits $14,000 in an account that pays 4.5% compounded
monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits
or withdrawals are made during this period?
i Click the icon to view some finance formulas.
The value of the account will be $
(Round to the nearest dollar as needed.)
4
Answers
Answer:
The value of the account will be $5,628
Step-by-step explanation:
Step-by-step explanation:
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
therefore
The value of the account will be $5,628
‼️‼️‼️‼️WILL MARK BRAINLIEST‼️‼️‼️‼️
Answers
Answer:
S = 2π(14^2) + 2π(14)(154)
= 2π(196) + 2π(2,156)
= 4,704π = 14,778.1 ft^2
Using 3.14 for π:
S = 4,704(3.14) = 14,770.6 ft^2
What is the equation through the points: (-7, -3), (1, 2)
ASAP please
Answers
The equation of the line passing through the points (-7, -3) and (1, 2) is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].
What is the equation of the line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
First, we determine the slope of the line.
Given the two points are (-7, -3) and (1, 2)
We can find the slope of the line by using the slope formula:
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values, we get:
m = (2 - (-3)) / (1 - (-7))
m = 5/8
Using the point-slope form, plug in one of the given points and slope m = 5/8 to find the equation of the line.
Let's use the point (-7, -3:
y - y₁ = m(x - x₁)
[tex]y - (-3) = \frac{5}{8}( x - (-7) ) \\\\y + 3 = \frac{5}{8}(x + 7 )\\\\y + 3 = \frac{5}{8}x + \frac{35}{8} \\ \\y = \frac{5}{8}x + \frac{35}{8} - 3\\\\y = \frac{5}{8}x + \frac{11}{8}[/tex]
Therefore, the equation of the line is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].
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P(JIK) = 0.35, P(KJ) = 0.95, P(K) = 0.3
What is P(J)?
O 0.1105
O 0.8143
O 0.8895
O 0.1857
Answers
The conditional value probability is solved and P ( J ) = 0.1105
Given data ,
P(JIK) = 0.35, P(KJ) = 0.95, P(K) = 0.3
We can use Bayes' theorem to find P(J):
P(J | K) = P(K | J) * P(J) / P(K)
0.35 = 0.95 * P(J) / 0.3
0.35 * 0.3 = 0.95 * P(J)
0.105 = 0.95 * P(J)
P(J) = 0.105 / 0.95
P(J) = 0.1105
Hence , the probability is P ( J ) = 0.1105
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Evaluate the determinant
1
03
03
0)2
w2
1 , where w is a cube root
co
2 1 o
of unity.
Answers
In this case, the cube root is = 0
Why is this so?We can use the rule Sarrus to evaluate the determinant
1 w w²
w w² 1
w² 1 w
Starting with the first column, we can wrte out the terms for the diagonal products and
then sum the terms for the products of the diagonal elements that wrap around
(1 x w² x w) +(w x 1 x w²) + (w² x w x w) - (w ² x w x 1) - (w x w² x w) - (1 x w x w ²)
Simplifying each term:
w³ + w³ + w³ - w³ -w³ - w³
We can see that all the terms cancel out, leaving us with a determinant of 0. So it is clear that
|1 w w²|
|w w² 1 |
|w² 1 w | = 0
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Evaluate the determinant 1 w w2 , w w2 1, w2 1 w. where w is a cube root of unity.
Function f is an exponential function. It predicts the value of a famous painting, in thousands of dollars, as a function of the number of years since it was last purchased.
What equation models this function?
ANSWER: 8(1.25)x just took the test
Answers
Answer:
[tex]f(t) = 8e^{0.223144t}[/tex]
A store has 300 televisions on order, and 90% are high definition. How many televisions on order are high
definition? You may find the bar model useful in completing this problem.
20% 30% 40%
70%
0%
0
10%
30
The store has
50% 60%
high-definition televisions on order.
80%
90%
100%
300
Answers
Answer:
90% of 300 = .90 × 300 = 270 high- definition televisions on order.
the set of five number each of which is divisible by 3
Answers
Answer:
{3, 6, 9, 12, 15}
Each of these numbers is divisible by 3
Step-by-step explanation:
where should the linear inequality y ≤ 3/2x + 3 be shaded?
Answers
Answer:
Step-by-step explanation:
it should be shaded at the 76
Find f(−3), f(0) and f(1) for the following function.
f(x)=2x
Answers
Answer:
-6, 0, 2Step-by-step explanation:
f(x)=2x
note: putting anything in the f(x) parentheses replaces x in the function with that value
so,
f(-3) = 2(-3) = -6
f(0) = 2*0 = 0
f(2) = 2(2) = 4
solve for x, neg x over 4 = 12 A 48 or B -3 or C 3 or D -48?
Answers
The solution for x is -48, the answer is D) -48.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It represents a value that can change based on the values assigned to the variables.
Starting with:
x:4 = 12
Multiplying both sides by -1 gives:
(-x÷4) = -12
Simplifying the left side:
x÷4 = -12
Multiplying both sides by 4 gives:
x = -48
Therefore, the solution for x is -48, the answer is D) -48.
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if you help I would be so thankful
Answers
Answer:
I put the answer on the attachment please look
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of $2600. What was the rate charged per hour by each mechanic if the sum of the two rates was $155
per hour?
Answers
the first mechanic charged $55 per hour and the second mechanic charged $100 per hour. we solve this by forming equation by by given data.
what is equation ?
An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables,
In the given question,
Let's assume that the first mechanic charged x dollars per hour and the second mechanic charged y dollars per hour.
From the problem, we know that:
The first mechanic worked for 20 hours, so he charged 20x dollars.
The second mechanic worked for 15 hours, so he charged 15y dollars.
Together, they charged a total of $2600, so we have:
20x + 15y = 2600
The sum of the two rates was $155 per hour, so we have:
x + y = 155
We can use these two equations to solve for x and y. First, we can rewrite the second equation as:
y = 155 - x
Then, we can substitute this expression for y into the first equation:
20x + 15(155 - x) = 2600
Simplifying and solving for x, we get:
20x + 2325 - 15x = 2600
5x = 275
x = 55
Now that we know x, we can use the second equation to find y:
y = 155 - x = 155 - 55 = 100
Therefore, the first mechanic charged $55 per hour and the second mechanic charged $100 per hour.
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answers
The solution for x in the equation (x – 7)^2 = 36 are x = 13 and x = 1
Solving for x in the equationWe can solve for x by taking the square root of both sides of the equation:
(x – 7)^2 = 36
Taking the square root of both sides:
x - 7 = ±6
Adding 7 to both sides:
x = 7 ± 6
Therefore, the values of x are:
x = 7 + 6 = 13
x = 7 - 6 = 1
So the correct answers are x = 13 and x = 1. The values x = -29 and x = 42 are not solutions to the equation.
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Statistics Help, pls help me
A nationwide award for high school students is given to outstanding students who are sophomores, juniors, or seniors (freshmen are not eligible). Of the award-winners, 65 percent are SENIORS, 23 percent JUNIORS, and 12 percent are SOPHOMORES.
Answers
a) The probability of selecting exactly 3 award-winners before selecting a SENIOR is 0.078875
b)The probability of selecting more than 2 award-winners before selecting a JUNIOR is 0.135437
c)The probability of selecting 2 or fewer award-winners before selecting a SOPHOMORE is 0.252744
Define probabilityProbability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.
(a) The probability of selecting a SENIOR is 0.65, and the probability of not selecting a SENIOR is 0.35.
Since we are selecting award-winners until we select a SENIOR, the first two selections must not be SENIORS, and the third selection must be a SENIOR.
the probability of selecting exactly 3 award-winners before selecting a SENIOR is:
P(not SENIOR) x P(not SENIOR) x P(SENIOR) = 0.35 x 0.35 x 0.65 = 0.078875
(b)Therefore, the probability of selecting more than 2 award-winners before selecting a JUNIOR is:
P(not JUNIOR) x P(not JUNIOR) x P(JUNIOR) = 0.77 x 0.77 x 0.23 = 0.135437
To find the probability of selecting more than 2 award-winners, we can subtract this value from 1, since the only other possibility is selecting exactly 2 award-winners before selecting a JUNIOR:
P(more than 2) = 1 - P(exactly 2) = 1 - (P(not JUNIOR) x P(JUNIOR) x P(not JUNIOR)) = 1 - (0.77 x 0.23 x 0.77) = 0.567911
(c) The probability of selecting a SOPHOMORE is 0.12, and the probability of not selecting a SOPHOMORE is 0.88.
Since we are selecting award-winners until we select a SOPHOMORE, we can keep selecting SENIORS and JUNIORS until we select a SOPHOMORE.
Therefore, the probability of selecting 2 or fewer award-winners before selecting a SOPHOMORE is:
P(SOPHOMORE) + P(not SOPHOMORE) x P(JUNIOR) x P(SOPHOMORE) + P(not SOPHOMORE) x P(not JUNIOR) x P(JUNIOR) x P(SOPHOMORE) = 0.12 + (0.88 x 0.23 x 0.12) + (0.88 x 0.77 x 0.23 x 0.12) = 0.252744
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what is the suface area of 11cm and 14cm
Answers
Answer:
429 i think
Step-by-step explanation:
In ΔFGH, g = 910 cm,
m∠G=98° and
m∠H=51°. Find the length of h, to the nearest 10th of a centimeter.
Answers
In ΔFGH, the length of h is 714.2 cm
Let us assume that in ΔFGH, f represents the opposite side to angle F, g represents the opposite side to angle G, and h represents the opposite side to angle H.
Consider the following figure.
Using sine rule for triangle FGH,
sin F/f = sin G/g = sin H/h
Consider equation sin G/g = sin H/h
sin(98°) / 910 = sin(51°) / h
We solve this equation for h.
h = (sin(51°) × 910)/ sin(98°)
h = (0.777 × 910)/ 0.99
h = 714.21
h = 714.2 cm
This is the required length of h.
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Solve for w.
w − 5
4
= 2
Answers
The value of the variable w is 56
What are algebraic expressions?Algebraic expressions are described as expressions that are composed of terms, variables, factors, coefficients and constants.
Also, algebraic expressions are made up of mathematical or arithmetic operations, such as;
AdditionBracketSubtractionParenthesesMultiplicationDivisionFrom the information given, we have the algebraic equation as;
w - 54 = 2
To determine the value of the variable, we take the steps;
collect the like terms
w = 2 + 54
Now, add the values
w = 56
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