Answer:
4x[tex]\sqrt{6x}[/tex]
Step-by-step explanation:
This can be written:
[tex]\sqrt{(3)(2)(2)(2)(2)xxx}[/tex] Pull out all the pairs. There are 2 pairs of 2 and 1 pair of x's
(2)(2)x[tex]\sqrt{(3)(2)x}[/tex] Clean up
4x[tex]\sqrt{6x}[/tex]
2. A construction supplier is determining which type of cement sells the best. The table shows the rates at which each type sold. A workday is 8 hours, and each pound of cement sells for 4.50. List the types of cements in order from highest to lowest unit rate of
A Forty pounds were sold in one day.
B 6 y=2 x, where x is in pounds and y is in hours
C After 3 hours, 45 worth had been sold.
D The ratio of days to pounds sold was 2: 60.
The cement kinds will be listed in order of highest to lowest unit rate of pounds per day: C > A > D > B.
The table shows the rates at which each type is sold. A workday is 8 hours, and each pound of cement sells for 4.50.
Type A cement,
Forty pounds were sold in one day.
unit rate = 40 pounds per day
Type B cement,
6y = 2x, where x is in pounds and y is in hours
Since the workday is 8 hours, so substitute the value of x = 8 and we get
6y = 2(8)
6y = 16
y = 16/6 = 2.67
This means the unit rate = 2.67 pounds per day
Type C cement,
After 3 hours, 45 worth had been sold.
After 8 hours,
The worth had been sold = 8×45/3 = 120
unit rate = 120 pounds per day
Type D cement,
The ratio of days to pounds sold was 2: 60.
So, unit rate = 60/2 = 30 pounds per day
So the types of cement in order from highest to lowest unit rate of pounds per day will be :
C > A > D > B
Learn more about the descending order here:
brainly.com/question/233644
#SPJ1
y varies directly as x. If y = 7 when x = 2, find y when x = 3.
Evaluate : -35 ÷ (-7) =
Answer:
-35/-7=5
Step-by-step explanation:
Diviser par de nombre négatif alors sa devient positif pareil pour la multiplication
Una docena de bananos cuesta $2.650. ¿Cuántas docenas podría comprar una persona con $22.500?. ¿Cuánto obtendría de devueltas? (ojo, existe más de una solución)
Podras comprar un total de 8 docenas, y sobrara $1.30
¿Cuantas docenas se pueden comprar con $22.50?
Sabemos que una docena de bananos cuesta $2.65, y queremos ver cuantas docenas se peden comprar con $22.50, para ver esto, debemos tomar el cociente entre la cantidad de dinero que tenemos y el precio de una docena.
Obtendremos:
$22.50/$2.65 = 8.49
Redondenado al proximo numero entero obtenemos 8, es decir, se pueden comprar 8 docenas.
La cantidad que sobra es:
$22.50 - 8*$2.65 = $1.30
Aprende mas sobre cocientes:
https://brainly.com/question/3493733
#SPJ1
The ratio of Lauren's jellybeans to Haley's jellybeans is 3:8. Lauren has 50 fewer jellybeans than Haley. How many jellybeans does Lauren have ?
Answer:
Lauren has 30 jellybeans
Step-by-step explanation:
Let x - Lauren
Let y = Haley
[tex]\frac{x}{y}[/tex] = [tex]\frac{3}{8}[/tex] Cross multiply
8x + 3y
x = y - 50 Substitute y - 50 into the equation above for x
8(y -50) = 3y
8y -400 = 3y Subtract 8y from both sides
-400 = -5y Divide both sides by -5
80 = y This is Haley's jellybeans
x = y = 50
x = 80 - 50
x = 30 This is Lauren's jellybeans.
Which expression means “Twice the difference of w and the square of 6”
Answer:
[tex]2(w-6^2)[/tex]
Step-by-step explanation:
We are doubling the difference, so we first need to find the difference. Our two numbers are [tex]w[/tex] and [tex]6^2[/tex] (you can also write 36 but that is how the problem states it). Therefore, the equation for that is [tex]w-6^2[/tex]. Then, if we double it, we get [tex]2(w-6^2)[/tex].
Differentiate the function with respect to x. Shot steps
The given function y = sec⁻¹(x³) is differentiated as dy/dx = 3x/√(x² - 1).
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = Lim h --> 0 (f(x + h) - f(x)) /(x + h - x).
Its geometric meaning is the slope of tangent of the function at a given point.
The given function is as below,
y = sec⁻¹(x³)
The given function is a composite function of sec⁻¹x and x³.
In order to differentiate it, first differentiate x³ and then sec⁻¹x as follows,
dx³/dx = 3x²
And, dsec⁻¹x /dx = 1/x√(x² - 1)
Now, differentiation of sec⁻¹(x³) is given as,
d sec⁻¹(x³)/dx = 3x²/(x√(x² - 1))
= 3x/√(x² - 1)
Hence, the differentiation of the given function is 3x/√(x² - 1).
To know more about differentiation click on,
https://brainly.com/question/24898810
#SPJ1
In a binomial situation, n = 4 and π = 0.30. Find the probabilities for all possible values of the random variable, x (0, 1, 2, 3, 4, 5, 6).
The corresponding probabilities of the random variables x = (0, 1, 2, 3, 4, 5, and 6) are (0.2401, 0.4116, 0.2646, 0.0756, 0.0081, 0, and 0)
How find the probabilities for all possible values of the random variable?Since we are dealing with a binomial probability distribution. We are going to use the binomial distribution formula for determining the probability of x successes:
P(x = r) = nCr . π^r . q^n-r
Given: n = 4 and π = 0.30, q = 1 - π = 1 - 0.30 = 0.70 and x = (0, 1, 2, 3, 4, 5, 6)
P(x = 0) = 4C0 × 0.3⁰ × 0.7⁴⁻⁰ = 0.2401
P(x = 1) = 4C1 × 0.3¹ × 0.7⁴⁻¹ = 0.4116
P(x = 2) = 4C2 × 0.3² × 0.7⁴⁻² = 0.2646
P(x = 3) = 4C3 × 0.3³ × 0.7⁴⁻³ = 0.0756
P(x = 4) = 4C4 × 0.3⁴ × 0.7⁴⁻⁴ = 0.0081
P(x = 5) = 0
P(x = 6) = 0
Note: P(x = 5) and P(x = 6) are 0 because their x (5 and 6) is greater than the n (4)
Therefore, the probabilities of the random variables x(0, 1, 2, 3, 4, 5, and 6) are 0.2401, 0.4116, 0.2646, 0.0756, 0.0081, 0, and 0 respectively
Learn more about binomial distribution on:
brainly.com/question/29241256
#SPJ1
2) The chess club plans to fundraise $780, which is to be divided evenly among the members, Initially there are x participants, but then 2 more participants come forward, causing each participant to fundraise $8 less. Create an equation that represents the situation and can be used to salve for x, the initial number of participants,2) The chess club plans to fundraise $780, which is to be divided evenly among the members. Initially there are x participants, but then 2 more participants come forward, causing each participant to fundraise $8 less. Create an equation that represents the situation and can be used to solve for x, the initial number of participants.
An equation that represents the situation is 780/x and the initial number of participants is 95.
Equation:
An equation is the combination of number, variables and the mathematical operators such as addition, subtraction, multiplication and division etc.
Given,
The chess club plans to fundraise $780, which is to be divided evenly among the members. Initially there are x participants, but then 2 more participants come forward, causing each participant to fundraise $8 less.
Here we need to find the equation that represents the situation and then we have to find the initial number of participants.
According to the given question,
Total amount for fundraise = $780
Number of participants = x
Here we know that the amount is divided evenly among the members.
So, the equation is written as.
=> 780/x
And the other part of the condition is, 2 more participants come forward, causing each participant to fundraise $8,
So, it can be written as,
=> 780 / (x+2) = 8
=> x + 2 = 780/8
=> x + 2 = 97
=> x = 95
Therefore, there are 95 initial number of participants.
To know more about Equation here.
https://brainly.com/question/10413253
#SPJ1
A red purse contains $7, and a black purse contains $10. Each package contains X red purses and Y black purses. If there are N packages (N ≥ 2) and the total value of them is $2021 and if each of X, Y, and N are positive integers, what is X+Y+N?
If each of X, Y, and N are positive integers, then the value of X+Y+N is 212.1
What are system of inequalities?A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.
WE are given that A red purse contains $7, and a black purse contains $10. Each package contains X red purses and Y black purses.
X = 7
Y = 10
If there are N packages (N ≥ 2) and the total value of them is $2021
X + Y = One packages
N packages = N(X + Y ) = 10 N
if each of X, Y, and N are positive integers, then;
10 N = 2021
N = 2021/10
N = 202.1
Therefore, X+Y+N = 10 + 202.1 = 212.1
Learn more about solutions to the system of inequalities here:
https://brainly.com/question/16339562
#SPJ1
2. aₙ-1=aₙ-1 ÷ 2 where a₁=50 for n≥2
The nth term of the sequence is aₙ = 48 + 2n
How to determine the value of nth term?The definition of the function is given as
a₁= 50
aₙ = aₙ₋₁ + 2
The above definitions imply that we simply add 2 to the previous term to get the current term
Using the above as a guide, we have:
The common difference, d = 2
First term, a = 50
The nth term of the sequence is calculated as
aₙ = a₁ + (n - 1)* d
Substitute the known values in the above equation
So, we have the following representation
aₙ = 50 + (n - 1)* 2
So, we have
aₙ = 50 + 2n - 2
Evaluate the like terms
aₙ = 48 + 2n
Hence, the nth term is aₙ = 48 + 2n
Read more about sequence at
brainly.com/question/7882626
#SPJ1
Your car dealer is willing to lease you a new car for $140 a month for 36 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 6.4 percent, what is the current value of the lease?
If your cost of money is 6.4 percent, what is the current value of the lease is equal to $820.0054.
What is a lease?In Economics, a lease can be defined as a contractual agreement between a lessor and lessee, which avails the lessee an opportunity to make use of an asset, while making payments in instalment to the lessor for a specific period of time.
Mathematically, the current (present) monetary value of a lease can be calculated by using this formula:
Current value, PV = [Annuity × (1 + r) × [1 - (1 + r)^{-n}]/r]
Where:
PV represents the current value of an ordinary annuity.r represents the interest rate per period.n represents the number of periods.Note: r = 0.064/12 = 0.0053333
Substituting the given parameters into the formula, we have;
Current value, PV = [144 × (1 + 0.0053333) × [1 - (1 + 0.0053333)^{-36}]/0.0053333]
Current value, PV = [144 × (1.0053333) × [1 - (1.0053333)^{-36}]/0.0053333]
Current value, PV = [144 × (1.0053333) × [1 - 0.8257290]/0.0053333]
Current value, PV = [144 × (1.0053333) × [0.174271/0.0053333]
Current value, PV = 25.095024 × 32.6760167
Current value, PV = $820.0054.
Read more on current value on annuity here: https://brainly.com/question/27882683
#SPJ1
2. A rectangle has a length that is half its
width. Define a variable to represent the
unknown quantity. Then write an expression
to represent the perimeter of the rectangle.
(Example 5)
The Perimeter of the given Reactangle is 6*length
Whta is a Rectanglee?
A rectangle is a quadrilateral with four right angles in Euclidean plane geometry. It can alternatively be classified as an equiangular quadrilateral since all of its angles are equal; or a parallelogram with a right angle. A square is a rectangle with four equal-length sides.
Solution:
Let,
the length be l
and breadth be b
According to the question,
l = (1/2)b
We know that Perimeter of Rectangle = 2(length + breadth)
From the variable mentioned above
Perimeter = 2*(l+b)
Perimeter = 2*(l + 2l)
Perimeter = 2*(3l)
Perimeter = 6l
The Perimeter of the given Reactangle is 6*length
To learn more about Rectangle from the given link
https://brainly.com/question/2607596
#SPJ1
Answer:
Let x be the width of the rectangle.
The expression to represent the perimeter of the rectangle is 3x.
Step-by-step explanation:
Definition of the variable:
Let x be the width of the rectangle.If the rectangle has a length that is half its width, then:
[tex]\textsf{Width} = x[/tex][tex]\textsf{Length} = \dfrac{1}{2}x[/tex]The perimeter of a two-dimensional shape is the distance all the way around the outside. Therefore, the perimeter of a rectangle is twice the sum of its length and width.
[tex]\begin{aligned}\textsf{Perimeter of the rectangle}&=2 \left(\;\sf length+width\; \right)\\& = 2\left(\dfrac{1}{2}x+x\right)\\& = 2 \left(\dfrac{3}{2}x\right)\\& = 3x\end{aligned}[/tex]
Therefore, an expression to represent the perimeter of the rectangle is:
[tex]\textsf{$3x$ \;\;(where\;$x$ is the width of the rectangle)}.[/tex]You are choosing between two different prepaid cell phone planes. The first plan charges a rate of 26 cents per minute. The second plan charges charges a monthly fee of $19.95 plus 11 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable?
If we use more than 133 minutes then the 2nd plan will be preferable.
Given:
The first plan charges a rate of 26 cents per minute. The second plan charges charges a monthly fee of $19.95 plus 11 cents per minute.
26 cents = $0.26
Let m be the minutes
19.95 + .17m < .32m
Subtract .17m from both sides
19.95 < .32m - .17m
19.95 < .15m
Divide both sides by .15
19.95/.15 < m
133 < m
Learn more about the charges here:
https://brainly.com/question/19886264
#SPJ1
If y 1/x and y = 2 when x = 13, find the equation that connects x and y.
The relation for x and y is given as y = 26/x. The correct answer is option (B).
What is Proportionality?When two quantities have some dependence in their values they can be said proportional to each other.
It can be of two types such as direct and indirect.
The direct proportionality means the values of both the quantities are increasing or decreasing at the same time while the indirect proportionality implies value of one quantity is increasing while the other is decreasing.
Given that,
The proportionality relation between x and y as
y ∝ 1/x
And, y = 2 at x = 13.
Suppose k is the constant of proportionality.
Then, y = k/x
Substitute y = 2 and x = 13 in the above equation to obtain,
2 = k/13
=> k = 26
Thus, by substituting the value of k the equation can be written as y = 26/x.
Hence, the equation that relates x and y is y = 26/x.
To know more about proportionality click on,
brainly.com/question/22620356
#SPJ1
Jim is a preschool teacher. While he was getting ready for his class's snacktime, he put 6 carrots on each plate. If he used 48 total carrots, which equation could be used to determine the number of plates, p, that he used? (Picture shows answer choices)
The equation that can be used to determine the number of plates p, that he used is 6p = 48.
How to represent a situation with an equation?Jim is a preschool teacher. While he was getting ready for his class's snack time, he put 6 carrots on each plate.
He used 48 total carrots. The equation that could be used to determine the number of plates, p, that he used can be represented as follows:
let
p = number of of plates
Therefore,
6 carrots are put on each plate.
He has 48 carrots.
Hence, the equation is 6p = 48
p = 48 / 6
p = 8
Therefore,
number of plates = 8
learn more on equation here: https://brainly.com/question/15014611
#SPJ1
The number of plates he used is can be calculated by 6p = 48
How to determine this?
He was said to put 6 carrots on each plates
And used 48 total carrots altogether
p representing the number of plates
That is, 6 carrots in p places
6 carrots × p
= 6p
Given that 48 carrots used altogether
6p = the total number of carrots
Therefore, 6p = 48
Read more about Word problem
https://brainly.com/question/29529084
#SPJ1
Select all expressions that are equivalent to 2x+3x+8-3x-2. 2x+6 2x+10 65x-3x+6 (5x-3x+10
Answer:
Step-by-step explanation:
2x+3x+8-3x-2 = 2x + 6
-3x-10=14
How do u solve this with working?
Transporssy method in maths anyone?
Answer: x = -8
Step-by-step explanation:
1. Add 10 to both sides
-3x = 14 + 10
2. Simplify 14 + 10 to 24
-3x = 24
3. Divide both sides by -3
x = [tex]-\frac{24}{3}[/tex]
4. Simplify [tex]\frac{24}{3}[/tex] to 8
x = -8
X
60°
70° find x can you please help me
Answer:
50 degrees
Step-by-step explanation:
sum of all three angles on any triangle is equal 180 degrees so first we add the first 2 given angles
70+60
130
Now we subtract from 180 to find the unknown angle
180-130
50 degrees
Hopes this helps please mark brainliest
x + 60° + 70 = 180°
( sum of interior angle of triangle is 180° )
x + 130° = 180°
x = 180° - 130°
x = 50°
hope it helps...
2 power 8 multiply by A power 5 by 4 power 3 multiply by a power 3
The value of the equation is 2² x A ²
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be D
D = 2 power 8 multiply by A power 5 / 4 power 3 multiply by a power 3
So , on substituting the values in the equation , we get
D = 2⁸ x A⁵ / 4³ x A³
Now , 2⁸ / 4³ can be simplified as
4³ = 2⁶
So ,
2⁸ / 2⁶ = 2 ⁸⁻⁶
= 2²
And , A⁵ / A³ can be simplified as
A⁵ / A³ = A⁵⁻³
= A²
So , the equation becomes ,
D = 2⁸ x A⁵ / 4³ x A³
D = 2² x A²
D = ( 2A )²
Hence , the value of the equation is D = 2² x A²
To learn more about equations click :
https://brainly.com/question/10413253
#SPJ1
Solve x = 36, where x is a real number.
Simplify your answer as much as possible.
The value obtained after solving the expression will be equal to (-1, 1).
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both.
Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given in for the mention in the question,
x² = 36
x = ±6
Therefore, the values are -6, and +6.
To know more about the expression:
https://brainly.com/question/14083225
#SPJ1
() 10 % of Glen's coins are from Denmark. If he has 11 coins from Denmark, how many
coins does Glen have in his entire collection?
Pick the model that represents the problem.
0%
0
0%
0
10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Submit
11
10% 20% 30% 40% 50% 60% 70% 80% 90%
?
How many coins does Glen have in his entire collection?
coins
?
100%
11
Glens have 110 coins in his entire collection.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Glens coins from Denmark are eleven 11.
These 11 coins are 10% of his entire coins.
We need to find how many coins Glens has.
Let x be the entire collection of Glens coins
10/100x=11
0.1x=11
Divide both sides by 0.1
x=110
Hence, Glens have 110 coins in his entire collection.
To learn more on Percentage click:
https://brainly.com/question/28269290
#SPJ1
Use the image to answer the question.
Rectangular prism with dimensions 0.5 feet by 1.5 feet by 4 inches.
© 2018 StrongMind
What is the surface area of the figure in square inches?
Enter your answer as a number, like this: 42
The surface area of the figure in square inches will be 17.5 inch².
What is a rectangular prism?It is defined as a six-faced shape, a type of hexahedron in geometry. It is a three-dimensional shape. It is also called a cuboid.
It is given that, Rectangular prism with dimensions 0.5 feet by 1.5 feet by 4 inches.
Length(l) = 0.5 ft = 6 inch
Width(w) = 1.5 ft = 18 inches
Height(h) = 4 inches
The surface area of the figure in square inches is found as,
S = 2(lw + lh + wh)
S=2(6×8 + 8×4 +4×6)
A = 17.5 inch²
Thus, the surface area of the figure in square inches will be 17.5 inch².
Learn more about the rectangular prism here:
brainly.com/question/21308574
#SPJ1
3. You are looking to test whether the mean resting heart rate for people who exercise regularly is
less than the mean resting heart rate for people who do not. You randomly sample 17 people
that exercise regularly and compute a sample mean of 69.4 bpm and a sample standard
deviation of 4.57 bpm. You randomly sample 16 people that do not exercise regularly and
compute a sample mean of 73.25 bpm and a sample standard deviation of 3.30 bpm. We are
interested in finding out if the new approach is better at a 2% significance level.
a. State the hypotheses to be tested.
b. The test resulted in a t-value of -2.779 with 29 degrees of freedom. Compute the P-value.
Detail how you got your number.
c. Based on your P-value, what decision do you make at a 2% significance level: Reject H0 or
do not reject H0?
d. Based on your decision what conclusion can you make about comparing the two sets of
people?
a. The hypothesis to be tested are given as follows:
Null: [tex]H_0: \mu_d \leq 0[/tex]Alternative: [tex]H_1: \mu_d > 0[/tex]b. The p-value is of: 0.0047.
c. The decision is of: Reject the null hypothesis.
d. The conclusion is of: There is enough evidence to conclude that the mean rate is less for people who exercise regularly.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence to conclude that the heart rate is less, than is, if the difference is not negative, hence:
[tex]H_0: \mu_d \leq 0[/tex]
At the alternative hypothesis, it is tested if there is enough evidence to conclude that the heart rate is less, that is, if the difference is negative, hence:
[tex]H_1: \mu_d > 0[/tex]
What are the p-value, decision and conclusion?The parameters to the p-value are given as follows:
t = -2.779.29 degrees of freedom.We have a left-tailed test, as we are testing if the mean is less than a value, hence, using a t-distribution calculator, the p-value is of:
0.0047.
Since the p-value is less than the critical value, the decision and the conclusion are given as follows:
Decision: Reject the null hypothesis.Conclusion: There is enough evidence to conclude that the mean is less.More can be learned about the test of an hypothesis at https://brainly.com/question/13873630
#SPJ1
Zhang invests $2600 in two different accounts. The first account paid 11 %, the second account paid
5 % in interest. At the end of the first year he had earned $220 in interest. How much was in each
account?
$ At 11%
$ At 5%
Step-by-step explanation:
Zhang invests $2,600 in two different accounts. The first account paid 11%, the second account paid 5% in interest. At the end of the first year he had earned $220 in interest. How much was in each account?
11% = 0.11
in account 1: $220/0.11 = $2,000
in account 2: $2,600 - $2,000 = $600
$2,000 At 11%
$600 At 5%
The function f(x) is graphed below. How many points on the graph represent a relative minimum? PLEASE need help i don't understand. Need by TONIGHT!!!
The number of point on this graph that represent a relative minimum is one, which is point b.
What is a function?In Mathematics, a function simply refers to a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair (x, y)on a graph.
What is a relative minimum?A relative minimum can be defined as the lowest point or valley point on the graph of a function. Additionally, all of the points that are located to the left and right of the lowest point (valley point) on a graph must be larger than the relative minimum.
By critically observing the graph of function f(x), we can reasonably and logically deduce the following information:
Point b is a relative minimum.Point d is an absolute minimum.Point f is a relative maximum.Read more on relative minimum here: https://brainly.com/question/9180672
#SPJ1
7cm is not correct please I’m so confused
Answer:
10 cm
Step-by-step explanation:
since DE is probably equal to AD which is 17 we subtract the length of the side of CD to find CE
Length CD can be found because it is equal to AB which is 7 cm so we subtract
17-7=10
Hopes this helps please mark brainliest
Answer:
CE = 10
Step-by-step explanation:
Because they are congruent:
AD = 17, that means DE = 17
AB = 7, that means CD = 7
To find what CE is, we start with the full length:
DE
and by subtracting CD (that's part of the length), we can get CE.
DE - CD = CE
Just substitute the values in:
17 - 7 = 10
CE = 10
So there's the answer, but check this out:
CE + CD = DE
10 + 7 = 17
what is the solution for 15= 1/2 + 3/2x + 10
Answer:
x = 3
Step-by-step explanation:
Find all values of m for which the equation has two real solutions.
(m - 3)r² + 9r - 2 = 0
Given equation to us is , [tex](m-3)r^2+9r-2=0[/tex] .
The given equation is a quadratic equation and it has two real solutions if it's discriminant is greater than or equal to 0 .
For a quadratic equation in standard form of
[tex]ax ^{2} + bx + c = 0[/tex]
the discriminant is given by b² - 4ac .
On comparing wrt to Standard form, we have ;
[tex]a = m - 3[/tex][tex]b = 9[/tex][tex]c = - 2[/tex]Now we have,
[tex]\longrightarrow b^2-4ac \geq 0\\\\\longrightarrow 9^2-4(m-3)(-2)\geq 0\\\\\longrightarrow 81 +8(m-3)\geq 0 \\\\\longrightarrow 81 +8m-24\geq 0 \\\\\longrightarrow 8m \geq 24-81 \\\\\longrightarrow 8m \geq -57 \\\\\longrightarrow \underline{\underline{ m \geq \dfrac{-57}{8}}}[/tex]
Therefore for all values greater than or equal to -57/8 the equation will have a real solution .
And we are done!
The equation (m-3)r² + 9r -2 = 0 will have two real solution for the value of m, greater than or equal to -57/8.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The standard form of equation of power two is ax²+bx+c =0 .
The given equation,
(m-3)r² + 9r -2 = 0
Compare the given equation with standard equation ax²+bx+c =0,
The value of a=m-3, b=9 and c=-2
An equation has two real solutions if a discriminant of the equation is greater than or equal to zero.
⇒D ≥ 0
⇒b²-4ac ≥ 0
Substitute the value of a, b and c,
⇒9² - 4×(m-3)(-2) ≥ 0
⇒81 +8m - 24 ≥ 0
⇒8m ≥ -57
⇒ m ≥ -57/8
For the values of m greater than or equal to -57/8, the equation have two real solutions.
To know more about Equation on:
https://brainly.com/question/187506
#SPJ1
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.
xy = 6, x = 0, y = 6, y = 8
The volume of the solid obtained by rotating the region bounded by the given curves about the x-axis is 48π
Volume of the Solid:
Volume refers the measure of how much space an object takes up and it is measured by the number of unit cubes it takes to fill up the solid.
Given,
Here we have to use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.
xy = 6, x = 0, y = 6, y = 8.
Here we know that,
xy = 6
Then the value of x is obtained as,
=> x = 6/y
Now, the volume of the solid is calculated with the given interval [6,8] as.
=> V = 2π ∫₆⁸ y x (6/y)/dy
=> 2π∫₆⁸ 6/dy
When we differentiate the equation, then we get,
=> 24π[y]₆⁸
=> 24π [8 - 6]
=> 24π [2]
=> 48π
Therefore, the volume of the solid is 48π.
To know more about Volume of Solid here.
https://brainly.com/question/12649605
#SPJ1
