To place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet. Let's discuss it in detail below. Here are the dimensions of the bench press machine, which can help determine the amount of space required to fit two bench press machines in a small area:
The length of the bench press machine is between 48 inches and 54 inches.
The width of the bench press machine is between 28 inches and 32 inches.
The height of the bench press machine is between 48 inches and 56 inches.
Based on the above dimensions of the bench press machine, two machines can be placed in a small area of 10 feet by 10 feet. However, for safe use, the following guidelines should be followed:
There should be at least 6 feet of distance between the two bench press machines. There should be at least 3 feet of clearance in the front of the bench press machine to allow for safe movement during exercises. There should be at least 2 feet of clearance behind the bench press machine to allow for a safe exit in case of an emergency.
Thus, to place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet.
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Can i get assistance with this?
Answer:
see attached
Step-by-step explanation:
You want the given triangle dilated by a factor of -3 about point A.
DilationTo find the image point corresponding to a pre-image point, multiply the pre-image point's distance from A by the dilation factor. The negative sign means the distance to the image point is measured in the opposite direction.
In the attached figure, the chosen point is 4 units up and 5 units right of A. Its image in the dilated figure is 3·4 = 12 units down, and 3·5 = 15 units left of A.
This same process can be used to locate the other vertices of the triangle's image.
22 The regular selling price is a 22" tube television is $389. The markdown rate is 33%. Use the
percent paid to determine the sale price.
A. $245.34
C. $260.63
B. $267.89
D. $287.56
The Sale price is C. $260.63.
What is selling price?Selling price is the price at which a product or service is sold by a business or seller to a customer. It is the amount of money that a customer must pay in order to purchase the product or service. The selling price is typically determined by factors such as production costs, competition, supply and demand, and profit margins.
What is sale price?Sale price is the discounted price at which a product or service is sold for a limited period of time. It is usually a lower price than the regular price, and it is offered to customers as an incentive to make a purchase. Sale prices can be determined by applying a discount or markdown to the regular selling price.
In the given question,
To find the sale price, we need to first calculate the amount of the markdown:
Markdown = Regular Price x Markdown Rate
Markdown = $389 x 0.33
Markdown = $128.37
The sale price is then the regular price minus the markdown:
Sale Price = Regular Price - Markdown
Sale Price = $389 - $128.37
Sale Price = $260.63
Therefore, the answer is C. $260.63.
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Suppose that s is the position function of an object, given as s(t) = 2t - 7. We compute the instantaneous velocity of the object at t = 6 as follows. Use exact values. First we compute and simplify (6 +h). s(6 + h) = Then we compute and simplify the average velocity of the object between t = 6 and t = 6 + h. 8(6+h) - s(6) h = Rationalize the numerator in the average velocity. (If it applies, simplify again.) $(6 + h) - $(6) h The instantaneous velocity of the object att = 6 is the limit of the average velocity as h approaches zero. s(6 + h) – $(6) v(6) lim h -0
The instantaneous velocity of the object at t = 6 is 2.
Suppose that s is the position function of an object, given as s(t) = 2t - 7. We compute the instantaneous velocity of the object at t = 6 as follows. Use exact values. First we compute and simplify (6 + h). s(6 + h) = 2(6 + h) - 7 = 12 + 2h - 7 = 2h + 5Then we compute and simplify the average velocity of the object between t = 6 and t = 6 + h.8(6+h) - s(6) h = 8(6 + h) - (2(6) - 7) h= 8h + 56
Then, to rationalize the numerator in the average velocity. (If it applies, simplify again.)$(6 + h) - $(6) h(h(h) + 56)/(h(h)) = (8h + 56)/h The instantaneous velocity of the object att = 6 is the limit of the average velocity as h approaches zero.s(6 + h) – $(6) v(6) lim h -0s(6 + h) – s(6) v(6) lim h -0Using the above calculation, we get:s(6 + h) – s(6) / h lim h -0s(6 + h) = 2(6 + h) - 7 = 2h + 5So,s(6 + h) – s(6) / h lim h -0(2h + 5 - (2(6) - 7)) / h= (2h + 5 - 5) / h = (2h / h) = 2
Therefore, the instantaneous velocity of the object at t = 6 is 2.
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1(1/2)= 1 1/2 draw number line and represent this
|-----|-----|-----|----|-----|-----|--│--|-----|----|-----|
-5 -4 -3 -2 -1 0 1 │ 2 3 4 5
1 1/2
On this number line, the tick mark labeled "1 1/2" is located halfway between the integer values of 1 and 2.
To represent the number 1 1/2 on a number line, we need to draw a horizontal line with evenly spaced tick marks. Each tick mark represents a specific value on the number line. Since 1 1/2 is a mixed number that includes a whole number (1) and a fraction (1/2), we need to locate it between the integer values of 1 and 2. The tick mark for 1 1/2 should be halfway between these two integers, which means it would be located at the midpoint of the line segment that connects the tick marks for 1 and 2. By placing the tick mark for 1 1/2 in the correct position on the number line, we can accurately represent this number visually.
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Find the interest refund on a 35-month loan with interest of $2,802 if the loan is paid in full with 13 months remaining.
Answer: $1,071.54
Step-by-step explanation:
To find the interest refund, first we need to calculate the total interest charged on the loan. We can do this by multiplying the monthly interest by the number of months in the loan:
Monthly interest = Total interest / Number of months
Monthly interest = $2,802 / 35
Monthly interest = $80.06
Total interest charged on the loan = Monthly interest x Number of months
Total interest charged on the loan = $80.06 x 35
Total interest charged on the loan = $2,802.10
Now we need to calculate the interest that would have been charged for the remaining 13 months of the loan:
Interest for remaining 13 months = Monthly interest x Remaining months
Interest for remaining 13 months = $80.06 x 13
Interest for remaining 13 months = $1,040.78
Finally, we can find the interest refund by subtracting the interest for the remaining 13 months from the total interest charged on the loan:
Interest refund = Total interest charged - Interest for remaining months
Interest refund = $2,802.10 - $1,040.78
Interest refund = $1,074.32
Therefore, the interest refund on the loan is $1,074.30.
what is the z-score for the 75th percentile of the standard normal distribution is: 0.67 1.645 1.28 -0.67 -1.28
The z-score for the 75th percentile of the standard normal distribution is given by 0.67 that is option A.
The most significant continuous probability distribution is the Normal Distribution, often known as the Gaussian Distribution. It is also known as a bell curve. The normal distribution represents a large number of random variables either nearly or exactly.
I found one that shows the following:
Z value Table entry
0.67 0.7486
0.68 0.7517
As a result, the Z value for 0.75 is between 0.67 and 0.68.
Interpolation yields the z value of 0.6745.
If you have a TI-84 calculator, you may calculate the z value as follows:
VARS - 2nd (this will show the DISTR menu)
To select invNorm, press 3.
Enter the value for the area/table (0.75)
If you press enter, it will return the z value.
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Complete question:
what is the z-score for the 75th percentile of the standard normal distribution is:
0.67 1.645 1.28 -0.67 -1.28Suppose Z follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places. (a) P(Z < 0.79) = Х 5 ? (b) P(Z > 0.75) (c) P(-1.06 < Z< 2.17) =
The probabilities Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75).
The probability of Z > 0.75 is 1 - 0.77337 = 0.22663
The probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968
Suppose Z follows the standard normal distribution. The probabilities using the ALEKS calculator are given below.(a) P(Z < 0.79) = 0.78524. (rounded to 5 decimal places)(b) P(Z > 0.75) = 1 - P(Z < 0.75) = 1 - 0.77337 = 0.22663. (rounded to 5 decimal places)(c) P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968. (rounded to 5 decimal places). In the standard normal distribution, the mean is equal to zero and the standard deviation is equal to 1. The notation for a standard normal random variable is z. Z is a random variable with a standard normal distribution and P(Z) denotes the probability of the random variable Z. Suppose z follows a standard normal distribution then the probability of Z < 0.79 is P(Z < 0.79) = 0.78524. So, the answer is 0.78524(rounded to 5 decimal places).Suppose z follows a standard normal distribution then the probability of Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75). Therefore, the probability of Z > 0.75 is 1 - 0.77337 = 0.22663(rounded to 5 decimal places).Therefore, the probability of -1.06 < Z< 2.17 can be found by finding the probability of Z < 2.17 and then subtracting the probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968(rounded to 5 decimal places).
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Use a ruler and pair of compasses to make an accurate drawing of line
AB and its perpendicular bisector, as shown. You must show all of your
construction lines.
Mark point C on your drawing.
Measure the length of AC in your drawing to 1 d.p.
Step-by-step explanation:
1. Draw a line of 8cm.
2. Take a compass and keep it in the length of more than 8 cm.
3. Draw an arc from point A and B which will intersect at point between A and B.
4. Draw a straight line from the arc.
5. You will find out that the line will be drawn exactly between A and B at 4cm.
Reduce each expression to a polynomial
((y-b)^(2))/(y-b+1)+(y-b)/(y-b+1)
The given expression ((y-b)²/(y-b+1)+(y-b)/(y-b+1) after being reduced to a polynomial, can be represented as y-b.
In order to reduce the given equation to a polynomial, we are required to simplify and combine like terms. First, we can simplify the expression in the numerator by expanding the square:
((y-b)²/(y-b+1) = (y-b)(y-b)/(y-b+1) = (y-b)²/(y-b+1)
Now, we can combine the two terms in the equation by finding a common denominator:
(y-b)²/(y-b+1) + (y-b)/(y-b+1) = [(y-b)² + (y-b)]/(y-b+1)
Next, we can combine the terms in the numerator by factoring out (y-b):
[(y-b)² + (y-b)]/(y-b+1) = (y-b)(y-b+1)/(y-b+1)
Finally, we can cancel out the common factor of (y-b+1) in the numerator and denominator to get the polynomial:
(y-b)(y-b+1)/(y-b+1) = y-b
Therefore, the equation ((y-b)²)/(y-b+1)+(y-b)/(y-b+1) after being simplified, is equivalent to the polynomial y-b.
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At which values in the interval [0, 2π) will the functions f (x) = 2cos2θ and g(x) = −1 − 4cos θ − 2cos2θ intersect?
a: theta equals pi over 3 comma 4 times pi over 3
b: theta equals pi over 3 comma 5 times pi over 3
c: theta equals 2 times pi over 3 comma 4 times pi over 3
d: theta equals 2 times pi over 3 comma 5 times pi over 3
The values in the interval [0, 2π) for which the two points would intersect as required is; Choice C; theta equals 2 times pi over 3 comma 4 times pi over 3.
What values of θ make the two functions intersect?Recall from the task content; the given functions are;
f (x) = 2cos2θ and g(x) = −1 − 4cos θ − 2cos2θ
Therefore, for intersection; f (θ) and g(θ):
2 cos²θ = −1 − 4cos θ − 2cos²θ
4cos²θ + 4cosθ + 1 = 0
let cos θ = y;
4y² + 4y + 1 = 0
y = -1/2
Therefore; -1/2 = cos θ
θ = cos-¹ (-1/2)
θ = 2π/3, 4π/3.
Ultimately, the correct answer choice is; Choice C; theta equals 2 times pi over 3 comma 4 times pi over 3.
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if a watch costs $40 and you must pay 6.5% sales tax how much will the tax be ?
Answer:$2.60
Step-by-step explanation:40*0.065
Answer:42.06
Step-by-step explanation:
An amount of money is divided among A, B and C in the ratio 4: 7:9 A receives R500 less than C. Calculate the amount that is divided.
Answer:
We know that A receives R500 less than C, so we can write:
4x = 9x - 500
Solving for x, we get:
5x = 500
x = 100
Now we can calculate the amounts received by each person:
A = 4x = 4(100) = R400
B = 7x = 7(100) = R700
C = 9x = 9(100) = R900
To check our answer, we can verify that the ratios of the amounts received by A, B, and C are indeed 4:7:9:
A:B = 400:700 = 4:7
B:C = 700:900 = 7:9
Therefore, the total amount divided is:
400 + 700 + 900 = R2000
So the amount that is divided is R2000.
Step-by-step explanation:
The total amount of money divided is R2000.
What is the ratio?Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We are given that;
The ratio of A, B and C= 4:7:9
Now,
Let's start by assigning variables to the unknowns in the problem. Let's call the total amount of money "T". Then, if A receives 4x, B receives 7x, and C receives 9x, where "x" is some constant, we can write:
4x + 500 = C's share
We can also write an equation to represent the fact that the three shares add up to the total amount:
4x + 7x + 9x = T
Simplifying this equation, we get:
20x = T
Now we can substitute the first equation into the second equation and solve for x:
4x + 7x + (4x + 500) = 20x
15x + 500 = 20x
500 = 5x
x = 100
Now we can find the individual shares by multiplying x by the appropriate ratio factor:
A's share = 4x = 400
B's share = 7x = 700
C's share = 9x = 900
Finally, we can check that these add up to the total amount:
400 + 700 + 900 = 2000
Therefore, by the given ratio the answer will be R2000.
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Brittany needed new tires for her truck. She went to the auto shop and bought 4 tires on sale for $85.95 each. The salesman told her that she saved a total of $96.16. If Brittany saved the same amount on each tire, what was the original price of each tire?
The best solution gets brainlist
Answer:
$109.99
Step-by-step explanation:
The original price of each tire is [tex]\[/tex][tex]109.99[/tex]
Solution:Take the amount saved and divide by 4 to find the amount saved on each tire
[tex]96.16\div4 =24.04[/tex]
Add that to the sale price of each tire to find the original price
[tex]85.95+24.04 =109.99[/tex]
Therefore, The original price is $109.99.
Select the correct solution for the expression. 2 5 + 3 8 2 5 + 3 8 A. 2 5 + 3 8 = 5 13 2 5 + 3 8 = 5 13 B. 16 40 + 15 40 = 31 40 16 40 + 15 40 = 31 40 C. 10 40 + 24 40 = 34 40 10 40 + 24 40 = 34 40 D. 2 5 + 3 8 = 6 40
In response to the stated question, we may state that As a result, the equation proper answer is: B. 16/40 + 15/40 = 31/40
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
We must identify a common denominator for the two fractions in order to solve the formula 2/5 + 3/8. Because 40 is the lowest common multiple of 5 and 8, we can transform both fractions to have a denominator of 40:
2/5 = 16/40
3/8 = 15/40
We can now sum the two fractions:
16/40 + 15/40 = 31/40
As a result, the proper answer is:
B. 16/40 + 15/40 = 31/40
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round 0.956 to one decimal place
Answer: 0.96
Step-by-step explanation:
To round 0.956 to one decimal place, we need to look at the second decimal place (the hundredths place), which is 5. Since 5 is greater than or equal to 5, we need to round up the first decimal place (the tenths place), which is 9. Therefore, the rounded number to one decimal place is:
0.956 rounded to one decimal place = 0.96
A surfboard is in the shape of a rectangle and semicircle. The perimeter is to be 4m. Find the maximum area of the surfboard correct to 2 places.
The maximum area of the surfboard correct to 2 places is 0.67 m².
Given that a surfboard is in the shape of a rectangle and a semicircle, and its perimeter is to be 4m. We need to find the maximum area of the surfboard, correct to 2 decimal places.
Let the radius of the semicircle be 'r' and the length and breadth of the rectangle be 'l' and 'b' respectively. Perimeter of the surfboard = [tex]4m => l + 2r + b + 2r = 4 => l + b = 4 - 4r[/tex] -----(1)
Area of surfboard = Area of rectangle + Area of semicircle Area of rectangle = l × b Area of semicircle = πr²/2 + 2r²/2 = (π + 2)r²/2Area of surfboard = l × b + (π + 2)r²/2 -----(2)
We have to maximize the area of the surfboard. So, we have to find the value of 'l', 'b', and 'r' such that the area of the surfboard is maximum .From equation (1), we have l + b = 4 - 4r => l = 4 - 4r - bWe will substitute this value of 'l' in equation (2)
Area of surfboard = l × b + (π + 2)r²/2 = (4 - 4r - b) × b + (π + 2)r²/2 = -2b² + (4 - 4r) b + (π + 2)r²/2Now, we have to maximize the area of the surfboard, that is, we need to find the maximum value of the above equation.
To find the maximum value of the equation, we can differentiate the above equation with respect to 'b' and equate it to zero. d(Area of surfboard)/db = -4b + 4 - 4r = 0 => b = 1 - r Substitute the value of 'b' in equation (1),
we get l = 3r - 3Now, we can substitute the values of 'l' and 'b' in the equation for the area of the surfboard.
Area of surfboard =
[tex]l × b + (π + 2)r²/2 = (3r - 3)(1 - r) + (π + 2)r²/2 = -r³ + (π/2 - 1)r² + 3r - 3[/tex]
[tex]-r³ + (π/2 - 1)r² + 3r - 3 = -0.6685 m² \\[/tex]
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Does someone mind helping me with this problem? Thank you!
the answer to the problem that you need to is 1024
Given the following key, what polynomial is modeled by the diagram below?
The polynomial function modeled by the given diagram is given as follows:
p(x) = 3x² - 7x - 6.
How to obtain the polynomial function?The polynomial function modeled by the given diagram is obtained considering the keys of the problem, which are the terms represented by each figure.
The polynomial is constructed as follows:
3 large non-shaded squares: 3x².Two non-shaded rectangles: 2x.Nine shaded rectangles: -9x.Six shaded small squares: -6.Then the expression used to construct the polynomial is given as follows:
p(x) = 3x² + 2x - 9x - 6.
Combining the like terms, the polynomial function is defined as follows:
p(x) = 3x² - 7x - 6.
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Find the value of x.
Answer:
x=1.9
Step-by-step explanation:
[tex]\frac{x}{4.6} =\frac{4.6}{11}[/tex]
[tex]11x=21.16[/tex]
[tex]X=1.9[/tex]
Write the equation of a line that is perpendicular to y=½x - 9 and passes through the point (3, -2).
Answer:
y = - 2x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{2}[/tex] x - 9 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (3, - 2 ) into the partial equation
- 2 = - 2(3) + c = - 6 + c ( add 6 to both sides )
4 = c
y = - 2x + 4 ← equation of perpendicular line
how does the graph of the function g(x) = 2x – 3 differ from the graph of f(x) = 2x?
Answer: The graph of function g(x) is shifting down by 3 (vertical shift) because the -3 is not part of x but y (the whole graph). Originally there is no y-intercept and the f(x) function crosses the origin, but now there is a y-intercept at (0, -3)
Which exspression is equivalent to 9(4/3m-5-2/3m+2)
By answering the presented question, we may conclude that Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
To simplify the expression,
[tex]a(b+c) = ab + ac\\9(4/3m-5-2/3m+2) = 9(4/3m - 2/3m - 5 + 2)\\= 9(2/3m - 3)\\= 6m - 27[/tex]
Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.
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the radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.6 in/s. at what rate is the volume of the cone changing when the radius is 144 in. and the height is 138 in.?
Answer:
Let's use the formula for the volume of a right circular cone to solve this problem:
V = (1/3)πr^2h
We are given that the radius is increasing at a rate of 1.4 in/s and the height is decreasing at a rate of 2.6 in/s. We want to find the rate at which the volume is changing when the radius is 144 in. and the height is 138 in. In other words, we want to find dV/dt when r = 144 and h = 138.
Using the chain rule of differentiation, we can express the rate of change of the volume as follows:
dV/dt = (dV/dr) (dr/dt) + (dV/dh) (dh/dt)
To find dV/dr and dV/dh, we differentiate the formula for the volume with respect to r and h, respectively:
dV/dr = (2/3)πrh
dV/dh = (1/3)πr^2
Substituting the given values and their rates of change, we have:
dV/dt = (2/3)π(144)(138)(1.4) + (1/3)π(144)^2(-2.6)
dV/dt = 55,742.4 - 1,994,598.4
dV/dt = -1,938,856 in^3/s
Therefore, when the radius is 144 in. and the height is 138 in., the volume of the cone is decreasing at a rate of approximately 1,938,856 cubic inches per second.
Step-by-step explanation:
Joan has a credit limit of $900. Her new balance is $450. What is Joan's available credit?
Hi!
Let's write this out.
Her limit is $900, and she's used $450. So, we subtract 450 from 900.
900-450 = 450.
So, she has $450 available credit left.
Hope this helps!
~~~PicklePoppers~~~
Answer: your credit utilization ratio on that card would be 50% but the answer is 450
Step-by-step explanation:
900-450 = 450
I need helppp, I’ll give brainliest
The set of all possible y-values for the function h constitutes its range. The range is therefore [-3, 0].
what is range ?The collection of all feasible output values (dependent variable) of a function is known as the range in mathematics. It is the totality of all possible numbers that the function can accept as input (an independent variable) and output. On the number line, the range is frequently represented by an interval or group of intervals. For instance, the range can be written as [-3, 3] if the domain of a function f(x) is [-2, 2] and its output numbers fall within [-3, 3].
given
The collection of all x-values for which h(x) is specified is the domain of the function h.
The graph's [-2, 4] domain can be determined by looking at the graph, which shows that it begins at x=-2 and concludes at x=4.
The set of all possible y-values for the function h constitutes its range. Looking at the graph, we can see that it takes all values between y=-3 and y=0, and that it begins at y=-3.
The range is therefore [-3, 0].
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The complete question is :- The entire graph of the function h is shown in the figure below. Write the domain and range of h as intervals or unions of intervals.
-2
-3-
4-
domain =
range =
If 140 men working 10 hours a day can build a house in 16 days, find out how many men will build same kind of house in 12 days by working 13 hours a day?
We need 144 men to build the house in 12 days working 13 hours a day.
Let M be the number of men needed to build the house in 12 days working 13 hours a day.
140 x 10 x 16 = M x 13 x 12
Simplifying the equation, we get:
22400 = 156M
Dividing both sides by 156, we get:
M = 144.1
An equation in mathematics is a statement that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The expressions on either side can be numbers, variables, or combinations of both. The equation expresses that the values of the expressions on both sides are equivalent.
Equations play a fundamental role in many areas of mathematics and are used to model various real-world situations, such as physics, engineering, and finance. They can be solved using various techniques, such as substitution, elimination, or graphing, to find the values of the variables that satisfy the equation.
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Shade in the regions represented by the inequalities
Answer:
Step-by-step explanation:
see diagram
Determine wheter the given vale of the varible is a soultion of the equatiom1/3 h=6 h=2
No, the given value of h=2 is not a solution of the equation 1/3h=6.
All the students in the sixth grade either purchased their lunch or brought their lunch from home on Monday.
• 24% of the students purchased their lunch.
• 190 students brought their lunch from home.
How many students are in the sixth grade?
The number of students that are in the sixth grade is given as follows:
250 students.
How to obtain the number of students?The number of students is obtained applying the proportions in the context of the problem.
We know that all students in the sixth grade either purchased their lunch or brought their lunch from home on Monday, and 24% of the students purchased their lunch, hence 76% of the students brought their lunch from home.
190 students brought their lunch from home, which is equivalent to 76% of the number of students, hence the number of students is given as follows:
0.76n = 190
n = 190/0.76
n = 250 students.
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some rate functions require algebraic manipulation or simplification to set the stage for undoing the chain rule or other antiderivative techniques. find an equivalent closed form for each function.a. S π / π /4 5t+4 / t² + 1 dtHint : begin by writing as a sum of two functions ____ previewb. S π/t 4tan (t) dt Hint : begin by using a trig identity to change the form of the rate function___ preview
the given form of the rate function:[tex]tan² (t) + 1 = sec²[/tex](t)
Therefore, we can write the given function as:c (t) dtUsing integration by substitution, we haveu = tan (t) ⇒ du = sec² (t) dt
Therefore,S [tex]π/t tan (t) sec² (t) dt= S u du= ln |tan (t)| + C[/tex]Thus, the equivalent closed form of the given function is:S π/t 4tan (t) dt= 4 ln |tan (t)| + C
a. S π/π/4 5t+4/t² + 1 dt equivalent closed formThe question demands to find an equivalent closed form for each function. So let's find the equivalent closed form for the given functions:a. S π/π/4 5t+4/t² + 1 dt
Hint: begin by writing as a sum of two functionsNow, we need to write the given function as a sum of two functions. Let's first write the numerator of the function as a sum of two functions.
Using the formula, a²-b² = (a+b)(a-b), we have5t + 4 = (2 + √21)(√21 - 2)Therefore, we can write the numerator of the function as follows:5t + 4 = (√21 - 2)² - 17Using this in the given function,
we haveπ/π/4 [(√21 - 2)² - 17]/t² + 1 dtLet's further simplify the numeratorπ/π/4 [21 + 4 - 4√21 - 17t² + 34t - 17] / (t² + 1) dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dtLet's now find the closed form of this function using the integration formulaS f(x) dx = ln |f(x)| + C Therefore, the equivalent closed form of the function is:
S π/π/4 5t+4/t² + 1 dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dt= - π/2 ln |t² + 1| + 34 π/2 arctan (t) - 17 π/2 t + 2 π/√21 arctan [(2t-√21)/ √21] + Cb. S π/t 4tan (t) dt equivalent closed formNow, let's find the equivalent closed form of the second given function.b. S π/t 4tan (t)
dtHint: begin by using a trig identity to change the form of the rate function Let's now use the following trig identity to change
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