The value of [tex]\( y \)[/tex] when x = 6 is 16.
Given that [tex]\( y \)[/tex] is inversely proportional to [tex]\( x \)[/tex], we can write the relationship as:
[tex]\[ y = \frac{k}{x} \][/tex]
where [tex]\( k \)[/tex] is the constant of proportionality.
First, we need to determine the value of [tex]\( k \)[/tex]. We are given that [tex]\( y = 24 \)[/tex] when [tex]\( x = 4 \)[/tex].
[tex]\[ 24 = \frac{k}{4} \][/tex]
Solving for k:
[tex]\[ k = 24 \times 4 = 96 \][/tex]
Now that we have the value of [tex]\( k \)[/tex], we can find the value of [tex]\( y \)[/tex] when [tex]\( x = 6 \)[/tex]:
[tex]\[ y = \frac{96}{6} \][/tex]
[tex]\[ y = 16 \][/tex]
What is the integral of 1/x?
Final answer:
The integral of 1/x is the natural logarithm of the absolute value of x, plus an integration constant C. This expression is central to calculations in many areas of science and mathematics.
Explanation:
The integral of 1/x is known as the natural logarithm of the absolute value of x, plus a constant of integration, commonly referred to as C. In mathematical terms, this is expressed as:
[tex]\( \int \frac{1}{x} dx = \ln(|x|) + C \)[/tex]
The natural logarithm arises due to the fundamental properties of the integral, and it's significant as it appears frequently across various fields of science and mathematics. While the basic form of integration of 1/x involves the natural logarithm, in applied examples like the cases mentioned above, where one works with additional functions or domain restrictions, the integral may lead to more complex expressions or even vanish under certain symmetry conditions.
Tank 1 initially contains 50 gals of water with 10 oz of salt in it, while tank 2 initially contains 20 gals of water with 15 oz of salt in it. water containing 2 oz/gal of salt flows into tank 1 at a rate of 5 gal/min and the well-stirred mixture flows from tank 1 into tank 2 at the same rate of 5 gal/min. the solution in tank 2 flows out to the ground at a rate of 5 gal/min. if x1(t) and x2(t) represent the number of ounces of salt in tank 1 and tank 2, respectively, set up but do not solve an initial value problem describing this system.
Compare the value of the
4 in 40 and 400
Consider a line l with positive x- and y- intercepts. Suppose l makes an angle of with the positive x- axis. What is the slope of l in terms of theta?
A motorboat takes 3 hours to travel 108 km going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Curt is installing a picket fence around his garden which is 45.45 ft by 14.63 ft. When he gets to the hardware store he finds that each picket fence slat is two feet wide. If Curt does not want any spaces between each slat, use estimation to determine how many slats of fencing he should buy.
for f(x) = x^3-7X^2+8x+16 find f(10) using synthetic division
Angle BCA is congruent to angle DAC, and angle BAC is congruent to angle DCA by:
the vertical angle theorem.
the alternate interior angles theorem.
the reflexive property.
None of the choices are correct.
Angle BAC is congruent to angle DCA by the alternate interior angles theorem. Option B is correct.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
here,
The pro[perty of parallel lines states that when two parallel lines intersect by the same transversal line the alternate interior angle will be equal as also the alternate exterior angles.
So,
Line BC and AB are parallel lines and AC is a transversal line,
So,
Angle BAC = angle DCA
Thus, angle BAC is congruent to angle DCA by the alternate interior angles theorem. Option B is correct.
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If f(x)=2x^2sqrt(x-2), complete the following statement f(6)
The value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex] is 82
How to determine the function value?The function is given as:
[tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex]
Substitute 6 for x
[tex]f(6)=2 * 6^2 + 5\sqrt{6-2}[/tex]
Evaluate the difference
[tex]f(6)=2 * 6^2 + 5\sqrt{4}[/tex]
Evaluate the exponents
f(6)=2 * 36 + 5 * 2
Evaluate the sum of products
f(6) = 82
Hence, the value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex] is 82
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What is 4.76 hours converted to min and sec
If m and n are positive integers such that the greatest common factor of [tex] m^{2} n^{2}[/tex] and [tex] m n^{3}[/tex] is 45, then which of the following could n equal?
(A) 3
(B) 5
(C) 9
(D) 15
(E) 45
Lena bought 10 pounds of potatoes for $5.50 write the cost as cents per pound
A flagpole cast a shadow 16 feet long at the same time a pole 9 feet high casts a shadow 6feet long what is the height in feet of the flagpole
Write an equation of a line that is perpendicular to the given line and that passes through the given point.
-x + 5y= 14; (-5, -2)
A. Y=-5x-27
B.y=-1/5x-27
C. Y=-1/5x-15
D. Y=5x-27
Susan invests
2
times as much money at
8%
as she does at
4%
. If her total interest after
1
year is
$800
, how much does she have invested at each rate?
Final answer:
To find how much Susan has invested at each rate when she invests 2 times as much money at 8% as she does at 4%, create and solve an equation based on the total interest earned.
Explanation:
Susan has invested $x at 4% interest rate and $2x at 8% interest rate.
Given that the total interest after 1 year is $800, we can create the equation: $x(0.04) + $2x(0.08) = $800.
Solving the equation, we find that Susan has $3,000 invested at 4% and $6,000 invested at 8%.
A jacket is on sale for $15 off. As part of a one-day sale, a 20% discount is applied to all purchases. If x represents the original price of the jacket, which expression represents the final price of the jacket during this sale? 0.2x – 3 0.8x – 12 0.8x – 15 0.2x – 15
0.8x – 12
Explanation:The sale price is (x-15). After the 20% discount, the final price is 0.80 times the sale price, so is ...
... final price = 0.80×(x -15) = 0.80x -12
Answer:
The correct option is B.
Step-by-step explanation:
Let the original price of the jacket be x.
A jacket is on sale for $15 off. As part of a one-day sale, a 20% discount is applied to all purchases.
The price of jacket after $15 off is [tex]x-15[/tex].
Then 20% discount is applied, so the final price of the jacket is
[tex]P=(x-15)(1-\frac{20}{100})[/tex]
[tex]P=(x-15)(1-0.2)[/tex]
[tex]P=(x-15)(0.8)[/tex]
[tex]P=0.8x-12[/tex]
The final price of the jacket during this sale is 0.8x-12. Therefore the correct option is B.
53 ℃ below zero degrees
What is after 100,99,07,94,90
Each canvas bag will hold exactly 5 pounds of kings tomatoes. How many bags will be necessary to hold 5 kg worth of these same tomatoes? (1 kg = 2.25 pounds)
1 kg = 2.25 pounds
5*2.25 = 11.25 pounds
11.25/5 = 2.25 bags
so you would need 3 bags
the formula I=square root w/r gives the electric current I amperes that flows through an appliance, where W is the power in watts and R is the resistance in ohms. which set of numbers best describes the value of I for the given values of W and R? ( 42.) W=100,R=25 ( 43.)W=100,R=50
Final answer:
The value of I for the given values of W and R can be calculated using the formula I = [tex]\sqrt{(W/R)[/tex]. For W = 100 and R = 25, the value of I is 2 amperes. For W = 100 and R = 50, the value of I is approximately 1.41 amperes.
Explanation:
The formula I = [tex]\sqrt{(W/R)[/tex] gives the electric current in amperes that flows through an appliance, where W is the power in watts and R is the resistance in ohms.
To determine the value of I for the given values of W and R, we can simply substitute the values into the formula. For the first set of numbers, W = 100 and R = 25:
[tex]I = \sqrt{(100/25)} = \sqrt{(4)} = 2[/tex] amperes.
For the second set of numbers, W = 100 and R = 50:
[tex]I = \sqrt{(100/50)} = \sqrt{(2) }[/tex]≈ 1.41 amperes.
Therefore, the value of I for the first set of numbers (W = 100, R = 25) is 2 amperes, and the value of I for the second set of numbers (W = 100, R = 50) is approximately 1.41 amperes.
In a certain grocery store, strawberries cost $5.92 per pound ( 5.92 dollars/lb ). what is the cost per ounce?
Answer:
$,37 dollars per ounce of strawberries
Step-by-step explanation:
We have to remember that there are 16 ounces in one pound so in order to calculate the cost per ounce, we just divide the cost per pound by 16:
5,92/16= ,37
SO the cost per ounce of strawberries when the price per pound is 5,92 dollars will be 0,37 dollars.
Hello, I'm working on a project and I've been stumped.
How would I find the central ark of a ferris wheel? I'm using the London Eye ferris wheel for my project, and so far I know it has a diameter of 120 meters and 32 cars. It has a circumference of 377m and an area of 11,310m.
How can that information help me? Please include all steps and a clear explanation, and give the answer in degrees. Thank you.
a circle has 360 degrees
the ferris wheel has 32 cars so the circle is broken up into 32 sections
the central angle would be the angle between 2 of the cars
so divide 360 by 32
360/32 = 11.25 degrees
The Greasy Grab Bag claims that customers can make 20 different meal combinations from the menu items. If the Greasy Grab Bag has 4 sandwiches, 3 sides, and 2 drinks, which of the following is correct?
The correct number of different meal combinations that customers can make from the menu items at the Greasy Grab Bag is 24.
To determine the number of different meal combinations, we need to consider that each meal consists of one sandwich, one side, and one drink. Given that there are 4 sandwiches, 3 sides, and 2 drinks to choose from, we can calculate the total number of combinations by multiplying the number of choices for each category together.
The number of sandwich choices is 4, the number of side choices is 3, and the number of drink choices is 2. Therefore, the total number of meal combinations is calculated as follows:
Total combinations = Number of sandwich choices — Number of side choices — Number of drink choices
Total combinations = [tex]$4 \times 3 \times 2$[/tex]
Now, let's calculate the total number of combinations:
Total combinations =[tex]$4 \times 3 \times 2 = 12 \times 2 = 24$[/tex]
Thus, there are 24 different meal combinations that customers can make, which means the Greasy Grab Bag's claim of 20 different meal combinations is incorrect. The correct number is 24.
If 12 bumper stickers cost $8.64, then how much do 18 cost
The proportion is solved and the cost of 18 bumper stickers is $ 12.96.
Given data:
To find out how much 18 bumper stickers cost, use a proportion since the cost of bumper stickers is directly proportional to the number of stickers.
Cost of 12 bumper stickers / Number of 12 bumper stickers = Cost of 18 bumper stickers / Number of 18 bumper stickers
On simplifying the proportion:
$8.64 / 12 = x / 18
Now, solve for x (the cost of 18 bumper stickers):
x = ($8.64 / 12) * 18
x = $12.96
Hence, 18 bumper stickers cost $12.96.
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what is the value of x in the equation 5(4x-10)+10x=4(2x-3)+2(x-4) ?
-7/4
-1/4
3/20
3/2
Answer:
[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Here, the given expression is,
[tex]5(4x-10)+10x=4(2x-3)+2(x-4)[/tex]
By distributive property,
[tex]20x - 50 + 10x = 8x - 12 + 2x - 8[/tex]
By combining like terms,
[tex]30x -50=10x-20[/tex]
Adding 50 on both sides,
[tex]30x=10x-20+50[/tex]
[tex]30x = 10x + 30[/tex]
Subtracting 10x on both sides,
[tex]20x = 30[/tex]
Divide both sides by 20,.
[tex]x=\frac{3}{2}[/tex]
Hence, LAST option is correct.
let A and B be nxn matrices such that AB is singular prove that either A or Bis singular
Explain why we need more than one digit to express certain quantities
What if the atom has no charge
The equation of the line of best fit of a scatter plot is y = −4x − 6. What is the slope of the equation?
−6
−4
4
6
Convert the measurement as indicated.
26ft= _ yd _ ft