The value of d when F = 0.7 Newton's by solving with inverse variation is 0.61 meters to 2 D.P
How to find inverse variation?Let
F = force in Newton'sd = distance in metersF = k/ d²
Where k = constant of proportionality
If F = 0.045 Newtons and d = 2.4 metres
F = k/ d²
0.045 = k / 2.4²
cross product
k = 0.045 × 2.4²
k = 0.2592
Find d when F = 0.7 Newton's
F = k/ d²
0.7 = 0.2592 / d²
cross product
0.7 × d² = 0.2592
0.7d² = 0.2592
divide both sides by 0.7
d² = 0.2592 / 0.7
d² = 0.370285714285714
find the square root of both sides
d = √0.370285714285714
d = 0.6085110634045
d = 0.61 to 2 decimal place.
Therefore, d is equal to 0.61 meters to 2 decimal place if F is 0.7 Newton's.
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Similar Figures / Proportion (Level 1)
Triangle OPQ is similar to triangle RST. Find the measure of side ST. Round your
answer to the nearest tenth.
Rounded to the nearest tenth, the measure of side ST is 8.0.
How to find measure of sides?In order to find the measure of side ST, you will need to use the concept of similarity. If two triangles are similar, then their corresponding sides are in proportion. If we let x be the measure of side ST, then we can set up a proportion using the given information:
[tex]OP/PQ = ST/RQ[/tex]
We also know that
[tex]OP/PQ = 2/3[/tex]
and
[tex]RQ = 12[/tex]
So we can substitute these values into the proportion and solve for x:
[tex](2/3) = ST/12[/tex]
[tex]ST = (2/3) * 12[/tex]
[tex]ST = 8[/tex]
Rounded to the nearest tenth, the measure of side ST is 8.0.
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Animal House Rescue is holding a fundraiser raffle. They sell 2,980 tickets for $1 each for a prize telescope valued at $425. What is the expected gain or loss to a participant purchasing ten tickets?
Answer:
Gain: $415
Loss: $10
Step-by-step explanation:
money earned - money spent = gain/loss
The gain is when the participant wins the telescope:
telescope = $425 ==> money earned
10 tickets * $1 = $10 for tickets ==> money spent
$425 - $10 = $415
Loss is when the participant doesn't get the telescope:
$0 ==> money earned (No money earned)
10 tickets * $1 = $10 for tickets ==> money spent
$0 - $10 = -$10 gained
-$10 gained ==> $10 lost
Show that the vector field defined by the vector function v=xyz(yzi^xzj^xyk^) i conervative
The process to show the vector field V(x,y,z) as conservative is show below and the scalar potential f is [tex]f(x,y,z) =xyz^{2} + e^{\pi }[/tex] .
A Vector field can be called as conservative if we are able to find the potential function "f" , whose gradient is field .
The Gradient is vector that is made from partial derivatives of potential function .
The Vector function is given as , V(x,y,z) = [tex](yz^{2} )i + (xz^{2} )j + (2xyz)k[/tex] ,
So , we can write the partial derivatives function of potential function as :
[tex]\frac{\partial f}{\partial x} = yz^{2}[/tex] ; [tex]\frac{\partial f}{\partial y} = xz^{2}[/tex] ; [tex]\frac{\partial f}{\partial z} = 2xyz[/tex],
On Antidifferentiating any of the above three partial derivatives ,
we get ; [tex]f=xyz^{2} + C[/tex] , here the constant C can take any value ,
so , we take C as [tex]e^{\pi }[/tex] .
Therefore , the potential Function is [tex]f(x,y,z) =xyz^{2} + e^{\pi }[/tex] .
The given question is incomplete , the complete question is
Show that the vector field defined by the vector function V(x,y,z) = (yz²)i + (xz²)j + (2xyz)k is conservative by finding a scalar potential f .
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What is a 3 variable equation called?
Equations with three variables that are linear. Ax + by + cz = r is referred to as a linear equation in three variables.
what is linear equation ?A linear equation is one that has the form y=mx+b in algebra. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
equations with three variables that are linear. Ax + by + cz = r is referred to as a linear equation in three variables if all four variables—a, b, c, and r—are real values and not equal to 0.
(The x, y, and z are the "three variables"). The coefficients of the equation are designated by the numerals a, b, and c.
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Find the value of x then classify the triangle.
Answer:
x= 35⁰ - obtuse triangle
Step-by-step explanation:
since the sum of angles of the triangle = 180⁰
(3x-5) + (x+10) + (x) =180⁰
5x+5= 180
(subtracting 5 from both sides)
5x=180-5
5x= 175
(dividing by 5)
x= 35⁰
so the angles of the triangle are
(3x-5) = 105-5= 100⁰
(x+10) = 45⁰
(x) = 35⁰
then this triangle is an obtuse triangle
A club plans to sell tote bags. The club members estimate they will sell 100 tote bags when the bags are priced at $11 each. For every price increase of $1, they estimate they will sell 10 fewer bags.
What is the estimated revenue, in dollars, when the bags are priced at $13 each?
(revenue = price × number sold)
1) 1,300
2) 1,100
3) 1,040
4) 880
The estimated revenue, in dollars, that the club will generate when the bags are priced at $13 each is 3) 1,040.
What is the revenue formula?The revenue formula is the multiplication of the number of units sold and the price per unit.
To determine the total revenue, we must first ascertain the unit price and the quantity sold.
We know that market forces and the competitive environment determine the quantity sold or supplied.
The demand for tote bags at $11 = 100 units
Decrease in demand for every $1 price increase = 10 units
When the price is $13 each, the units to be sold = 80 (100 -10 x 2)
The total revenue at $13 each = $1,040 (80 x $13)
Total revenue at $12 each = $1,080 (90 x $12)
Total revenue at $11 each = $1,100 (100 x $11)
Thus, we can conclude that the club generates less revenue when it increases its price per tote bag from $11 to $13, justifying the interactions between supply, demand, and cost.
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please i need help! anything will help
Answer:
a = 3 or -3
Step-by-step explanation:
a^2 -8 = 1
a^2 = 1 + 8
a^2 = 9
a = - [tex]\sqrt{9}[/tex] or [tex]\sqrt{9}[/tex]
a = 3 or -3
Answer: a = 3, -3
Step-by-step explanation:
Since we want to find what values of a, or x when substituted into the function, equal 1, we will set the function equal to 1 and solve for x.
Given:
f(x) = x² - 8
Set equal to 1:
1 = x² - 8
Subtract 1 from both sides of the equation:
x² - 9 = 0
Difference of squares factoring:
(x - 3)(x + 3) = 0
Answers:
x = 3, -3
So,
a = 3, -3
hi can someone pls help me
:)
Which mixed number is equal to 35
Answer:
35 [tex]\frac{0}{1}[/tex]
Step-by-step explanation:
Is infinity times 0 still 0?
Yes, infinity times 0 is still 0 because if we multiply 0 to any number is 0.
Yes, infinity times 0 is still 0 because if we multiply 0 to any number is 0.
0 * 0 * 0 * 0= 0
Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present. It is the only integer (and, in fact, the only real number) that is neither negative nor positive. A number which is not zero is said to be nonzero. A root of a function f is also sometimes known as "a zero of f."
The Schoolhouse Rock segment "My Hero, Zero" (Multiplication Rock, Season 1, Episode 2, 1973) extols the virtues of zero with such praises as, "My hero, zero Such a funny little hero But till you came along We counted on our fingers and toes Now you're here to stay And nobody really knows How wonderful you are Why we could never reach a star Without you, zero, my hero How wonderful you are."
Zero is commonly taken to have the factorization 0=0·1 (e.g., in the Wolfram Language's FactorInteger[n] command). On the other hand, the divisors and divisor function sigma_k(0) are generally taken to be undefined, since by convention, n|0 (i.e., n divides 0) for every n except zero.
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SOMEONE HELP ME PLSSSS
simplify (pic below)
Answer:
10^11
Step-by-step explanation:
This question helps you practice some exponent rules. To "fix" a negative exponent you push it across the fraction bar. The 10^-3 on the bottom becomes a 10^3 on the top. See image.
Then, when you have 10^8 • 10^3, that is when you are multiplying, you add the exponents.
10 ^ (8+3)
= 10^11
see image
sutton is listing the prime factorazation for 220 what is the last factor she needs 2 square root of 5
Answer:
4.472135955
Step-by-step explanation:
What is the midpoint of 1 and 2 and 3 and 4?
The midpoint of 1 and 2 and 3 and 4 is (2,3).
The formula for midpoint = (x1 + x2)/2, (y1 + y2)/2.
The end of a line at a point that is equally distant from both ends, a time interval between an event's beginning and end.
The point on a graph or figure where the figure stops might be referred to as the endpoint. It can be the point joining the sides of a polygon (the vertex), the common endpoint of two rays making an angle, the two extreme points of a line segment, the one end of a ray.
Use numbers, fractions, mixed numbers, or decimals to enter two points. The midpoint calculator displays the required research:
Halfway between the two specified pointsOne endpoint and a midpoint are provided.The separation of two endpoints.Additionally, the calculator offers a link to the Slope Calculator, which will solve and display the work necessary to identify the slope, line equations, and x and y intercepts for any given pair of points.To learn more about midpoint:
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A certain map shows two roads. Road A is 1 1/5 miles long but is 1 4/5 inches on the map. What is the unit rate for inches per mile on the map. If road B is 2 miles long, how long is road B on the map ?
The length of the map would be 3 inches.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: length of the road as 6/5 miles and on the map 9/5 inches and thus 1 mile = 1.5 inches and therefore the length of the 2 mile road on the map is 2×1.5=3 inches
Hence, The length of the map would be 3 inches.
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Let C be between D and E. Use the Segment Addition Postulate to solve for n.
DC = 5n – 30
CE = 6n – 25
DE = 44
A. N = 13
B. N = 4
C. N = –5
D. N = 9
Segment Addition Postulate states that n has a value of 9 when DC = 5n - 30 and CE = 6n - 25 and DE = 44.
what is equation ?A mathematical equation is a formula that connects two statements using the equal sign (=) to denote equivalence. An algebraic equation is a mathematical statement that establishes the equality of two mathematical expressions. For example, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematical equations are used to express the connection between two phrases on either side of a letter. There is frequently just one variable, which is also the symbol. example: 2x - 4 = 2.
given
DE = DC + CE
44 = 5n – 30 + 6n – 25
44 = 11n - 55
44 + 55 = 11n
n = 9
Segment Addition Postulate states that n has a value of 9 when DC = 5n - 30 and CE = 6n - 25 and DE = 44.
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The height of an equilateral triangular based prism is 30 cm. If the area of one base of the prism is 16√3 cm², find the area of the rectangular surfaces of the prism.
The area of one base of the triangular prism is given as 16√3 square cm, and since the base is equilateral, the sides of the triangle are of equal length.
The formula to calculate the area of an equilateral triangle is (sqrt(3)/4) * s^2 where s is the length of a side of the triangle.
So, plugging in the given area of base, 16√3, we can find the length of a side of the equilateral triangle, s.
16√3 = (sqrt(3)/4) * s^2
s = (4*16√3)/sqrt(3) = 16√3 cm
Now we can use the height of the prism, which is given as 30 cm, to find the area of the rectangular surface.
Area of the rectangular surface = 2 * base area * height = 2 * 16√3 * 30 cm²
This simplifies to:
960√3 cm²
So the total area of the rectangular surface of the prism is 960√3 square cm.
A distribution of exam scores has mean 60 and standard deviation 18. If each score is doubled, and then 5 is subtracted from that result, what will be the mean and standard deviation, respectively, of the new scores
If each score is doubled, and then 5 is subtracted from that result, then the mean and standard deviation will be 115 and 36 respectively.
What will be the mean and standard deviation?A huge group of test results has a mean of 60 and a standard deviation of 18. If each score is doubled and then 5 is deducted from the result, the mean and standard deviation are “ mean = 115; standard deviation = 36”. Mean = 2 x 60 -5 = 120 -5 = 115
2 x 18 = 36 standard deviation
The mean is the average and is calculated as the sum of all the results from the example divided by the total number of events.
The standard deviation (SD) is a statistic used to assess the degree of variation or dispersion in a set of data values.
A low standard deviation indicates that the information points slant toward being near the mean of the set, whereas an exclusive expectation deviation or a high standard deviation indicates that the information points tilt toward being near the mean of the set.
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d minus 2 = 4.6 please help meeee im not good at mathhh
[tex]d-2=4.6[/tex]
Add 2 to both sides:
[tex]d-2+2=4.6+2[/tex]
[tex]\fbox{d = 6.6}[/tex]
How do you solve 5t 35?
The answer to this question will t = 8. The first step to solving this equation is to combine the like terms by adding the two numbers together.
In this case, 5t + 35 = 40t. The next step is to divide both sides of the equation by the coefficient of the variable, which in this case is 5. When you do this, you get 40t/5 = t. Therefore, the answer to 5t + 35 is t = 8.
A coefficient is an integer that is either multiplied by the variable it is associated with or written alongside the variable. A coefficient is, in other words, the numerical factor of a term that contains both constants and variables. For instance, the coefficient in the expression 2x is 2.
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How do you reflect over Y =- 4?
What is the meaning of △?
Meaning of the △ is: the given symbol is the representation of the geometrical figure triangle.
Different symbols used to represent the different geometrical figures.The given symbol has three sides.Symbol also represents three interior angles.When three sides intersect with each other it represents the vertices.The triangle represents the 2 dimensional shape.Sum of all the measure of the three interior angles is equal to 180 degree.Symbol of triangle in the geometrical shape is given by △.There are different shape such as square, rectangle, circle and many more.Therefore, the meaning of the given symbol △ is the representation of the triangle.
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Santos walks 222 kilometers south and then a certain number of kilometers east. He ends 555 kilometers away from his starting position. How many kilometers east did Santos walk
Answer:
4.6 km
Step-by-step explanation:
You want to know how many kilometers east Santos walked to end up 5 km from his starting position after walking 2 km south.
DistanceThe distance Santos is from his starting position will be the hypotenuse of a right triangle with one leg 2 km. Using the Pythagorean theorem, we can find the length of the other leg.
c² = a² + b²
5² = 2² + b²
21 = b²
b = √21 ≈ 4.583
Santos walked about 4.6 km east.
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PLEASE HELP ASAP I WILL GIVE BRAINLIEST!!!
Answer:
try -5
Step-by-step explanation:
mainly because it says -3 plus 5 and there's only 4 and 5 so It can't really go further
Answer:try -5
Step-by-step explanation:
mainly because it says -3 plus 5 and there's only 4 and 5 so It can't really go further
1. You have cup of flour in a bin and
7
-
2
8
-
3
cup of flour in a bag. To determine
whether you have enough flour for a
3
recipe that needs 1 cups of flour,
4
should you use an estimate, or is an
exact answer required? Explain.
The exact value is required. In this case, they don't have enough for 1 3/4 cups of flour.
How to express the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.
From the information, the person had 2/3 cup of flour in a bin and 7/8 flour was still in the bag. In this case, it should be noted that they also wanted to know of they had enough for 1 3/4 cups of flour.
This will be calculated thus:
= 2/3 + 7 / 8
= 16/24 + 21/24
= 37 / 24.
= 1 13 / 24
This is not enough for 1 3/4 cups of flour.
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80 people were laying out on the beach. Clouds started forming, and it looked like it was going to rain. 42 people left. What is a reasonable estimate for the percentage of people that left the beach?
Select the best answer from the choices provided.
A. 10%
B. 25%
C. 50%
D. 75%
Answer:
C. 50%
Step-by-step explanation:
Since 40 is half of 80, and 50% means half, and 42 out of 80 is close to half, then 42 out of 80 is close to 50%.
Answer: C. 50%
Answer:
b25
Step-by-step explanation:
beacuse that is a rain and reasonable he percentage
The first term of a sequence is 13 The term -to-term rule is take away 5 work out the 4th term
Answer:
a₄ = - 2
Step-by-step explanation:
to calculate a term in the sequence subtract 5 from the previous term
give first term a₁ = 13 , then
a₂ = a₁ - 5 = 13 - 5 = 8
a₃ = a₂ - 5 = 8 - 5 = 3
a₄ = a₃ - 5 = 3 - 5 = - 2
Can someone help on this?
Answer:
x=0 and y=36
Step-by-step explanation:
30 + 6 equals 36 but it is negative so you would add 30 to negative thirty to get to zero and go into the positive numbers. So if you add 6 more you would have positive 6. so it it 36 y is 36
i need help asap please
Step-by-step explanation:
the range is (-32, 28)
note that when the bubble is not filled in it should be an open bracket
Estimate the difference by rounding each number to the nearest whole number and then subtracting.
10.04 − 6.3
Answer:
Estimate of difference is 4.
Step-by-step explanation:
10.04 = 10 to nearest whole number
6.3 = 6 to nearest whole number.
10 - 6 = 4.
SinA + cosA = √2, prove that tanA + cotA = 2
[tex]sin(A)+cos(A)=\sqrt{2}\hspace{10em}tan(A)+cot(A)=2 \\\\[-0.35em] ~\dotfill\\\\ tan(A)+cot(A)=2\implies \cfrac{sin(A)}{cos(A)}+\cfrac{cos(A)}{sin(A)}=2 \\\\\\ \cfrac{sin^2(A)+cos^2(A)}{cos(A)sin(A)}=2\implies \boxed{\cfrac{1}{cos(A)sin(A)}=2} \\\\[-0.35em] ~\dotfill[/tex]
[tex]sin(A)+cos(A)=\sqrt{2}\implies (~~sin(A)+cos(A)~~)^2=(\sqrt{2})^2 \\\\\\ sin^2(A)+2sin(A)cos(A)+cos^2(A)=2 \\\\\\ 2sin(A)cos(A)+sin^2(A)+cos^2(A)=2\implies 2sin(A)+1=2 \\\\\\ 2sin(A)cos(A)=1\implies \boxed{2=\cfrac{1}{cos(A)sin(A)}}[/tex]
now, another way to look at this identity will be as a unified system of equations
[tex]\begin{cases} (~~sin(A)+cos(A)~~)^2=2\\\\ ~~ ~tan(A)+cot(A)=2 \end{cases}\implies (~~sin(A)+cos(A)~~)^2=tan(A)+cot(A)[/tex]
and we'd end up with the same rigamarole.