Answer:
30 cm²
Step-by-step explanation:
Formula : [tex]Area = \frac{hb}{2}[/tex]
Devonte is studying for a history test he uses 1/8 of a side of one sheet of paper to write notes for each history event he fills 2 full sides of one sheet paper. which expression could be used to find how many events
The expression to find the number of events is: (1 event) / (1/8 side) = (n events) / (1/4 sides).
Devonte is studying for a history test and uses 1/8 of a side of one sheet of paper to write notes for each history event. He fills 2 full sides of one sheet of paper. To find out how many events he wrote notes for, you can set up an expression using the given information.
Since Devonte uses 1/8 of a side for each event, and he fills 2 sides, you can calculate the total amount of space he used by multiplying the fractions: (1/8) * 2. This simplifies to 2/8 or 1/4. Now, you can set up a proportion to find the number of events (n) that Devonte wrote notes for:
(1 event) / (1/8 side) = (n events) / (1/4 sides)
Cross-multiply to solve for n:
1 * (1/4) = n * (1/8)
1/4 = n/8
To find n, multiply both sides by 8:
(8) * (1/4) = n
2 = n
So, Devonte wrote notes for 2 history events using the 2 full sides of one sheet of paper. The expression to find the number of events is: (1 event) / (1/8 side) = (n events) / (1/4 sides).
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Complete Question:
Devonte is studying for a history test. He uses 1/8 of a side of one sheet of paper to write notes for each history event. He fills 2 full sides of one sheet of paper. Which expression could be used to find how many events Devonte makes notes for?
the perimeter of an isosceles triangle is 12x^2-5x +4 cm find the length of one of its equal sides
Answer:
4x² - x + 2--------------------------
Let the equal sides be both marked as ?
Use the perimeter formula to determine one of the equal sides.
P = 2(?) + x(4x - 3)Substitute the expression for the perimeter and find the value of ?
12x² - 5x + 4 = 2(?) + x(4x - 3)12x² - 5x + 4 = 2(?) + 4x² - 3x2(?) = 12x² - 5x + 4 - 4x² + 3x2(?) = 8x² - 2x + 4? = 4x² - x + 2Hence the length of each of equal sides is 4x² - x + 2.
A circle of radius 6 is centred at the origin, as shown.
The tangent to the circle at point P crosses the y-axis at (0, -14).
Work out the coordinates of point P.
Give any decimals in your answer to 1 d.p.
Answer:
P = (5.4, -2.6)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
As the given circle has a radius of 6 units and is centred at the origin, the equation of the circle is:
[tex]x^2+y^2=36[/tex]
The formula for the equation of the tangent line to a circle with the equation x² + y² = a² is:
[tex]\boxed{y = mx \pm a \sqrt{1+ m^2}}[/tex]
where:
m is the slope.a is the radius of the circle.To find the slope of the equation of the tangent line to the circle that passes through the point (0, -14), substitute a = 6, x = 0 and y = -14 into the formula and solve for m:
[tex]\implies -14 = m(0) \pm 6 \sqrt{1+ m^2}[/tex]
[tex]\implies -14 = \pm 6 \sqrt{1+ m^2}[/tex]
[tex]\implies \pm\dfrac{14}{6} =\sqrt{1+ m^2}[/tex]
[tex]\implies \left(\pm\dfrac{14}{6}\right)^2 =1+m^2[/tex]
[tex]\implies m^2= \left(\pm\dfrac{14}{6}\right)^2-1[/tex]
[tex]\implies m^2=\dfrac{40}{9}[/tex]
[tex]\implies \sqrt{m^2}= \sqrt{\dfrac{40}{9}}[/tex]
[tex]\implies m=\pm\sqrt{\dfrac{40}{9}}[/tex]
[tex]\implies m=\pm\dfrac{2\sqrt{10}}{3}[/tex]
The slope-intercept form of a straight line is y = mx + b, where m is the slope and b is the y-intercept.
As the slope of the given tangent line is positive, and the y-intercept is (0, -14), the equation of the tangent line is:
[tex]\boxed{y=\dfrac{2\sqrt{10}}{3}x-14}[/tex]
As point P is the point of intersection of the circle and the tangent line, substitute the tangent line into the equation of the circle and solve for x:
[tex]x^2+\left(\dfrac{2\sqrt{10}}{3}x-14\right)^2=36[/tex]
Expand the brackets:
[tex]x^2 +\dfrac{40}{9}x^2-\dfrac{56\sqrt{10}}{3}x+196=36[/tex]
Subtract 36 from both sides of the equation:
[tex]\dfrac{49}{9}x^2-\dfrac{56\sqrt{10}}{3}x+160=0[/tex]
Multiply both sides of the equation by 9:
[tex]49x^2-168\sqrt{10}x+1440=0[/tex]
Rewrite the equation in the form a² - 2ab + b²:
[tex](7x)^2-2 \cdot 7 \cdot 12\sqrt{10}x+(12\sqrt{10})^2=0[/tex]
Apply the Perfect Square formula: a² - 2ab + b² = (a - b)²
[tex](7x-12\sqrt{10})^2=0[/tex]
Solve for x:
[tex]7x-12\sqrt{10}=0[/tex]
[tex]7x=12\sqrt{10}[/tex]
[tex]x=\dfrac{12\sqrt{10}}{7}[/tex]
To find the y-coordinate of point P, substitute the found value of x into the equation of the tangent line:
[tex]y=\dfrac{2\sqrt{10}}{3}\left(\dfrac{12\sqrt{10}}{7}\right)-14[/tex]
[tex]y=\dfrac{2\sqrt{10}\cdot 12\sqrt{10}}{3\cdot 7}\right)-14[/tex]
[tex]y=\dfrac{240}{21}-14[/tex]
[tex]y=\dfrac{80}{7}-\dfrac{98}{7}[/tex]
[tex]y=-\dfrac{18}{7}[/tex]
Therefore, the exact coordinates of point P are:
[tex]\left(\dfrac{12\sqrt{10}}{7}, -\dfrac{18}{7}\right)[/tex]
The coordinates of point P to 1 decimal place are:
[tex](5.4, -2.6)[/tex]
1 ml =
a
litres
ii)
b
ml = 1 litre
iii) 1 cl =
c
litres
iv)
d
cl = 1 litre
v) 1 cl =
e
ml
vi)
f
cl = 1 ml
The corresponding measure of the parameters are;
i. 1ml = 0. 001 liter a.
ii. 1000ml = 1 liter b.
iii. 1 cl = 0. 01 liter c.
iv. 10dcl = 1 liter d.
v. 1cl = 100ml e.
v. 0. 01 cl = 1ml f.
How to determine the valuesTo convert the factors, we need to know the following conversion rates.
We have;
1 milliliter = 0. 001 liter
1 centiliter = 0. 01 liter
1 deciliter = 0. 1 liter
1 cubic centimeter = 1 millimeter
Hence, the sizes are determined by the corresponding factor.
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Complete question:
Convert the following to their equivalent measurement for each letter
i. 1 ml = a liters
ii) b ml = 1 liters
iii) 1 cl = c liters
iv)d cl = 1 liters
v) 1 cl = e ml
vi) f cl = 1 ml
what’s the coefficients of the polynomials?
The numbers preceding a variable
Step-by-step explanation:The coefficients are the number before the variable.
Finding Coefficients
All variables are multiplied by some coefficient. Sometimes those coefficients are one or another number. Take the variable 5x. The coefficient is 5. Since 5 is the number that comes before the variable, it is the coefficient. Additionally, the variable x has a coefficient of 1 because x is multiplied by 1.
Polynomial Example
Every variable within a polynomial can have a unique variable. For example, 3x⁶+5x³+2x². The first coefficient is 3, then 5, then 2. Coefficients are simply the constants that a variable is multiplied by. It does not matter what the variable is or the exponent.
i really need help with someone who really understands pythagorean therom please help i will give away brainliest and a lot of points just please help me and can someone please stop reporting this question
Answer:
Perry would need to place his ladder 6.63 ft away from the base of the basketball hoop in order to reach the hoop.
Hope this helps!
Step-by-step explanation:
The Pythagorean theorem is [tex]a^{2} +b^{2} =c^{2}[/tex].
It is given that c is 12 and b is 10, so that would be:
[tex]c^{2} -b^{2} =a^{2}[/tex]
[tex]12^{2} -10^{2} =a^{2}[/tex]
144 - 100 = [tex]a^{2}[/tex]
44 = [tex]a^{2}[/tex]
a = [tex]\sqrt{44}[/tex]
a = 6.6332...
( c is the length of the ladder, b is the height of the hoop, and a is the distance between the ladder and the basketball hoop )
The parabolas y=x^2 and y=-x^2-4x+6 are graphed below. What are they-values of the solutions to this system of equations
Answer:
y = 2.25
Step-by-step explanation:
The solutions are the points of intersection of the 2 graphs.
This magic grid contains number sequences that increase in steps. What is the missing number? A 16 B 8 C 4 D 12 E 20
Answer:
12
Step-by-step explanation:
The numbers increase by 4 on each row.
Jaime is cutting shapes out of cardboard to make a piñata. One of the shapes is shown in a
coordinate grid
c. (0,10)
d. (3,2)
e. (9,0)
f. (3,-2)
g (0,-10)
h. (3,-2)
a. (-9,0)
(it’s the shape of a star)
What is the length of side AB? Round your answer to the nearest tenth of a unit.
Show your work.
The length of side AB is 6.3 units.
How to find the length of side ABThe length of side AB is solved using the distance formula below
AB = √((x₂ - x₁)² + (y₂ - y₁)²
where
(x₁, y₁) = (-9, 0) and
(x₂, y₂) = (-3, 2).
AB = √((-3 - (-9))² + (2 - 0)²)
AB = √(6² + 2²)
AB = √(40)
AB = 2√(10)
AB = 6.3245
AB = 6.3 to the nearest tenth
Therefore, the length of side AB is 6.3 units.
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(a) Find an equation of the tangent plane to the surface at the given point. z = x2 - y2, (5, 4, 9) X-5 (b) Find a set of symmetric equations for the normal line to the surface at the given point. Х y z 10 -8 -1 y - 4 Z - 9 10 -8 -1 Ox - 5 = y - 4 = Z - 9 X + 5 y + 4 Z +9 10 -8 -1 Ox + 5 = y + 4 = 2 + 9 =
z - 9 = 10(x - 5) - 8(y - 4) this is the equation of the tangent plane at the point (5, 4, 9). (x - 5)/10 = (y - 4)/(-8) = (z - 9)/(-1). These are the symmetric equations for the normal line to the surface at the given point.
(a) To find the equation of the tangent plane to the surface z = x^2 - y^2 at the point (5, 4, 9), we first need to find the partial derivatives with respect to x and y:
∂z/∂x = 2x
∂z/∂y = -2y
Now, we evaluate these at the given points (5, 4, 9):
∂z/∂x(5, 4) = 2(5) = 10
∂z/∂y(5, 4) = -2(4) = -8
Using the tangent plane equation:
z - z₀ = ∂z/∂x (x - x₀) + ∂z/∂y (y - y₀)
Plugging in the values:
z - 9 = 10(x - 5) - 8(y - 4)
This is the equation of the tangent plane at the point (5, 4, 9).
(b) The normal vector to the surface at the given point is given by the gradient vector (∂z/∂x, ∂z/∂y, -1) = (10, -8, -1). To find the symmetric equations for the normal line, we use the point-normal form:
(x - x₀)/a = (y - y₀)/b = (z - z₀)/c
Plugging in the point (5, 4, 9) and the normal vector components (10, -8, -1):
(x - 5)/10 = (y - 4)/(-8) = (z - 9)/(-1)
These are the symmetric equations for the normal line to the surface at the given point.
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Complete the description of a real-world situation that might involve three linear equations in three variables.
you are trying to find the ages of three people. you know the sum of all three ages, the sum of the first two ages and blank (the answer choices are twice the third or the third age squared), and the sum of the first and third ages and blank (the answer choices are twice the second or the square root of the second)
* just to be clear there are two blanks and two possible answer choices for each
A real-world situation that might involve three linear equations in three variables is trying to determine the ages of three siblings.
Let's call them A, B, and C. We know that the sum of all three ages is a certain value, let's say it's 60. We also know the sum of the first two ages is either twice the third age or the third age squared. For example, if the sum of the first two ages is twice the third age, we could write it as A + B = 2C.
Alternatively, if the sum of the first two ages is the third age squared, we could write it as A + B = C^2. Similarly, we know the sum of the first and third ages is either twice the second age or the square root of the second age. So, we could write it as A + C = 2B or A + C = sqrt(B).
We now have three linear equations in three variables that we can use to solve for the ages of the three siblings. By solving the system of equations, we can find out how old each sibling is.
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Nick used his credit card to make several large purchases, and now owes the credit card company $4,273 plus 32% interest. His mother gave him $500 for h
birthday. Which is the most responsible choice he can make regarding his birthday money?
A He can put $250 into a savings account that pays 3. 8% interest and pay down his credit card debt with the rest.
B. He can put all the birthday money in the 3. 8% savings account
о
C. He can use all the money to pay down his credit card debt.
O D. He can invest $200 in the stock market and pay down his credit card debt with the rest.
The most responsible choice for Nick regarding his birthday money would be option C, which is to use all the money to pay down his credit card debt.
This is because credit card debt generally comes with high- interest rates, and it can be grueling to pay off the debt if the interest keeps adding up. By using the$ 500 to pay down his credit card debt, Nick can reduce the quantum he owes and, as a result, pay lower interest in the long run. Options A and D suggest unyoking the plutocrat between paying down debt and investing/ saving, which may not be the stylish choice given Nick's current fiscal situation.
Option B suggests putting all the plutocrat into a savings regard with a lower interest rate, which would not be as effective in reducing his credit card debt. thus, option C is the most responsible choice for Nick.
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o produto de dois números é 54 seu MMC é 18 Qual o MDC desse número?
Porfavor explique
Answer:
o MDC de 6 e 9 é 3.
O produto de dois números é 54 e o seu MMC é 18. Precisamos encontrar o MDC desses dois números.
Primeiro, encontramos os dois números cujo produto é 54: 6 e 9.
Então, fatoramos cada número em seus fatores primos: 6 = 2 x 3 e 9 = 3 x 3.
O MDC de 6 e 9 é o produto dos fatores primos comuns, elevados à menor potência. Neste caso, o único fator primo comum é 3, elevado à primeira potência.
Portanto, o MDC de 6 e 9 é 3.
0. 587. Write this value in
scientific notation.
. 0.587 in scientific notation is 5.87 x 10^-1.
Find out the scientific notation of the given value?Scientific notation is a way of writing numbers that are very large or very small in a compact and standardized way. In scientific notation, a number is expressed as a coefficient multiplied by 10 raised to some power.
For example, the number 0.587 can be written in scientific notation as 5.87 x 10^-1. The coefficient 5.87 is obtained by moving the decimal point one place to the right, while the negative exponent -1 indicates that the decimal point has been moved one place to the left, to the tenth place.
Scientific notation is commonly used in scientific and engineering fields where very large or very small numbers are often encountered, and it allows for easier calculation and comparison of these values.
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Find the directional derivative of f(x, y, z) = 23 – x²y at the point (3,-1, -2) in the direction of the vector v=(-1,-4,-4).
The directional derivative of f(x, y, z) = z³ – x²y at the point (3,-1, -2) in the direction of the vector v=(-1,-4,-4) is -234/√33.
The function is f(x, y, z) = z³ – x²y
We have to find directional derivative at the point (3, -1, -2)
In the direction vector v = (-1, -4, -4)
The gradient of the function is
∇f(x, y, z) = ∂f/∂x [tex]\hat{i}[/tex] + ∂f/∂y [tex]\hat{j}[/tex] + ∂f/∂z [tex]\hat{k}[/tex]
∇f(x, y, z) = ∂/∂x(z³ – x²y) [tex]\hat{i}[/tex] + ∂/∂y(z³ – x²y) [tex]\hat{j}[/tex] + ∂/∂z(z³ – x²y) [tex]\hat{k}[/tex]
∇f(x, y, z) = -2xy[tex]\hat{i}[/tex] - x²y[tex]\hat{j}[/tex] + 3z²[tex]\hat{k}[/tex]
At the point (3, -1, 4).
∇f(3, -1, 4) = -2(3)(-1)[tex]\hat{i}[/tex] - (3)²(-1)[tex]\hat{j}[/tex] + 3(4)²[tex]\hat{k}[/tex]
∇f(3, -1, 4) = 6[tex]\hat{i}[/tex] + 9[tex]\hat{j}[/tex] + 48[tex]\hat{k}[/tex]
The length of the vector is
|v| = √[(-1)² + (-4)² + (-4)²]
|v| = √[1 + 16 + 16]
|v| = √33
To normalize the vector we have
n = (-√33/33, -4√33/33, -4√33/33)
The directional derivative is
∇f(x, y, z) · n = (6, 9, 48) · (-√33/33, -4√33/33, -4√33/33)
∇f(x, y, z) · n = -6√33/33 - 36√33/33 - 192√33/33
∇f(x, y, z) · n = (-6 - 36 - 192)√33/33
∇f(x, y, z) · n = -234√33/33
∇f(x, y, z) · n = -234/√33
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This is math and I need help.
The inequality that can be used to determine the number of outfits Jason can purchase while staying within his budget is 68.54 o ≤ 274.16.
Solving the inequality gives:
o ≤ 4
How to find the inequality ?The total cost of items that Jason spends on :
= 217. 34 + 36. 32 + 12. 18
= $ 265. 85
The amount that Jason has left from the $ 540 is:
= 540 - 265. 85
= $ 274. 16
If each outfit costs $ 68. 54 then the inequality that would help stay in budget is:
68.54 o ≤ 274.16
Solving this, gives:
o ≤ 274. 16 / 68.54
o ≤ 4
In conclusion, Jason can purchase up to 4 biking outfits while staying within his budget.
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Help how do I solve for x???
The value of x that makes line A and B parallel is 13.
What is the value of x?Two Angles are Supplementary when they add up to 180 degrees.
From the diagram:
Angle 1 = 9x + 24
Angle 2 = 3x
Angle 1 and angle 2 are supplementary as their sum equals 180 degrees making line A and B parallel.
Hence:
Angle 1 + Angle 2 = 180°
Plug in the values
9x + 24 + 3x = 180
Solve for x
Collect like terms
9x + 3x = 180 - 24
12x = 156
Divide both sides by 12
12x/12 = 156/12
x = 56/12
x = 13
Therefore, the value of x is 13.
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The volume of this rectangular prism is 216 cubic inches. What is the value of L?
After leveling the sand box, the height of the sand box is 1.57 in
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
The volume of a cuboid is expressed as;
V = l × w × h
V = 30 × 20 × 5
V = 3000 in³
After leveling, the volume decreases by 1680 in³, therefore the new volume of the sand box is
3000-1680 = 1320
Therefore the new height of the sand is calculated as;
1320 = 30 × 28 × h
1320 = 840h
divide both sides by 840
h = 1320/840
h = 1.57 in
therefore the height of the remaining sand is 1.57
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Si al triple de la edad que tengo, se quita mi edad aumentada en 8 años, tendría 36 años. ¿Qué edad tengo?
damePor lo tanto, la edad que tienes es de aproximante 14.67 años.
Si al triple de la edad que tengo, se quita mi edad aumentada en 8 años, tendría 36 años. ¿
Podemos plantear este problema como una ecuación algebraica. Si llamamos "x" a la edad que tienes, la ecuación sería:
3x - 8 = 36
Ahora, despejamos la variable "x" para encontrar su valor:
3x = 36 + 8
3x = 44
x = 44/3
.Este resultado nos indica que nuestra edad actual es de aproximadamente 14.67 años. Es importante tener en cuenta que la solución no es un número entero, lo cual puede parecer inusual para una edad, pero es una respuesta matemáticamente correcta según la ecuación planteada en el problema.
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Adcb is a rectangle. ac = 16 and bd = 2x + 4, find the value of x.
In a rectangle, the diagonals are equal in length. So we can write the equation: AC = BD or 16 = 2x + 4. Solving for x, we get x = 6.
A car with a mass of 1200 kg and traveling 40 m/s east runs into the back of a parked truck with a mass of 2000 kg. After the collision the car and truck do not stick together, but the car is stopped. If momentum is conserved, what would the velocity of the truck be after the collision?
The velocity of the truck after the collision would be 24 m/s east.
The law of conservation of momentum states that the momentum of a closed system remains constant if no external forces act on it. In this case, we can assume that the car and the truck form a closed system.
The momentum of an object is given by its mass multiplied by its velocity, p = mv. Initially, the momentum of the system is:
p_initial = m_car * v_car + m_truck * v_truck
where m_car and v_car are the mass and velocity of the car, and m_truck and v_truck are the mass and velocity of the truck.
After the collision, the car is stopped, so its velocity is 0. The momentum of the system after the collision is:
p_final = m_car * 0 + m_truck * v'_truck
where v'_truck is the velocity of the truck after the collision.
Since momentum is conserved, we can set p_initial equal to p_final:
m_car * v_car + m_truck * v_truck = m_truck * v'_truck
Solving for v'_truck, we get:
v'_truck = (m_car * v_car + m_truck * v_truck) / m_truck
Substituting the given values, we have:
v'_truck = (1200 kg * 40 m/s + 2000 kg * 0 m/s) / 2000 kg
v'_truck = 24 m/s east
Therefore, the velocity of the truck after the collision would be 24 m/s east.
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During a workout, Kelly spent 10½ minutes and burned a total of 504 calories. How many calories did she burn per minute?\
Answer:
48 calories per (each) minute.
Step-by- Step
=
Which one is it please help thank you.
The students who attend Memorial High School have a wide variety of extra-curricular activities to choose from in the after-school program. Students are 38% likely to join the dance team; 18% likely to participate in the school play; 42% likely to join the yearbook club; and 64% likely to join the marching band. Many students choose to participate in multiple activities. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors. If Event A = sophomore or junior, what is Event A'?
Event A' has a probability of 50% (25% for freshmen + 25% for seniors).
To determine Event A', we need to first identify what Event A represents. Event A is the probability that a student is a sophomore or junior. Since students have equal probabilities of being freshmen, sophomores, juniors, or seniors, the probability of Event A is 50% (25% for sophomores + 25% for juniors).
Event A' is the complement of Event A, which means it includes the other two grade levels not included in Event A, in this case, freshmen and seniors. Therefore, Event A' is the probability that a student is a freshman or a senior. Since students have equal probabilities of being in each grade level, Event A' also has a probability of 50% (25% for freshmen + 25% for seniors).
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The volumes of two similar solids are 857.5 mm^3 and 540 mm^3. The surface area of the smaller solid is 108 mm^2. What is the surface area of the larger solid?
*
147 mm^2
68 mm^2
16 mm^2
216 mm^2
Answer:
147 mm^2
Step-by-step explanation: The surface area has to be more, but not double the smaller figures surface area therefore the answer is 147 mm^2
The requried surface area of the larger solid is approximately 147 mm². Option A is correct.
What is surface area?The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
Let's call the larger solid's surface area S.
Since the two solids are similar, their volumes have a ratio of (side length)³. Let's call the ratio of the side lengths of the larger to the smaller solid as k. Then:
[tex](k^3)(540 mm^3) = 857.5 mm^3[/tex]
Simplifying the above equation, we get:
[tex]k = (857.5/540)^{(1/3)}[/tex] =7/6
So, the larger solid is about 7/6=1.183 times bigger than the smaller solid in terms of side length. Since the surface area has a ratio of [tex](side length)^2[/tex], we can find the surface area of the larger solid by:
[tex]S = (1.183^2)(108 mm^2) \approx 147 mm^2[/tex]
Therefore, the surface area of the larger solid is approximately 147 mm². Answer: A.
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What is the volume of the prism, measured in cubic inches
Answer:
360 cubes
Step-by-step explanation:
A maker of homemade candles makes a scatter plot to show data of the diameter of a candle and the total burn time of the candle. A line of best fit of this data is T = 6. 5d + 11. 8, where T is the total burn time, in hours, and d is the diameter of the candle, in inches. Approximately how long is the total burn time of a candle with a diameter of 0. 5 inch?
answers: A. 2 hours B. 5 hours
C. 10 hours D. 15 hours
Answer:
The given line of best fit is: T = 6.5d + 11.8
We can use this equation to estimate the total burn time for a candle with a diameter of 0.5 inches:
T = 6.5(0.5) + 11.8
T = 3.25 + 11.8
T = 15.05
So, according to the line of best fit, the total burn time of a candle with a diameter of 0.5 inch would be approximately 15.05 hours.
Therefore, the answer is D. 15 hours.
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840x - x2 A company's revenue for selling x (thousand) items is given by R(x) = x2 +840 Find the value of x that maximizes the revenue and find the maximum revenue. X= maximum revenue is $ 2
The value of x that maximizes revenue is x 28.99 and maximum revenue is $1680 (thousand).
The revenue function for a company that sells x (thousand) items is R(x) = x² + 840. To find the value of x that maximizes revenue, we need to differentiate the revenue function, set it equal to zero and solve for x. The maximum revenue can then be calculated by substituting the value of x into the revenue function.
Revenue function: R(x) = x² + 840
To find the value of x that maximizes revenue, we differentiate the revenue function with respect to x:
dR/dx = 2x
Setting this equal to zero, we get:
2x = 0
x = 0
However, this value does not make sense in the context of the problem, as the company cannot sell 0 items. Therefore, we need to consider the critical points of the function, which occur when dR/dx = 0 or is undefined.
dR/dx = 0 when 2x = 0, so x = 0 is a critical point.
dR/dx is undefined when x = ±√840, so these are also critical points.
We can use the second derivative test to determine which critical point corresponds to a maximum. The second derivative of the revenue function is:
d²R/dx² = 2
At x = 0, d²R/dx² = 2 > 0, so this critical point corresponds to a minimum.
At x = ±√840, d²R/dx² = 2 > 0, so these critical points correspond to a minimum.
Therefore, the value of x that maximizes revenue is x = √840 ≈ 28.99 (thousand items).
To find the maximum revenue, we substitute x = √840 into the revenue function:
R(√840) = (√840)² + 840 = 1680
So the maximum revenue is $1680 (thousand).
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There are 90 children in year 6 at woodland junior school
they are split into three classes
class
number n class
27
6m
6p
33
6t
30
each child chose football or netball or hockey.
in 6m, 13 children chose hockey.
the rest of the class were split equally between football and netball.
in 6p, 9 children chose netball
twice as many children chose football as chose hockey
in 6t the ratio of children who chose
football to netball to hockey was 1:2:3
complete this table
class
number in class
football
netball
hockey
6м
27
13
6p
33
6t
30
In Year 6 at Woodland Junior School, there are 90 children split into three classes of 14, 24, and 12 on the basis of there selection of sports. In 6M, 14 not chose hockey, and the rest of the class was split equally between football and netball. In 6P, 24 not chose netball, 16 chose football, and 8 choose hockey In 6T, the ratio of football to netball to hockey was 1:2:3. The completed table is shown.
To complete the table, we need to distribute the remaining children who did not choose their sport in each class. Here's how we can calculate it
In 6M, the number of children who did not choose hockey is 27 - 13 = 14.
Since the rest of the class was split equally between football and netball, each of these two sports will have 14/2 = 7 children.
In 6P, the number of children who did not choose netball is 33 - 9 = 24.
Since twice as many children chose football as chose hockey, we can write the number of footballers as 2x, and the number of hockey players as x. Then we have 2x + x + 9 = 33, which gives x = 8. Therefore, we have 16 children who chose football, and 8 children who chose hockey. The number of children who did not choose any of these two sports is 33 - 16 - 8 - 9 = 0.
In 6T, the ratio of children who chose football to netball to hockey was 1:2:3. Let's call the number of children who chose netball as 2x, and the number of children who chose hockey as 3x. Then we have x + 2x + 3x = 30, which gives x = 6. Therefore, we have 6 children who chose football, 12 children who chose netball, and 18 children who chose hockey.
Thus, the completed table is shown.
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Which shows 71. 38 in word form? O A seventy-one thirty-eighths O B. Seventy-one and thirty eighths O c. Seventy-one and thirty-eight tenths D. Seventy-one and thirty-eight hundredths E seventy-one and thirty-eight thousands
The number 71.38 can be written in word form as "seventy-one and thirty-eight hundredths." The correct answer is option D.
In decimal notation, the number 71.38 can be broken down into its whole number and decimal parts. The whole number part is 71, and the decimal part is 0.38.
In a decimal number, the digits to the right of the decimal point represent fractions of a whole. Each digit to the right of the decimal point has a place value that is a power of 10.
In word form, the decimal part 0.38 is read as "thirty-eight hundredths." Therefore, when combined with the whole number 71, the correct word form is "Seventy-one and thirty-eight hundredths."
Therefore option D is the correct answer.
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Find the derivative y = cos(sin(14x-13))
To find the derivative of y = cos(sin(14x-13)), we will use the chain rule.
Let's start by defining two functions:
u = sin(14x-13)
v = cos(u)
We can now apply the chain rule:
dy/dx = dv/du * du/dx
First, let's find dv/du:
dv/du = -sin(u)
Next, let's find du/dx:
du/dx = 14*cos(14x-13)
Now we can put it all together:
dy/dx = dv/du * du/dx
dy/dx = -sin(u) * 14*cos(14x-13)
But we still need to substitute u = sin(14x-13) back in:
dy/dx = -sin(sin(14x-13)) * 14*cos(14x-13)
So the derivative of y = cos(sin(14x-13)) is:
dy/dx = -14*sin(sin(14x-13)) * cos(14x-13)
To find the derivative of the function y = cos(sin(14x - 13)), we can use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.
Let u = sin(14x - 13), so y = cos(u). Now we find the derivatives:
1. dy/du = -sin(u)
2. du/dx = 14cos(14x - 13)
Now, using the chain rule, we get:
dy/dx = dy/du × du/dx
dy/dx = -sin(u) × 14cos(14x - 13)
Since u = sin(14x - 13), we can substitute back in:
dy/dx = -sin(sin(14x - 13)) × 14cos(14x - 13)
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