The equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]
What do we mean by equations?An equation is a mathematical declaration composed of two expressions joined by an equal sign. An equation is 3x - 5 = 16. By solving this equation, we obtain the value of the variable x as x = 7.To find the equation:
When we differentiate the function [tex]y=6 \sec (x)-12 \cos (x)[/tex], we get:
[tex]\begin{aligned}y^{\prime} &=\frac{d}{d x}(6 \sec (x)-12 \cos (x)) \\&=6 \frac{d}{d x}(\sec (x))-12 \frac{d}{d x}(\cos (x)) \\&=6 \sec (x) \tan (x)+12 \sin (x)\end{aligned}[/tex]
The slope of the tangent line is given by this derivative at the point [tex]x=\frac{\pi}{3}[/tex]:
[tex]y^{\prime}\left(\frac{\pi}{3}\right)=6 \sec \left(\frac{\pi}{3}\right) \tan \left(\frac{\pi}{3}\right)+12 \sin \left(\frac{\pi}{3}\right)=18 \sqrt{3}[/tex]The general equation y applies to the tangent line passing through the point [tex](a, y(a))[/tex] on the curve [tex]y(x)-y(a)=y^{\prime}(a)(x-a)[/tex].The tangent line in this case passes through the point [tex]\left(\frac{\pi}{3}, y\left(\frac{\pi}{3}\right)\right)=\left(\frac{\pi}{3}, 6\right)[/tex] and has the slope [tex]y^{\prime}\left(\frac{\pi}{3}\right)=18 \sqrt{3}[/tex].As a result, this tangent line has the equation: [tex]y-6=18 \sqrt{3}\left(x-\frac{\pi}{3}\right)[/tex]
Therefore, the equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]
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The correct question is given below:
Find the equation of the tangent line to the curve y = 6 sec (x) at the point ([tex]\pi[/tex]/3, 6). Give your answer in the form y = mx + b where m is the slope and b is the y--intercept.
The functions are defined:
f(x) = -2x
g(x) = 2x + 5
h(x) = x² + 3x-10
Calculate the indicated function values.
ƒ(6²)
The indicated function value is f(6²) = -72
How to calculate the indicated function values?The function definitions are given as
f(x) = -2x
g(x) = 2x+ 5
h(x) = x^2 + 3x - 10
The function f(6²) means that x = 6² in f(x)
So, we have
f(6²) = -2(6²)
Evaluate
f(6²) = -72
Hence, the indicated function value is f(6²) = -72
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A 40g rock is lowered into 20ml the water rose to 45ml what is the density
PLEASE HELP ME
Answer:
40g/25ml
Step-by-step explanation:
The density formula is Mass/Volume. The rock is stated to have a mass of 40g, and the 20ml of water was displaced by 25ml, so, the rock has a volume of 25ml.
When drawing a line, use
_____ to show that the line continues endlessly in both directions. (Fill in the blank)
when drawing a line use arrows to show that the line continues endlessly in both directions.
A small apartment has a 10ft by 10ft bedroom, a 5ft by 5ft bathroom, and a single multi-use 14ft by 18ft living room/kitchen. what is the total square footage (area) of the apartment?
The total square footage (area) of the apartment is 337 square feet.
It is given in the question that, In a small apartment:-
Dimensions of the bedroom = 10 ft by 10ft
Dimensions of the bathroom = 5 ft by 5 ft
Dimensions of the living room/kitchen = 14 ft by 18 ft
We have to find the total square footage (area) of the apartment.
We know that,
Area of square = [tex]side^2[/tex]
Hence,
Area of the bedroom = 100 square feet
Area of the bathroom = 25 square feet
Area of the living room/ kitchen = 212 square feet
Hence,
Total square footage of the apartment = 100 + 25 + 212 = 337 square feet.
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Find the circumference
and the area of a circle with radius 9 m.
Use the value 3.14 for and do not round your answers. Be sure to include the correct units in your answers.
Answer:
56.52m is the circumference. The area is 254.34[tex]m^{2}[/tex]
Step-by-step explanation:
The equation for the circumference of a circle is c=2πr with r being the radius. So 2(3.14)(9)=56.52m. The area equation for a circle is A=π[tex]r^{2}[/tex] so it would be (3.14)(9)^2 or (3.14)(81) which equals 254.34[tex]m^{2}[/tex]
help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help
Answer:
1. -10x+36
2. 24x+121
3. 2x-8xy+32y
4. 50x-10xy+y^2
Step-by-step explanation:
i think dis right
Answer:
see explanation
Step-by-step explanation:
using the following expansions
a² + 2ab + b² = (a + b)²
a² - 2ab + b² = (a - b)²
1
x² - 12x + 36
with a = x and b = 6 , then
x² - 12x + 36 = x² - 2(x)(6) + 6² = (x - 6)²
2
x² + 22x + 121
with a = x and b = 11 , then
x² + 22x + 121 = x² + 2(x)(11) + 11² = (x + 11)²
3
x² - 8xy + 16y²
with a = x and b = 4y , then
x² - 8xy + 16y² = x² - 2(x)(4y) + 16y² = (x - 4y)²
4
25x² - 10xy + y²
with a = 5x and b = y , then
25x² - 10xy + y² = 25x² - 2(5x)(y) + y² = (5x - y)²
Evaluate the indefinite integral. (use c for the constant of integration.) x5 1 x12 dx
The evaluation of the given indefinite integral is (1/8)Tan⁻¹(x⁸) + C.
What is indefinite integral?A function that performs the antiderivative of another function is known as an indefinite integral. It can be represented visually as an integral symbol, a function, and finally a dx. A differentiable function F whose derivative is equal to the original function f is referred to as an antiderivative, inverse derivative, primitive function, primitive integral, or indefinite integral of a function f in calculus.So,
∫[x⁷ / (1 + x¹⁶)]dx = ∫[x⁷ / (1 + (x⁸)²]dxNow, u = x⁸. Then, du = 8x⁷dx. So, x⁷dx = (1/8)du.So, we obtain: (1/8)∫[du / (1 + u²)] = (1/8)Tan⁻¹u + C = (1/8)Tan⁻¹(x⁸) + CTherefore, the evaluation of the given indefinite integral is (1/8)Tan⁻¹(x⁸)+C.
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The correct question is given below:
Evaluate the indefinite integral. (use c for the constant of integration.)
x⁷/1+x¹⁶ dx
please help me with this i will mark as brainliest
Answer:
SHOWN BELOW!!!!
Step-by-step explanation:
KEEP IN MIND ----> *Square root of a number is a value, which on multiplication by itself gives the original number. The square root is an inverse method of squaring a number.*
Alright so the first equation C^2 - 49 = 0
Step 1 : Add 49 to both sides
C^2 - 49 + 49 = 0 + 49
C^2 = 49
Step 2 : Take the square root
(squ root) C^2 = (squ root)49
C = +/- (squ root) 49
Final answer ---> C = 7 OR C = -7
2.) 4S^2 - 100 = 0
Step 1 : Add 100 to both sides
4S^2 - 100 + 100 = 0 + 100
4S^2 = 100
Step 2 : Divide both sides by 4
4S^2/4 = 100/4
S^2 = 25
Step 3 : Take the square root
(squ root) S^2 = (squ root) 25
S = +/- (squ root) 25
Final answer ---> S = 5 OR S = -5
3.) 9x^2 = 324
Step 1: Divide both sides by 9.
9x^2/9 = 324/9
x^2 = 36
Step 2: Take the square root
squ root) x^2 = (squ root) 36
x = +/- (squ root) 36
Final answer ---> x = 6 OR x = -6
Which set of values contains no integers?
A. {-5, 9/3, 7.2}
B. {2.2361, 4, 7.8}
C. {-12, -3.33, 2.6458}
D. {-23/5, 2.4495, 5.1}
Answer:
D
Step-by-step explanation:
Integers found in:
A: -5, 9/3 = 3
B: 4
C: -12
Hope this helped! ^^
Marcie cooked dinner for herself. The original recipe has a serving size of 3 and requires three and three sevenths pounds of chicken. How many pounds of chicken will be needed for a single serving?
one and one seventh pounds
nine and three sevenths pounds
two over 49 pounds
three sevenths pounds
Using proportions, the number of pounds that will be needed for a single serving is: one and three seventh pounds.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The number of pounds for 3 people is given by:
[tex]3 \frac{3}{7} = 3 + \frac{3}{7} = \frac{24}{7}[/tex]
Hence, for one person, the number of pounds can be divided by three(multiplied by 1/3), hence:
[tex]\frac{24}{7} \times \frac{1}{3} = \frac{24}{21}[/tex]
24 divided by 21 has a quotient of 1 and remainder of 3, hence as a mixed number, the amount is:
one and three seventh pounds.
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Answer:
Step-by-step explanation:
the awnser is cerrot.
HELP ME
your revenue function is f(x) = 3x. How does this affect your profit for 100 downloads?
Answer:
It affects it by profit for 100 downloads is for $90 greater.
Step-by-step explanation:
Profit - 90% * revenue - 50
p(x) - 0.9 * f(x) - 50
=0.9 * 3x - 50
=2.7x - 50
Now find the profit for 100 downloads: p(100) = 2.7 * 100 - 50 =220
220 - 130 = 90
Express the mass of 49,000 molecules of oxygen in scientific notation.
grams
Answer: 49,000 molecules = 4.9*10⁴ molecules
Step-by-step explanation:
49,000=
49*10³=
4.9*10⁴ molecules
f(x) = -x² - 8x - 16; Find ƒ(-3)
f(-3) = -1
Step-by-step explanation:We can find an unknown y-value by plugging an x-value into a given function.
Function Notation
Before we answer this question, we need to understand the notation of the equation. In function notation, the equation is given in terms of f(x).
"f(x)" represents the y-value of a function at the point "x".For example, f(-3) represents the value of y when x = -3.
Finding f(3)
As stated above, to find f(-3) we need to plug -3 in for x. *Remember to use PEMDAS when solving.* This creates the new equation:
f(-3) = -(-3)² - 8(-3) - 16Then, distribute the exponent.
f(-3) = -9 - 8(-3) - 16Next, multiply.
f(-3) = -9 - (-24) - 16Distribute the negative.
f(-3) = -9 + 24 - 16Finally, add the remaining terms.
f(-3) = -1This means that when x = -3, y or f(-3) = -1.
Meena and some friends are going to the movies. at the theater, they sell a bag of popcorn for $5.50 and a drink for $3.50. how much would it cost if they bought 5 bags of popcorn and 7 drinks? how much would it cost if they bought p bags of popcorn and d drinks?
It would cost-
$27.50 for the 5 bags of popcorn.$24.50 for the 7 drinks.What is cost?In common parlance, cost is the monetary value of products and services purchased by producers and consumers.
Cost is the measure of a alternative opportunities foregone when one good or activity is chosen over others in a basic economic sense. This fundamental cost is commonly known as opportunity cost.Total cost refers to all expense incurred in achieving a specific level of output; dividing such total cost by the quantity generated yields average or unit cost.Total cost = (fixed cost) x Number of units produced.
The cost of a bag of popcorn for $5.50.
The number of popcorn bags bought are 5.
Total cost for 5 bags of popcorn are-
$5.50 ×5 = $27.50.
Thus, Total cost for 5 bags of popcorn bags are $27.50.
The cost of 1 drink is $3.50.
The total number of drinks bought is 7.
Total cost = $3.50×7 = $24.50
Thus, the total cost for the drinks is $24.50.
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help me with this ques. (need solution and answer both) thanks so much <3
Answer:
1.) 27a^11 + 18a^9 -72a^7
2.) 6p^4q^3 - 10p^3q + 4p^2q3
Step-by-step explanation:
1.) Distribute and do the math
-9a^5 x (-3a^6) - 9a^5 X (-2a^4) - 9a^5 x 8a^2
27a^11 + 18a^9 -72a^7
2.) Distribute and do the math
2pq^2q x 3p^2q^2 - sp^2q x 5p + 2p^2q x 2q^2
6p^4q^3 - 10p^3q + 4p^2q3
If you can play the piano, then you can play a musical instrument. kiyo can play a musical instrument.
use the law of detachment to write a true statement. if the law of detachment can't be used, explain.
Law of Detachment can't be applied here.
What is Law of Detachment ?The Law of Detachment says that we must detach ourselves from the result or outcome in order to allow what we desire to materialize in the physical universe. When we have done our part, we must learn to let go of the outcome for things to materialize. And once we do let go, it's when things materialize.
Given:
If you can play the piano, then you can play a musical instrument.
kiyo can play a musical instrument.
So, as Kiyo can play a musical instrument, that does not necessary mean he can play a piano.
There could be any other musical instrumental, not only piano.
So, the hypothesis do not have to be true.
Hence, the condition is not fulfilled, Law of Detachment can't be applied here.
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Given the binary number 1011, what is the next consecutive binary value? (what happens when you add 1 to 1011)? explain how you arrived at your answer.
The next consecutive binary value of 1011 = 1100
Binary numbers only consist of two digits: 0 and 1. So there are some specific rules for addition in binary. They are:
0 + 0 = 00 + 1 = 11 + 1 = 10(read as one zero and corresponds to the binary value of 2)1 +1 + 1 = 11 (read as one one one and corresponds to the binary value of 3)Here 1011 is a binary number and to find the its next consecutive binary value, we have to add 1 to 1011.
i.e., 1 0 1 1 +
1
------------------
1 1 0 0
The 0 in the one's place is got by adding 1 + 1 = 10 and 1 is supposed to be a carry to the ten's place. The 0 in the ten's place is got from adding this carry 1 and 1, which again gives 10 and 1 is carry to next place. Now 0 + 1 = 1 and finally we get, 1011 + 1 = 1100.
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Someone pls help with this !! Tyyy
Answer:
a , b , e , f
Step-by-step explanation:
Find the surface area of the cube shown below. A. 66 cm2 B. 121 cm2 C. 726 cm2 D. 1,331 cm2
Answer:
66
Step-by-step explanation:
What is the absolute value of:
-3|2y-3|+2=-20
Answer:
Exact Form:
y = 31/6, −13/6
Decimal Form:
y = 5.16,−2.16
Mixed Number Form:
y = 5 1/6,−2 1/6
Last year, 63 new houses were built in a neighborhood. So far 6/7 of them have been sold. How many new houses have been sold this year?
Write your answer in simplest form
Answer is 54. Here is a trick for you. Write 63 as a fraction, with the denominator as 1. 63/1. Then insert the fraction you are calculating, 6/7: (6*63)/7*1. Do the multiplication, 6*63=378, 7*1=7. Then write as 378/7. What's 378/7? Your answer 54.
12. Which is the simplified expression of -8(2m + 9k-13)?
-16m+9k-13
A.-16m +9k - 13
B. -16m - 72k + 104
C. -16m-72k - 104
D. 16m - 72k - 104
-16m - 72k + 104 is the simplified expression .
What does a math expression mean?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)Expression can be a commonly used word or phrase or a means of expressing your ideas, emotions, or sentiments. The idiom "a penny saved is a penny earned" is a prime example. A smile is an illustration of an expression.the simplified expression of -8(2m + 9k-13)
= -8(2m + 9k-13)
= -16m - 72k + 104
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4 12 ➗ 1 12
what is the quotient?
The quotient of the fraction 4/12 ÷ 1/12 is 4.
What do we mean by fractions?A fraction is a small part of a larger whole.In arithmetic, the number is expressed as a quotient, which is the numerator divided by the denominator.In a simple fraction, both are integers.A complex fraction has a fraction in the numerator or denominator.In mathematics, there are three major types of fractions.The three types are proper fractions, improper fractions, and mixed fractions.Fractions are terms with a denominator and a numerator.So, evaluation of 4/12 ÷ 1/12:
4/12 ÷ 1/124/12 × 12/1 (Reciprocal)4/1 (12 - 12 cancel)4Therefore, the quotient of the fraction 4/12 ÷ 1/12 is 4.
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If the sample variance for a frequency distribution consisting of hourly wages was computed to be 10, what is the sample standard deviation?
The sample standard deviation is (B) $3.16.
What is the sample standard deviation?The sample standard deviation is defined as the root-mean-square of the differences between observations and the sample mean: A significant deviation is defined as two or more standard deviations from the mean. The lowercase Greek letter (sigma) for the population standard deviation or the Latin letter s for the sample standard deviation is most commonly used in mathematical texts and equations to represent standard deviation. For example, if the sample variance for a frequency distribution of hourly wages is 10 and the sample standard deviation is $3.16.Therefore, the sample standard deviation is (B) $3.16.
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The complete question is given below:
If the sample variance for a frequency distribution consisting of hourly wages was computed to be 10, what is the sample standard deviation?
A. $4.67
B. $3.16
C. $1.96
D. $10.00
Evaluate the function.
f(x) = 2x² – 3x – 1
Find f(8)
Given ~
[tex] \tt \: f(x) = 2x² – 3x – 1[/tex]
[tex] \: [/tex]
put the value of x=8 in given function ~
[tex] \tt \: f(8) = 2 ({8})^{2} - 3(8) - 1[/tex]
[tex] \: [/tex]
[tex] \tt \: f(8) = 2 (64) - 3(8) - 1[/tex]
[tex] \: [/tex]
[tex] \tt \: f(8) = 128 - 24 - 1[/tex]
[tex] \: [/tex]
[tex] \tt \: f(8) = 104 - 1[/tex]
[tex] \: [/tex]
[tex] \underline { \boxed{ \tt \red{f(8) = 103}}}{ \green ✓}[/tex]
[tex] \: [/tex]
hope helps ~
Simplify the radical expression that does NOT simplify to 10.
Answer:
A.
Option A√10 ≈ 3
2 × 3 ≈ 6
Option B√25 = 5
√4 = 2
5 × 2 = 10
Option C[tex]\frac{300}{3}=100\\\sqrt{100}\\100=10^2\\\sqrt{10^2}\\\sqrt{10^2}=10[/tex]
Option D[tex]1000=10^3\\\sqrt[3]{10^3}\\\sqrt[3]{10^3}=10(\mathrm{Radical\:rule)}\\[/tex]
Thus,
option A. is correct.
HELP!!! what is the quadratic formula????
Rodolfo le da una vuelta a la manzana en 4 minutos; Ricardo, en 5 minutos y Rena to, en 6 minutos. ¿En cuánto tiempo existirán si empiezan a hacer el recorrido desde el mismo punto?
Rodolfo, Rena y Ricardo se encuentran después de 6 minutos en la salida si todos comienzan su viaje desde el mismo punto.
Rodolfo tarda unos 4 minutos en dar la vuelta a la manzana.
Ricardo tarda 5 minutos en dar la vuelta a la manzana.
Rena tarda 6 minutos en dar la vuelta a la manzana.
Digamos que los tres comienzan el viaje desde el mismo punto A.
Rena tarda 6 minutos, Ricardo tarda un minuto menos que Rena y Rodolfo tarda 2 minutos menos que Rena.
Por lo tanto,
Rena es la que más tarda en dar la vuelta a la manzana y será la última en salir.
Por lo tanto, Rodolfo, Ricardo y Rena se encontrarán después de 6 minutos en la salida.
Todas se reúnen después de 6 minutos en la salida.
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Rory has 3 pounds of ground turkey to make meatballs.He uses 3/8 pound per to make 6 meatballs. How many 1/8 pound meatballs can Rory make with the remaining turkey?
He can make 2 meat balls from the remaining turkey.
Total pounds of ground turkey available = 3 pounds.
Turkey used to make 6 meat ball = 3 / 8 of 3 pounds = 9 / 8 pounds
Turkey used to make 1 meat ball = 9 / 8 ÷ 6 = 3 / 16
1 / 8 meat = 1/ 8 of 3 = 3 / 8 pound of meat.
Number of meatballs made = 3 / 8 × 16 / 3 = 2
Therefore, he can make 2 meat balls from the remaining turkey.
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What is the scientific results to 5,97 X 1024 kg
The scientific results to 5.97 x [tex]10^{24}[/tex] kg is the Earth's mass.
What is the Earth's mass?The Earth has a mass of 5.9 sextillion tonnes, which is a significant amount of mass. The Earth's mass is approximately 5.97 x [tex]10^{24}[/tex] kg, with a standard error of 6 x [tex]10^{20}[/tex] kg. The mass of a planet is difficult to measure exactly due to its size, therefore this number has varied over time as we have developed better measuring techniques.Astronomers use the Earth's mass as a reference point when calculating the masses of other planets, including rocky terrestrial planets and exoplanets.To learn more about the Earth's mass visit:
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