Answer: 18
Step-by-step explanation:
The least common denominator of [tex]\frac{7}{9}[/tex] and [tex]\frac{5}{6}[/tex] is going to be a multiple of 9 and 6. Let us list them out:
9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90
6: 6, 12, 18, 24, 30, 36, 42, 28, 54, 60
You can see I bolded and underlined 18. Why? This is the first common multiple of 9 and 6 so it is our least common denominator (LCD).
differentiate the following with respect to x
irrelevant answers will be reported
Answer:
[tex]\displaystyle y' = - \frac{e^{x^2 + 7} \sqrt{\csc 5x} \Bigg[ \bigg[ 5 \cot (5x) - 4x \bigg] \sin (3x + 4) - 6 \cos (3x + 4) \Bigg] }{2}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
[tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]:
[tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]:
[tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle y = e^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)}[/tex]
Step 2: Differentiate
Apply Derivative Rule [Product Rule]:∴ we have found the derivative of the function.
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Learn more about differentiation: https://brainly.com/question/26836290
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
To find the derivative of the function [tex]\displaystyle\sf\:y=e^{x^{2}+7}\sin(3x+4)\sqrt{\csc(5x)}}[/tex] with respect to [tex]\displaystyle\sf x[/tex], we'll use the chain rule and product rule.
Let's break down the function into its individual parts:
[tex]\displaystyle\sf u= e^{x^{2}+7}[/tex]
[tex]\displaystyle\sf v= \sin(3x+4)[/tex]
[tex]\displaystyle\sf w= \sqrt{\csc(5x)}}[/tex]
Now, let's differentiate each part separately:
Using the chain rule, the derivative of [tex]\displaystyle\sf u= e^{x^{2}+7}[/tex] is:
[tex]\displaystyle\sf \dfrac{du}{dx}= (2x)e^{x^{2}+7}[/tex]
Using the chain rule, the derivative of [tex]\displaystyle\sf v= \sin(3x+4)[/tex] is:
[tex]\displaystyle\sf \dfrac{dv}{dx}= 3\cos(3x+4)[/tex]
To differentiate [tex]\displaystyle\sf w= \sqrt{\csc(5x)}}[/tex], we can rewrite it as [tex]\displaystyle\sf w= (\csc(5x))^{1/2}[/tex]. Using the chain rule, the derivative of [tex]\displaystyle\sf w[/tex] is:
[tex]\displaystyle\sf \dfrac{dw}{dx}= \dfrac{1}{2}(\csc(5x))^{-1/2}(-\cot(5x))(5)[/tex]
Simplifying the derivative [tex]\displaystyle\sf \dfrac{dw}{dx}[/tex]:
[tex]\displaystyle\sf \dfrac{dw}{dx}= -\dfrac{5\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]
Now, using the product rule, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] can be calculated as follows:
[tex]\displaystyle\sf \dfrac{dy}{dx}= \dfrac{du}{dx} \cdot v \cdot w + u \cdot \dfrac{dv}{dx} \cdot w + u \cdot v \cdot \dfrac{dw}{dx}[/tex]
Substituting the values of [tex]\displaystyle\sf \dfrac{du}{dx}[/tex], [tex]\displaystyle\sf \dfrac{dv}{dx}[/tex], and [tex]\displaystyle\sf \dfrac{dw}{dx}[/tex]:
[tex]\displaystyle\sf \dfrac{dy}{dx}= \left((2x)e^{x^{2}+7}\right) \cdot \sin(3x+4) \cdot \sqrt{\csc(5x)} + e^{x^{2}+7} \cdot \left(3\cos(3x+4)\right) \cdot \sqrt{\csc(5x)} - e^{x^{2}+7} \cdot \sin(3x+4) \cdot \dfrac{5\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]
Simplifying further:
[tex]\displaystyle\sf \dfrac{dy}{dx}= \left(2xe^{x^{2}+7}\right) \sin(3x+4) \sqrt{\csc(5x)} + 3e^{x^{2}+7}\cos(3x+4) \sqrt{\csc(5x)} - \dfrac{5e^{x^{2}+7} \sin(3x+4) \cot(5x)}{2\sqrt{\csc(5x)}}[/tex]
Therefore, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] is:
[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x]\sin(3x+4) - 3e^{x^{2}+7}\sqrt{\csc(5x)}\cos(3x+4) - \dfrac{5e^{x^{2}+7}\sin(3x+4)\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]
Simplifying further, we have:
[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x \sin(3x+4) - 6e^{x^{2}+7}\cos(3x+4)\sqrt{\csc(5x)}[/tex]
Therefore, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] is:
[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x]\sin(3x+4) - 6e^{x^{2}+7}\cos(3x+4)\sqrt{\csc(5x)}[/tex]
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
Two sides of a parallelogram are 110 feet and 850 feet. The measure of the angle between these sides is 157 Find the area of the parallelogram to the nearest square foot.
Answer: 36533
Step-by-step explanation:
Prove that cos⁻¹ (12/13) + sin⁻¹ (3/5) = sin⁻¹ (56/65)
Answer:
See below ↓
Step-by-step explanation:
We need to prove :
⇒ cos⁻¹ [tex]\frac{12}{13}[/tex] + sin⁻¹ [tex]\frac{3}{5}[/tex] = tan⁻¹ [tex]\frac{56}{65}[/tex]
Let's simplify the LHS.
cos⁻¹ [tex]\frac{12}{13}[/tex] + sin⁻¹ [tex]\frac{3}{5}[/tex]Convert the inverse cos and sin functions into inverse tan functions
tan⁻¹ [tex]\frac{5}{12}[/tex] + tan⁻¹ [tex]\frac{3}{4}[/tex][∴This can be found taking a right triangle and labeling the sides, and then using Pythagorean Theorem, we can find the missing side and take the ratio of tan]Identity
tan⁻¹ x + tan⁻¹ y = tan⁻¹ [tex]\frac{x+y}{1-xy}[/tex]Using this identity, we can simplify our earlier equation!
⇒ tan⁻¹ [(5/12 + 3/4)/(1 - (5/12 x 3/4))]
⇒ tan⁻¹ [(20 + 36) / (48 - 15)
⇒ tan⁻¹ (56/65)
⇒ RHS
⇒ Proved ∴√
[tex]\text{L.H.S}\\\\=\cos^{-1} \dfrac{12}{13} + \sin^{-1} \dfrac 35\\\\=\sin^{-1} \dfrac 5{13} + \sin^{-1} \dfrac 35\\\\[/tex]
[tex]=\sin^{-1}\left[\dfrac 5{13}\sqrt{1- \left(\dfrac 35 \right)^2} + \dfrac 35\sqrt{1-\left(\dfrac 5{13} \right)^2} \right]\\\\=\sin^{-1} \left(\dfrac 5{13} \sqrt{1-\dfrac 9{25} }+\dfrac 35 \sqrt{1-\dfrac{25}{169}} \right)\\\\=\sin^{-1} \left(\dfrac 5{13} \sqrt{\dfrac{16}{25}}+\dfrac 35 \sqrt{\dfrac{144}{169}} \right)\\\\=\sin^{-1} \left(\dfrac{5}{13} \cdot \dfrac 45 + \dfrac 35 \cdot \dfrac{12}{13} \right)\\[/tex]
[tex]=\sin^{-1} \left(\dfrac 4{13} +\dfrac{36}{65}\right)\\\\=\sin^{-1} \left(\dfrac{20}{65} + \dfrac{36}{65} \right)\\\\=\sin^{-1} \left(\dfrac{20+36}{65} \right)\\\\=\sin^{-1} \left(\dfrac{56}{65} \right)\\\\=\text{R.H.S}[/tex]
? need in a day or 2 please! Is worth 23 points and brainiest!
Answer:
60 feet
Step-by-step explanation:
The easiest way to do this is to go answer by answer with the triangle area formula :)
Formula: A=hb/2
H = height
B: base
Now lets solve this :)
Choice 1: 50 feet
50 x 20 = 1000
1000/2 = 500
Choice 2: 40 feet
Since 40 feet is smaller than the 50, we know this will not be correct :)
Choice 3: 120 feet
120 x 20 = 2400
2400/2 = 1200
Choice 4: 60 feet
60 x 20 = 1200
1200/2 = 600
The correct answer is 4, 60 feet :)
Have an amazing day!!
Please rate and mark brainliest!!
Complete the table
I WILL MARK BRAINLIEST AND GIVE THANKS
Answer:
Step-by-step explanation:
hours Cost
0 $15
1 $15 + 2.50 = $17.50
2 $15 + 2.50(2) = $15 + 5 = $20
3 $15 + 2.50(3)= $15 + 7.50 = $22.50
4. $15 + 2.50(4)= $15 + 10 = $25
Help plsss 60 points
Step-by-step explanation:
please mark me as brainlest
Answer:
a) 5, -3, -4, 0
b) Curve B
Step-by-step explanation:
Given equation:
[tex]y=x^2-4x[/tex]
Inputting the values of x into the equation to find the missing values of y:
[tex]x=-1 \implies y=(-1)^2-4(-1)=5[/tex]
[tex]x=1 \implies y=(1)^2-4(1)=-3[/tex]
[tex]x=2 \implies y=(2)^2-4(2)=-4[/tex]
[tex]x=4 \implies y=(4)^2-4(4)=0[/tex]
[tex]\large\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} x & -1 & 0 & 1 & 2 & 3 & 4 & 5\\\cline{1-8} y & 5 & 0 & -3 & -4 & -3 & 0& 5\\\cline{1-8}\end{array}[/tex]
According to the table:
y-intercept of the curve = (0, 0)x-intercept of the curve = (4, 0)Therefore, Curve B matches the graph of [tex]y=x^2-4x[/tex]
Brandon paid $70 for 20 gallons of
gasoline. How much did he pay per
gallon?
Answer:
$3.50
Step-by-step explanation:
For this question, you just take the price paid and divide it by the number of gallons. In this case, you get $3.50 per gallon.
A cone-shaped lampshade has a height of 18 cm and a slant height of 19.5 cm. Find the lateral surface area of the lampshade.
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{19.5^2-18^2}=r\implies \sqrt{56.25}=r \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} r=radius\\ h=height\\ \stackrel{slant~height}{\sqrt{r^2+h^2}}\\[-0.5em] \hrulefill\\ r=\sqrt{56.25} \end{cases}\implies \begin{array}{llll} LA=\pi \sqrt{56.25}\stackrel{slant~height}{(19.5)} \\\\\\ LA\approx 459.46~cm^2 \end{array}[/tex]
solve for x. -5 + 5x = -(1 - 6x)
- 5 + 5x = - 1 + 6x
- 5 + 5 + 5x = - 1 + 5 + 6x
5x = 4 + 6x
5x - 6x = 6x - 6x + 4
- x = 4
x = - 4
Answer:
The answer is that x = -4.
Step-by-step explanation:
You first take away the parenthesis so it would look like this: -5+5x=-1+6x
Then, you add 5 to both sides of the problem: -5+5x+5=-1+6x+5
Then, you simplify it down: 5x=6x+4
You then subtract 6x from each side: 5x-6x=6x+4-6x
Then simplify again: -x=4
Then, divide both sides by -1: -x/-1 = 4/-1
Then simplify to get x = -4.
HELP!:
x^2 + 6x + 9 = ?
This is a factorizing question!! I need help, quickly!
Answer:
nasa pic yung answer
Step-by-step explanation:
hope its help
correct me if im wrong
Answer:
x=-3 x=-3
Step-by-step explanation:
You have the equation x^2+6x+9=0. So we are tying to find two terms that add to 6 but multiply to 9. Those numbers are 3 and 3. So now we have x^2+3x+3x+9=0. Then factor it to get (x+3) and (x+3) then to isolate x do x+3=0, x=-3 (move 3 to the other side to get x=-3).
Maria has 32 tickets to sell.She sold 4/6 of them.How many did she sell?
Answer:
22 tickets
Step-by-step explanation:
4/6 is 2/3
2/3 of 32 is 21 .3
Can't sell 0.3 of a ticket, so round up.
22 tickets
Four beakers contain water as shown below.
Which two beakers of water can be combined to fill one beaker to exactly 1,000 mL?
beaker B and beaker C
beaker B and beaker C
beaker A and beaker C
beaker A and beaker C
beaker A and beaker B
beaker A and beaker B
beaker A and beaker D
beaker A and beaker D
Answer:
A&C
Step-by-step explanation:
It would be A because it has 750 mL and C because it has 250mL and 750+250=1000
Also can you mark brainlyist you dont have to
Type SSS, SAS, ASA, AAS, or HL to
justify why the TWO LARGER triangles are congruent.
m
BE = BC
Answer: AAS
Step-by-step explanation:
-
Use inverse operations to write the inverse of f(x) = x +
3/2
Answer:
I believe the correct answer is f^-1 (x) = x - 3/2
Here's Francesca's description of the scatterplot:
There is a strong nonlinear association between group size and time. There don't seem to be any outliers.
What, if anything, is missing from this description?
Choose 1 answer:
A:Form
B: Direction
C: Strength
D: Outliers
E: Nothing is missing: this is a complete description.
You are deciding between First National Bank and Liberty Bank. They both offer checking and savings accounts. First National charges a $10 fee to receive checks and charges $2.50 per ATM transaction. Liberty Bank has no check fee but charges $3.25 per ATM transaction. How many times do you need to be charged an ATM fee before you are paying the same amount of money in fees at both banks?
Step 1: Define your variables - Look at the question statement. What are you being asked to find?
Step 2: Write 2 equations that use those unknown variables
Step 3: Solve the system of equations
Step 4: State your solution. What does it mean in the context of the word problem?
What is the value of x?
Answer:
30 degrees
Step-by-step explanation:
because if its 60 at the bottom and 30 on the left it only makes sense that it would be 30 on the right.
Also can you mark brainlyest you dont have to thoe
Find the diameter of the circle with the given circumference. Use 3.14 . C=16 cm
Answer:
5.1 cm
Step-by-step explanation:
The equation for the circumference of a circle is 2πr or πd.
So, we can plug in 16 and 3.14 to get 16 = 3.14×diameter.
Divide both sides by 3.14 to get approximately 5.1 cm.
Hope that helps! :)
What is the volume of this figure?
6004 in³
6624 in³
9936 in³
10,488 in³
The volume of the figure is the amount of space in the figure
The volume of the figure is 10488 cubic inches
How to determine the volume?The figure is a composite figure, and it contains:
A rectangular prism A triangular prismThe volume (V1) of the rectangular prism is:
V1 = Length * Width * Height
V1 = 18 in * 23 in * 16 in
V1 = 6624 cubic inches
The volume (V2) of the triangular prism is:
V2 = 0.5 * Base * Width * Height
V2 = 0.5 * 23 in * 16 in * 21 in
V2 = 3864 cubic inches
Add the volumes of both figures
V = V1 + V2
V = 6624 cubic inches + 3864 cubic inches
V = 10488 cubic inches
Hence, the volume of the figure is 10488 cubic inches
Read more about volumes at:
https://brainly.com/question/1972490
Answer:
The answer is D: 10488
Step-by-step explanation:
need help with this one its "Find the slope of the line y = 7x + 9/16" please help
Answer:
slope = 7
Step-by-step explanation:
Slope-intercept form of a linear equation: y = mx + b
(where m is the slope, and b is the y-intercept)
Therefore, for the equation: y = 7x + 9/16
Slope = 7y-intercept = 9/16Suppose a ferris wheel is moving at a constant rate of 8 inches per second. if the diameter of the wheel is 60 feet, how long will it take the ferris wheel to make a complete revolution ?
Answer: If you want you can put 480 seconds or 8 minutes.
480 seconds = 8 minutes
Step-by-step explanation:
8 inches multiply by 60 feet
48 ounce bag of granola each month how many pounds if granola does she eat each year
Answer:
12 months = 1 year48 ounce bag of granola per month.
T = 48x
Where 'x' represents the months.
Replace x with 12, because we want to know how many ounces she eats each year.
T = 48x
T = 48(12)
T = 576 ounces, she eats each year.
A company has an opportunity to bid on three contracts. determine which would be the best investment given the information in the table below. probability of profit and loss by contract contract profit, probability of profit probability to break even loss, probability of loss southeast $45,000, 50% 30% $6,000, 20% southwest $60,000, 35% 40% $10,000, 25% california $112,000, 20% 40% $40,000, 40% southeast southwest california all contracts include a probability for loss.
The best investment of the company is in southeast contract. The probability of profit of this contract is maximum 50% and of loss is minimum 20%.
What is probability?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
A company has an opportunity to bid on three contracts. Probability of profit and loss by all three contract is listed in the table below.
Contract profit, (P)* of profit, (P)* to break even loss, (P)* of loss
Southeast $45,000, 50% 30% $6,000, 20% Southwest $60,000, 35% 40% $10,000, 25% California $112,000, 20% 40% $40,000, 40%The company which will give the maximum profit probability and minimum loss probability will be the best investment.
In the above table, the southeast contract has the maximum probability of profit, which is 50% among all the contracts. Similarly, it has the lowest probability of loss, which is 20%.
Thus, the best investment of the company is in southeast contract. The probability of profit of this contract is maximum 50% and of loss is minimum 20%.
Learn more about the probability here;
https://brainly.com/question/24756209
Answer:
It's A. Southeast
Step-by-step explanation:
In Zoe's grade, there are 90 students. Currently, 90% of them are enrolled in health. How many students are enrolled in health?
Answer: 81
Step-by-step explanation:
90% is the same as 0.9
We can multiply .9 by 90 to see how many students are enrolled in health
0.9×90=81.0
Answer:
[tex]\huge\boxed{\sf 81\ students }[/tex]
Step-by-step explanation:
Total students = 90
Enrolled in health:
= 90 % of 90
[Key: "of" means "to multiply" and "%" means "out of hundred"]
[tex]\displaystyle = \frac{90}{100} \times 90\\\\= 9 \times 9\\\\= 81[/tex]
So, 81 students are enrolled in health.
[tex]\rule[225]{225}{2}[/tex]
Find the perimeter.
Write your answer as a fraction or as a whole or mixed numbe
5 1 cm
10
5 cm
10
Bloc
5
cm
10
5 cm
10
Answer:
20 2/5 cm
Step-by-step explanation:
4 ( 5 1/10)
4 × 51/10
2×51/5
0.4x51
=20 2/5
if f(x)=2x^2-3x+4, find f(x+3)
Step-by-step explanation:
well, the approach is totally simple : we use (x+3) everywhere where we have "x" in the function expression.
so,
f(x+3) = 2(x+3)² - 3(x+3) + 4 =
= 2(x² + 6x + 9) - 3x - 9 + 4 =
= 2x² + 12x + 18 - 3x - 9 + 4 =
= 2x² + 9x + 13
Angel and Jaden were at track practice. The track is 2/5 kilometers around.
Angel ran 1 lap in 2 minutes.
Jayden ran 3 laps in 5 minutes
How many minutes does it take Jayden to run 1 kilometer?
Answer:
See below ↓
Step-by-step explanation:
Information we need
Jayden runs 3 laps in 5 minutesSolving
Time taken by Jayden to run 2/5 kilometers (1 lap) = 5/3 minutesTime taken to run 1 km = Time taken to run 2/5 km x 5/2 Time taken to run 1 km = 5/3 x 5/2 ⇒ 25/6 minutes (improper fraction form)⇒ 4 1/6 minutes (mixed number form)⇒ 4.17 minutes (decimal form)The Sum of the measures of angle X & Y is 90 degrees
The measure of angle X is 6x
The measure of angle Y is 24
what is the value of X?
Step-by-step explanation:
X + Y = 90
Y = 24
X = 6x
X + 24 = 90
X = 66
x = X/6 = 66/6 = 11
Sam has been running his swimming pool cleaning business now for five years. He is considering enlarging his service area to a 100 mile radius, which would require two new offices in different parts of town. He would like to take out a business loan to cover the cost of expansion. The profits for Sam's business over the last 5 years are outlined in the table below. According to this information, what would be the best estimate for Sam to quote as expected profits in the next year in his new business plan? Business Year Net Profit 1 $43,502. 25 2 $47,417. 45 3 $51,685. 02 4 $56,336. 68 5 $61,406. 98 a. $66,477. 28 b. $66,933. 60 c. $72,003. 91 d. $72,957. 63.
Thus, the best estimate for Sam to quote as expected profits in the next year in his new business plan is $66,933.60.
What is net profit?Net profit is the amount of a business earn after deducting all the expenditure over it.
Sam has been running his swimming pool cleaning business now for five years. He is considering enlarging his service area to a 100 mile radius, which would require two new offices in different parts of town.
He would like to take out a business loan to cover the cost of expansion. The profits for Sam's business over the last 5 years are outlined in the table below.
Business Year Net Profit 1 $43,502.25 2 $47,417.45 3 $51,685.02 4 $56,336.68 5 $61,406.98Using the regression graph, the quadratic equation we get for this data as,
[tex]y=192.4493x^2+3318.1733x+39998.214[/tex]
For the 6 year value,
[tex]y=192.4493(6)^2+3318.1733(6)+39998.214\\y\approx 66835.43[/tex]
This value is much near to the option b which is $66,933.60.
Thus, the best estimate for Sam to quote as expected profits in the next year in his new business plan is $66,933.60.
Learn more about the Net profit here;
https://brainly.com/question/4177260
Pick the biggest number.
A0.193 B0.26 C0.6 D0.308
Answer:
Hello fellow Human! ^ω^
The answer is option D. 0.308
Step-by-step explanation:
We are going to Compare the digits starting with the greatest place value.
The Number 0.193 Is not the biggest number. However, 0.193 is bigger than 0.26 and 0.60.The number 0.193 is smaller than the number 0.308.
Therefore, the answer is Option D. 0.308
Hope this helps!
Have an Awesome Friday!