Answer:
It is actually very simple:
Notice that they don't actually do the square of 49 and 64. For some reason, they do the square root of the values without squaring them. If we were to do it in the right way, the answer would be:
[tex]49^{2} +64^{2} = c^{2}[/tex]⇔ 2401+4096 = [tex]c^{2}[/tex] ⇔ 6497 = [tex]c^{2}[/tex] ⇔ [tex]\sqrt{6497}[/tex] = [tex]\sqrt{c^{2} }[/tex] ⇔ 80,6 ≈ c
I believe this is the answer. I hope I had helped :)
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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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]
The times of all 15 year olds who run a certain race are approximately normally distributed with a given mean mu = 18 sec and standard deviation sigma = 1.2 sec. what percentage of the runners have times less than 14.4 sec? 0.15% 0.30% 0.60% 2.50%
The percentage of the runners having times less than 14.4 sec is 0.15%. Then the correct option is A.
What is normal a distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The times of all 15 years old who run a certain race are approximately normally distributed with a given mean μ = 18 sec and standard deviation σ = 1.2 sec.
The percentage of the runners has times less than 14.4 sec.
Then the z-score will be given as
[tex]\rm z = \dfrac{X - \mu}{\sigma }\\\\\\z = \dfrac{14.4 - 18}{1.2}\\\\\\z = -3[/tex]
Then the percentage will be
[tex]\rm P(z < -3)=0.00135 = 0.135 \% \approx 0.15 \%[/tex]
More about the normal distribution link is given below.
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Answer:
A. 0.15%
Step-by-step explanation:
edge 2022
Will choose Brainliest.
Jessica and Martha each have a bag of cookies with unequal quantities. They have 30 cookies total between the two of them. Each of them ate 6 cookies from their bag. The product of the number of cookies left in each bag is not more than 80.
How many more cookies will Jessica have than Martha?
If x represents the number of cookies Jessica started with, complete the statements below.
The inequality that describes the relationship between the number of cookies each one of them has is x^2- _ x + 224 ≥ 0
Jessica has at least
_ cookies more than Martha.
That part is total cookies as per algebraic formula x^2-(a+b)x+ab=0
Hence
The inequality is
[tex]\\ \rm\rightarrowtail x^2-30x+224>=0[/tex]
[tex]\\ \rm\rightarrowtail (x-14)(x-16)>=0[/tex]
[tex]\\ \rm\rightarrowtail 14\leqslant x\leqslant 16[/tex]
Solution range
[14,16]Atleast means the range
16-142Atleast 2 more than Martha
Charles buys 60 packs of pens.
There are 14 pens in each pack.
Each pack costs £4.50.
Charles sells each pen for 70p but he only manages to sell
2
3
of the pens.
How much profit did he make?
Answer:
£122
Step-by-step explanation:
Total no. of pens :- 60× 14= 840
Cost of all pens :- £270
Total no. of pens sold :- 560
Cost of those pens :- £392
Profit = £122Charles made a profit of £122, By selling (2/3)rd of his pens.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Charles buys 60 packs of pens and there are 14 pens in each pack.
If each pack costs £4.50.
So, The Total cost is,
= £(60×4.50).
= £270.
The total number of pens is,
= (14×60).
= 840, And he manages to sell (2/3) of it which is,
= (2/3)×840.
= 560.
Now, The total money made by him is,
= 540×0.7.
= £392.
Therefore, The profit he made is £(392 - 270) = £122.
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A researcher is studying the relationship between the number of TVs owned by a family and the size of the family's electric bill. After collecting data, he finds that the relationship is best modeled by the equation B = 2.43T + 95.66, where B is one month's electric bill in dollars and T is the number of TVs owned by the family. Which of these is a good interpretation of the y-intercept of this model?
Answer:
Step-by-step explanation:
No choice is given but here is the general interpretation.
Y-intercept is where the plot crosses the y-axia at x=0. In this case, x is T which represents number of TVs owned by the family. T=0 meaning there is no TV and B = 96.66 is the one month's electric bill in dollars for all other appliances in the home.
Given function
B=2.43T+95.66Now
Compare to slope intercept form y=mx+b
Slope=m=2.43Y intercept=b=95.66Here y intercept may be the fixed charge .
A rectangle has an area of 91.7 square inches and a base of 13.1 inches. What is the height?
Answer:
7 inches
Step-by-step explanation:
The area of a rectangle A is equal to its length times its width (or base times height if you want to put it that way.)
Since A = b*h, h = A/b. Plugging in values gives you 91.7/ 13.1 = 7 inches.
So the answer is 7 inches.
which expression is equavilent to the epression -3(4x - 2) - 2x?
A. -8x
B. -16
C. -14 - 2
D. -14 + 6
Answer:
D
Step-by-step explanation:
-3(4x - 2) - 2x
-12x + 6 -2x
-14x + 6
Manny has 36 coins in
his piggybank.
3 of the coins are silver dollars.
• The remaining coins are dimes (10€), quarters (25€) and nickels (5¢).
• There is an equal number of dimes, quarters and nickels.
How many nickels does Manny have?
Answer:
q=50
d=22
Step-by-step explanation:
Divide 2.875 x 106 by 2.3 x 103.
Answer:
1.25 x 10^3
Step-by-step explanation:
i took the test
For his car, Sam spent $138.96 on speakers and $142.89 on new tires. In total, how
much did Sam spend on car parts?
Answer:
Same spent $281.85 or approximately $282
Which is an equivalent fraction for
?
A
12\frac{1}{2}
2
1
B
26\frac{2}{6}
6
2
C
46\frac{4}{6}
6
4
D
32\frac{3}{2}
2
3
Answer:
I believe the answer is C
Step-by-step explanation:
Select the true statement about trend lines.
O A. A trend line should be as close as possible to the points.
O B. A trend line connects the points.
O C. A trend line goes through the first and last points.
D. A trend line is always horizontal.
SUBMIT
The statement that is true about trend lines is: A. A trend line should be as close as possible to the points.
What is a Trend Line?A trend line, which can also be called the line of best fit, is a straight line that represents the pattern of a data, which can be positive or negative.
A trend line does not necessarily need to connects all the points, but goes through some points to show the pattern. It may not even be necessary to go through any of the points, what's improtant is for the trend line to be close to as many points as possible.
Therefore, the statement that is true about trend lines is: A. A trend line should be as close as possible to the points.
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Can anyone help me with this one Question on volume The diameter of a cylinder is 1 yd. The height is 12 yd. Find the volume of the cylinder.
Answer:
9.42 cube.yd
Step-by-step explanation:
Volume of cylinder= πr^2h
3.14 × 0.5 × 0.5 × 129.42 cube.ydA company is designing a new cylindrical water bottle. The volume of the bottle will be 176 cm ^3. The height of the water bottle is 7.8 cm. What is the radius of the water bottle? Use 3.14 for pi
Step-by-step explanation:
volume = 176 cm³
height = 7.8
radius = ?
pi = 3.14
volume of cylinder = πr²h
176 = 3.14 × r² × 7.8
176 = 24.492 × r²
176/24.4 = r²
7.21 = r²
√7.21 = r². ( Using long division )
r = 2.69 ( approx. )
the standard form of a linear equation is the form ______________
Answer:
Ax+By=C
Step-by-step explanation:
:)
Angle FGH is a right angle.
The measure of angle JGH is 50.
The measure of angle FGJ is
What is the value of x?
Answer:
since its a triangle then angles have to be 90 (the right angle) and 50 (which is given)
180-90-50 = 40
Answer = 40
Step-by-step explanation:
Solve the system of equations below. Thankyou!
Answer:
x = - 9
y = 5
Step-by-step explanation:
EQ1 + EQ2
Substitute the value of X in either EQ1 or EQ2
Identify the initial amount in the following exponential function: y = 2.3(1.32)
Please answer soon
(-2 • -4)^2 = ?
Answer:
64
Step-by-step explanation:
(-2(-4))^2
8^2
64
hope that helps
What is the sum product pattern? Correct answer gets BRAINLY!!!!!!!!!!!!!!!!!!!! Pls hurry!!!!!!!!!!!
The sum-product pattern
If the polynomial is of the form x 2 + b x + c x^2+bx+c x2+bx+cx, squared, plus, b, x, plus, c and there are factors of c that add up to b.
I am not sure what you meant but hopefully you meant this
Answer:
If the polynomial is of the form x2 + bx + cx²+bx+cx2+bx+cx, squared, plus, b, x, plus, c and there are factors of c that add up to b.
Step-by-step explanation:
Do mark BRAINLIEST
a parabola has focus of (5 2) and directrix y=0.where is the parabola's vertex
keeping in mind that the vertex will be half-way between the directrix and the focus point, in this case the directrix is below the focus point, meaning is a vertical parabola, Check the picture below.
If a 45-45-90° triangle's leg has a length of 18 units, what is the length of the hypotenuse?
Answer:
25.45584...
Step-by-step explanation:
The length of the hypotenuse can be found using the pythagorean theorem: [tex]a^{2} +b^{2} =c^{2}[/tex] So in this situation, the solution can be found by solving [tex]\sqrt{2(18)^{2} }[/tex]
Darrin graphs the following inequality: y > -3x -5. Does the side of the line with all solutions (the shaded region) include the test point (0,0)?
Yes it does include the test point (0, 0)
equation: y > -3x -5Find y-intercept: y > -3(0) -5 y > -5Find x-intercept:y > -3x -5switch sides
-3x - 5 < 0-3x < 5Multiply both sides by -1 reverses the inequality
x > -5/3Thus, the following (0, 0) comes under the following x > -5/3 and y > -5
Find the area of the figure below. You may assume all sides are perpendicular.
Multiple answer choice
23
19
27
17
Answer:
I think the answers is 27, just add all of those squares.
Write a numerical expression to represent the phrase.
the difference of 4 cubed and 25
Hello!
First, "the difference" of 2 numbers means you subtract these numbers.
Then, 4 cubed is written as follows:
4³
Subtract:
4³-25
[If necessary] Evaluate:
64-25
39
Hope everything is clear.
Let me know if you have any questions!
Always remember: Knowledge is power!
The perimeter of a notebook is 28
inches. The area is 48 square inches.
What are the dimensions of the
notebook?
Area = length x width
Half the perimeter = length + width
half the perimeter = 14 inches.
Find 2 numbers when added together = 14 and when multiplied together = 48
6 + 8 = 14
6 x 8 = 48
the dimensions are 6 inches by 8 inches
Kyle has a storage box that is 2 ft. Long, 3 ft. High, and has a volume of 12 ft. 3. Myla has a storage box that is 4 ft. High, 2 ft. Long, and has a volume of 16 ft. 3. What are the widths of Kyle and Myla's boxes? Explain how you know.
The widths of Kyle's and Myla's boxes for the considered case are obtained as: width of Kyle's box = 2 ft, width of Myle's box = 2 ft
How to find the volume of a right rectangular prism?Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:
[tex]V = a\times b \times c \: \: unit^3[/tex]
A storage box oftenly has the shape of a right rectangular prism.
We're specified that:
For Kyle's box:
Volume of the box = 12 cubic ftLength of the box = 2 ftHeight of the box = 3 ftWidth of the box = x ft (suppose)For Myla's box:
Volume of the box = 16 cubic ftLength of the box = 4 ftHeight of the box = 2 ftWidth of the box = y ft (suppose)Using the formula for volume of right rectangular prism to find the missing widths:
Case 1: For Kyle's box:[tex]12 = 2 \times 3 \times x\\12 = 6 \times x\\\text{Dividing both the sides by 6}\\2= x\\x = 2 \: \rm ft[/tex]
Case 2: For Myla's box:[tex]16 = 4 \times 2 \times y\\16 = 8 \times x\\\text{Dividing both the sides by 8}\\2= y\\y = 2 \: \rm ft[/tex]
Thus, the widths of Kyle's and Myla's boxes for the considered case are obtained as: width of Kyle's box = 2 ft, width of Myle's box = 2 ft
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Briefly describe a predatory/prey boom bust graph.
Answer:
This can lead to cyclical patterns of predator and prey abundance, where prey increase in number and then, with abundant food, predator number increases ...
Step-by-step explanation:
Proportional ratios : If I mow 75 % of 150 square meters of my grass, how much did I mow?
Answer:
You mowed 112.5 square meters of your grass.
Step-by-step explanation:
First, convert the percentage to a fraction.
75% = 3/4
Then to find 75% of 150, multiply 3/4 and 150.
(3/4) * 150
(3*150)/4
450/4
112.5
We can now say that 75% of 150 is 112.5, meaning you mowed 112.5 square meters of your grass.
Answer:
[tex]\huge\boxed{\sf 112.5 \ m^2\\}[/tex]
Step-by-step explanation:
Grass mowed:
= 75% of 150 m²
[Key: "of" means "to multiply" and "%" means "out of 100"]
[tex]\displaystyle = \frac{75}{100 } \times 150\\\\= \frac{75 \times 15}{10} \\\\= \frac{1125}{10} \\\\= 112.5 \ m^2\\\\\rule[225]{225}{2}[/tex]
What quadrilaterals can you draw that have two sides with length 8 cm and two sides with length
5 cm?
Which of these quadrilaterals can have two sides with length
8 cm and two sides with length 5 cm?
Select all that apply.
OA. Trapezoid
OB. Square
OC. Parallelogram
OD. Rectangle
E. Kite
Answer:
C. parallelogram
D. rectangle
E. kite
Step-by-step explanation:
Cannot be the square because all sides are the same. A trapezoid can have two sides the same, but not two pairs of equal sides. The remaining shapes can have two pairs of equal length sides. see image.