Answer:
[tex] \frac{dy}{dx} = - \frac{ {x}^{3} }{ {y}^{3} } [/tex]
Step-by-step explanation:
Differentiate both sides of the equation (consider y as a function of x).
[tex] \frac{d}{dx} ( {x}^{4} + {y}^{4} (x)) = \frac{d}{dx} (16)[/tex]
the derivative of a sum/difference is the sum/difference of derivatives.
[tex]( \frac{d}{dx} ( {x}^{4} + {y}^{4} (x))[/tex]
[tex] = ( \frac{d}{dx} ( {x}^{4} ) + \frac{d}{dx} ( {y}^{4} (x)))[/tex]
the function of y^4(x) is the composition of f(g(x)) of the two functions.
the chain rule:
[tex] \frac{d}{dx} (f(g(x))) = \frac{d}{du} (f(u)) \frac{d}{dx} (g(x))[/tex]
[tex] = ( \frac{d}{du} ( {u}^{4} ) \frac{d}{dx} (y(x))) + \frac{d}{dx} ( {x}^{4} )[/tex]
apply the power rule:
[tex](4 {u}^{3} ) \frac{d}{dx} (y(x)) + \frac{d}{dx} ( {x}^{4} )[/tex]
return to the old variable:
[tex]4(y(x) {)}^{3} \frac{d}{dx} (y(x)) + \frac{d}{dx} ( {x}^{4} )[/tex]
apply the power rule once again:
[tex]4 {y}^{3} (x) \frac{d}{dx} (y(x)) + (4 {x}^{3} )[/tex]
simplify:
[tex]4 {x}^{3} + 4 {y}^{3} (x) \frac{d}{dx} (y(x))[/tex]
[tex] = 4( {x}^{3} + {y}^{3} (x) \frac{d}{dx} (y(x)))[/tex]
[tex] = \frac{d}{dx} ( {x}^{4} + {y}^{4} ))[/tex]
[tex] = 4( {x}^{3} + {y}^{3} (x) \frac{d}{dx}(y(x))) [/tex]
differentiate the equation:
[tex]( \frac{d}{dx} (16)) = (0)[/tex]
[tex] = \frac{d}{dx} (16) = 0[/tex]
derivative:
[tex]4 {x}^{3} + 4 {y}^{3} \frac{dy}{dx} = 0[/tex]
[tex] \frac{dy}{dx} = - \frac{ {x}^{3} }{ {y}^{3} } [/tex]
What is the value of the expression 4x^3 – 3x when x = 6?
Multiply.
(b - 7)(2b +9)
(b - 7)(2b + 9) = (Simplify your answer.)
Answer:
foil method
add/subtract like terms
Step-by-step explanation:
b×2b=2b²
b×9=9b
-7×2b=-14b
-7×9=-63
-14b+9=-5
=2b²-5b-63
What is the arc length of arc cd in the circle below. The circle has a radius of 6ft and an angle measure of 30
9514 1404 393
Answer:
π ft ≈ 3.14 ft
Step-by-step explanation:
The angle is 1/12 of the number of degrees in a circle, so the arc length will be 1/12 of the circumference of the circle.
C = 2πr
1/12C = 2/12π(6 ft) = π ft ≈ 3.14 ft
The arc length is about 3.14 feet.
11/13 = v/7 round to the nearest tenth
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The owner has 8 employees. Seven of them
earn $ 210, $200, $190, $180, $300, $150,$90 a
day. What does the 8th employee get paid, if the
average pay for all 8 employees is $200?
whats equivalent to (4r+ 3) +(-2r+ 4)
Answer:
2r+7
Step-by-step explanation:
(4r+3)+(−2r+4)
Combine 4r and −2r to get 2r.
2r+3+4
Add 3 and 4 to get 7.
2r+7
:)
If no sides of a triangle have the same length, the triangle is called scalene
(pronounced SKAY-leen). And, as you might remember, if the triangle has at
least two sides that are the same length, the triangle is called isosceles. Use the
markings or description in each diagram below to decide if AABC is isosceles or
scalene. Assume the diagrams are not drawn to scale.
Answer:
a. isosceles
b. isosceles
c. scalene
Please I need the answers if it is for today please if you can in edited photography, it is before 9 o'clock At that time I have to go to sleep please, I give a crown :(
Answer:
mkhhikbyjhggfikmnikkfyujikok
Write 28.63 in expanded notation and word form.
Answer:
Answer below
Step-by-step explanation:
Expanded form : 20 + 8 + 0.6 + 0.03
Expanded form is a way of writing numbers to see the individual math value of digits.
Word form: twenty eight point six three.
HOPE THIS HELPED
select the code requirements when it is located in a crawl space You may select more than one.
Answer:
your gonna have to give me more details
Step-by-step explanation:
is this even a question
Can someone help me with this one pleaseee!!!!
f(2)=3 divide by 2x-5
Answer:
[tex]f(2) = \frac{3}{2x - 5} [/tex]
Fully factorise: 4x2−25
NEED ANSWER ONLY DON'T SHOW STEPS. URGENT!!!
a. (2x+5)(2x−5)
b. (2x−5)(2x−5)
c. (4x+5)(x−5)
d. (3x+20)(x+5)
Answer:
The correct choice is option a. (2x+5)(2x−5)
Answer:
Option a. (2x+5)(2x-5)
Step-by-step explanation:
4x2 - 25
Furthermore, this is the difference of squares formula we will use to factor 4x^2-25:
a2 - b2 = (a + b) • (a − b)
As you can see, our problem does not look like the left side of the formula, so first we have to convert our problem to match the left side like so:
4x2 - 25 = (2x)2 - 52
Now that it matches, we can simply plug in 2x for a and 5 for b into the formula to get the factors of 4x^2-25:
(2x + 5) • (2x − 5)
________________________________
I know this is urgent but still I gave you the explanation so that whenever you're confused with questions like that then these steps can help you.
A rectangular picture frame has length three inches longer than twice it’s width. The perimeter is 36 inches. Find the width of the frame.
a.) 5in
b.) 7in
c.) 10in
d.) 11in
Answer:
A. 5 in
Step-by-step explanation:
Let w represent the width of the frame.
If the length is 3 inches longer than twice the width, it can be represented by 2w + 3.
Use the perimeter formula, p = 2l + 2w. Plug in the perimeter and 2w + 3 as l, and solve for w:
p = 2l + 2w
36 = 2(2w + 3) + 2w
36 = 4w + 6 + 2w
36 = 6w + 6
30 = 6w
5 = w
So, the width of the frame is 5 inches.
The correct answer is A. 5 in
5. Name the property of real numbers illustrated by the equation. (1 point)
Answer:
distributive property
please help me, if you help then thanks!
Answer:
B. [tex] {a}^{ - 7 - 10} [/tex] (second option)
Step-by-step explanation:
[tex] \frac{ {a}^{ - 7} }{ {a}^{10} } [/tex]
[tex] {a}^{ - 7 - 10} [/tex]
[tex] - 7 - 10 = - (7 + 10) = - 17[/tex]
If a = 3+2✓2 then find the value of a^2+1/a^2
Pls answer first to answer get the brainliest crown
Pls answer ASAP
Answer: 34
Step-by-step explanation:
[tex]a=3+2\sqrt{2} \\\\\dfrac{1}{a} =\dfrac{1}{3+2\sqrt{2}} =\dfrac{3-2\sqrt{2}}{(3+2\sqrt{2})(3-2\sqrt{2})} =\dfrac{3-2\sqrt{2}}{3^2-2^2*2} =3-2\sqrt{2}\\\\\\a+\dfrac{1}{a} =3+2\sqrt{2}+3-2\sqrt{2}=6\\\\(a+\dfrac{1}{a})^2=6^2=36=a^2+\dfrac{1}{a^2}+2\\\\\\a^2+\dfrac{1}{a^2}=36-2=34\\[/tex]
Compare: 7/20 O 35%
who answers first get brainlest
Step-by-step explanation:
7/20
=0.35
35%
=35/100
=0.35
Hence, 7/20=35%
Choose the equation that satisfies the data in the table.
-15 0 15
х
[
y
0
2
4
Answer:
B. y = [tex]\frac{2}{15} X + 2[/tex]
Step-by-step explanation:
I. Given x = 15 and y = 4
4 = [tex]\frac{2}{15}(15) + 2[/tex]
4 = 2+2
4 = 4 true
II. Give x = 0 and y = 2
2 = [tex]\frac{2}{15}(0) + 2[/tex]
2 = 0 + 2
2 = 2 true
III. Given x = -15 and y = 0
0 = [tex]\frac{2}{15}(-15) + 2[/tex]
0 = -2 + 2
0 = 0 true
Good luck.
help help help
Find d
A. 74
B. 14
C. 16
D. 76
Answer:
D
Step-by-step explanation:
b/c 90 - 14 = 76 .........
What number is 1/2 of 3/4
Answer
1.5/4
Step-by-step explanation:
An equation is shown below: 4x+2(x-3) = 4x+2x-11 Solve the equation and write the number of solutions. Name one property you used to solve this equation
Answer:
4x + 2(x - 3) = 4x + 2x - 11 4x + 2x - 6 = 4x + 2x - 11 6x - 6 = 6x - 11 6x - 6x = -11+ 6 O = -5...incorrect...this has no solution...0 solutions one property used was the distributive property :2(x - 3) = 2x - 6
Where would you find the point (-10,0)
Answer:
Step-by-step explanation:
the x axis
Ivan’s desserts made a batch of fresh scones with 4/5 of a pound of butter and 1/2 of a pound of sugar. How much more butter than sugar was used?
Kayla Koolbeck has $37.60 un her checking account. She uses her debit card to make purchases of $25.99 and $19.34, which overdraws his account. His bank charges her account antes overdraft Dee of $25.00. She then deposits her paycheck for $58.66 from her part-time job ay Subway. What is the balance in ver account?
Answer:
33.66
Step-by-step explanation:
if (a+b)=3 and ab=2, find the value of a2+b2
Answer: so a^2 + b^2 = 5
Step-by-step explanation:
(a+b) = 3
ab = 2
so
(a+b)^2 = 3^2
a^2 + 2ab + b^2 = 9
or, a^2 + 2*2 + b^2 = 9
or, a^2 + 4 + b^2 = 9
or, a^2 +b^2 = 9-4 = 5
Which of the following is equivalent to the radical expression below when
x20?
VAX 1X+7
A. x 47
B. VAXA + 20%
C. VAMAX
D. X* 20%
Answer:
B in the photo
Step-by-step explanation:
another way to write the problem:
square root is also taking the 1/2 power:
[tex](4x)^{1/2} * (x+7)^{1/2} \\[/tex]
since they are raised to the same power:
[tex](4x * (x+7))^{1/2}\\(4x^2 + 28x)^{1/2}\\\\=\sqrt{4x^2 + 28x}[/tex]
Rewrite 14 / 25 and 11 / 20 so that they have a common denominator
The fraction equivalent of the given fractions with the same denominator is written as [tex]\frac{56}{100} \ and \ \frac{55}{100}[/tex]
The given parameters include:
[tex]\frac{14}{25} \ and \ \frac{11}{20}[/tex]
To rewrite the given fractions to have the same denominator, we must find the LCM of the denominators;
The prime factorization of 25 = 5²
The prime factorization of 20 = 5 x 2²
The LCM of the two numbers = 5² x 2² = 25 x 4 = 100
The fractions can rewritten as follows;
[tex]\frac{14}{25} \ = \frac{14}{25} \times \frac{4}{4} = \frac{14 \times 4}{25 \times 4} = \frac{56}{100} \\\\\frac{11}{20} \ = \frac{11}{20} \times \frac{5}{5} = \frac{11 \times 5}{20 \times 5} = \frac{55}{100}[/tex]
Thus, the fraction equivalent of the given fractions with the same denominator is written as [tex]\frac{56}{100} \ and \ \frac{55}{100}[/tex]
Learn more here: https://brainly.com/question/17248258
Find the value of 9 - [4 2 - (3 + 2)]. 8 6 -2
Answer:
-2
Step-by-step explanation:
9 - [4^2 - (3 + 2)]
PEDMAS says parentheses first
Work from the inside out
9 - [4^2 - (5)]
9 - [16-5]
9 - [11]
Subtract
9-11
-2
Find two rational numbers between the root of 2 and root 3
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Answer:
1.5 and 1.6
Step-by-step explanation:
√2 ≈ 1.41421356...
√3 ≈ 1.7320508...
1.5 and 1.6 are between these numbers
__
If you need the ratio of integers, these numbers are 3/2 and 8/5.