Given:
The function is:
[tex]y=-\dfrac{3\sqrt{x^5}}{4}[/tex]
To find:
The value of [tex]\dfrac{dy}{dx}[/tex].
Solution:
We have,
[tex]y=-\dfrac{3\sqrt{x^5}}{4}[/tex]
It can be written as
[tex]y=-\dfrac{3}{4}x^{\frac{5}{2}}[/tex] [tex][\because \sqrt[n]x=x^\frac{1}{n}][/tex]
Differentiate with respect to x.
[tex]\dfrac{dy}{dx}=-\dfrac{3}{4}\times \dfrac{5}{2}x^{\frac{5}{2}-1}[/tex] [tex][\because \dfrac{d}{dx}x^n=nx^{n-1}][/tex]
[tex]\dfrac{dy}{dx}=-\dfrac{15}{8}x^{\frac{5-2}{2}}[/tex]
[tex]\dfrac{dy}{dx}=-\dfrac{15}{8}x^{\frac{3}{2}}[/tex]
[tex]\dfrac{dy}{dx}=-\dfrac{15}{8}\sqrt{x^3}[/tex]
Therefore, the value of [tex]\dfrac{dy}{dx}[/tex] is [tex]-\dfrac{15}{8}\sqrt{x^3}[/tex].
The legs of a right triangle measure 5 and 8. What is the length of the hypotenuse?
[tex]\sqrt{89}[/tex]
Hope This Helps You!
Good Luck Studying ^-^
Write the equation of a line in slope-intercept form with a slope of 2 and
passes through the point (-3,1)
Answer:
y = 2x + 1
Step-by-step explanation:
Hope this helps!
Find two positive consecutive integers such that the square of the first added to three times the second is 24
Answer:
3 and 5
Step-by-step explanation:
Let the two consecutive odd integers be x and x + 2.
Now,
The given statement is
[tex]x^2 + 3 \times (x+2)=24\\x^2 + 3x+6-24 = 0 \\x^2 + 3x-18 = 0\\x^2+6x-3x-18=0\\x(x+6)-3(x+6)=0\\(x-3)(x+6)=0\\x=3,-6[/tex]
Taking x=3.
Hence, two consecutive odd integers are 3 and 5.
Which one of these statements correctly states Pythagoras' Theorem for the following diagram?
a) d 2 = e 2 − f 2
b) d 2 = e 2 + f 2
c) e 2 = d 2 + f 2
d) f 2 = d 2 + e 2
Answer:
I couldn't really read the problem that well, but if there's an e^2+f^2=d^2, then that's probably the correct option.
Step-by-step explanation:
6. If f(x) = -2x2 + x - 5, what is f(3)?
Answer:
If you use the formula it should help for your answer.
Step-by-step explanation:
Laura invested $1000 in a college saving account for her children that had an annual interest rate of 11% compounded continuously after 20 years how much money is in her account
Answer:
$2200
Step-by-step explanation:
1000*11%*20=2200
Plz help will give brainliest!
Answer:
8.7
Step-by-step explanation:
I need help with this math problem on get more math the photo is at the top
Answer:
30
Step-by-step explanation:
6x5=30 Just took the test and got 100%
factor out the gcf from each polynomial 30x^2-18x^3+6x^4
Answer:
43
Step-by-step explanation:
what is the slope of the line that passes through 4,-2 and -8,6
Answer:
Slope is -2/3
Step-by-step explanation:
Please can someone give me correct answer to this problem.
I will mark you brainliest for the correct answer.
Please help!!!!!!!!!!!!!!!!!!!
what is 2 copies of 1/6
find the product of (5x+4)(5x-4)
Answer:
25x² - 16
Step-by-step explanation:
Given
(5x + 4)(5x - 4)
Each term in the second factor is multiplied by each term in the first factor, that is
5x(5x - 4) + 4(5x - 4) ← distribute parenthesis
= 25x² - 20x + 20x - 16 ← collect like terms
= 25x² - 16
Which of these is a Pythagorean Triple?
1,1 square root of 2.
1, square root of 3, 2
11, 50, 51
20, 21, 29
Answer:
1, 1, sqrt of 2
WILL GIVE BRAINLIEST
(Photo is recommended)
What is the value of the expression 4 4? ____
62c + 86 = 32
A. -1.90
B. -.87
C. .35
D. 4.63
Answer:B
62ç=32-86
62c=-54
C=0.87
2.
Brian was reading a novel. He said, “If I take the sum of the number of the page I'm on
with the number of the page on its right, I get 425." Which page is Brian on?
How many hundredths are in the number 2912.468
Answer:
6
Step-by-step explanation:
Pind the distance between -5 and 8.
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8 9 10 11 12 13
The distance is 12
Edit: I did it wrong, sorry
---
hope it helps
Answer:
The distance between the two points is 13 units
Step-by-step explanation:
on a graph, to find the distance you can either count each square/unit or you could add the points together not counting if they're negative or not
basically just add them in absolute value |-5| + 8= 13
hope this helps <3
What are the value/s of x if: *
36x2 – 25 = 0 ?
8 folders cost $25.20. Write an equation to determine the cost of 3 folders.
Answer:
9 dollars and 45 cents
Step-by-step explanation:
First find the price of one folder.
$25.20 divided by 8 = $3.15
Then, multiply by 3.
$3.15 x 3 = $9.45
(I accidentally used 3.18 instead of 3.15. Someone corrected me.)
Answer:
25.20 divided by 8 = $3.15 x 3 = 9.45
Step-by-step explanation:
used a calculator, Hope this helps!
The coordinates of the vertices for the figure HIJK are H(0, 5), I(3, 3), J(4, –1), and K(1, 1). To determine if it is a parallelogram, use the converse of the parallelogram diagonal theorem. This states that if the diagonals, then the quadrilateral is a parallelogram. The midpoint of HJ is and the midpoint of IK is (2, 2). Therefore, HIJK is a parallelogram because of the diagonals, which means they bisect each other.
Answer:
In ΔHKJ and ΔHIJ
HK=IJ=√17
HI=KJ=√13
HJ=HJ [Common}
ΔHKJ ≅ ΔHIJ [SSS]
Now consider ΔHKI AND ΔKJI
HK=IJ=√17
HI=KJ=√13
KI=KI [Common]
ΔHKI ≅ ΔKJI [SSS]
Now the converse of Parallelogram diagonal theorem also states that if diagonals of a Quadrilateral divides it into two congruent triangles then it is a parallelogram.
Hence the given Quadrilateral is a Parallelogram.
Step-by-step explanation:
Leo has a lock box with a volume of 312 cubic inches. The box is 4 inches high and 13 inches long. What is the width of the box?
Answer:
6in
Step-by-step explanation:
Given data
Volume of the lockbox= 312 cubic inches
Height= 4in
Length= 13in
Width= ???
The expression for the volume of box is
V= L*W*H
substitute
312=13*W*4
312=52W
W= 312/52
W=6 in
Hence the width is 6in
please give solutions kindly write and send pic in my whatsap no.( eight zero one seven zero zero zero nine five zero)
Answer:
You simply take the values away from 180°.
a) 180-85-65 = 30°
b) 180-37-63=80°
c) 180-52-78=50°
d) 180-102-58=20°
e) 180-100-60=20°
f) 180-105-25=50°
g) 180-127-23=30°
would the answer be 36?
Answer:
No, it would be 72
Step-by-step explanation:
In similar triangles, the sides are different but the angles are the same. You still had a great guess though :)
Pls give brainliest
Need a bit of help, please. :D
Answer:
c.
Step-by-step explanation:
Please note that the angle A and B are somewhat close to 45deg, so we expect AC and BC to be close in length.
We can drop answer a on that basis.
We can also drop abswer d on the basis that AC is longer than AB there and that cannot be the case in a right triangle.
We can verify that for both b and c the Pythagoras theorem holds, so we need to choose the answer that fits the angles A and B. Te can check the tan of the angle to get the ratio between BC and AC.
tan(48.8deg) ~= 1.1423
1.6/1.4 ~= 1.1429; close enough.
So we choose answer c.
Okay have posted the next question.
Answer:
1. only 1 unique triangle can be made
2. only 1 unique triangle can be made
3. multiple triangles are possible
4. True
5. True
6. False
7. only 1 unique triangle can be made
8. only 1 unique triangle is possible
9. multiple triangles are possible
10. no triangle is possible
Step-by-step explanation:
Ask in comments if you got any questions.
Answer:All are correct I think.
Step-by-step explanation:
Help PLEASE 10pts CMON PEOPLE I NEED TO FINISH THIS TODAY
Answer:
451054547.5Since total sum of interior angles of a triangle is 180 Do the calculation you will get it
which pic you choose
.............that apple do be looking good doe........ : /
Right answer gets brainlist
Answer:
(-7-2)....................hope this helps
