Find the gradient of the curve y = x^5/2 at the point where x = 4
Given:
The equation of the curve is:
[tex]y=x^{\frac{5}{2}}[/tex]
To find:
The gradient of the given curve at the point where [tex]x = 4[/tex].
Solution:
We have,
[tex]y=x^{\frac{5}{2}}[/tex]
Differentiate with respect to x.
[tex]y'=\dfrac{5}{2}x^{\frac{5}{2}-1}[/tex] [tex][\because \dfrac{d}{dx}x^n=nx^{n-1}][/tex]
[tex]y'=\dfrac{5}{2}x^{\frac{3}{2}}[/tex]
Substituting [tex]x=4[/tex], we get
[tex]y'=\dfrac{5}{2}(4)^{\frac{3}{2}}[/tex]
[tex]y'=\dfrac{5}{2}(2^2)^{\frac{3}{2}}[/tex]
Using properties of exponents, we get
[tex]y'=\dfrac{5}{2}(2)^{2\times \frac{3}{2}}[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
[tex]y'=\dfrac{5}{2}(2)^{3}[/tex]
[tex]y'=\dfrac{5}{2}(8)[/tex]
[tex]y'=20[/tex]
Therefore, the gradient of the given curve at the point where [tex]x = 4[/tex] is 20.
Which set of integers is in order from least to greatest? a. 1, -2, 3, 4, -5. b. -5, 4, 3, -2, 1. c. -2, -5, 1, 3, 4 d. -5, -2, 1, 3, 4.
Answer:
Step-by-step explanation:
Negative numbers have the least value and (-1) is the greatest negative value
So, d is arranged in least to greatest order
d) -5 , - 2 , 1 , 3 , 4
Answer:
The answer is D.
Step-by-step explanation:
D is the one that has the order from least to greatest.
1. A baseball coach graphs some data and finds the line of
best fit. The equation for the line of best fit is
y = 0.32x - 20.51, where x is the number of times at bat and
y is the number of hits.
How many hits should he expect from a player who is at bat
175 times?
A) 35 hits
B) 49 hits
C) 609 hits
D) 62 hits
Answer:
It's answer B, 49 hits. I got it right
Help plzzzzz help me
Answer: 10 < x < 60, or x is from 10 to 60
Step-by-step explanation: A domain of a graph consists of all of the input values shown on the x-axis while the range consists of all of the output values shown on the y-axis. Since the question asks to find the domain, you should look at the values of the graph from left to right. The domain includes all real numbers. Notice the black horizontal line on the graph and match up the beginning of it and the end of it with the values on the x-axis. The line begins at an x-value of 10 and ends at an x-value of 60; therefore, the domain (x-values) is from 10 to 60.
747 = (9 times x) + 9
Answer:
x=82
Step-by-step explanation:
You start of with subtracting both sides with 9
then you divide both side with 9
Remember the rule that whatever you do to one side, you have to do to the other side. So, how do we find x? The objective when we are simplifying equations like this is to isolate x. We need to make x lonely on one side. So let's try!
747 = 9x + 9
What is the first step to making x lonely? Usually try to use the property of addition or subtraction because it makes things 10x easier. So, using the idea of using addition or subtraction, let's make x lonely by minusing 9 on both sides.
747 = 9x + 9
- 9 - 9 (Remember we have to do the same thing to both sides!)
738 = 9x
Now we have 9 times x = 738. Hm, how do we make x lonely even more? What if divide both sides by 9. We are dividing both sides by 9 because this way, the 9 times will cancel out and disappear. Look:
738 = 9x
÷9 ÷9
82 = x
And there we go, we made x completely lonely and found out x = 82!
WILL GIVE BRAINLIEST!
The slope of a line is 2/5
What is the slope of any line perpendicular to this line? (If an answer is undefined, enter UNDEFINED.)
Step-by-step explanation:
Explanation:
First, we must solve the equation for y to determine the slope: y = 2x + 3/2
By looking at the coefficient in front of x, we know that the slope of this line has a value of 2. To fine the slope of any line perpendicular to this one, we take the negative reciprocal of it:
slope = m , perpendicular slope = – 1/m
slope = 2 , perpendicular slope = – 1/2
Answer:
the slope would be -5/2
Explanation:
the perpendicular slope of a line is the negative reciprocal and the negative reciprocal of 2/5 is -5/2
Which of the following is equal to
5
?
4
А
B
-6).
С
-(0)
D
-()
Answer:
D
Step-by-step explanation:
the negative signs in the numerator and denominator negate each other.
The steps below show the incomplete solution to find the value of m for the equation 5m − 2m + 4 = −1 + 12: Step 1: 5m − 2m + 3 = −1 + 12 Step 2: 5m − 2m + 3 = 11 Step 3: 3m + 3 = 11 Which of these is most likely the next step? (5 points) a 3m = 3 b 3m = 8 c 3m = 16 d 3m = 18
Given:
Consider the equation is:
[tex]5m-2m+3=-1+12[/tex]
Some steps of the solution are given.
To find:
The next step of the solution.
Solution:
Step 1: The given equation is:
[tex]5m-2m+3=-1+12[/tex]
Step 2: Simplifying right hand side.
[tex]5m-2m+3=11[/tex]
Step 3: Simplifying left hand side.
[tex]3m+3=11[/tex]
These steps are already given. So, the next step is:
Step 4: Subtracting 3 from both sides.
[tex]3m=8[/tex]
Therefore, the correct option is (b).
A relation R={(4,3)(5,4)(6,5)}then write its inverse
Answer:
R'={(3,4)(4,5)(5,6)}
Step-by-step explanation:
R={(4,3)(5,4)(6,5)}
R'={(3,4)(4,5)(5,6)}
A rectangle with area
126
square inches has a length that is four less than two times the width. Find the length and the width of the rectangle.
Answer:
Step-by-step explanation
width is 9. length is 14
What is the area of the triangle?
Answer:
289m2
Step-by-step explanation:
The mathematical formula for the area of the triangle is:
base x height / 2
Does the following equation represent a circle? Why or why not? X^2-y^2=4
Answer:
solution given:
yeah it represent circle
as it is in the form:
(x-h)²+(y-k)²=r²
where
centre(h,k)=(0,0)
radius [r]=2 units
– x + 7 = 13
X = ?
What is X
what is the radius of the cylinder
Answer:
5.99
Step-by-step explanation:
brainliest pwease??
The volume of a cylinder can be found with the following equation
[tex]V = r^2h\pi[/tex]
After inputting the known information we get
[tex]980\pi = r^220\pi \\\\[/tex]
Which simplifies to
radius = 7 or (-7)
For proof's sake, we can try the equation again with the known radius
[tex]980\pi = r^220\pi \\980\pi = (7^2)20\pi \\980\pi = (49)20\pi \\980\pi = 980\pi \\[/tex]
And because the radius is being squared, it can either be negative or positive.
help please i’ll really appreciate it
Answer:
704
Step-by-step explanation:
We need to find the volume of pyramid and cube and plus.
volume of pyramid
l-Base length
w-Base width
h-Pyramid height
Vp==lwh /3=8·8·9 /3=192
Volume of pyramid and cube
a-Edge
Va=a³=8³=512
V=Va+Vp=512+192=704
An athlete did one round around a circle of radius 42m.what is the total distance covered by him
Answer:
Again
Step-by-step explanation:
Answer:
42000cm
Step-by-step explanation:
42m======42000cm
help its for math will give brainly Find the area of the hexagon.
Answer:
the area of the hexagon is 68 cm²
Step-by-step explanation:
Let us observe the image a little, we can find the area of the hexagon equals to the area of the large rectangle minus 4 small triangles surrounding the hexagon. The area of the rectangle is 8 × 12 is 96 cm². The area of 1 small triangle is 4 × 3.5 ÷ 2 = 7, there are 4 triangles, so the total area is 4 × 7 = 28. So the hexagon's area is 96 - 28 = 68 cm²
Hope this will help❤️
I will mark Brainliest if u help meee
Answer:
Same y-intercept
Step-by-step explanation:
They have the same y-intercept of 2
look a y intercept is where the function crosses the y axis or when x is 0
In the chart y=2 when x =2 meaning a y intercept of 2
in the graph u can see the line going through the y intercept at (0,2)
So they have the same y-intercept
please help ill give brainliest answer!
Answer:
x=54, acute scalene triangle
Step-by-step explanation:
1st Question:
Triangle SRT has two congruent sides, making it an isosceles triangle.
In isosceles triangles, the two base angles are congruent.
This means that in the question, ∠SRT equals ∠STR, so let's call them both x.
The sum of the interior angles of a triangle add to 180, so
∠RST+∠SRT+∠STR=180
Substitute ∠RST for 72 and ∠SRT+∠STR for x
72+2x=180
2x=108
x=54
2nd Question:
Again, using the sum of the interior angles of a triangle, we can say
42+88+∠DFE=180
∠DFE=50
All the angles in the triangle are less than 90°, meaning they are all acute. Also, none of the sides are labeled as congruent, so it is an acute scalene triangle
someone please answer this fast 35cos(78)
Answer:
−30.02310826357
Step-by-step explanation:
−30.02310826357
answer the question for brainilest and 30 points
HELP THIS IS DUE TODAY
Answer:
7) circumference = 11.78 ft
8) arc NMP = 198° or 27.63 ft
Step-by-step explanation:
7) circumference = πd = (3.14) (3 3/4) = 11.78 ft
8) radius = 8 ft
diameter = 2 x 8 = 16 ft
arc NM + arc QP = 360° - 162° - 162° = 36°
arc NM = arc QP because they are arcs of vertical angles.
arc QP = 18°
arc NMQ = 180°
arc NMP = 180° + 18° = 198°
circumference = πd = (3.14)(16) = 50.24 ft
(198°/360°)(50.24) = 27.63 ft
Explain why triangle ABC is similar to triangle CFE
Answer:
It's exactly the same, except the size
Step-by-step explanation:
Answer:
They are similar because if you look at the length of 2 of the sides that you know
Triangle ABC has side length 1 and 2 or 1:2
CFE has sides length 2 and 4 or 2:4 and 2:4 can also be written as [tex]\frac{2}{4}[/tex] which is a fraction, and fractions can be simplified to 1:2.
So they are similar but just one is bigger then the other.
You and a friend are trying to decide whether going to the movie theater or renting a film to watch at home would cost less. At Theater
Y, the cost of a ticket for young adults ages 10-18 is $7.75. A medium drink costs $2.50 and a small popcorn costs $2.50. Conversely,
it costs $4.50 to rent a movie, $1.50 for a 2 liter of cola, and $2.00 for a bag of microwave popcorn. Which option would cost less and
by how much?
Home by $17.50
Theater Y by $8.00
Theater Y by $17.50
Home by $8.00
Answer:
Home by $17.50
Step-by-step explanation:
Home by 17.50 because when going to the theater you have to consider all the costs of everything you will be purchasing so there will be 2 tickets for yourself and your friend 2 drinks and 2 small popcorns when you add all of these up it will look like this 7.75+7.75+2.50+2.50+2.50+2.50 = 25.50 then I will subtract this from the at home cost so 25.50 - 4.50 - 1.50 - 2.00 = 17.50 So it's cheaper home by 17.50
pleaseeee help I’ll mark you as Brainly if the answers correct with no link just tell me please
Answer:
Step-by-step explanation:
25-2t=0
2t=25
t=25/2=12.5 hrs.
Answer:
Step-by-step explanation:
12 hours and 30 minutes because every hr is 2 degrees so 30 minutes is 1 degree
What is the slope of the line through (–5,2) and (6,7) in the standard (x,y) coordinate plane?
9
9
5
5
-5
-5
5
11
5 over 11
−
5
11
Step-by-step explanation:
[tex]slope = \frac{\triangle \: y}{\triangle \: x} \\ = \frac{(7 - 2)}{(6 - ( - 5))} \\ = \frac{5}{11} \\ slope = (5 ,11)[/tex]
Please help will mark you brainiest
Answer:
c
Step-by-step explanation:
A university law school accepts 7 out of every 12 applicants. If the school accepted 686 students, find how many applications they received.
The school had applicants
Answer:
1176 applications
Step-by-step explanation:
7:12 accepted:applied
686 = 7
686 / 7 = 98
98 x 12 = 1176
What does y equal in the equation ? 6 - 2y = -8
Answer:
7
Step-by-step explanation:
because 6 plus 8 equals 2y then 14 equals 2y the divide each side by 2 so y equals to 7
find cos B 52 b 65 a 39
Answer:
hi
Step-by-step explanation:
i think it is 52/65
hope it helps
have a nice day