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.
Help me please! I need to get this done to go outside :(
Answer:
98ft.
Step-by-step explanation:
Question is asking for the total square feet of laminate wood to cover the entire retail store. Add all the sides together to get your answer.
I can really use this help please
Answer:
1. 60 2. 120
Step-by-step explanation:
plz give brailiest
Answer:
1. 60
2. 120
Step-by-step explanation:
the opposite angle is 60
180 - 60 = 120
find the standard deviation of: 141, 116, 117, 135, 126, 121
Answer:
Please see photos for simplified result
Step-by-step explanation:
please answer fast! calculate the value of x. C is center of the circle. (attached image)
Si tuvieras que formar un cuadrado de 196 baldosas cuadradas iguales, ¿Cuantas deberías poner en cada fila?
Answer:
Respuesta. entonces como respuesta deben colocarse 14 filas por 14 columnas de baldosas para que quede un cuadrado. SALUDOS!
(X-2/3)^2+y^2 =36
What is its center?
What is its radius
Answer:
0(2/3; 0)
Step-by-step explanation:
Is x+y is an algebraic expression?
1. Yes
2. No
3. Cannot be identified
4. None of these
I will mark the brainiest for the correct answer!!
simplify the expression below. (x^25)^-5/(x^-3)^48
pls pls help for math
Answer and Step-by-step explanation:
The answer would be D. 82%.
All we need to do is add together the amount that can swim.
We do this because all of the numbers added together equals 1, so the parts that are split off represent the percentages (in decimal form) of the total amount of people.
0.34 + 0.48 = 0.82.
Multiply by 100 and we get 82%.
#teamtrees #PAW (Plant And Water)
Please help and also include an explanation so I know how you got the answer.
Answer:
x = 15
Step-by-step explanation:
We know that 4x° + 8x° make a straight angle of 180°.
4x° + 8x° = 180°
12x° = 180°
12x = 180
x = 180/12 = 15
Answer:
x=15
Step-by-step explanation:
I gotcha bro
The line C is straight and straight lines are 180°
so 180° = 4x + 8x = 12x ----> 180 = 12x ---> then divide both sides by 12
180/12 = 15 and 12x/12 = x
so 15 = x or x = 15
How many ounces are in 1 pint?
Huilan's age is two times Thomas's age. The sum of their ages is 21 . What is Thomas's age?
Answer:
Thomas age is 7
Step-by-step explanation:
X + 2x =21
3x=21
x=7
What is the ratio for sin A?
3/4
3/5
4/5
4/3
Place the numbers 40 and 100 into the proportion. (Whole)(percents) ----------- (Part) what goes where?
Answer:
Step-by-step explanation:
Hard to tell how the question should read.
40/100 = 40%
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Proportion means writing in fraction form as numerator and denominator.
40/100 = 40%
The proportion of 40 and 100 is 40%.
What is a percentage?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have.
40 and 100.
Proportion means writing in fraction form as numerator and denominator.
So,
If we write 40/100 we get 40%.
This means 40 out of 100.
Thus,
40/100 = 40%
The proportion of 40 and 100 is 40%.
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ5
A gift box has dimensions of: 8 1 2 inches, 5 1 2 inches, and 2 1 2 inches, respectively. how many cubes with side lengths of 1 2 inches would be needed to fill the gift box?
Number of 1/2-inch cubes length-wise = 8 1/2 ÷ 1/2 = 17
Number of 1/2-inch cubes width-wise = 5 1/2 ÷ 1/2 = 11
Number of 1/2-inch cubes height-wise = 2 1/2 ÷ 1/2 = 5
Number of 1/2-inch cubes = 17 x 11 x 5 = 935
------------------------------------------------------------
Answer: 935 1/2-inch cubes are needed.
------------------------------------------------------------
Find the length of the missing side.
a= in
b= in
c= in
80
Step-by-step explanation:
you take the square root of 82 squared minus 18 squared
¿Como resuelvo esta equación? Necesito ayuda.
2x·(1-x)= x-6
Answer:
x=-3/2 x=2
Step-by-step explanation:
2x(1-x)=x-6
2x-2x^2=x-6
subtract x from both sides
add 6 to both sides
x-2x^2+6=0
reorganize
-2x^2+x+6=0
factor
2x+3=0
x-2=0
solve both
2x+3=0
2x=-3
x=-3/2
now the other one
x-2=0
x=2
Sorry, I don't speak spanish.
CONGRUENT FIGURES
EACH SET OF SHAPES ARE CONGRUENT. FOR CACH SIDE OR
ANGLE LISTED BELOW CACH BLANK. WRITE THE
CORRESPONDING SIDE OR ANGLE TO CREATE YOUR CODE. Plz for the love of God help me this is so so over due
Answer:
p-o
u-t
e-l
s-d
r-w
b-z
a-n
Step-by-step explanation:
He dimensions are tripled. The new surface area would be times larger than the original surface area.
Answer:
The new surface area would be 9 times larger than the original surface area.
Step-by-step explanation:
Here we do not know what was the original shape, but we will see that it does not matter.
Let's start with a square of side length L.
The original area of this square will be:
A = L^2
Now if each dimension is tripled, then all the sides of the square now will be equal to 3*L
Then the new area of the square is:
A' = (3*L)^2 = (3*L)*(3*L) = 9*L^2 = 9*A
So the new surface area is 9 times the original one.
Now, if the figure was a circle instead of a square?
For a circle of radius R, the area is:
A = pi*R^2
where pi = 3.14
Now if the dimensions of the circle are tripled, the new radius will be 3*R
Then the new area of the circle is:
A' = pi*(3*R)^2 = pi*9*R^2 = 9*(pi*R^2) = 9*A
Again, the new area is 9 times the original one.
If the figure is a triangle?
We know that for a triangle of base B and height H, the area is:
A = B*H/2
If we triple each measure, we will have a base 3*B and a height 3*H
Then the new area is:
A' = (3*B)*(3*H)/2 = (3*3)*(B*H/2) = 9*(B*H/2) = 9*A
Again, the new area is 9 times the original area.
So we can conclude that for any shape, the new area will be 9 times the original area.
CAN SOMEONE PLZ HELP ME?? PLZ DO YOU KNOW ABOUT Coordinate Planes??!! plzzzzzz help
Answer:
Hey!
The X Value is 3, while the Y value is 6. In other words, it looks like this:
3, 6
Step-by-step explanation:
Hey!
The X Value is 3, while the Y value is 6. In other words, it looks like this:
3, 6
Answer:
(0.5,1.5)
Step-by-step explanation:
What is the area of triangle ABC in the simplest terms?
19. Find the value of:
4/3tan^2 30° + Sin^2 60° – 3Cos^2 30°+ 3tan^2. 60° - 2tan^2 45°
9514 1404 393
Answer:
107/18
Step-by-step explanation:
Your calculator and/or knowledge of trig function values can help you evaluate this.
= 4/3(1/3) +3/4 -3(3/4) +3(3) -2(1)
= 4/9 +3/4 -9/4 +9 -2
= 107/18
___
tan(30°) = 1/√3
tan(45°) = 1
tan(60°) = √3
sin(60°) = cos(30°) = √3/2
a.
8. Sarah has a garden that is 4 feet by 3 feet. What is the perimeter of Sarah's garden?
16 feet
b. 7 feet
c. 14 feet
d. 9 feet
Find a formula for the nth term
of the arithmetic sequence.
First term 2.5
Common difference -0.2
An = [? ]n +
Ali, Ben and Cathy share an amount of money in the ratio 6 : 9 : 10 What fraction of the money does Ben get?
there are 6+9+10=25 equal parts, so Ben has 9/25 of the total.
Gary’s soccer team plays 12 games in a season. Each game is 45 minutes long. His older brother, Hector, plays the same number of games, but each of his games lasts twice as long. How many minutes does Hector’s team play each season? Write and solve equations.
Answer:
1080 minutes
Step-by-step explanation:
12x45: garys team
45x2=90 : hector's team
12x90=1080
choose the bast description for the real number 34/3
Step-by-step Answer:
C and D are both correct as fractions. Numbers are NOT irrational because they are a fraction. And concluding decimals are both rational numbers. By using a known formula you can convert reaptedly decimals to a fraction.
A bar of soap is shaped like a right rectangular prism. The base is a rectangle that is 12 centimeters by 2 centimeters. The height is 3 centimeters. A second bar of soap is shaped like a square pyramid with the same volume as the first bar of soap. Each side of the base of the pyramid is 6 centimeters in length. What is the height of the pyramid?
Answer:
6 cm
Step-by-step explanation:
Volume of a Prism = base area x height =
Base area = length x width = 12 x 2 = 24 cm^2
Volume = 24 x 3 = 72 cm^3
Volume of a pyramid = 1/3( l x w x h)
72 = 1/3( 6x6 x h)
Multiply both sides of the equation by 3
216 = 36 x h
divide both sides by 36
h = 6
A cylindrical pipe is 25 ft long and has a volume of 900ft3 find it's approximate diameter to the nearest hundredth of a foot
Answer:
Diameter of the pipe ≈ 6.77 ft
Step-by-step explanation:
Volume of a cylinder = πr²h
Here, r = Radius of the cylindrical pipe
h = Length of the pipe
Volume of the pipe = 900 ft³
Length of the pipe = 25 ft
By substituting the given values in the formula,
900 = π(r)²(25)
r² = [tex]\frac{900}{25\pi}[/tex]
r = √11.459
r = 3.385
Diameter = 2(radius)
= 2(3.385)
= 6.77 ft
The diameter of the cylinderi is 6.77ft
Volume of a cylinderthe formula for calculating thevolume of a cylinder is given as
V = pi d²/4 × h
Given the following
V = 900ft³
h = 25ft
Substitute the given parameters
900 = 3.14 × d²/4 × 25
900 = 19.625d²
d² = 45.859
d = 6.77ft
Hence the diameter of the cylinderi is 6.77ft
learn more on cylinder here: https://brainly.com/question/23935577
One diagonal of the kite is three times as long as the other diagonal. If the area of the kite is 48 square meters, what is the length of each diagonal?
Given:
One diagonal of the kite is three times as long as the other diagonal.
The area of the kite is 48 square meters.
To find:
The length of each diagonal.
Solution:
We know that, the area of the kite is:
[tex]A=\dfrac{d_1d_2}{2}[/tex]
Where, [tex]d_1,d_2[/tex] are two diagonals of a kite.
It is given that, one diagonal of the kite is three times as long as the other diagonal.
Let [tex]d_1=3d_2[/tex]. Then the area of the kite is:
[tex]A=\dfrac{3d_2d_2}{2}[/tex]
[tex]A=\dfrac{3d_2^2}{2}[/tex]
The area of the kite is 48 square meters.
[tex]\dfrac{3d_2^2}{2}=48[/tex]
[tex]3d_2^2=2(48)[/tex]
[tex]d_2^2=\dfrac{96}{3}[/tex]
[tex]d_2^2=32[/tex]
Taking square root on both sides, we get
[tex]d_2=\sqrt{32}[/tex] [It is only positive because side length cannot be negative]
[tex]d_2=4\sqrt{2}[/tex]
Now,
[tex]d_1=3d_2[/tex]
[tex]d_1=3(4\sqrt{2})[/tex]
[tex]d_1=12\sqrt{2}[/tex]
Therefore, the diagonals of the kite are [tex]4\sqrt{2}[/tex] units and [tex]12\sqrt{2}[/tex] units.