please help :) thanks

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.

Answer:

hi

Step-by-step explanation:

i think it is 52/65

hope it helps

have a nice day

Answer:

289m2

Step-by-step explanation:

The mathematical formula  for the area of the triangle is:

base x height / 2

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

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

Answer:

C.14ײ+5

Step-by-step explanation:

Hope It Help

Brainliest please

Answer:

2 quarters, one nickel and two dimes

Step-by-step explanation:

2 quarters = 25 cents + 25 cents = 50 cents

Nickel is 5 cents

Two dimes is 10+10 = 20

50+20+5=75

Answer:

Step-by-step explanation:

It is expected the spinner to land on Red 1/5 times.

If the spinner is spun 40 times, then it should land on Red:

And it should not land on red:

Correct choice is D

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.

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

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).

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.

Answer:

Again

Step-by-step explanation:

Answer:

42000cm

Step-by-step explanation:

42m======42000cm

Answer:

Jacob sold 25 bars - chocolates and 15 peanut butter.

Step-by-step explanation:

Jacob sold 40 candy bars.

Let the bars - chocolate be x and peanut butter be y and made $65.

Now,

x + y = 40 ...(1)

2x + y = 65 ...(2)

Now, From equation (1) we get,

x + y = 40

x = 40 - y

Now, put the value of x = 40 - y in equation (2) we get,

2x + y = 65

2(40 - y) + y = 65

80 - 2y + y = 65

y = 80 - 65

y = 15

Now, put the value of y in equation (1)

x + y = 40

x + 15 = 40

x = 40 - 15

x = 25

The bars - chocolate = x = 25 and

peanut butter = y = 15

Thus, Jacob sold 25 bars - chocolates and 15 peanut butter.

-TheUnknownScientist

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.

Step-by-step explanation:

15) 13x = 130 x = 10

16) 16x+2+43x+1 = 180 59 x = 177 x = 3

17) 29x+3+31x-3 = 180 60x = 180 x = 3

18) 16x -5 + -5 + 22x = 180 38x = 190 x = 5

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

Answer:

They have atleast two or one left

Answer:

x = .06418

Step-by-step explanation:

2 + (9.2)−8x = 2.32

(9.2)−8x = 2.32 − 2

log (9.2)−8x = log .32

−8x log 9.2 = log .32

−8x log 9.2

−8 log 9.2

=

log .32

−8 log 9.2

x = .06418

Answer:

What website is this picture on. I can not see the picture.

Step-by-step explanation:

Answer:

−30.02310826357

Step-by-step explanation:

−30.02310826357

Answer:

the statement is a true statement

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

Answer:

Step-by-step explanation:

3 a) 6

3 b) 12

3 c) 12

4 a) 4/5

4 b) 10/9

4 c) 17/15

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!

Answer:

x=1/2,-5/2

Step-by-step explanation:

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

Answer:

4/3 is ur answer which is equal to 6.92820323028

which i B's side length

Step-by-step explanation: