Answer:
Remember that the gradient is equivalent o the derivative evaluated in one point.
And remember that if we have a function like:
f(x) a*x^n
The derivative is:
f'(x) = n*a*x^(n - 1)
Then knowing this, let's start:
a) y = x^2
the derivative is:
y' = 2*x
And we want to evaluate this in the point (3, 9), then we just need to replace x by 3.
y'(3) = 2*3 = 6
The gradient of y = x^2 at (3, 9) is 6.
b) y = -4*x^3
The derivative is:
y' = 3*(-4*x^2) = -12*x^2
And we want to evaluate this on (1, -4), then we need to replace x by 1.
y'(1) = -12*1^2 = -12
The gradient of y = -4*x^3 at (1, -4) is -12.
c) y = 2*x^4
The derivative is:
y' = 4*2*(x^3) = 8*x^3
And we want to evaluate this on (-1, 2), then we need to replace x by -1.
y'(-1) = 8*(-1)^3 = -8
The gradient of y = 2*x^4 at the point (-1, 2) is -8
d) y = 6*x
The derivative is:
y' = 6
We can see that here we do not have any dependence on x, so the gradient will be the same for all values of x, this means that the gradient at the point (2, 12) is 6.
A circle has radius 5 units and the equations of its two diameter are 2x-y=5 and x-3y+5=0.find the equations of the circle and show that it passes through the origin.
Answer:
is a required equation. but I forgot to show that it passes through the origin.sorry for that.we had done in previous grade.
What operation would you use to solve: x+7=10
Answer:
x=3
Step-by-step explanation:
x+7=10
x+7-7=10-7
x=3
Answer:
You would use subtraction
Step-by-step explanation:
To get 7 away, you need to subtract it
To find the quotient of
8
1
3, multiply 8 by
-100
- اند
O
3.
ОО
8.
Answer: 3 hope this helped (:
Carlo places 6 apple slices on one side of a pan balance and 12 orange slices on the other side. Each side weighs 48 grams.
What is the weight of one apple slice? One orange slice?
Answer:
apple slice = 8 grams
orange slide = 4 grams
Step-by-step explanation:
48/6 will give you the weight of each apple slice
48/12 will give you the weight of each orange slice
Pls help me I’m stuck
Step-by-step explanation:
8 gallons m miles
=
6 gallons 180 miles
or
8-m
6-180
If £29 =500 rubles how many £ are in 1,260 give your answer to 2dp
Based on the information given, it should be noted that the value of 1260 will therefore be £73.09.
Solving equationsFrom the information given, it was stated that £29 =500. Therefore, the equation to solve that of 1260 will go thus:
£29 =500
£1 = 500/29
£1 = 17.24
Therefore, 1260 will be:
= 1260/17.24
= £73.09
Learn more about equations on:
https://brainly.com/question/13763238
the number of employees for a certain company had been decreasing each year by 8%. If the company currently has 860 employees and this rate continues, fund the number of employees in 19 years.
Answer:
approximately 684 employees
Step-by-step explanation:
So this is an exponential equation since there is a dividing decrease, not just subtracting. The standard equation is,
[tex]y = a(b)^{x} [/tex]. [tex]a[/tex] is initial value (860 employees) and [tex]b[/tex] is the change [tex]-8%[/tex] or [tex]0.92[/tex]. The [tex]x[/tex] would be the period of time, [tex]19[/tex]. This equation would be [tex]y = 860(0.92)^{19} [/tex].
After solving, the equation would become the following: [tex]y = 860(0.92)^{19} = 176.387242442≈176[/tex]. After subracting the number of lost employees from orginal employees ([tex]860-176=684[/tex]), we see that the company will have approximately 684 employees left after 19 years.
What is the equation in slope-intercept form of the line that crosses the y-axis at 6 and is perpendicular to the line represented by y= (-4/9)x+5?
Answer:
y=(9/4)x+6
Step-by-step explanation:
If it crosses at 6 then it will be +6. A perpendicular line has a slope that is the opposite reciprocal of your current slope.
Darrell earns $75 per week walking dogs and cutting grass. He carns $10 more cutting grass than walking dogs. How much does Darrell
earn cutting grass?
PLEASE AM TIMED STEP BY STEP
Answer:
Here you go :)
Step-by-step explanation:
⚠️⚠️⚠️⚠️HELLPP⚠️⚠️⚠️
Use completing the square to solve for x in the equation (x-12)(x+4)-
O x= -1 or 15
O x= 1 or 7
x=4+ JAT
O x=4573
Answer:
x = 4 ± [tex]\sqrt{73}[/tex]
Step-by-step explanation:
d it is the answer all the way at the bottom
Seven people are going to share an 84-ounce bottle of soda. How many ounces will each person get to drink? Choose the correct equation and answer for this situation. I THINK THIS IS ABOUT RASIOS SO PLS HELP
Answer:
7 ÷ 84 = 84 = 12 ounces
_
7
Step-by-step explanation:
The equation will be 7x = 84. Then the number of ounces will each person get to drink will be 12.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Seven people are going to share an 84-ounce bottle of soda.
Let x be the number of the ounces bottle of soda of each person.
Then we have the equation will be
7x = 84
x = 84 / 7
x = 12
Then the number of ounces will each person get to drink will be 12.
More about the linear system link is given below.
https://brainly.com/question/20379472
#SPJ2
Which is the graph of y= 3/4x - 3?
Someone plz help me I will give brainliest
Answer:
275 non spectators
Step-by-step explanation:
1. Subtract
42,500 - 31,750 - 10,475 =
275
2. Get answer
275 non-spectators
In ΔIJK, k = 59 cm, i = 80 cm and ∠J=106°. Find the length of j, to the nearest centimeter.
Answer:
112 cm.
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. The types of triangles are scalene triangle, equilateral triangle, right angled triangle and obtuse triangle.
Cosine rule states that given a triangle with sides a, b, c and their corresponding angles opposite to the sides as A, B, C. Then:
[tex]a^2=b^2+c^2-2bc*cos(A)[/tex]
In triangle IJK:
We can find the length of j using cosine rule:
[tex]j^2=k^2+i^2-2ik*cos(J)\\\\substituting:\\\\j^2=59^2+80^2-2(80)(59)cos(106)\\\\j^2=3481+6400-(-2602)\\\\j^2=3481+6400+2602\\\\j^2=12483\\\\j=\sqrt{12483} \\\\j=112\ cm[/tex]
Could someone do this real quick
Answer: x= 5/7 or x= 0.714285
Step-by-step explanation:
The solution to the system of equations is (-7, 11). true or false
Which expression is equivalent to X
Step-by-step explanation:
[tex]{( {x}^{ \frac{4}{3} } {x}^{ \frac{2}{3} })}^{ \frac{1}{3} } = {( {x}^{ \frac{4 + 2}{3} } ) }^{ \frac{1}{3} } = {( {x}^{2} ) }^{ \frac{1}{3} } \\ = {x}^{ \frac{2}{3} } [/tex]
Paula bought 8 pairs of socks. She paid $104. Two pairs of socks cost the same amount. How much did each of the others pairs of socks cost?
Answer:
The other socks cost 9$.
Step-by-step explanation:
Please help me asap!!
Answer:
the second one ( - 3, -6)
Step-by-step explanation:
I used the method of substitution
Answer:
(-3, -6)
Step-by-step explanation:
A machine can make 14,400 screws in 8 hours. A second machine can make twice as many screws. What is the constant of proportionality (k) between the number of screws (y) and the number of hours (x) for the second machine?
Answer:
1800 screws per hour
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLIEST! Solve |3x – 1| = |x+1| by graphing.
it wold be (0,1) and (2,3)
Answer:
Step-by-step explanation:
greta has piece of cloth that is 9 yards long she cut it into pieces that are each 1\3 how many pieces does greta have now
Answer:
27
Step-by-step explanation:
9 divided by 1/3 is 27
Can someone could explain the part of simplifying rational expressions where it is x is not equal to a number. I've had a hard time understanding how to get that answer. The picture is an example in my notes.
Answer:
yeah it is bcoz if x is -1 then x+1 will be
-1+1 which is 0 and ur whole equation will say
now thats a lot of damage
Find the product of the term 3ab
-2x + y = 3
what does x equal
Answer:
Step-by-step explanation:
-2x+y=3
-2x=3-y
x=[tex]\frac{3-y}{-2}[/tex]
Please help! I am pretty sure that is correct, however looking for confirmation. Thanks you
Answer:
yes you did right answer
What’s the X coordinate of the vertex
Step-by-step explanation:
f(x) = (x + 3)(x - 5)
In a Quadratic curve, the x-coordinate of the vertex is equidistant to the x-intercepts. (If they exist)
In f(x), our x-intercept are x = -3 and x = 5.
=> (-3 + 5)/2 = 1.
Hence the x-value of the vertex is 1.
3(2x + 1) = 6(5x - 4)
Answer:
X= 9 over 8 or 9/8
Step-by-step explanation:
hopefully this helps
Answer:
9/8 or 1.125 or 1 1/8
Step-by-step explanation:
How do I find the y-intercept of a graph?
Answer:
the y intercept on a graph is the line that goes up and down
Step-by-step explanation:
Step-by-step explanation:
Every point on the y-axis has 0 as its x-coordinate. The y-intercept is the point of intersection of the graph and the y-axis.
To find the y-intercept, let x = 0 in the equation of the graph and solve for y. The value of y is the y-intercept.
For example, what is the y-intercept of
2x + 3y = 6
Let x = 0.
2(0) + 3y = 6
Solve for y.
3y = 6
y = 2
The y-intercept is 2.
