The approximate directional derivative of f at point p in the direction of q is 0.
To approximate the directional derivative of f at point p in the direction of q, we can use the formula:
Df(p;q) ≈ ∇f(p) · u
where ∇f(p) represents the gradient of f at point p, and u is the unit vector in the direction of q.
First, let's compute the gradient ∇f(p) at point p:
∇f(p) = (∂f/∂x, ∂f/∂y)
Since f(p) = 15, the function f is constant, and the partial derivatives are both zero:
∂f/∂x = 0
∂f/∂y = 0
Therefore, ∇f(p) = (0, 0).
Next, let's calculate the unit vector u in the direction of q:
u = q - p / ||q - p||
Substituting the given values:
u = (3.03, 3.96) - (3, 4) / ||(3.03, 3.96) - (3, 4)||
Performing the calculations:
u = (0.03, -0.04) / ||(0.03, -0.04)||
To find ||(0.03, -0.04)||, we calculate the Euclidean norm (magnitude) of the vector:
||(0.03, -0.04)|| = sqrt((0.03)^2 + (-0.04)^2) = sqrt(0.0009 + 0.0016) = sqrt(0.0025) = 0.05
Therefore, the unit vector u is:
u = (0.03, -0.04) / 0.05 = (0.6, -0.8)
Finally, we can approximate the directional derivative of f at point p in the direction of q using the formula:
Df(p;q) ≈ ∇f(p) · u
Substituting the values:
Df(p;q) ≈ (0, 0) · (0.6, -0.8) = 0
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A rectangle has a length of 2x+7 and a width of 3x+8. Write and simplify an expression for the perimeter of that rectangle.
A perimeter is a sum of lengths of sides of a lateral.
[tex]2x+7+3x+8=5x+15[/tex].
Dana is buying Grandparents Day gifts at the mall. She spends $13.75 on a teacup for her grandmother. She spends
4
5
of that on a coffee mug for her grandfather. How much money does Dana spend in all?
Answer:
$24.75
Step-by-step explanation:
4/5 of 13.75 = 11
11+13.75= 24.75
Dana spends $24.75 in all.
What is an Equation ?An equation is a mathematical statement that equates two algebraic expression by an equal sign.
The data given in the question is
Dana spends $13.75 on a teacup for her grandmother
She spends 4/5 of that on a coffee mug for her grandfather.
The total amount she spends is given by $x
The equation becomes
x = 13.75 + (4/5) * 13.75
x = $24.75
Therefore she spends $24.75 in all.
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pls pls help me! Trousers bought 1400 dollars with 20% discount. How much is the original price?
Answer:1120 dollars. Δ
Step-by-step explanation:You will pay $1120 for a item with original price of $1400 when discounted 20%. In this example, if you buy an item at $1400 with 20% discount, you will pay 1400 - 280 = 1120 dollars.
#I hope this helps!!!
~Regards~
44014137
The cost of 9 scarves is $56.25. What is the unit price?
Answer:
6.25
Step-by-step explanation:
hhhheeeepppp pleas e e e e e e e e e e e e e e branlist
Answer:
27
Step-by-step explanation:
a+b/2 times h
thats teh formula for the area of a trapezoid so a and b are the top and bottom sides of the trapezoid
so 6 on the bottom and 3 on the top
add those and it equals 9 then divide by 2 gives us 9/2
then the height would be 6
so we multiply 9/2 by 6 giving us 54/2
simplified equals 27 so ur answer would be 27 units squared
Answer:27
Step-by-step explanation:
> Find the area of a circle with diameter 12 yd. Use the value 3.14 and do not round your answer. Be sure to include the correct unit in your answer. 12 yd
[tex]area = \pi {r}^{2} [/tex]
[tex]area = (3.14) {(6)}^{2} [/tex]
[tex]area = (3.14)(36)[/tex]
[tex]area = 113.04 \: yd[/tex]
S
3 ft
Find the area of this figure.
Round your answer to the
nearest hundredth. Use
3.14 to approximate .
4 ft
5 ft
5 ft
A = [ ? ] ft2
Notice that only half of the circle is included in the figure!
9514 1404 393
Answer:
26.13 ft²
Step-by-step explanation:
The total area is twice the area of the right triangles plus half the area of a circle of radius 3 ft.
Semicircle area = (1/2)(πr²)
semicircle area = (1/2)(3.14)(3 ft)² = 14.13 ft²
The area of the two right triangles is ...
total triangular area = (3 ft)(4 ft) = 12 ft²
Then the area of the figure is ...
figure area = semicircle area + total triangular area
= 14.13 ft² + 12 ft² = 26.13 ft²
Answer: 26.13
Step-by-step explanation:
the ratio of red marbles to blue marbles in a bag is 3:4. which of the following is a possible total number of marbles is it 21, 30, 32, or 40.
Answer:
21
Step-by-step explanation:
so if the ratio is 3:4
then we can also write the ratio as 3x:4x
where the total is 7x marbles and we see we have to chose the one that is divisible by 7 which is 21.
if my answer helped please mark as brainliest.
10squared correct to 6 decimal places
Answer:
3.162278
Step-by-step explanation:
√10= 3.16227766
then find the millionths place which is 3.16227766
then you round that number based on the number to the right of it which is a 6 so you round it up
so the answer is 3.162278
Divide. Express your answer in simplest form.
11/12 ÷ 3/4=
Answer:
11/9
hope this helped :)
Step-by-step explanation:
Answer:
Step-by-step explanation:
11 / 12 = 0,91 and a periodic 6
3 / 4 = 0,75
11 / 12 = 3 / 4 = 0,916 ÷ 0,75
Please helpppp i just want to know if i sm doing it right
9514 1404 393
Answer:
b) -9.8t +18
Step-by-step explanation:
b) The instantaneous rate of change is the derivative of the height function. The power rule is separately applied to each term, and the results added.
power rule: d/dx(x^n) = nx^(n-1)
Then the derivative is ...
dh/dt = 2(-4.9t^1) +18(1 ·t^0)
dh/dt = -9.8t +18
__
If you haven't been introduced to derivatives as such, then you find the instantaneous rate of change by finding the average rate of change over a vanishing interval.
[tex]\dfrac{dh}{dt}=\displaystyle\lim\limits_{h\to 0}{ \dfrac{h(t+h)-h(t)}{h}}\\\\\dfrac{dh}{dt}=\lim\limits_{h\to 0}\dfrac{(-4.9(t+h)^2+18(t+h)+23)-(-4.9t^2+18t+23)}{h}\\\\\dfrac{dh}{dt}=\lim\limits_{h\to 0}\dfrac{-4.9(2th+h^2)+18h}{h}=\lim\limits_{h\to 0}{(-9.8t +18 -4.9h)}\\\\ \boxed{\dfrac{dh}{dt}=-9.8t +18}[/tex]
A country trying to decide whether to join the United Nations must determine whether it is willing to: O A. give up its own national laws in favor of international laws set by the UN. O B. occasionally go against its own interests in favor of international priorities. O C. supply a large number of military forces to the UN standing army. O D. leave any regional intergovernmental organizations it has already joined.
Answer:
to guarantee equality for all
Step-by-step explanation:
The league of nations was created to prevent another global war
10 is 70% of what number? If necessary, round to the nearest tenth.
Answer:
The required answer is 7.
Step-by-step explanation:
=10*70/100
=7
Select whether each equation has no solution, one solution, or infinitely many solutions.( I need help)
Answer:
1. one solution
2. one solution
3. no solution
Step-by-step explanation:
1. x = 0
2. x = -¾
3. 0
Answer:
1.one solution
2.one solution
3. no solution
4. infinitly solution
Step-by-step explanation:
(-3, -14) and (0, -9)
Answer: -26
Step-by-step explanation: hope this helps :)
Whats 4x+2=2(x+6) ?
Just want to see your answers
Answer:
x = 5
Step-by-step explanation:
4x + 2 = 2(x + 6)
4x + 2 = 2x + 12 (after you distribute the 2)
add and subtract like terms
4x - 2x = 12 - 2
2x = 10
x = 5
you can double check by substituting the x with 5 in the equation
4 (5) + 2 = 2(5 + 6)
20 + 2 = 2(11)
22 = 22
plz solve it and help me for it
Given:
Base angle of an isosceles triangle is 15 degrees more than its vertical angle.
To find:
The measure of each angle of the triangle.
Solution:
Let x be the vertical angle. Then,
One base angle = x+15 degrees
We know that base angles of an isosceles triangle are equal.
Another base angle = x+15 degrees
Now, the sum of all angles of a triangle is 180 degrees by the angle sum property.
[tex]x^\circ+(x+15)^\circ+(x+15)^\circ=180^\circ[/tex] (Angle sum property)
[tex](3x+30)^\circ=180^\circ[/tex]
[tex]3x+30=180[/tex]
[tex]3x=180-30[/tex]
[tex]3x=150[/tex]
Divide both sides by 3.
[tex]x=\dfrac{150}{3}[/tex]
[tex]x=50[/tex]
The measure of base angles is
[tex](x+15)^\circ=(50+15)^\circ[/tex]
[tex](x+15)^\circ=65^\circ[/tex]
Therefore, the measure of angles are 50°, 65° and 65°.
an anchor line for a tower needs to be replaced the tower is 96ft tall. the anchor line is 105ft long. how far from the tower can it be placed, to the from the nearest tenth
a). 142.3ft
b). 42.5ft
c). 9ft
d). 60 ft
Answer: 42.5ft
Step-by-step explanation: The wording in your question is a little unclear. I assume that you are looking for how far the anchor line is from the base of the tower.
If so, you can use the Pythagorean Theorem.
a^2 + b^ = c^2
96^ + b^2 = 105^2
Solve for b, gives you about 42.53ft round up and it is 42.5 ft :)
Happy to help
[tex]18 \div 36[/tex]
Answer:
0.5
Step-by-step explanation:
help, please I don't understand
Answer:
The second top one. if they have ANY repeating y values its not a function
Step-by-step explanation:
Which ordered pair is on the graph of the function? O (-1,2) O (6,-3) O (-2,-4) O (-6, 4)
Answer:
(6, -3)
Step-by-step explanation:
PLEASE HELP RN
If cot theta = 8/7, which equation represents cotangent theta? cotangent theta = StartFraction StartRoot 15 EndRoot Over 8 EndFraction cotangent theta = StartFraction StartRoot 15 EndRoot Over 7 EndFraction cotangent theta = StartFraction 7 StartRoot 15 EndRoot Over 15 EndFraction cotangent theta = StartFraction 8 StartRoot 15 EndRoot Over 15 EndFraction
Answer:
The second option, [tex]\frac{\sqrt{15}}{7}[/tex]
Step-by-step explanation:
Edge '21
The equation for cot θ is √15/7. Therefore, option B is the correct answer.
Given that, cosec θ=8/7.
We need to find the ratio of cot θ.
What is the ratio of cot θ?The ratio of cot θ is cot θ=Adjacent/Opposite.
As we know, cosec θ=Hypotenuse/Opposite.
So, 7²+x²=8²
⇒x=√15
Now, cot θ=√15/7.
The value of cot θ is √15/7. Therefore, option B is the correct answer.
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En la tabla 1.8 se presentan los puntos de ebullición aproximados de algunos elementos de la tabla periodica flúor -180 hidrogeno -253 argón -186 helio -269 nitrógeno -196 neón -246 ¿Cuál es el elemento químico con el mayor punto de ebullición?¿ y con el menor?
Answer:
Lowest boiling point = helium.
Highest boiling point = fluorine
Step-by-step explanation:
Given :
fluorine -180
hydrogen -253
argon -186
helium -269
nitrogen -196
neon -246
Arranging the boxing points of each chemical element on a number line, the least which will be located to the leftmost part is Helium with a boiling point of - 269 ; while the highest will be fluorine which is - 186°C
1 point
Which of the following lists is ordered correctly from greatest to least?
A. 1 lb, 2 lbs., 18 oz., 49oz.
B. 2 lbs., 49 oz., 18 oz., 1 lb.
C. 49 oz., 2 lbs., 18 oz., 1 lb.
D. 2 lbs., 49 oz., 1 lb., 18 oz.
Answer: C
Step-by-step explanation:
1 lb = 16 oz
2 lb = 32 oz
18 oz = 18 oz
49 oz = 49 oz
I am not a professional, I am simply using prior knowledge!
Note- It would mean the world to me if you could mark me brainliest!
solve for x for the first and second question.
Answer:
Step-by-step explanation:
I assume the figures are parallelograms, then
1). KL = MJ and
12x - 22 = 7x - 2
12x - 7x = 22 - 2
5x = 20
x = 4
2). m∠RQT + m∠QTS = 180°
(The picture is not clear and I might be wrong about coefficients by x for ∠RQT and ∠QTS)
(3x + 5)° + (9x - 17)° = 180°
12x - 12 = 180
12x = 192
x = 16
WILL GIVE BRAINLIEST
Answer:
Step-by-step explanation:
MN/sin72=10/sin18
MN=30.8
Mark scored 138 points in 6 games. How many points did he score per game?
Answer:
23 Points
Explanation:
The answer you are looking for is 23 points per game.
To find this answer, you simply divide 138 by 6.
I hope this helps!
Complete this statement using >, <, or =
0.248_____0.259
Answer:
Here the most appropriate answer is '>'
Thus it will be 0.248 > 0.259
Felix said quadrilateral ABCD is a parallelogram because
BE = DE. What was his error?
Answer:
There is no angle E in the quadilateral presented in the question. Also, the angles he used are not on opposite side.
Step-by-step explanation:
To classify a quadrilateral is a parallelogram, a quadrilateral with both pairs of opposite sides must be parallel or congruent, that is in a quadrilateral ABCD, angle AB must equal CD and angle AD must equal BC.
Hence, when Felix said quadrilateral ABCD is a parallelogram because of BE = DE. His error was that "there is no angle E in the quadrilateral presented in the question and the angle he used are not on opposite side"
If AD=8 and BD=4, what is the length of DC⎯⎯⎯⎯⎯⎯?
The figure shows right triangle C A B with altitude A D to hypotenuse B C.
DC = 4
DC = 20
DC = 8
DC = 16
Answer:
the answer should be 16!