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Please assist with these geometry problems

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Answer:

The maximum rate of change of the given function is equal to 3√2.

The direction at which the vector points is given by the unit vector [tex]\displaystyle \frac{\sqrt{2}}{2} \hat{\i} + \frac{\sqrt{2}}{2} \hat{\j}[/tex].

General Formulas and Concepts:
Pre-Calculus

Vectors

Calculus

Differentiation

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]

Derivative Rule [Basic Power Rule]:

Multivariable Calculus

Partial Derivatives

Gradient:
[tex]\displaystyle \nabla f(x, y, z) = \frac{\partial f}{\partial x} \hat{\i} + \frac{\partial f}{\partial y} \hat{\j} + \frac{\partial f}{\partial z} \hat{\text{k}}[/tex]

Gradient Property [Addition/Subtraction]:
[tex]\displaystyle \nabla \big[ f(x) + g(x) \big] = \nabla f(x) + \nabla g(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle f(x, y) = x^2y^2 + xy - 10[/tex]

[tex]\displaystyle \text{Point} \ (1, 1)[/tex]

Step 2: Find Maximum Rate of Change

∴ the maximum rate of change of the given function f(x, y) is equal to 3√2.

Step 3: Find Direction

∴ we have found the direction of the gradient.

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Topic: Multivariable Calculus

Unit: Directional Derivatives

Answer:

15 ft

Step-by-step explanation:

I'm not sure but I think u add them together to get ur answer

hope it helps

Answer: 21

Step-by-step explanation:

1. Simplify the quadratic equation into its standard form

Formula : ax^2+bx+c=0

Subtract  from both sides:

x^2-10x+25=51

x^2-10x+25-51=0

x^2-10x-26=0

Use the standard form,  ax^2+bx+c=0, to find the coefficients of our equation.

x^2-10x-26=0

a=1

b=-10

c=-26

The quadratic formula gives us the roots for ax^2+bx+c=0, in which a, b and c are numbers (or coefficients), as follows :

x=(-b±sqrt(b^2-4ac))/(2a)

to get the result :

x=(10±sqrt(204))/2

Simplify 204  by finding its prime factors:

The prime factorization of 204 is 2^2*3*17

x_2=-2.141

Answer:

x = 5 ± √51

Step-by-step explanation:

x² - 10x + 25 = 51

x² - 10x + 25 - 51 = 51 - 51

x² - 10x - 26 = 0

Factors with a product of -26 and a sum of -10:

NONE! Solve by completing the square (see attachment)

Step 1: Rearrange

x² - 10x + 25 = 51

x² - 10x = 26

Step 2: Add (b/2)² to both sides

x² - 10x + (-10/2)² = 26 + (-10/2)²

x² - 10x + 25 = 51

Step 3: Factor and solve

(x - 5)² = 51

x - 5 = √51

x = 5 ± √51

Answer:

500,000 + 4,000 + 40 + 7

Step-by-step explanation:

<1 = 180°-102° = 78° (the extended angle is 180°)

<2 = <5 = 58°

<3 = 180° - 78° - 58° = 44° (the sum of the angles inside of a triangle is 180°)

<4 = 180° - 44° - 58° = 78° = <1 (the extended angle is 180°)

Answer:

23/10

Step-by-step explanation:

and put the denominator as it is

[tex]\boxed{\rm{pls\:refer\:to\:explanation}}[/tex]

Step-by-step explanation:

First multiply the whole part (2) times the denominator (10) :

20

Add the numerator (3) :

23

That's the numerator of our improper fraction .

The denominator stays the same .

[tex]\boxed{\frac{23}{10}}[/tex]

[tex]\footnotesize\text{hope\:helpful}[/tex]

Answer:

A=LxW

Step-by-step explanation:

cut the shape into easier pieces then go to one piece and x the W with the L for example 4x5 then x them and youll get your area like this A=LxW = 20=4x5 like that then do the same for the other pieces then once you x them all add them and youll get the whole area for your shape

hoped it helped :)

Answer:

x=36

Divide the corresponding side (16) by 4/7

Answer:

x=36

Divide the corresponding side (16) by 4/7

Step-by-step explanation:

x=16×9/4=36

Your median is 5 because that is the number that is mentioned the most.

A median is a number that i said the most.

And in the pic your median is 7.

Hope this helps you :0

Answer:

The digit 5 is equal to is 5,000 :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

The thousandth digit!

Step-by-step explanation:

Answer:

y = 1

Step-by-step explanation:

Given

⇒ y = kx⁴

Finding the proportionality constant, k

Finding y

Answer:

24:37

Simplify the ratio by dividing by the GCF, in this case, two.

[tex]\frac{48 / 2}{74 / 2} = \frac{24}{37}~also~known~as~24:37[/tex]

Answer:

The answer is 75

Step-by-step explanation:

Answer:

First,you need to find the components of each force.

Answer: 10/8 = 1 1/4

Step-by-step explanation:

2x5 =10

4x2 =8

10/8= 1 2/8 = 1 1/4

Answer:

add all of them together (x and y’s) the divide the sum by the amt of numbers

Step-by-step explanation:

Answer:

1. 0

2. -2.5

3. 5

4.  -2.5

5.  -4

Step-by-step explanation:

Did this by adding the scores together and then dividing by the number of scores added

Recall that for all [tex]z\in\Bbb C[/tex],

[tex]\displaystyle e^z = \sum_{n=0}^\infty \frac{z^n}{n!}[/tex]

Then

[tex]\displaystyle \frac{e^{z^2}}{z^3} = \frac1{z^3} \sum_{n=0}^\infty \frac{z^{2n}}{n!} = \boxed{\sum_{n=0}^\infty \frac{z^{2n-3}}{n!}}[/tex]

Answer: 8

just guessed it

Answer:

$573.50 per week

Step-by-step explanation:

wages =  40 hr/wk * 7.25 $/hr   $290 per week

tips   90 tables * ( 21*.15) = 283.50

total    290 + 283.5 = 573.50  

Answer:

x > 4 or x < -1

Step-by-step explanation:

[tex]2x - 3 > 5[/tex]

[tex]2x > 8[/tex]

[tex]x > 4[/tex]

[tex]2x - 3 < - 5[/tex]

[tex]2x < - 2[/tex]

[tex]x < - 1[/tex]

Answer:

  f(x) = 2 -2^x

Step-by-step explanation:

The graph has a horizontal asymptote at y = 2. It has a slope that doubles in each unit interval. This tells you it is an exponential function with a base of 2, and a vertical translation of 2. The curve downward, rather than upward, means the function has been reflected across a horizontal line.

__

An exponential function of the form ...

  y = a·b^x

will have a horizontal asymptote at y=0. The asymptote here is y=2, so 2 has been added to the function value.

The slope of the above function (y=a·b^x) will be multiplied by a factor of 'b' when x increases by 1. Your graph has a slope (rise/run) of -1 for x between 0 and 1, a slope of -2 for x between 1 and 2, and a slope of -4 between x=2 and 3. This behavior indicates that b=-2/-1 = -4/-2 = 2.

The function so far looks like ...

  y = a·2^x +2

Using x=0, we can find the value of 'a'.

  1 = a·2^0 +2

  -1 = a . . . . . . . . subtract 2

Then the function is ...

  f(x) = -2^x +2

Answer:

Can't answer this without knowing the height of the rectangle ...

Step-by-step explanation:

Answer: 3.2

Step-by-step explanation: Trust me, I got it right.

Answer:

here

Step-by-step explanation:

if you need more explanation comment on this

Answer:

$77.514

Step-by-step explanation:

28.6 x 1.74 + 27.75 =  77.514

Answer:

Step-by-step explanation:

The following inequality can be solved by separating the term x from one side.

4x+15≥x+6

First, subtract by 15 from both sides.

4x+15-15≥x+6-15

Solve.

4x≥x-9

Then, you subtract by x from both sides.

4x-x≥x-9-x

Solve.

3x≥-9

Divide by 3 from both sides.

3x/3≥-9/3

Solve.

Divide the numbers from left to right.

-9/3=-3

[tex]\Longrightarrow: \boxed{\sf{x\geq -3}}[/tex]

I hope this helps, let me know if you have any questions.

Answer:

x ≥ -3

Step-by-step explanation:

To determine the solution to the inequality, we need to isolate the variable and its coefficient on one side of the equation. Furthermore, isolate the variable by dividing the coefficient by both sides of the equation. The inequality obtained after doing these steps is the solution to the inequality.

Given inequality:

As said above, let's isolate "x" and it's coefficient on one side of the equation. This can be done by subtracting "x + 15" to both sides of the equation.

As said above, let's further isolate "x" by dividing the coefficient of "x" to both sides of the equation.

Therefore, the solution is x ≥ -3.

a) The first five terms in the sequence is 100, 95, 90, 85 and 80

b) The nth term of the sequence will be 100 + (n - 1)(5) = 5n + 95

Sequences are set of values arranged in a particular order. Given the recursive formula for a sequence expressed as;

an=an-1-5

If the first term a1 = 100, then;

a2 = a1 - 5
a2 = 100 - 5
a2 = 95

For the third term

a3= a2 - 5
a3= 95 - 5
a3 = 90

The other two terms will be 85 and 80

a) The first five terms in the sequence is 100, 95, 90, 85 and 80

b) The nth term of the sequence will be 100 + (n - 1)(5) = 5n + 95

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Based on the current income to Frenza, and the proposed expansion amount, the net income and return on equity for the three options are:

Don't Expand:

Debt financing:

Equity financing:

Net income will remain at $100,000.

Return on equity would be:

= Net income / Equity

= 100,000 / 400,000

= 25%

Income goes to $150,000.

Net income:
= Income - interest

= 150,000 - (8% x 160,000)

= $137,200

Return on equity:

= 137,200 / 400,000

= $34.3%.

Income goes to $150,000.

No interest payment so net income is $150,000.

Return on equity:

= 150,000 / (400,000 + 150,000 new equity)

= 26.8%

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Answer:

By simplifiying the expression we get

−x+4

Answer:

-x+4

Step-by-step explanation:

Subtract: 37-33

Combine like terms: 6x-7

Rearrange terms: -x+4

Using the slope intercept formula, the equation for the line in slope intercept form is y = -x - 4

The slope intercept equation can be describe as follows:

y = mx + b

where

Therefore,

(-4, 0)(1, -5)

m = -5 - 0 / 1 + 4 = -5 / 5 = -1

Therefore, let's find b using (1, -5)

-5 = -1(1) + b

-5  = -1 + b

b = -5 + 1

b = -4

Therefore, the equation is y = -x - 4

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