(X+y)^16 what is the answer

What is the anwser to the math problem

Mariulka [41]

Answer:

whats the problem

Step-by-step explanation:

4 0

4 years ago

Item 3 Find the distance from point $A$ to $\overleftrightarrow{XZ}$ . Round your answer to the nearest tenth. Triangle X Z A an

vovikov84 [41]

Answer:

3.2

Step-by-step explanation:

Given the coordinates

X(4, -3)

Y(2, 1.5)

A(3, 3)

Z(4,-1)

We are to find the distance from point A to XZ

First let us get the coordinate XZ

According to vector notation XZ = Z-X

XZ = (4,-1)-(4,-3)

XZ = [(4-4),-1-(-3)]

XZ = (0, 2)

Next is to find the distance from A(3, 3) to XZ(0,2) using the formula for calculating the distance between two points.

D = √(x2-x1)²+(y2-y1)²

x1 = 3, y1 = 3, x2 = 0, y2 = 2

D = √(0-3)²+(2-3)²

D = √9+1

D = √10

D = 3.16

Hence the distance from point A to XZ to nearest tenth is 3.2

4 0

3 years ago

Find the area of the region enclosed by the graphs of these equations. (CALCULUS HELP)

sergiy2304 [10]

Answer:

$\displaystyle A = \frac{20\sqrt{15}}{3}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Terms/Coefficients
Graphing
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Area - Integrals

U-Substitution

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Area of a Region Formula: $\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx$

Step-by-step explanation:

Step 1: Define

F: y = √(15 - x)

G: y = √(15 - 3x)

H: y = 0

Step 2: Find Bounds of Integration

Solve each equation for the x-value for our bounds of integration.

F

Set y = 0: 0 = √(15 - x)
[Equality Property] Square both sides: 0 = 15 - x
[Subtraction Property of Equality] Isolate x term: -x = -15
[Division Property of Equality] Isolate x: x = 15

G

Set y = 0: 0 = √(15 - 3x)
[Equality Property] Square both sides: 0 = 15 - 3x
[Subtraction Property of Equality] Isolate x term: -3x = -15
[Division Property of Equality] Isolate x: x = 5

This tells us that our bounds of integration for function F is from 0 to 15 and our bounds of integration for function G is 0 to 5.

We see that we need to subtract function G from function F to get our area of the region (See attachment graph for visual).

Step 3: Find Area of Region

Integration Part 1

Rewrite Area of Region Formula [Integration Property - Subtraction]: $\displaystyle A = \int\limits^b_a {f(x)} \, dx - \int\limits^d_c {g(x)} \, dx$
[Integral] Substitute in variables and limits [Area of Region Formula]: $\displaystyle A = \int\limits^{15}_0 {\sqrt{15 - x}} \, dx - \int\limits^5_0 {\sqrt{15 - 3x}} \, dx$
[Area] [Integral] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle A = \int\limits^{15}_0 {(15 - x)^{\frac{1}{2}}} \, dx - \int\limits^5_0 {(15 - 3x)^{\frac{1}{2}}} \, dx$

Step 4: Identify Variables

Set variables for u-substitution for both integrals.

Integral 1:

u = 15 - x

du = -dx

Integral 2:

z = 15 - 3x

dz = -3dx

Step 5: Find Area of Region

Integration Part 2

[Area] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle A = -\int\limits^{15}_0 {-(15 - x)^{\frac{1}{2}}} \, dx + \frac{1}{3}\int\limits^5_0 {-3(15 - 3x)^{\frac{1}{2}}} \, dx$
[Area] U-Substitution: $\displaystyle A = -\int\limits^0_{15} {u^{\frac{1}{2}}} \, du + \frac{1}{3}\int\limits^0_{15} {z^{\frac{1}{2}}} \, dz$
[Area] Reverse Power Rule: $\displaystyle A = -(\frac{2u^{\frac{3}{2}}}{3}) \bigg|\limit^0_{15} + \frac{1}{3}(\frac{2z^{\frac{3}{2}}}{3}) \bigg|\limit^0_{15}$
[Area] Evaluate [Integration Rule - FTC 1]: $\displaystyle A = -(-10\sqrt{15}) + \frac{1}{3}(-10\sqrt{15})$
[Area] Multiply: $\displaystyle A = 10\sqrt{15} + \frac{-10\sqrt{15}}{3}$
[Area] Add: $\displaystyle A = \frac{20\sqrt{15}}{3}$

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Area Under the Curve - Area of a Region (Integration)

Book: College Calculus 10e

3 0

3 years ago

The angle θ lies in Quadrant II .

Andreyy89

let's keep in mind that, in the II Quadrant, cosine is negative and sine, is positive.

cosine is adjacent/hypotenuse, however the hypotenuse is simply a radius unit, and thus is never negative, so in the -(2/3) the negative must be the numerator, -2.

$\bf cos(\theta )=\cfrac{\stackrel{adjacent}{-2}}{\stackrel{hypotenuse}{3}}\impliedby \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{3^2-(-2)^2}=b\implies \pm\sqrt{5}=b\implies \stackrel{\textit{II Quadrant}}{+\sqrt{5}=b}~\hfill tan(\theta )=\cfrac{\stackrel{opposite}{\sqrt{5}}}{\stackrel{adjacent}{-2}} \\\\\\ ~\hspace{34em}$

6 0

4 years ago

Suppose the owner of a local apple orchard has 4 half-bushels of apples to sell. He loads them on his truck, and drives his rout

NikAS [45]

Answer:

a) The orchard owner's expected profit from driving the route is $33.

b) The standard deviation of the profit is $27.28

Step-by-step explanation:

a) Data and Calculations:

Apples to sell = 4 half-bushels

Price of each half-bushel sold = $40

Sales revenue = $160 ($40 *4)

Cost of driving the route = $15

Expected values:

Event Probability Revenue Profit Expected Profit

No Sales 40% $0 ($15) ($0 - $15) ($6.00)

Selling 1 half-bushel 30% $40 $25 ($40 - $15) $7.50

Selling 2 half-bushels 10% $80 $65 ($80 - $15) $6.50

Selling 3 half-bushels 10% $120 $105 ($120 - $15) $10.50

Selling 4 half-bushels 10% $160 $145 ($160 - $15) $14.50

Total expected profit = $33

Event Expected Profit Mean Squared

Difference

No Sales ($6.00) -39 1,521

Selling 1 half-bushel $7.50 -25.5 650.25

Selling 2 half-bushels $6.50 -26.5 702.25

Selling 3 half-bushels $10.50 -22.50 506.25

Selling 4 half-bushels $14.50 -18.50 342.25

Sum of squared differences 3,722

Mean of squared differences = 744.4 (3,722/5)

Standard deviation = square root of the mean

= 27.28

= $27.28

3 0

3 years ago