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anzhelika [568]
3 years ago
13

A summer camp counselor wants to find a length x in feet across a lake as represented in the sketch to the left

Mathematics
1 answer:
Nata [24]3 years ago
8 0

The question is incomplete and without a picture. I found similar question as follows:

A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. The lengths represented by AB, EB, BD and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and the angle AEB and the angle CBD have the same measure. What is the value of x?

Answer:

1600ft

Step-by-step explanation:

Angle AEB and CBD is the same value.

Referring to the picture, since ABC and DBE are straight lines and crosses each other at B, the angle DBC and EBA are equal.

Since we have 2 equal angle, the third angle must be the same as well.

Therefore we can conclude that both ABE and CBD are similar triangle but with different factor with;

AB similar to BC

EB similar to BD

AE similar to CD

To find the factor between ABE and CBD,

EB / BD = 1400 / 700 = 2

So x, which is AE must be a factor of 2 to CD

AE = 2*800 =1600ft

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Need more information. You said which of the following and didn't put any questions under it
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Adam’s car traveled 465.3 miles on 16.5 gallons of gas. Which equation can be used to determine the average number of miles that
grandymaker [24]

Answer:

465.3 = 16.5x

Step-by-step explanation:

We can determine the miles per gallon  by taking the number of miles driven and dividing by the gallons

465.3 /16.5 =x

Rewriting by multiplying each side by 16.5

465.3 = 16.5x

7 0
3 years ago
Read 2 more answers
The difference between two numbers is 275.the smaller number is 236 what is the sum of both numbers​
kirza4 [7]

Answer:

747

Step-by-step explanation:

let the 2 numbers be x and y with x > y, then

x - y = 275 ( the difference of the 2 numbers ) and

x - 236 = 275 ( the smaller number y = 236 )

Add 236 to both sides

x = 511

Thus x = 511 and y = 236, thus

x + y = 511 + 236 = 747

7 0
3 years ago
Help evaluating the indefinite integral
Dafna11 [192]

Answer:

\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }

General Formulas and Concepts:
<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:
\displaystyle (cu)' = cu'

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

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Integration

  • Integrals

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 Methods: U-Substitution and U-Solve

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify given.</em>

<em />\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx

<u>Step 2: Integrate Pt. 1</u>

<em>Identify variables for u-substitution/u-solve</em>.

  1. Set <em>u</em>:
    \displaystyle u = 4 - x^2
  2. [<em>u</em>] Differentiate [Derivative Rules and Properties]:
    \displaystyle du = -2x \ dx
  3. [<em>du</em>] Rewrite [U-Solve]:
    \displaystyle dx = \frac{-1}{2x} \ du

<u>Step 3: Integrate Pt. 2</u>

  1. [Integral] Apply U-Solve:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du
  2. [Integrand] Simplify:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du
  3. [Integral] Rewrite [Integration Property - Multiplied Constant]:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du
  4. [Integral] Apply Integration Rule [Reverse Power Rule]:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C
  5. [<em>u</em>] Back-substitute:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }

∴ we have used u-solve (u-substitution) to <em>find</em> the indefinite integral.

---

Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27746485

---

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

Unit: Integration

5 0
2 years ago
the size of the second application is 3.45 MB less than he first application. What is the size of the second application
mr_godi [17]

The size of the second application given the size of the first application and the expression ( x - 3.45 mb) for the size of the second application is 293.55 MB.

<h3>Equation</h3>

Let

  • Size of the first application = x

  • Size of the second application= x - 3.45 mb

For instance,

if the size of the first application is 297 MB

Size of the second application= x - 3.45 mb

= 297 MB - 3.45 MB

= 293.55 MB

Therefore, the size of the second application given the size of the first application and the expression for the size of the second application is 293.55 MB

Learn more about equation:

brainly.com/question/2972832

#SPJ1

6 0
2 years ago
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