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3 years ago

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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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

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Answer:

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Step-by-step explanation:

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3 years ago

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The difference between two numbers is 275.the smaller number is 236 what is the sum of both numbers

kirza4 [7]

Answer:

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Step-by-step explanation:

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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:
Calculus

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]:

f(x) = cxⁿ
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:

Step 1: Define

Identify given.

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution/u-solve.

Set u:
$\displaystyle u = 4 - x^2$
[u] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = -2x \ dx$
[du] Rewrite [U-Solve]:
$\displaystyle dx = \frac{-1}{2x} \ du$

Step 3: Integrate Pt. 2

[Integral] Apply U-Solve:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du$
[Integrand] Simplify:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du$
[Integral] Apply Integration Rule [Reverse Power Rule]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C$
[u] 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 find the indefinite integral.

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

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

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

Unit: Integration

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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

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