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2 years ago

Find the missing length indicated

Mathematics

1 answer:

Gemiola [76]2 years ago

8 0

Answer:

Step-by-step explanation:

According to Euclidian theorem

x^2 = 144*81

x^2 = 11664

x = 108

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SoMeonE plZ hAlp me lol

jeka94

C.√93

A=17

B=14

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3 0

2 years ago

A. Evaluate ∫20 tan 2x sec^2 2x dx using the substitution u = tan 2x.

irakobra [83]

Answer:

The integral is equal to $5\sec^2(2x)+C$ for an arbitrary constant C.

Step-by-step explanation:

a) If $u=\tan(2x)$ then $du=2\sec^2(2x)dx$ so the integral becomes $\int 20\tan(2x)\sec^2(2x)dx=\int 10\tan(2x) (2\sec^2(2x))dx=\int 10udu=\frac{u^2}{2}+C=10(\int udu)=10(\frac{u^2}{2}+C)=5\tan^2(2x)+C$ . (the constant of integration is actually 5C, but this doesn't affect the result when taking derivatives, so we still denote it by C)

b) In this case $u=\sec(2x)$ hence $du=2\tan(2x)\sec(2x)dx$ . We rewrite the integral as $\int 20\tan(2x)\sec^2(2x)dx=\int 10\sec(2x) (2\tan(2x)\sec(2x))dx=\int 10udu=5\frac{u^2}{2}+C=5\sec^2(2x)+C$ .

c) We use the trigonometric identity $\tan(2x)^2+1=\sec(2x)^2$ is part b). The value of the integral is $5\sec^2(2x)+C=5(\tan^2(2x)+1)+C=5\tan^2(2x)+5+C=5\tan^2(2x)+C$ . which coincides with part a)

Note that we just replaced 5+C by C. This is because we are asked for an indefinite integral. Each value of C defines a unique antiderivative, but we are not interested in specific values of C as this integral is the family of all antiderivatives. Part a) and b) don't coincide for specific values of C (they would if we were working with a definite integral), but they do represent the same family of functions.

3 0

2 years ago

Find the simple interest on 7,200 at 3/4% for 5 years

lakkis [162]

Answer:

$7474.08

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Simple Interest Rate Formula: $\displaystyle A = P(1 + r)^t$

A is final amount
P is principle (initial) amount
r is rate
t is time (in years)

Step-by-step explanation:

Step 1: Define

P = 7200

r = 0.75% = 0.0075

t = 5

Step 2: Solve for A

Substitute in variables [Simple Interest Rate Formula]: $\displaystyle A = 7200(1 + 0.0075)^5$
(Parenthesis) Add: $\displaystyle A = 7200(1.0075)^5$
Evaluate exponents: $\displaystyle A = 7200(1.03807)$
Multiply: $\displaystyle A = 7474.08$