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1 year ago

If x = 14 cm, y = 7 cm, and z = 8 cm, what is the surface area of the figure?

Mathematics

1 answer:

Nat2105 [25]1 year ago

8 0

Formula for sufrace area of rectangular prisms: S= 2 (lw + lh + wh)

for the first prism, x=14, plug 14 into 2(x)--> 2(14)=28

7,8,28

S= 2 [7(8)+7(28)+8(28)]

S= 2 (28+196+224)

S= 2(448)

S= 896

for the second prism, x is just 14

7,8,14

S= 2 [7(8)+7(14)+8(14)]

S= 2 (28+98+112)

S= 2(238)

S= 476

Add the two sufrace areas we found and the answer will be

D) S= 1,372

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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.

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2 years ago

Simplify. (-8n + 11) + (2n -3)

Rasek [7]

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Hope this helps :)

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2 years ago

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