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3 years ago

Jhonny has read 115 pages of a 305-page book. He reads 10 pages each day. How many days will it take to finish?

Mathematics

1 answer:

WINSTONCH [101]3 years ago

7 0

Answer:

It will take 19 days until johnny finishes reading the book.

Step-by-step explanation:

305=115+10x

190=10x

x=19

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Differentiate y=x⁴(1-2x⁵)⁶(5-8x³)².

Liula [17]

Step-by-step explanation:

Let $y(x)=f(x)g(x)h(x)$ where

$f(x) = x^4$

$g(x)= (1 -2x^5)^6$

$h(x)= (5 - 8x^3)^2$

so that

$y(x) = x^4(1 -2x^5)^6(5 - 8x^3)^2$

Recall that the derivative of the product of functions is

$y'(x)=f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)$

so taking the derivatives of the individual functions, we get

$f'(x) = 4x^3$

$g'(x) = 6(1 - 2x^5)^5(-10x^4)$

$h'(x) = 2(5 - 8x^3)(-24x^2)$

So the derivative of y(x) is given by

$y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2 + x^4 6(1 -2x^5)^5(-10x^4)(5 - 8x^3)^2 + x^4(1 -2x^5)^6 2(5 - 8x^3)(-24x^2)$

$y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 60x^8(1 -2x^5)^5(5 - 8x^3)^2$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 48x^6(1 -2x^5)^6 2(5 - 8x^3)$

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2 years ago

What is a formula for the nth term of the given sequence? 36, 24, 16...

SpyIntel [72]

Answer:

The formula to find the nth term of the given sequence is 54 · $\frac{2}{3} ^{n}$

Step-by-step explanation:

The formula for nth term of an geometric progression is :

$a_{n} = \frac{a_{1}(r^{n})}{r}$

In this example, we have $a_{1}$ = 36 (the first term in the sequence) and

r = $\frac{2}{3}$ (the rate in which the sequence is changing).

Knowing what the values for r and $a_{1}$ are, now we can solve.

$a_{n} = \frac{a_{1}(r^{n})}{r}$ = $\frac{36 (\frac{2}{3} ^{n}) }{\frac{2}{3} }$ = 54 · $\frac{2}{3} ^{n}$

Therefore, the formula to find the nth term of the given sequence is

54 · $\frac{2}{3} ^{n}$

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2 years ago

Pattern A follows the rule "add 3" and Pattern B follows the rule "add 4." Pattern A 1 4 7 10 13 Pattern B 5 9 13 17 21 Which or

IceJOKER [234]

Answer:

(1,5) (7,13) (10,17) (7,13)

Step-by-step explanation:

1 4 7 10 13

5 9 13 17 21

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1 year ago

What is the cube of 8? O A. 2 O B. 64 C.53 O D. 24

VMariaS [17]

Answer:

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Step-by-step explanation:

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1 year ago

Given the function g(x)=−2x−8, evaluate g(0).

Vera_Pavlovna [14]

Answer:

g(0) = -8

Step-by-step explanation:

When you plug in a zero for the x the equation will look like

g(0) = -2(0) - 8

-2 times 0 = 0 so g(0) = -8

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2 years ago