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2 years ago

Find the slope of the line that passes through (8, 3) and (1, 9).

Mathematics

1 answer:

leonid [27]2 years ago

3 0

Answer:

$-\frac{6}{7}$

Step-by-step explanation:

⇒ $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

⇒ $m = \frac{9 - 3}{1 - 8}$

⇒ $m = \frac{6}{-7}$

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A can of tuna has a volume 18pi cm3 and a height of 2 cm. Find the area of the label that wraps around the entire can and does n

Sphinxa [80]

Answer:

The area of the label is $12\pi\ cm^{2}$

Step-by-step explanation:

step 1

Find the radius

we know that

The volume of the cylinder (can of tuna) is equal to

$V=\pi r^{2} h$

In this problem we have

$V=18\pi\ cm^{3}$

$h=2\ cm$

substitute and solve for r

$18\pi=\pi r^{2} (2)$

Simplify

$18=r^{2}(2)$

$r^{2}=9$

$r=3\ cm$

step 2

<em>Find the lateral area of the can</em>

The lateral area of the cylinder (can of tuna) is equal to

$LA=2\pi rh$

we have

$r=3\ cm$

$h=2\ cm$

$LA=2\pi (3)(2)=12\pi\ cm^{2}$

5 0

2 years ago

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

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

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

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

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

3 0

2 years ago

twice the sum of the number and negative seven is eight. Find the number. Round your answer to the nearest integer, if necessary

Ugo [173]

The number that twice the sum of it and negative seven is eight is 11.

<h3>How to find the number ?</h3>

Twice the sum of the number and negative seven is eight. The number can be found as follows:

let

the number = x

According to the word expression, twice the value of the addition of x and minus seven is equals to 8. Hence, we will find the value of x in the equation formed from the words expression.

The variable x is the required number.

Therefore,

2(x + (-7)) = 8

2(x - 7) = 8

open the brackets

2(x - 7) = 8

2x - 14 = 8

add 14 to both sides of the equation

2x - 14 = 8

2x - 14 + 14 = 8 + 14

2x = 22

divide both sides by 2

x = 22 / 2

x = 11

learn more on numbers here: brainly.com/question/11234992

#SPJ1

3 0

8 months ago

Order least to greatest 1/2, 0.55, 5/7

Nataliya [291]

1/2<0.55<5/7
This is the order from least to greatest

8 0

3 years ago

Read 2 more answers

Someone help me with number 1 and 2 please

adell [148]

1 is 25
2 is 7.42
if you need explanation please comment and let me know

7 0

2 years ago