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3 years ago

What is the slope of the line that passes through the points (6, -3) and (1, 7)

Mathematics

1 answer:

BARSIC [14]3 years ago

3 0

Answer:

-2

Step-by-step explanation:

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How do you solve this question? Any help appreciated!

fiasKO [112]

$\bf \displaystyle \int\limits_{1}^{e}\cfrac{1}{t}\cdot dt\\\\
-------------------------------\\\\
\textit{doing substitution}\\\\
u=\cfrac{1}{t}\implies u=t^{-1}\implies \cfrac{du}{dt}=-t^{-2}\implies \cfrac{du}{dt}=-\cfrac{1}{t^2}\\\\\\ -t^2du=dt\\\\
-------------------------------\\\\
\displaystyle \int\limits_{1}^{e}u\cdot -t^2du\impliedby \textit{now, let's do some substitution on the "t"}\\\\
-------------------------------\\\\$

$\bf u=\cfrac{1}{t}\implies t=\cfrac{1}{u}\implies t^2=\cfrac{1^2}{u^2}\implies t^2=\cfrac{1}{u^2}\\\\
-------------------------------\\\\
\displaystyle \int\limits_{1}^{e}u\cdot -\cfrac{1}{u^2}\cdot du\implies -1\int\limits_{1}^{e}\cfrac{1}{u}\cdot du\implies \left. -ln|u| \cfrac{}{}\right]_1^e$

$\bf \left. -ln\left( \frac{1}{t} \right) \cfrac{}{}\right]_1^e\implies 
\left[ -ln\left( \frac{1}{e} \right) \right]-\left[ -ln\left( \frac{1}{1} \right) \right]\implies 
\left[ -ln\left( e^{-1}\right) \right]-\left[ -ln\left( 1\right) \right]
\\\\\\\
[-(-1)]-[-(0)]\implies 1-0\implies 1$

8 0

3 years ago

(x^3- 2x^2 - 1) /( x - 1)

lesya [120]

Answer:

Quotient= x^2 + x + 1

Remainder= 0

Step-by-step explanation:

4 0

3 years ago

What is the sum of the arithmetic series: s10 = -20, d = 4, a1 =?

Otrada [13]

<h2>Step-by-step explanation:</h2><h3> $\green\star$ Given</h3>

$\blue\star$ s10 = -20

$\blue\star$ n = 10

$\blue\star$ an = -20

$\green\star$ solution

$\green\star$ s10 = n\2 [a+(n-1)d]

$\green\star$ -20 = 10a2[a+(10-1)4]

$\green\star$ -4 = a +36

$\green\star$ a1 = -40

$\small\boxed{a = -40}$

Hope it helps.

Hope it helps

8 0

3 years ago

Read 2 more answers

Uma piscina possui 5 m de comprimento, 3 m de largura e 2,5 m de profundidade. Calcule: a) A quantidade de azulejo necessária pa

Westkost [7]

Answer:

a) 70 azulejos

b) 37500 litros

c) 37.5m³

Step-by-step explanation:

A piscina tem 5 m de comprimento, 3 m de largura e 2,5 m de profundidade.

Comprimento = 5m

Largura = 3m

Profundidade (altura) = 2,5 m

Calcular:

a) A quantidade de ladrilhos necessária para cobrir a piscina

Isso é calculado como a área de superfície da votação

A = 2 (wl + hl + hw)

A = 2 × (3 × 5 + 2.5 × 5 +2.5 × 3)

A = 70 m²

Observe que:

1 m² = 1 azulejo

70 m² = 70 azulejos

b) A quantidade de água que pode caber na piscina.

1 m³ = 1000 litres

O volume de uma piscina = Comprimento × Largura × Altura

= 5m × 3m × 2.5m

= 37.5m³

1 m³ = 1000 litros

37.5m³ =

37.5 × 1000 litros

= 37500 litros

c) seu volume em m³

O volume de uma piscina = Comprimento × Largura × Altura

= 5m × 3m × 2.5m

= 37.5m³

7 0

3 years ago

I need help i don't get it !!!!!

joja [24]

Answer:

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 30 = x/8

8 sin 30 =x

8 (1/2) = x

4 0

3 years ago

Read 2 more answers