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2 years ago

What is the sum of the first 14 terms of the sequence -11+(-18)+(-25)+(-32)...

1 answer:

6 0

The difference between -11 and -18 is -7
the difference between -18 and -25 is -7
the difference between -25 and -32 is -7

therefore we can say that the difference between all of the terms will be -7.

the first term is -11 -> call this a
the difference is -7 -> call this d
the number of terms is 14 -> call this n

use the equation (sum of) $_{n}$ = $\frac{n}{2}$ (2a + (n-1)d)

(sum of) $_{n}$ = $\frac{14}{2}$ (2 x -11 + (14-1)-7)

= -7(-22 + (13 x -7))
= -7(-22 + -91)
= -7(-111)
= 777

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Given that lim x → 2 f ( x ) = 1 lim x → 2 g ( x ) = − 4 lim x → 2 h ( x ) = 0 limx→2f(x)=1 limx→2g(x)=-4 limx→2h(x)=0, find the

VashaNatasha [74]

Answer:

According what I can read, I have the following statements:

$\lim_{x \to 2} f(x) = 1$

$\lim_{x \to 2} g(x) = -4$

$\lim_{x \to 2} h(x) = 0$

a) Applying properties of limits

$\lim_{x \to 2} f(x) + 5g(x) = \lim_{x \to 2} f(x) + 5 \lim_{x \to 2} g(x) = 1 + 5*-4 = -19$

b) Applying properties of limits

$\lim_{x \to 2} g(x)^{3} = {(\lim_{x \to 2} g(x))}^{3} = (-4)^{3} = -64$

c) Applying properties of limits

$\lim_{x \to 2} \sqrt{f(x)} = \sqrt{\lim_{x \to 2} f(x)} = \sqrt{1} = 1$

d) Applying properties of limits

$\lim_{x \to 2} 4*g(x)*f(x) = 4*\lim_{x \to 2} g(x)*\lim_{x \to 2} f(x) = 4*-4*1 =-16$

e) Applying properties of limits

$\lim_{x \to 2} g(x)*h(x) = \lim_{x \to 2} g(x)*\lim_{x \to 2} h(x) = -4*0 =0$

f) Applying properties of limits

$\lim_{x \to 2} g(x)*h(x)*f(x) = \lim_{x \to 2} g(x)*\lim_{x \to 2} h(x)*\lim_{x \to 2} f(x = -4*0*1 =0$

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3 years ago

A train is traveling at a constant speed and goes 17 kilometers in 8 minutes. How far will the train travel in 60 minutes.

allsm [11]

Answer:

Distance B = 1275 kilometers.

Step-by-step explanation:

Let the two distances and time be A and B respectively.

Given the following data;

Distance A = 17 kilometers.

Time A = 8 minutes.

Distance B =?

Time B = 60 minutes.

First of all, we would find the constant speed;

Speed = distance/time

Substituting into the equation, we have;

Speed = 17/8

Speed = 2.125 km/m

Now, to find the distance B;

Distance B = speed * time

Distance B = 2.125 * 60

Distance B = 1275 km

3 0

2 years ago

55 POINTS!!!!!!

vladimir1956 [14]

A
c
d
b
c
a
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5 0

3 years ago

Determine the perimeter of this shape.

Sindrei [870]

Answer: perimeter = 70.54 cm

Step-by-step explanation:

Perimeter of a shape is the distance around it.

Perimeter of the arc of the bigger semicircle is

π × r

= 3.14 × 7 = 21.98 cm

Perimeter of the arc of the smaller semicircle(handle) is

π × r

= 3.14 × 3 = 9.42 cm

Perimeter of the arc of the smallest semicircle(inner part of the handle) is

π × r

= 3.14 × 1 = 3.14 cm

Therefore, the perimeter of the shape would be

21.98 + 9.42 + 3.14 + 7 + 7 + 10 + 10 + 2 = 70.54 cm

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2 years ago

Which is greater 0.086 or 86%

cupoosta [38]

Hey there!

In order to find out which one is greater, lets convert both of them into percents.

To convert a decimal into a percent, simply multiply the decimal by 100 or move the decimal two places to the right.

So!
0.086 × 100 = 8.6%

Now, we know that 0.086 is equal to 8.6% So, the correct answer is 86%

86% is greater than 0.086.

Thank you for being part of the Brainly community!

3 0

2 years ago