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3 years ago

Which statement about the function is true?

Mathematics

1 answer:

bonufazy [111]3 years ago

5 0

Answer:

The answer is The function is decreasing for all real values of x

where

-1<x<4.

Step-by-step explanation:

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How is the sum expressed in sigma notation? 11 + 17 + 23 + 29 + 35 + 41

Ann [662]

<h3>The sum expressed in sigma notation is:</h3>

$11+17+23+29+35+41=\sum\limits_{i=1}^{6}5+6i$

Solution:

Given that,

11 + 17 + 23 + 29 + 35 + 41

We have to express the sum in sigma notation

Analyse the series

5 + 6(1) = 11

5 + 6(2) = 17

5 + 6(3) = 5 + 18 = 23

5 + 6(4) = 5 + 24 = 29

5 + 6(5) = 5 + 30 = 35

5 + 6(6) = 5 + 36 = 41

Thus the series goes on like this:

5 + 6(n) , where n = 1 to 6

This can be expressed in sigma notation as:

$11+17+23+29+35+41=\sum\limits_{n=1}^{6}5+6n$

We can expand the sigma notation and verify the results

$\sum\limits_{i=1}^{6}5+6i=(5+6(1))+(5+6(2))+(5+6(3))+(5+6(4))+(5+6(5))+(5+6(6))\\\\\\\sum\limits_{i=1}^{6}5+6i=(5+6)+(5+12)+(5+18)+(5+24)+(5+30)+(5+36)\\\\\\\sum\limits_{i=1}^{6}5+6i=11+17+23+29+35+41$

8 0

3 years ago

Read 2 more answers

If the volume of a sphere is equal to the volume of a cube, what is the ratio of the edge of the cube to the radius of the spher

Pachacha [2.7K]

Answer: The answer is (C) 1.61.

Step-by-step explanation: Given that the volume of a sphere is equal to the volume of a cube. We are to find the ratio of the edge of the cube to the radius of the sphere.

Let, 'r' be the radius of the sphere and 'e' be the edge of the cube. Then, the volume of the sphere is given by

$V_s=\dfrac{4}{3}\pi r^3,$

and the volume of the cube is

$V_c=e^3.$

According to the question, we have

$V_s=V_e\\\\\Rightarrow \dfrac{4}{3}\pi r^3=e^3\\\\\\\Rightarrow \dfrac{4}{3}\times\dfrac{22}{7}r^3=e^3\\\\\\\Rightarrow 88r^3=21e^3\\\\\Rightarrow 4.44r=2.75e\\\\\Rightarrow \dfrac{e}{r}=\dfrac{4.44}{2.75}\\\\\Rightarrow e:r=1.61.$

Thus, the correct option is (C) 1.61.

4 0

3 years ago

Show that B = {[a, b) ⊂ ℝ | a < b} is a basis for a topology on ℝ

loris [4]

Answer:

Remember that a set $\mathcal{B}$ is a base for some topology on $\mathbb{R}$ if satisfy the following properties:

1. $\mathbb{R}=\cup\{B: B\in\mathcal{B}\}$

2. For $B, B^* \in \mathcal{B}$ , If $p\in B\cap B^*$ then exist $B_p\in\mathcal{B}$ such that $p\in B_p\subset B\cap B^*$ .

Now, for $B=\{[a,b)\subset\mathbb{R}| a < b\}$ we verify the above properties:

1. It's clear that $\mathbb{R}=\cup_{a,b \text{ with }a$

2. Let $B=[a,b), B^*=[c,d) \in \mathcal{B}, p\in B\cap B^*$ . Without loss of generality suppose that $a$ . Then $c\leq p < b$ , this implies that $p\in[c,b)$ and $B_p=[c,d) \in \mathcal{B}$ and $B_p\subset B\cap B^*$ .

Then, B satisfy the two properties. This show that B is a basis for a topology in $\mathbb{R}$

6 0

3 years ago

PLEASE HELP ASAP

oksano4ka [1.4K]

Answer:

Step-by-step explanation:

need the length and height of the triangle on the left

3 0

3 years ago

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. (07.01) Karolyn is arranging her art project, science project, and math project on her desk. The tree diagram below shows the

mash [69]

The tree diagram shows that there are a total of six sample spaces.

math------science

art

science---math

art---math

science

math---art

art---science

math

science---art

Based on the tree diagram, the probability that the science project is first is two over six. This is because science appears first in two out of the six sample spaces (boldened).

8 0

4 years ago

Read 2 more answers