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3 years ago

Can someone help me please

Mathematics

1 answer:

Ksenya-84 [330]3 years ago

7 0

Answer:

im not sure because im not good at these question but ill let you know when i figure it o

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Can somebody prove this mathmatical induction?

Flauer [41]

Answer:

See explanation

Step-by-step explanation:

1 step:

n=1, then

$\sum \limits_{j=1}^1 2^j=2^1=2\\ \\2(2^1-1)=2(2-1)=2\cdot 1=2$

So, for j=1 this statement is true

2 step:

Assume that for n=k the following statement is true

$\sum \limits_{j=1}^k2^j=2(2^k-1)$

3 step:

Check for n=k+1 whether the statement

$\sum \limits_{j=1}^{k+1}2^j=2(2^{k+1}-1)$

is true.

Start with the left side:

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}\ \ (\ast)$

According to the 2nd step,

$\sum \limits_{j=1}^k2^j=2(2^k-1)$

Substitute it into the $\ast$

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}=2(2^k-1)+2^{k+1}=2^{k+1}-2+2^{k+1}=2\cdot 2^{k+1}-2=2^{k+2}-2=2(2^{k+1}-1)$

So, you have proved the initial statement

4 0

3 years ago

Which expression represents the volume, in cubic

muminat

Given:

The composite figure.

To find:

The volume of the given composite figure.

Solution:

Given composite figure contains a cuboid and a pyramid.

Length, breadth and height of the cuboid are 8, 6 and 4 respectively.

Volume of a cuboid is

$V_1=length\times breadth\times height$

$V_1=(8)(6)(4)$

Length and breadth of the pyramid is same as the cuboid, i.e., 8 and 6 respectively.

Height of pyramid = 10 - 4 = 6

Volume of a pyramid is

$V_2=\dfrac{1}{3}\times length\times breadth\times height$

$V_2=(\dfrac{1}{3})(8)(6)(6)$

The volume of composite figure is

$V=V_1+V_2$

$V=(8)(6)(4)+(\dfrac{1}{3})(8)(6)(6)$

It can be written as

$V=(\dfrac{1}{3})(8)(6)(6)+(8)(6)(4)$

Therefore, the correct option is A.

3 0

3 years ago

3 friends are selling items at a bake sale. May makes $23.25 selling bread. Inez sells gift baskets and make 100 times as much a

Zigmanuir [339]

Answer:

May: $23.25

Inez: $2325

Jo: $232.5

Step-by-step explanation:

Inez makes 100 times as much as May. Since May makes $23.25, move the decimal point two places to the right to multiply the number by 100. You will get $2325. Jo makes 1/10 of the money Inez makes. Pretend there is a decimal point at the end of 2325. Move the decimal point one place to the left to divide by 10. You will get $232.5.

8 0

3 years ago

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Which logarithmic equation is equivalent to the exponential equation below? E^a=28.37

Alex_Xolod [135]

1. To solve this problem, it is important to know that the logarithmic functions and the exponential functions are inverse. Then, you have:

e^a=28.37
 a=ln(28.37)

2. Therefore: Which logarithmic equation is equivalent to the exponential equation e^a=28.37? As you can see, the answer for this question is:

a=ln(28.37)

7 0

3 years ago

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The base of a triangle is 3 cm and the height is 5 cm. What mathematical operation(s) described must be performed in order to fi

Firdavs [7]

Answer:

Step-by-step explanation:

To find the area of a triangle, one must multiply the base by the height then divide by 2.

So, the area of this triangle would be 7.5

6 0

3 years ago

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