Solve each equation. e. log:(6x

25=10+5k What does k equal? I need help!

Lunna [17]

The answer is 3.

First do 25 - 10 and you get 15

The final step is to do 15 divided by 5 and you get the final answer which is 3.

7 0

3 years ago

Read 2 more answers

The expression 5x+7x can be simplified into which of the following ?

zvonat [6]

Answer:

12x

Step-by-step explanation:

You can add the like terms (which have x)

5x+7x=12x

8 0

3 years ago

How can i prove this property to be true for all values of n, using mathematical induction.

chubhunter [2.5K]

Proof -

So, in the first part we'll verify by taking n = 1.

$\implies \: 1 = {1}^{2} = \frac{1(1 + 1)(2 + 1)}{6}$

$\implies{ \frac{1(2)(3)}{6} }$

$\implies{ 1}$

Therefore, it is true for the first part.

In the second part we will assume that,

$\: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} = \frac{k(k + 1)(2k + 1)}{6} }$

and we will prove that,

$\sf{ \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 1 + 1) \{2(k + 1) + 1\}}{6}}}$

$\: {{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 2) (2k + 3)}{6}}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k (k + 1) (2k + 1) }{6} + \frac{(k + 1) ^{2} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k(k+1)(2k+1)+6(k+1)^ 2 }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)\{k(2k+1)+6(k+1)\} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2 +k+6k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2+7k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(k+2)(2k+3) }{6}$

Henceforth, by using the principle of mathematical induction 1²+2² +3²+....+n² = n(n+1)(2n+1)/ 6 for all positive integers n.

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8 0

2 years ago

Farmer Samantha has a cylindrical grain silo with a diameter of 12 feet and a height of 40 feet. The silo is filled with grain t

sammy [17]

Answer:

161,234 pounds of grain will remain in the silo

Step-by-step explanation:

In this question, we are to calculate the amount of grains that will be left in a silo if 20 cows feed on the content for 100 days.

Firstly, we need to calculate the amount of grains present in the silo.

This we can do by first calculating the volume of the silo. Since it is cylindrical in shape, we apply the formula for the volume of a cylinder.

Mathematically, the volume of a cylinder is

V = pi * r^2 * h

Here we have the r = D/2 = 12/2 = 6 feet and h = 40 feet. Plugging this , we have;

V = pi * 6^2 * 40 = 1440pi cubic feet

Now, per cubic feet, we have a weight of 48 pounds. The weight of grains thus present in the silo is thus;

1440pi * 28 = 1440 * pi * 48= 69,120pi pounds of grain

Let’s calculate what the cows would feast on. That would be 20 * 28 * 100 = 56,000 pounds of grains

Now we need to know what will remain. We just need to subtract what is consumed by the cows from we have inside the silo

What is inside the silo would be 69,120 * 22/7 = apprx 217,234 pounds

What will remain is thus 217,234 - 56,000 = 161,234 pounds of grain

3 0

3 years ago

i was doing this task in math and I came across this: x-12x=0.88x . can someone plz explain why is this equal to this? I underst

valkas [14]

1x-12x=0.88x

11x=0.88x

-11x=0.88x-0.88x

-11.88x=0x

-11.88x=0

Isolate x

3 0

2 years ago

Solve each equation. e. log:(6x – 3) = 2