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Svetach [21]
3 years ago
7

Please answer this correctly

Mathematics
1 answer:
Serggg [28]3 years ago
3 0

Answer:

502 m²

Step-by-step explanation:

We require to find b before calculating the surface area.

The volume (V) of a cuboid is calculated as

V = lbh ( l is length, b is breadth and h is height )

Here V = 510, l = b, b = 10 and h = 3, thus

b × 10 × 3 = 510

30b = 510 ( divide both sides by 30 )

b = 17

--------------------------

The opposite faces of a cuboid are congruent, thus

top/bottom area = 2(17 × 10) = 2 × 170 = 340 m²

front/back area = 2(17 × 3) = 2 × 51 = 102 m²

sides area = 2(10 × 3) = 2 × 30 = 60 m²

Surface area = 340 + 102 + 60 = 502 m²

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If 2k, 5k-1 and 6k+2 are the first 3 terms of an arithmetic sequence, find k and the 8th term​
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Answer:

see explanation

Step-by-step explanation:

The common difference d of an arithmetic sequence is

d = a_{2} - a_{1} = a_{3} - a_{2}

Substitute in values and solve for k, that is

5k - 1 - 2k = 6k + 2 - (5k - 1)

3k - 1 = 6k + 2 - 5k + 1

3k - 1 = k + 3 ( subtract k from both sides )

2k - 1 = 3 ( add 1 to both sides )

2k = 4 ⇒ k = 2

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The n th term of an arithmetic sequence is

a_{n} = a_{1} + (n - 1)d

a_{1} = 2k = 2 × 2 = 4 and

d = 5k - 1 - 2k = 3k - 1 = (3 × 2) - 1 = 5

Hence

a_{8} = 4 + (7 × 5) = 4 + 35 = 39

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3 years ago
What is the value of p?
sveta [45]

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Step-by-step explanation:

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Log10 (2x + 1) - logio(3x - 2) = 1​
Pavlova-9 [17]

Answer: x=3/4

Step-by-step explanation:

To solve, first express the left side as one logarithm. To do so, apply the quotient rule which is log_bM/N=log_bM-log_bN .

log((2x+1)/(3x-2))=1

Then, express the equation to its equivalent exponential form to eliminate the logarithm.

Note that the exponential form of log_b M=a is M=b^a .

Since the base of the logarithm in the given equation is not written, it indicates that its base is 10.

So re-writing the equation, it becomes:

log_10((2x+1)/(3x-2))=1

And its exponential form is:

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(2x+1)/(3x-2)=10

Now that the equation has no more logarithm, the next step is to remove the x in the denominator.

To do so, multiply both sides by 3x-2.

(3x-2)*(2x+1)/(3x-2)=10*(3x-2)

2x+1=30x-20

Next, combine like terms.

To combine 30x and 2x, bring them together on one side of the equation. So, move 2x to the right side by subtracting both sides by 2x.

2x-2x+1=30x-2x-20

1=28x-20

To combine 20 and 1, bring them together on the side opposite the term with x. So, add both sides by 20.

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And, divide both sides by 28 to have x only at the right side.

21/28=(28x)/28

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Hence, the solution to the given equation is x=3/4 .

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Step-by-step explanation:

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