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3 years ago

How do I solve this?

Mathematics

1 answer:

ohaa [14]3 years ago

5 0

Answer:

Step-by-step explanation:

$x=e^{2t}-1\\y=e^t\\squaring\\\\y^{2}=e^{2t}\\Hence ~x=y^{2}-1$

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Find the length of side x in simplest radical form with a rational denominator<br><br>

HACTEHA [7]

Answer:

$x = \sqrt{2}$

Step-by-step explanation:

$\tan 30 \degree = \frac{x}{ \sqrt{6} } \\ \\ \frac{1}{ \sqrt{3} } = \frac{x}{ \sqrt{6} } \\ \\ x = \frac{ \sqrt{6} }{ \sqrt{3} } \\ \\ x = \frac{ \: \sqrt{3} \times \sqrt{2} }{ \sqrt{3} } \\ \\ x = \sqrt{2}$

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3 years ago

For some integer n, the first, the third and the fifth terms of an arithmetic sequence are respectively 3n, 5n – 6, and 11n + 8.

Mazyrski [523]

Answer:

a₄=8n+1= -39.

Step-by-step explanation:

1) if a₁=3n; a₃=5n-6 and a₅=11n+8, then it is possible to calculate the difference according to 0.5(a₅-a₃)=0.5(a₃-a₁). Then

2) 0.5(11n+8-5n+6)=0.5(5n-6-3n); ⇔ 6n+14=2n-6; ⇔ n= -5.

3) if n=-5, then the 4th term is:

$a_4=\frac{a_5+a_3}{2}; \ = > \ a_4=\frac{11n+8+5n-6}{2}=8n+1;$

or a₄=-39.

8 0

2 years ago

If 7 giant solar power plants generate 1.3 gigawatts (GW) of energy to power 900,000 homes, how many gigawatts can 21 giant sola

Mice21 [21]

Answer:

2,700,000 homes

Step-by-step explanation:

6 0

3 years ago

The perimeter of a rectangular garden is 338 m.

Natasha_Volkova [10]

Answer:

l=95

Step-by-step explanation:

Perimeter is all the sides add up. So the equation if you know two of the sides, it should be: 338=(2*74)+(2*l)

5 0

3 years ago

Read 2 more answers

The sum of the first 5 terms of an AP is 30 and the sum of the four term from T6 to T9 (inclusive) is 69. Find the AP

Ainat [17]

Answer: The AP = 1, ⁷/₂, 6, ¹⁷/₂, 11 ..............

Step-by-step explanation:

From the first statement,

S₅ = ⁵/₂(2a + ( n - 1 )d } = 30

5(2a + 4d )d = 60

10a + 20d = 60

reduce to lowest term to easy calculation by dividing through by 10

a + 2d = 6 -----------------------------------1

second statement

sum of the next 4 terms inclusive

T₉ = ⁹/₂(2a + 8d ) = 69

9(2a + 8d ) = 30 + 69

18a + 72d = 99 x 2

18a + 72d = 198

divide through by 18 to reduce to lowest time

a + 4d = 11 ------------------------------------------2

Now solve the two equation simultaneously to find a and d

a + 2d = 6

a + 4d = 11

-2d = -5

d = ⁵/₂.

Now substitute for d to get a

a + 2(⁵/₂) = 6

a + 5 = 6

a = 6 - 5

a = 1.

Therefore the AP = 1 , ⁷/₂ , 6 , ¹⁷/₂ , 11 , ..............

7 0

3 years ago