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andreev551 [17]

2 years ago

7

If you start with 1 marble in a jar and double the amount of marbles in a jar every minute, you will fill the jar in 60 minutes.

How many minutes will it take for the jar to be half full?

1 answer:

Nady [450]2 years ago

5 0

Answer: 59min

Step-by-step explanation:

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Can anyone help me with 9th-grade geometry?

katovenus [111]

Answer:

See below.

Step-by-step explanation:

From the given info the 2 triangles are isosceles with AE = FR and ET = RP because the 2 sets of base angles are equal.

As the base angles are congruent m < E = m < R.

So the are 2 triangles are congruent by SAS, ASA and AAS.

7 0

3 years ago

Solve the initial value problem where y′′+4y′−21 y=0, y(1)=1, y′(1)=0 . Use t as the independent variable.

igor_vitrenko [27]

Answer:

$y = \frac{7}{10} e^{3(t - 1)} + \frac{3}{10}e^{-7(t - 1)}$

Step-by-step explanation:

y′′ + 4y′ − 21y = 0

The auxiliary equation is given by

m² + 4m - 21 = 0

We solve this using the quadratic formula. So

$m = \frac{-4 +/- \sqrt{4^{2} - 4 X 1 X (-21))} }{2 X 1}\\ = \frac{-4 +/- \sqrt{16 + 84} }{2}\\= \frac{-4 +/- \sqrt{100} }{2}\\= \frac{-4 +/- 10 }{2}\\= -2 +/- 5\\= -2 + 5 or -2 -5\\= 3 or -7$

So, the solution of the equation is

$y = Ae^{m_{1} t} + Be^{m_{2} t}$

where m₁ = 3 and m₂ = -7.

So,

$y = Ae^{3t} + Be^{-7t}$

Also,

$y' = 3Ae^{3t} - 7e^{-7t}$

Since y(1) = 1 and y'(1) = 0, we substitute them into the equations above. So,

$y(1) = Ae^{3X1} + Be^{-7X1}\\1 = Ae^{3} + Be^{-7}\\Ae^{3} + Be^{-7} = 1 (1)$

$y'(1) = 3Ae^{3X1} - 7Be^{-7X1}\\0 = 3Ae^{3} - 7Be^{-7}\\3Ae^{3} - 7Be^{-7} = 0 \\3Ae^{3} = 7Be^{-7}\\A = \frac{7}{3} Be^{-10}$

Substituting A into (1) above, we have

$\frac{7}{3}B e^{-10}e^{3} + Be^{-7} = 1 \\\frac{7}{3}B e^{-7} + Be^{-7} = 1\\\frac{10}{3}B e^{-7} = 1\\B = \frac{3}{10} e^{7}$

Substituting B into A, we have

$A = \frac{7}{3} \frac{3}{10} e^{7}e^{-10}\\A = \frac{7}{10} e^{-3}$

Substituting A and B into y, we have

$y = Ae^{3t} + Be^{-7t}\\y = \frac{7}{10} e^{-3}e^{3t} + \frac{3}{10} e^{7}e^{-7t}\\y = \frac{7}{10} e^{3(t - 1)} + \frac{3}{10}e^{-7(t - 1)}$

So the solution to the differential equation is

$y = \frac{7}{10} e^{3(t - 1)} + \frac{3}{10}e^{-7(t - 1)}$

6 0

3 years ago

Yooo im from k12 please help me rqqq!!!

jek_recluse [69]

$\sf \: 12x^{4} ( - 56x^{3} {y}^{2} )$

Multiplying a positive and a negative equals a negative: (+)×(-)=(-)

$\sf \: { - 12x}^{4} \times 56 {x}^{3} {y}^{2}$

Calculate the product

$\boxed{ \tt - 672x^{7} {y}^{2} }$

3 0

2 years ago

Read 2 more answers

Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink. What fraction of the bouquet is pink

Vladimir [108]

Answer:

b) 7 over 12 or (7/12)

Step-by-step explanation:

The number of white roses = 5

Therefore,

The number of pink roses= 12-5

= 7

So the fraction will be

Pink roses/ total roses

= 7/12

3 0

3 years ago

Read 2 more answers

Wat the Pythagorean theorem

alexandr402 [8]

The Pythagorean theorem:

The theorem that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

<h2>The Pythagorean Theorem</h2><h3>Discoverer: Pythagoras</h3>

In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides. These calculations were discovered just as a tool of the ancient civilization of Babylonians who used it to divide up farmland; this was roughly 1,000 years before the birth of the discoverer, Pythagoras, a Greek philosopher.

The formula comes like this:
$a^2+b^2=c^2$

5 0

2 years ago