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Bas_tet [7]
3 years ago
15

If the general solution of a differential equation is ​y(t)equals=Upper C e Superscript negative 4 t Baseline plus 7Ce−4t+7​, wh

at is the solution that satisfies the initial condition ​y(0)equals=1010​?
Mathematics
2 answers:
Maru [420]3 years ago
8 0

Answer:

y(t) = 3e^{-4t}+7

Step-by-step explanation:

y(t) = Ce^{-4t}+7

At <em>y</em>(0) = 10, when <em>t</em> = 0, <em>y</em> = 10.

y(0) = 10 = Ce^{-4\times0}+7

10 = C+7

C = 3

Hence, the solution is

y(t) = 3e^{-4t}+7

Anuta_ua [19.1K]3 years ago
5 0

Answer:

a

Step-by-step explanation:

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Find the directional derivative of g(x, y) = xey − yex , 2x x − y at the point (1, 0) in the direction v = 3i + 4j
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7 0
3 years ago
Find an equation of a line passing through the point (8,9) and parallel to the line joining the points (2,7) and (1,5).
TiliK225 [7]

Answer:

2x - y - 7 = 0

Step-by-step explanation:

Since the slope of parallel line are same.

So, we can easily use formula,

y - y₁ = m ( x ₋ x₁)

where, (x₁, y₁) = (8, 9)

and m is a slope of line passing through (x₁, y₁).

and since the slope of parallel lines are same, so here we use slope of parallel line for calculation.

and, Slope = m = \dfrac{y_{b}-y_{a}}{x_{b}-x_{a}}

here, (xₐ, yₐ) = (2, 7)

and, (y_{a},y_{b}) = (1, 5 )

⇒ m = \dfrac{5-7}{1-2}

⇒ m = 2

Putting all values above formula. We get,

y - 9 = 2 ( x ₋ 8)

⇒ y - 9 = 2x - 16

⇒ 2x - y - 7 = 0

which is required equation.

3 0
3 years ago
Read 2 more answers
Gerry arrived at the bus stop x hours past noon. Dale arrived 4 hours later. Pat arrived at 5 P.M., x hours after Dale.
victus00 [196]

Answer:

<em>Gerry arrived at the bus station at 12:30 P.M.</em>

Step-by-step explanation:

From noon and 5:00 P.M. there are 5 hours.

Gerry, Dale, and Pat arrived at the bus stop within that interval, which means the sum of the times elapsed between their arrival times must be 5.

4 out of the 5 hours elapsed since Gerry and Dale's arrivals. This means there is only one hour left for twice x.

If twice x is one hour, then x is half an hour. Thus, the complete sequence of arrivals is:

Gerry arrived at the bus station at 12:30 P.M.

Dale arrived at the bus station at 4:30 P.M.

Pat arrived at the bus station at 5:00 P.M.

8 0
3 years ago
Annie wants to make several plates of apples apricots, so that each plate has the same number of apples and the same number of a
Vilka [71]

Answer:

Annie can make 4 plates with 8:4=2 apples and 20:4=5 apricots on each plate.

Step-by-step explanation:

Annie has  8 apples and 20 apricots.

Factor these numbers:

8=2\cdot 4=2\cdot 2\cdot 2\\ \\20=2\cdot 10=2\cdot 2\cdot 5

Find GCF(8,20):

GCF(8,20)=2\cdot 2=4

Hence, Annie can make 4 plates with 8:4=2 apples and 20:4=5 apricots on each plate.

3 0
3 years ago
Common factor of 35 and 49 is​
jonny [76]

Answer:

7

Step-by-step explanation:

35 / 7 = 5

49 /7 = 7

7 0
3 years ago
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