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3 years ago

What is the area of this trapezoid?

Mathematics

1 answer:

oee [108]3 years ago

8 0

Answer:

Step-by-step explanation:

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Lisa and Krystal are planning trips to ten countries this year. They have 14 countries on their bucket list, in how many ways ca

Salsk061 [2.6K]

Answer:

1,001 ways for them to decide.

Step-by-step explanation:

The order in which they will visit the countries is not important, so we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

10 countries from a set of 14. So

$C_{14,10} = \frac{14!}{10!(14-10)!} = 1001$

1,001 ways for them to decide.

8 0

3 years ago

What is the solution set to the inequality 2²-x≥6

madreJ [45]

Answer:

A is for apple

Step-by-step explanation:

abc

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3 years ago

Find the solution r(t)r(t) of the differential equation with the given initial condition: r′(t)=⟨sin9t,sin6t,9t⟩,r(0)=⟨4,6,3⟩

klemol [59]

$\mathbf r'(t)=\langle\sin9t,\sin6t,9t\rangle$

$\mathbf r(t)=\displaystyle\int\mathbf r'(t)\,\mathrm dt$

$\mathbf r(t)=\left\langle\displaystyle\int\sin9t\,\mathrm dt,\int\sin6t\,\mathrm dt,\int9t\,\mathrm dt\right\rangle$

$\displaystyle\int\sin9t\,\mathrm dt=\frac19\cos9t+C_1$

$\displaystyle\int\sin6t\,\mathrm dt=\frac16\cos6t+C_2$

$\displaystyle\int9t\,\mathrm dt=\frac92t^2+C_3$

With the initial condition $\mathbf r(0)=\langle4,6,3\rangle$ , we find

$\dfrac19\cos0+C_1=4\implies C_1=\dfrac{35}9$

$\dfrac16\cos0+C_2=6\implies C_2=\dfrac{35}6$

$\dfrac92\cdot0^2+C_3=3\implies C_3=3$

So the particular solution to the IVP is

$\mathbf r(t)=\left\langle\dfrac19\cos9t+\dfrac{35}9,\dfrac16\cos6t+\dfrac{35}6,\dfrac92t^2+3\right\rangle$

4 0

3 years ago

Find the midpoint of points A(-7,7) and B(-1,-3) graphically.

AfilCa [17]

Answer:

(3,5)

Step-by-step explanation:

Use the midpoint formula to find the midpoint of the line segment.

(3,5)

8 0

3 years ago

Whats the mean of 72+72+72+79+82+82+88?

creativ13 [48]

Answer:

78.1428571429

Step-by-step explanation:

6 0

2 years ago

What is the area of this trapezoid? ​

What is the area of this trapezoid?