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3 years ago

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A spider has 8 legs. An ant has 6 legs. There are a group of spiders and a group of ants. The groups have equal numbers of legs.

What is the least number of spiders and ants in each group? Show your work

1 answer:

Lemur [1.5K]3 years ago

8 0

There are three spiders and 4 ants in all

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Write the given second order equation as its equivalent system of first order equations. u′′−5u′−4u=1.5sin(3t),u(1)=1,u′(1)=2.5

lakkis [162]

Answer:

hi your question options is not available but attached to the answer is a complete question with the question options that you seek answer to

Answer: v = 5v + 4u + 1.5sin(3t),

0

1

4

5

0

1.5sin(3t)

1

2.5

Step-by-step explanation:

u" - 5u' - 4u = 1.5sin(3t) where u'(1) = 2.5 u(1) = 1

v represents the "velocity function" i.e v = u'(t)

As v = u'(t)

<em>u' = v</em>

since <em>u' = v </em>

v' = u"

v' = 5u' + 4u + 1.5sin(3t) ( given that u" - 5u' - 4u = 1.5sin(3t) )

= 5v + 4u + 1.5sin(3t) ( noting that v = u' )

so v' = 5v + 4u + 1.5sin(3t)

d/dt $\left[\begin{array}{ccc}u&\\v&\\\end{array}\right]$ = $\left[\begin{array}{ccc}0&1&\\4&5&\\\end{array}\right]$ $\left[\begin{array}{ccc}u&\\v&\\\end{array}\right]$ + $\left[\begin{array}{ccc}0&\\1.5sin(3t)&\\\end{array}\right]$

Given that u(1) = 1 and u'(1) = 2.5

since v = u'

v(1) = 2.5

note: the initial value for the vector valued function is given as

$\left[\begin{array}{ccc}u(1)&\\v(1)\\\end{array}\right]$ = $\left[\begin{array}{ccc}1\\2.5\\\end{array}\right]$

7 0

3 years ago

Four decreased by the product of a number and 7 is equal to 11

Nana76 [90]

Answer:

See image below:)

Step-by-step explanation:

5 0

3 years ago

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Answer 6s^5t x s^4t^2

babunello [35]

Answer:

6s⁹t³

Step-by-step explanation:

6s⁵t ₓ s⁴t² =

= 6ₓs⁵⁺⁴t¹⁺²

= 6s⁹t³

8 0

3 years ago

Read 2 more answers

Solve 5 tan x = 5√(3) for 0° ≤ x ≤ 180°.<br><br> a. 60°<br> b. 150°<br> c. 30°<br> d. 120°

ladessa [460]

Answer:

$\boxed{a.\:\:\:60\degree}$

Step-by-step explanation:

The given trigonometric equation is

$5\tan(x)=5\sqrt{3}$ for $0\degree \le x\le 180\degree$ .

We divide through by 5 to get;

$\tan(x)=\sqrt{3}$

We take the inverse tangent of both sides to obtain;

$x=tan^{-1}(\sqrt{3})$

$x=60\degree$

Since the tangent ratio is positive, it means $x$ could also be in the 3rd quadrant. But this is outside the given range.

Therefore the correct answer is A

6 0

3 years ago

What is the equation for the values in the table

devlian [24]

Step-by-step explanation:

Taking any two points through which the line passes;(-10,-3) and (-5,-1)

The equation of the line is given by

$\frac{y2 - y1}{x2 - x1} = \frac{y - y1}{x - x1}$

$=> \frac{ - 1 - ( - 3)}{ - 5 - ( - 10)} = \frac{y - ( - 3)}{x - ( - 10)} = \frac{y + 3}{x + 10}$

$=> \frac{ - 1 + 3}{ - 5 + 10} = \frac{y + 3}{x + 10}$

$=> \frac{2}{5} = \frac{y + 3}{x + 10}$

$=> 5(y + 3) = 2(x + 10)$

=> 5y+15 = 2x+20

=> 5y =2x+5

$=> y= \frac{2}{5} x + 1$

option C

8 0

3 years ago