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Daniel [21]
2 years ago
15

F is directly proportional to a.If F = 42 when a 7 finda when F = 18​

Mathematics
2 answers:
horrorfan [7]2 years ago
7 0

Answer:

a=3

Step-by-step explanation:

The formula for direct proportion is

f = ka

Let f= 42 and a = 7

42 = k*7

Divide each side by 7

42/7 = k7/7

6 =k

f = 6a

Let f = 18

18 = 6a

Divide each side by 6

18/6 = 6a/6

3 =a

crimeas [40]2 years ago
4 0

Answer:

a = 3

Step-by-step explanation:

Given that F is directly proportional to a, then the equation relating them is

F = ka ← k is the constant of proportion

To find k use the condition F = 42 when a = 7, thus

42 = 7k ( divide both sides by 7 )

6 = k

F = 6a ← equation of proportion

When F = 18, then

18 = 6a ( divide both sides by 6 )

3 = a

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Answer:

3rd graph down

Step-by-step explanation:

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looking at the points you can see that the points for the solid line are both the same so ignore those and go to the dashed lined ones.

on the first graph the points are (0,4)

plugging those into our equation gives us 0 + 2*4 <4

or 8<4 which doesnt make sense making 3 the correct graph

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2 years ago
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Which transformation will map an isosceles trapezoid onto itself? rotation by 180° about its center, reflection across a diagona
alukav5142 [94]

Answer:

The correct option is 4.

Step-by-step explanation:

The non parallel sides of an isosceles trapezoid are congruent.

The image of an isosceles trapezoid is same as the preimage of isosceles trapezoid if

1. Reflection across a line joining the midpoints of parallel sides.

2. Rotation by 360° about its center.

3. Rotation by 360° about origin.

If we rotate the trapezoid by 180° about its center, then the parallel sides will interchanged.

If we reflect the trapezoid across a diagonal, then the resultant figure will be a parallelogram.

If we reflect across a line joining the midpoints of the nonparallel sides, then the parallel sides will interchanged.

After rotation by 360° about the center, we always get an onto figure.

Therefore option 4 is correct.

6 0
2 years ago
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Answer:

a. The population does not become extinct in finite time.

Step-by-step explanation:

The model for the population of the fishery is

dP/dt = P(a-bP)-h, P(0) = P_0

If we rearrange and replace the constants we have:

\frac{dP}{P(7-P)-49/4} =dt\\\\-4 (\frac{dP}{4(P-7)P+49}) =dt\\\\-4 \frac{dP}{(2P-7)^2} =dt\\\\-4 \int\frac{dP}{(2P-7)^2} =\int dt\\\\-4(-\frac{1}{2(2P-7)})=t+C\\\\\frac{2}{2P-7}=t+C\\\\ t=0 \,\,\, P(0)=P_0\\\\\frac{2}{2P_0-7}=0+C\\\\C=\frac{2}{2P_0-7}

Now we can calculate if the population become 0 in any finite time

\frac{2}{2P-7}=t+\frac{2}{2P_0-7}\\\\\frac{2}{2*0-7}=t+\frac{2}{2P_0-7}\\\\-\frac{2}{7}=t+\frac{2}{2P_0-7}\\\\

To be a finite time, t>0

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We can conclude that the only finite time in which P=0 is when the initial population is 0.

Because P0 is a positive constant, we can say that the population does not become extint in finite time.

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Answer:

Simplifying

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Reorder the terms:

7 + 3n = 30

Solving

7 + 3n = 30

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Move all terms containing n to the left, all other terms to the right.

Add '-7' to each side of the equation.

7 + -7 + 3n = 30 + -7

Combine like terms: 7 + -7 = 0

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Step-by-step explanation:

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