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coldgirl [10]
2 years ago
11

A fruit basket contains oranges and grape fruits. One-third of the oranges and one-fourth of the grapefruits were spoiled. You t

hrew away 4 oranges and 7 grapefruits. How many peices of fruit were in the basket? ( write in algebraic form using the reciprocal property )
Mathematics
1 answer:
den301095 [7]2 years ago
5 0
So if 1/3 0f the oranges equals 4, than you times it by three to get 3/3, so there were 12 oranges and 28 grapefruits, so the answer is 40
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Consider the initial value problem y′+4y=48t,y(0)=9. y′+4y=48t,y(0)=9. Take the Laplace transform of both sides of the given dif
Nadusha1986 [10]

Answer:

sY(s)-y(0) +4Y(s) = 48 *\frac{1}{s^2}

Step-by-step explanation:

given is the Differential equation in I order linear as

y′+4y=48t,y(0)=9.

Take Laplace on both sides

L(y') +4L(y) = 48L(t)\\sY(s)-y(0) +4Y(s) = 48 *\frac{1}{s^2} \\Y(s) [s+4]=\frac{48}{s^2}+9\\Y(s) = \frac{1}{s^2(s+4)}+\frac{9}{s+4}

Now if we take inverse we get y(t) the solution

Thus the algebraic equation would besY(s)-y(0) +4Y(s) = 48 *\frac{1}{s^2}

8 0
1 year ago
The dot plots below show rainfall totals in the Highlands and Lowlands areas of a certain region.
Andre45 [30]

Options:

A. Both the Highlands and the Lowlands data points are evenly distributed around the center.

B. Both the Highlands and the Lowlands data points are clustered toward the left of the plot.

C. The Highlands data points are evenly distributed around the center, while the Lowlands data points are clustered toward the left of the plot.

D. The Highlands data points are clustered toward the left of the plot, while the Lowlands data points are evenly distributed.

Answer:

B. Both the Highlands and the Lowlands data points are clustered toward the left of the plot.

Step-by-step Explanation:

From the dot plots displaying rainfall totals for highland and lowland areas as shown in the diagram attached below, we can clearly observe that most of the dots on the plot tend to be more concentrated towards the left of the plot, compared to the concentration of dots toward the right of the plot.

Invariably, we can infer that data points for lowlands and Highlands are clustered toward the left of the plot.

Therefore, the statement that is true, comparing the shapes of the dot plot is B. "Both the Highlands and the Lowlands data points are clustered toward the left of the plot."

7 0
2 years ago
David proved the Law of Cosines with reference to ∆ABC using a different method. Arrange the steps of his proof in the correct s
AURORKA [14]

Answer: We can arrange the steps with help of below explanation.  

Step-by-step explanation:

Here ABC is a triangle,

Draw a perpendicular from BD to side AC ( construction)

where D\in AC

In the right triangle BCD, from the definition of cosine:

cos C =CD/ BC

CD= a cos C

Subtracting this from the side b, we see that

DA= b-acos C  

In the triangle BCD, from the definition of sine:

sin C =BD  / a

BD = a sin C  

In the triangle ADB, applying the Pythagorean Theorem

c^2  =BD^2 +DA^2  

Substituting for BD and DA from (2) and (3)

c^2 =(asinC)^2 +(b-acosC)^2  

⇒c^2 =a^2sin ^2C+b^2-2ab cosC+a^2 cos ^2C   ( On simplification)

⇒c^2 =a^2sin ^2C+a^2 cos ^2C+b^2-2abcos C

⇒c^2=a^2(sin^2C+cos^2C) +b^2-2abcosC

⇒c^2 = a^2+b^2-2abcosC (because,sin^2\theta+cos^2\theta =1 )


3 0
2 years ago
A movie theater was putting up their posters in the frames they had installed on the wall for upcoming attractions. They have 8
Serjik [45]

Answer:

1680

Step-by-step explanation:

Since there are 4 places (frames) to put up each poster, we think individually:

In the first place they can place ANY OF THE 8 POSTERS

In 2nd place, they can place ANY OF THE REMAINING 7 POSTERS

In 3rd place, they can place ANY OF THE REMAINING 6 posters

and

in last place, they can place ANY OF THE REMAINING 5 posters

The number of ways is the multiplication of them all, so:

8 * 7 * 6 * 5 ways = 1680 ways

7 0
2 years ago
Read 2 more answers
Investigate the following harvesting model both qualitatively and analytically. If a constant number h of fish are harvested fro
zalisa [80]

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

t=-\frac{2}{7}-\frac{2}{2P_0-7}=0\\\\-\frac{2}{2P_0-7}=\frac{2}{7}\\\\7-2P_0=7\\\\P_0=0

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.

5 0
2 years ago
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