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3 years ago

-2a 0b -2 × -5b 4 × -b

Mathematics

1 answer:

lakkis [162]3 years ago

8 0

Answer:

Step-by-step explanation:

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Nada is at the supermarket. She wants to buy a chocolate and a juice that both cost $10. How much will she pay at the cashier if

Illusion [34]

Total cost = Price of juice + price of chocolate + tax = 10 + 10 + [(16/100) x 20]

= 20 + 3.2

= $23.2

4 0

3 years ago

In a previous exercise we formulated a model for learning in the form of the differential equation dP dt = k(M − P) where P(t) m

GalinKa [24]

Answer:

$\frac{dP}{M-P}= kdt$

And we can integrate both sides of the equation using the following substitution:

$u= M-P, du =-dP$

And replacing we got:

$\int -\frac{du}{u} = kt +C$

$-ln (u)= kt+c$

If we multiply both sides by -1 we got:

$ln (u ) = -kt -c$

$ln (M-P) = -kt -c$

And using exponential in both sides of the equation we got:

$M-P = e^{-kt} e^{-c}$

And solving for P we got:

$P(t) = M- e^{-kt}e^{-c}$

And replacing $P_o =e^{-c}$ we got:

$P(t) = M - P_o e^{-kt}$

We can use the condition $P(0)=0$ and we got:

$0 = M -P_o e^0$

And we see that $M = P_o$ and replacing we got:

$P= M(1- e^{-kt})$

Step-by-step explanation:

For this case we aasume the following differential equation:

$\frac{dP}{dt}= k(M-P)$

Is a separable differential equation so we can do the following procedure:

$\frac{dP}{M-P}= kdt$

And we can integrate both sides of the equation using the following substitution:

$u= M-P, du =-dP$

And replacing we got:

$\int -\frac{du}{u} = kt +C$

$-ln (u)= kt+c$

If we multiply both sides by -1 we got:

$ln (u ) = -kt -c$

$ln (M-P) = -kt -c$

And using exponential in both sides of the equation we got:

$M-P = e^{-kt} e^{-c}$

And solving for P we got:

$P(t) = M- e^{-kt}e^{-c}$

And replacing $P_o =e^{-c}$ we got:

$P(t) = M - P_o e^{-kt}$

We can use the condition $P(0)=0$ and we got:

$0 = M -P_o e^0$

And we see that $M = P_o$ and replacing we got:

$P= M(1- e^{-kt})$

8 0

3 years ago

Omar wants to open an account for his grandchildren that he hopes will have

olga_2 [115]

Using compound interest, it is found that he must deposit $56,389.

Compound interest:

$A(t) = P(1 + \frac{r}{n})^{nt}$

A(t) is the amount of money after t years.
P is the principal(the initial sum of money).
r is the interest rate(as a decimal value).
n is the number of times that interest is compounded per year.
t is the time in years for which the money is invested or borrowed.

In this problem:

Hopes to have $80,000 in 20 years, thus $t = 20, A(t) = 80000$ .
Interest rate of 1.75%, thus $r = 0.0175$ .
Compounding monthly, thus $n = 12$
The investment is of P, for which we have to solve.

Then:

$A(t) = P(1 + \frac{r}{n})^{nt}$

$80000 = P(1 + \frac{0.0175}{12})^{12(20)}$

$P = \frac{80000}{(1 + \frac{0.0175}{12})^{12(20)}}$

$P = 56389$

He must deposit $56,389.

A similar problem is given at brainly.com/question/25263233

4 0

3 years ago

A tower casts a shadow that is 60 feet long when the angle of elevation of the sun is 65˚. How tall is the tower? Round answer t

r-ruslan [8.4K]

Answer: Tthe tower is 129 feet tall.

Step-by-step explanation:

According to trigonometry in a right triangle:

$\tan\theta =\dfrac{\text{Side opposite to }\theta}{\text{Side adjacent to }\theta}$

Let x be the height of the tower.

Given , $\theta=65^{\circ}$

Since tower stands vertical to the ground, that means it is making a right triangle with the shadow.

$\tan 65^{\circ}=\dfrac{x}{60}\\\\\Rightarrow\ 2.1445=\dfrac{x}{60}\ \ \text{[Using calculator]}\\\\\Rightarrow x= 2.1445\times60=128.67\approx129\text{ feet}$