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2 years ago

The number of players on Antonio’s basketball team increased by 20% from 2017 to 2018. If there were

Mathematics

1 answer:

yuradex [85]2 years ago

5 0

Answer:

14.4

Step-by-step explanation:

I subtracted 18-20% on a calculator lol

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If you were to write $190 as either $19 or $1,900, this mistake would be called a(n)

Verizon [17]

It would be called a mess up on ur paper

3 0

2 years ago

Waht is the elapsed time for 1:05 pm - 4:40 am

olga2289 [7]

Elapsed time from 105pm to 440am is 15 hours and 35 minutes.

8 0

2 years ago

Read 2 more answers

Bob purchased 2 hot dogs and 1 hamburger for S10. Later that day, Bob had to purchase more food and

Tom [10]

Answer:

Hotdog: $3.00

Hamburger: $4.00

Step-by-step explanation:

For the first time that Bob buys food, we can make an equation to find how much a single hotdog and a single hamburger costs, where:

x = cost of a hotdog

y = cost of a hamburger

He bought 2 hotdogs and 1 hamburger for $10, so the equation for his first time buying food is:

2x + y = 10

For the second time buying food, he bought 1 hotdog and 3 hamburgers for $15, so his equation would be:

x + 3y = 15

To find the value for x and y we need to solve this system of equations using the two equations we just came up with. We can do this multiple ways, but I'll be demonstrating the substitution method.

Using the second equation, we can solve for x by simply subtracting 3y from both sides:

x = 15 - 3y

We can then insert this value of x into the first equation so that way we are only dealing with one variable to solve - y:

2(15-3y) + y = 10

Distribute out the 2 into the paratheses, combine like terms, and then solve for y:

30 - 6y + y = 10

30 - 5y = 10

-5y = -20

y = 4

This means the cost for one hamburger is $4. But we still need to find the price of one hotdog, so we can insert this value of y into the equation we came up with earlier for x, and then solve for x:

x = 15 - 3y

x = 15 - 3(4)

x = 15 - 12

x = 3

So the price of one hotdog is $3 and the price of one hamburger is $4. Hope this helps.

3 0

2 years ago

Calculate s f(x, y, z) ds for the given surface and function. g(r, θ) = (r cos θ, r sin θ, θ), 0 ≤ r ≤ 4, 0 ≤ θ ≤ 2π; f(x, y, z)

Triss [41]

$g(r,\theta)=(r\cos\theta,r\sin\theta,\theta)\implies\begin{cases}g_r=(\cos\theta,\sin\theta,0)\\g_\theta=(-r\sin\theta,r\cos\theta,1)\end{cases}$

The surface element is

$\mathrm dS=\|g_r\times g_\theta\|\,\mathrm dr\,\mathrm d\theta=\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

and the integral is

$\displaystyle\iint_Sx^2+y^2\,\mathrm dS=\int_0^{2\pi}\int_0^4((r\cos\theta)^2+(r\sin\theta)^2)\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

$=\displaystyle2\pi\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac\pi4(132\sqrt{17}-\sinh^{-1}4)$

###

To compute the last integral, you can integrate by parts:

$u=r\implies\mathrm du=\mathrm dr$

$\mathrm dv=r\sqrt{1+r^2}\,\mathrm dr\implies v=\dfrac13(1+r^2)^{3/2}$

$\displaystyle\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac r3(1+r^2)^{3/2}\bigg|_0^4-\frac13\int_0^4(1+r^2)^{3/2}\,\mathrm dr$

For this integral, consider a substitution of

$r=\sinh s\implies\mathrm dr=\cosh s\,\mathrm ds$

$\displaystyle\int_0^4(1+r^2)^{3/2}\,\mathrm dr=\int_0^{\sinh^{-1}4}(1+\sinh^2s)^{3/2}\cosh s\,\mathrm ds$

$\displaystyle=\int_0^{\sinh^{-1}4}\cosh^4s\,\mathrm ds$

$=\displaystyle\frac18\int_0^{\sinh^{-1}4}(3+4\cosh2s+\cosh4s)\,\mathrm ds$

and the result above follows.

4 0

2 years ago

Find the positive solution of x when:<br><br> 25 = 4/x²

sladkih [1.3K]

1) Multiply both sides by x²

$25 {x}^{2} \: = \: 4$

2) Divide both sides by 25

${x}^{2} \: = \: \frac{4}{25}$

3) Square root both sides

$x \: = \: \frac{2}{5}$

Viola!

7 0

2 years ago