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3 years ago

Chris made hamburgers for his family and they each had a diameter of 3 in. If he made 16 hamburgers.

Mathematics

1 answer:

Alenkasestr [34]3 years ago

7 0

Answer:

The total area for all 16 hamburgers is 113.04 in².

Step-by-step explanation:

Given:

Chris made hamburgers for his family and they each had a diameter of 3 in.

If he made 16 hamburgers.

Now, to find the total area for all 16 hamburgers.

So, the diameter 3 in is given and we need first to find the radius:

$Radius\ (r)=\frac{Diameter}{2} =\frac{3}{2} =1.5\ in.$

Now, to get the area of a hamburger we put formula:

(Taking the value of π = 3.14.)

$Area=\pi r^2\\\\Area=3.14\times (1.5)^2\\\\Area=3.14\times 2.25\\\\Area=7.065\ in^2.$

Now. to get the total area of 16 hamburgers by multiplying 16 by the area of a hamburger:

$7.065\times 16\\\\=113.04\ in^2.$

Therefore, the total area for all 16 hamburgers is 113.04 in².

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Solve the differential equation. y' + 5xey = 0.

galben [10]

Answer:

The solution is $y = - ln(\frac{5}{2}x^{2} + C)$

Step-by-step explanation:

To solve the differential equation, we will find $y$

From the given equation, y' + 5xey = 0.

That is, $y' + 5xe^{y} = 0$

This can be written as

$\frac{dy}{dx} + 5xe^{y} = 0$

Then,

$\frac{dy}{dx} = - 5xe^{y}$

$\frac{dy}{e^{y}} = - 5x dx$

Then, we integrate both sides

$\int {\frac{dy}{e^{y}}} =\int {- 5x dx}$

$\int {e^{-y}dy }} =\int {- 5x dx}$

Then,

$-e^{-y} = -\frac{5}{2}x^{2} + C$

$e^{-y} = \frac{5}{2}x^{2} + C$

Then,

$ln(e^{-y}) = ln(\frac{5}{2}x^{2} + C)$

Then,

$-y = ln(\frac{5}{2}x^{2} + C)$

Hence,

$y = - ln(\frac{5}{2}x^{2} + C)$

5 0

3 years ago

5. Find the measures of the following. Round to the nearest whole number. (2 points)

chubhunter [2.5K]

Answer:

HT = 17 cm

<T = 58°

<H = 32°

Step-by-step explanation:

✔️Find HT:

Since it's a right triangle, we would apply the Pythagorean Theorem given as c² = a² + b²

Where,

a = HW = 15 cm

b = WT = 8 cm

c = HT

Plug in the values:

HT² = 15² + 8²

HT² = 289

HT = √289

HT = 17 cm

✔️Find <T by applying trigonometric ratio formula:

Recall: SOH CAH TOA

Reference angle (θ) = <T

HW = 15 cm = Opposite side length

WT = 8 cm = Adjacent side length

Apply CAH:

Cos θ = Adj/Hyp

Substitute

Cos T = 8/15

T = $cos^{-1}(0.5333)$

T ≈ 58°

✔️Find <H:

Sun of interior angles of a triangle = 180°

Therefore,

m<H + m<T + m<W = 180°

Substitute

m<H + 58° + 90° = 180°

m<H + 148° = 180°

m<H = 180° - 148°

m<H = 32°

4 0

3 years ago

Find the ratio 2 1/2 to 6 1/2

ivanzaharov [21]

Answer:

The ratio 2 1/2 to 6 1/2 is

$\frac{5}{13}\\or\\5:13$

Step-by-step explanation:

Ratio:

In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second.

It is also the Fraction

For example, if a bowl of fruit contains eight apples and six kiwis, then the ratio of apples to kiwis is eight to six.

i.e 8:6, which is equivalent to the ratio 4:3.

Now here,

$2\frac{1}{2}=\frac{4+1}{2}\\\\2\frac{1}{2}=\frac{5}{2}\\\\and\\\\6\frac{1}{2}=\frac{12+1}{2}\\\\6\frac{1}{2}=\frac{13}{2}$

Ratio of 2 1/2 to 6 1/2

$\frac{\frac{5}{2}}{\frac{13}{2}} = \frac{5}{13}\ \textrm{The number 2 will be cancelled from Numerator and Denominator} \\\\Hence,\\Final\ Ratio\ is\ 5 :13$

$\frac{5}{13}$

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4 years ago

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vova2212 [387]

The answer to your question is 3.666

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