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2 years ago

5

A population of 175 snails is increasing at an annual rate of 12%. what will the population

1 answer:

qaws [65]2 years ago

3 0

$\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &175\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ t=years\dotfill &10\\ \end{cases} \\\\\\ A=175(1 + 0.12)^{10}\implies A=175(1.12)^{10}\implies A\approx 543.52$

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Given sin thata = 2/5 and 0° < thata < 90°. find sin 2 thata

Andrej [43]

Recall the double angle identity:

$\sin2\theta=2\sin\theta\cos\theta$

With $\theta$ measuring between 0º and 90º, we know $\cos\theta>0$ . So from the Pythagorean identity, we get

$\sin^2\theta+\cos^2\theta=1\implies\cos\theta=\sqrt{1-\sin^2\theta}=\dfrac{\sqrt{21}}5$

Then

$\sin2\theta=2\dfrac25\dfrac{\sqrt{21}}5=\dfrac{4\sqrt{21}}{25}$

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4 years ago

Determine if line AB and line CD are parallel, perpendicular, or neither.

choli [55]

Answer:

AB and CD are parallel lines

Step-by-step explanation:

• Parallel lines have equal slopes

• The slopes of perpendicular lines are negative reciprocals

Calculate the slope m using the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

let (x₁, y₁ ) = A(1, 4) and (x₂, y₂ ) = B(3, 8)

m = $\frac{8-4}{3-1}$ = $\frac{4}{2}$ = 2

let (x₁, y₁ ) = C(- 1, 6) and (x₂, y₂ ) = D(3, 14)

m = $\frac{14-6}{3+1}$ = $\frac{8}{4}$ = 2

Since slope of AB and CD are equal then lines are parallel

3 0

3 years ago

Read 2 more answers

A self-tanning lotion advertises that a 4 -oz bottle will provide seven applications. Jen found a great deal on a 13 -oz bott

Alexxx [7]

4oz = 7 app
1oz = 1.75 app

13oz = 1.75 x 13
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3 years ago

Two angles are complementary.The larger angle is 30 degrees more than 4 times the smaller

gregori [183]

Answer:

Step-by-step explanation:

Remark

2 angles are complementary means that 2 angles add up to 90°. That is the guiding princeple behind the problem.

Givens

Let the smallest angle = x

Let the largest angle = 4x + 30

Equation

4x + 30° + x = 90° Combine like terms on the left

Solution

5x + 30 = 90 Subtract 30 from both sides.

5x + 30 - 30 = 90 - 30 Combine

5x = 60 Divide both sides by 5

5x/5 = 60/5

x = 12

Answer

smallest angle = 12
Larger angle = 4*12 + 30 = 78

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2 years ago

7(4g) + 3(5h) + 2 (-3g); g=1/2 , h= 1/3

Digiron [165]

7(4(1/2))+3(5(1/3))+2(-3(1/2))=
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3 years ago