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3 years ago

14

Mike's grandmother opened a savings account in Mike's name and deposited some money into the account. The account pays an annual

simple interest rate of 11%. After 14 years, the interest earned on the account was $3,080. How much money did Mike's grandmother deposit in the account?

1 answer:

algol [13]3 years ago

7 0

Answer:

Step-by-step explanation:

Bà của Mike đã mở một tài khoản tiết kiệm đứng tên Mike và gửi một số tiền vào tài khoản. Tài khoản trả lãi suất đơn giản hàng năm là 11%. Sau 14 năm, tiền lãi thu được trên tài khoản là $ 3,080

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110 meters of fencing are used to fence a rectangular pasture of 750 square meters of farmland. If the length of the pasture is

omeli [17]

Answer:

<h3>25m</h3>

Step-by-step explanation:

Perimeter of the rectangular pasture P = 2(L+W)

Area A = LW

L is the length

W is the width

Given

Perimeter = 110m

Area = 750m

If the length of the pasture is 40m longer than the width, then L = W+40

110 = 2L+2w

55 = L+W .....1

750 = LW.....2

Solving simultaneously

from 1; L = 55-W

substitute into 2;

750 = (55-W)W

750 = 55W-W²

-W²+55W -750 = 0

W²-55W+750 = 0

(W²-25W)-(30W+750) = 0

W(W-25)-30(W-25) = 0

(W-25)(W-30) = 0

W-25 = 0 and W-30 = 0

w = 25m and 30m

Since L = 55-W

L = 55-25 = 30m and;

L = 55-30 = 25m

Since we are told that length id longer than the width then, the width we are going to use is 25m

7 0

3 years ago

Please help this is for my son

Anuta_ua [19.1K]

Answer:

8 cookies left to be baked

Step-by-step explanation:

<u>Len</u>

Len bakes 1/3 of 30 cookies

To find 1/3 of 30, divide 30 by 3 then multiply by 1:

$\implies \frac{30}{3} \times1=10 \times 1=10$

Therefore, Len bakes 10 cookies

<u>Sallesh</u>

Sallesh bakes 2/5 of 30 cookies

To find 2/5 of 30, divide 30 by 5 then multiply by 2:

$\implies \frac{30}{5} \times2=6 \times 2=12$

Therefore, Sallesh bakes 12 cookies

<u>Cookies left to bake</u>

To calculate how many cookies are left to bake, subtract the found number of cookies Len and Sallesh have baked from 30:

30 - 10 - 12 = 8

So there are 8 cookies left to be baked.

3 0

2 years ago

Read 2 more answers

Find the equation of the line in slope-intercept form.Slope is 3/5 and (0, −2)

Nadya [2.5K]

Answer:

$y = \frac{3}{5}x - 2$

Step-by-step explanation:

Using the point slope form of a line equation, substitute m = 3/5 and the point (0,-2).

$y - y_1 = m(x-x_1)\\y --2 = \frac{3}{5}(x - 0)\\y + 2 = \frac{3}{5}x \\ y = \frac{3}{5}x - 2$

8 0

4 years ago

Can the sides of a triangle have lengths 5, 8, and 11? Yes or no

tiny-mole [99]

Answer:

no

Step-by-step explanation:

when you add 5 and 8 that will be 13. and according to the rules, both lengths of the triangle should add up to be greater then the other number in this case,11.

3 0

3 years ago

Help with num 3 please. thanks

Alja [10]

Answer:

a) $\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 0} = -1$

b) $\displaystyle \frac{dy}{dx} \bigg| \limits_{x = \frac{\pi}{2}} = -1$

General Formulas and Concepts:

<u>Pre-Calculus</u>

Unit Circle

<u>Calculus</u>

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Derivative Rule [Quotient Rule]: $\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Trigonometric Differentiation

Logarithmic Differentiation

Step-by-step explanation:

a)

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle y = ln \bigg( \frac{1 - x}{\sqrt{1 + x^2}} \bigg)$

<u>Step 2: Differentiate</u>

Logarithmic Differentiation [Chain Rule]: $\displaystyle \frac{dy}{dx} = \frac{1}{\frac{1 - x}{\sqrt{1 + x^2}}} \cdot \frac{d}{dx}[\frac{1 - x}{\sqrt{1 + x^2}}]$
Simplify: $\displaystyle \frac{dy}{dx} = \frac{-\sqrt{x^2 + 1}}{x - 1} \cdot \frac{d}{dx}[\frac{1 - x}{\sqrt{1 + x^2}}]$
Quotient Rule: $\displaystyle \frac{dy}{dx} = \frac{-\sqrt{x^2 + 1}}{x - 1} \cdot \frac{(1 - x)'\sqrt{1 + x^2} - (1 - x)(\sqrt{1 + x^2})'}{(\sqrt{1 + x^2})^2}$
Basic Power Rule [Chain Rule]: $\displaystyle \frac{dy}{dx} = \frac{-\sqrt{x^2 + 1}}{x - 1} \cdot \frac{-\sqrt{1 + x^2} - (1 - x)(\frac{x}{\sqrt{x^2 + 1}})}{(\sqrt{1 + x^2})^2}$
Simplify: $\displaystyle \frac{dy}{dx} = \frac{-\sqrt{x^2 + 1}}{x - 1} \cdot \bigg( \frac{x(x - 1)}{(x^2 + 1)^\bigg{\frac{3}{2}}} - \frac{1}{\sqrt{x^2 + 1}} \bigg)$
Simplify: $\displaystyle \frac{dy}{dx} = \frac{x + 1}{(x - 1)(x^2 + 1)}$

<u>Step 3: Find</u>

Substitute in <em>x</em> = 0 [Derivative]: $\displaystyle \frac{dy}{dx} \bigg| \limit_{x = 0} = \frac{0 + 1}{(0 - 1)(0^2 + 1)}$
Evaluate: $\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 0} = -1$

b)

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle y = ln \bigg( \frac{1 + sinx}{1 - cosx} \bigg)$

<u>Step 2: Differentiate</u>

Logarithmic Differentiation [Chain Rule]: $\displaystyle \frac{dy}{dx} = \frac{1}{\frac{1 + sinx}{1 - cosx}} \cdot \frac{d}{dx}[\frac{1 + sinx}{1 - cosx}]$
Simplify: $\displaystyle \frac{dy}{dx} = \frac{-[cos(x) - 1]}{sin(x) + 1} \cdot \frac{d}{dx}[\frac{1 + sinx}{1 - cosx}]$
Quotient Rule: $\displaystyle \frac{dy}{dx} = \frac{-[cos(x) - 1]}{sin(x) + 1} \cdot \frac{(1 + sinx)'(1 - cosx) - (1 + sinx)(1 - cosx)'}{(1 - cosx)^2}$
Trigonometric Differentiation: $\displaystyle \frac{dy}{dx} = \frac{-[cos(x) - 1]}{sin(x) + 1} \cdot \frac{cos(x)(1 - cosx) - sin(x)(1 + sinx)}{(1 - cosx)^2}$
Simplify: $\displaystyle \frac{dy}{dx} = \frac{-[cos(x) - sin(x) - 1]}{[sin(x) + 1][cos(x) - 1]}$

<u>Step 3: Find</u>

Substitute in <em>x</em> = π/2 [Derivative]: $\displaystyle \frac{dy}{dx} \bigg| \limit_{x = \frac{\pi}{2}} = \frac{-[cos(\frac{\pi}{2}) - sin(\frac{\pi}{2}) - 1]}{[sin(\frac{\pi}{2}) + 1][cos(\frac{\pi}{2}) - 1]}$
Evaluate [Unit Circle]: $\displaystyle \frac{dy}{dx} \bigg| \limit_{x = \frac{\pi}{2}} = -1$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Book: College Calculus 10e

4 0

3 years ago