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3 years ago

Please help, thanks.

Mathematics

2 answers:

zhannawk [14.2K]3 years ago

8 0

Answer:

-109

Step-by-step explanation:

As x changes from 1 to 2, 2 to 3, and 3 to 4, each change in x is 1. The corresponding changes in y from 19 to 15, from 15 to 11, and from 11 to 7, are each a change of -4 in y. For each change of 1 in x, the corresponding change in y is -4. From 4 to 33 in x, the change is 33 - 4 = 29. The corresponding change in y is 29 * (-4) = -116.

7 + (-116) = -109

sammy [17]3 years ago

7 0

Answer:

-109

Step-by-step explanation:

Arithmetic sequence formula:

an = a1 + d(n - 1) where d = -4 and a1 = 19

a(33) = 19 - 4(33-1)

a(33) = 19 - 4(32)

a(33) = 19 - 128

a(33) = -109

The missing term : -109

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3 years ago

Kari's paper cup holds 6 fluid ounces. If one ounce is equivalent to 29.6 milliliters, how many milliliters does her paper cup h

Degger [83]

Answer:

Equivalent measurements: teaspoon, ounce, pint, pound

You will find a table of equivalent measurements in the back of many cookbooks:

1 tablespoon = 3 teaspoons

1 cup = 16 tablespoon = 8 ounces

1/4 cup = 4 tablespoons

1/3 cup = 5 tablespoons plus 1 teaspoon

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1 gallon = 4 quarts

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Note that a pint is 16 ounces of volume, while a pound is 16 ounces of weight. The popular rhyme "A pint's a pound, the world around" can help you remember this, but keep in mind that they're not really equivalent.

Doubling a recipe can be easy (just put in two of each measurement), but what if you need to divide a recipe in half? Here are some measurements that may help:

Measurement 1/2 Measurement

1/8 teaspoon just a dash

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1/4 cup 2 tablespoons

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Step-by-step explanation:

7 0

3 years ago

Implicit differentiation Please help

Anvisha [2.4K]

Answer:

$y''(-1) =8$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Factoring

Calculus

Implicit Differentiation

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

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

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

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

Step-by-step explanation:

Step 1: Define

-xy - 2y = -4

Rate of change of the tangent line at point (-1, 4)

Step 2: Differentiate Pt. 1

Find 1st Derivative

Implicit Differentiation [Product Rule/Basic Power Rule]: $-y - xy' - 2y' = 0$
[Algebra] Isolate y' terms: $-xy' - 2y' = y$
[Algebra] Factor y': $y'(-x - 2) = y$
[Algebra] Isolate y': $y' = \frac{y}{-x-2}$
[Algebra] Rewrite: $y' = \frac{-y}{x+2}$

Step 3: Find y

Define equation: $-xy - 2y = -4$
Factor y: $y(-x - 2) = -4$
Isolate y: $y = \frac{-4}{-x-2}$
Simplify: $y = \frac{4}{x+2}$

Step 4: Rewrite 1st Derivative

[Algebra] Substitute in y: $y' = \frac{-\frac{4}{x+2} }{x+2}$
[Algebra] Simplify: $y' = \frac{-4}{(x+2)^2}$

Step 5: Differentiate Pt. 2

Find 2nd Derivative

Differentiate [Quotient Rule/Basic Power Rule]: $y'' = \frac{0(x+2)^2 - 8 \cdot 2(x + 2) \cdot 1}{[(x + 2)^2]^2}$
[Derivative] Simplify: $y'' = \frac{8}{(x+2)^3}$