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2 years ago

Can I please get help?!

Mathematics

1 answer:

Arisa [49]2 years ago

3 0

Answer:

The answer is d.

Step-by-step explanation:

x is "a number." When a variable and a number are next to each other, they are being multiplied. So it's 7 times a number. Then you take the product of that and add 2.

So, d is the correct answer. :D

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Liev is assembling a coffee table. The diagram below is from the instruction manual and shows the table after the first two legs

elixir [45]

Answer:

The support is 41 inches long.

Step-by-step explanation:

There's two ways we can do this: one with the diagonal formula and one without.

Since we know that Point C is halfway down leg A and that the table legs are 18 inches tall, Point C is 9 inches down leg A. The support, from Point C to Point D, will form a diagonal, the length of which we need to find. We know from the diagram that the width of the table is 24 inches and that its length is 32 inches. We have a height, length, and width for this problem, so let's imagine a rectangular prism, which has all three of those things, instead of a table. The formula for finding a rectangular prism's diagonal is $d = \sqrt{l^{2} + w^{2} + h^{2} }$ . Let's put in those numbers:

$d = \sqrt{32^{2} + 24^{2} + 9^{2} } = 41$

Therefore, the support is 41 inches long.

--------------------------------------------------------------------------------------------------------------

Another way you can do this is to use the Pythagorean Theorem twice: once to find the diagonal of the tabletop and another time for the support.

$24^{2} + 32^{2} = c^{2} \\576 + 1024 = c^2\\1600 = c^2\\\sqrt{1600} = \sqrt{c^2}\\ 40 = c$

Now that we know the corner-to-corner distance for the tabletop, we'll use that and the 9 inch distance for Point C to find the distance between C and D:

$9^{2} + 40^{2} = c^{2}\\ 81 + 1600 = c^2\\1681 = c^2\\\\sqrt{1681} = \sqrt{c^2} \\41 = c$

Again, the support is 41 inches long.

4 0

3 years ago

QUESTION 7 7.1 The fifth term of an arithmetic sequence is zero and the thirteenth term is equal to 16. Determine: the common di

pishuonlain [190]

Answer:

Step-by-step explanation:

The first term is our fifrth and 13th is our 9th term in the new sequence. So each step has to be 2. 2 * 8 = 16

3 0

2 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: $y'' = \frac{8}{(x+2)^3}$