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2 years ago

7/8y + 1/2 = 1 1/5 Solve for y.

Mathematics

1 answer:

abruzzese [7]2 years ago

3 0

Answer:

y = 4/5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Step-by-step explanation:

Step 1: Define

Identify

7/8y + 1/2 = 1 1/5

Step 2: Solve for y

Convert to improper fraction: 7/8y + 1/2 = 6/5
[Subtraction Property of Equality] Subtract 1/2 on both sides: 7/8y = 7/10
[Division Property of Equality] Divide 7/8 on both sides: y = 4/5

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Select all of the given trigonometric equations that are true statements. sin(180°) = cos(0°) cos(74°) = sin(16°) sin(20°) = cos

lara [203]

Answer:

Cos 74°= Sin 16°

Sin 20°= Cos 70°

Sin A°=Cos (90°- A°)

Step-by-step explanation:

This is because the three pairs are complementary i.e they add up to 90° and in trigonometric ratios, complementary ratios are equal.

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3 years ago

Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$

So altogether, $f(x,y)$ has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

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2 years ago

Jane drove 355 miles using 17 gallons of gas. At this rate, how many gallons of gas would she need to drive 284 miles?

Vlad [161]

I think it is 14 if my calculations are correct.

Hope it helps

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3 years ago

What ratios are equivalent to 12:3

nlexa [21]

Answer:

4:1

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A square room has a tiled floor with 81 square tiles. How many tiles are along an edge of the room?

Sladkaya [172]

Answer:

36 tiles

Step-by-step explanation:

Because the room is square, the numbers of tiles along the edge of the room were multiplied by the same number, meaning that:

81 = x²

So to find x, we must square root both sides of the equation:

$\sqrt{81} = \sqrt{x^2}$

x = 9

So the length of one side is 9 tiles. Now to calculate the circumference, as each side of a square is the same length, we can multiply this number by 4:

9 * 4 = 36

So there are 36 tiles along the edge of the room.

Hope this helps!

4 0

2 years ago