Mary had five and one-half dollars. She spent tw wo and one-fourth dollars on a snack. How much money does Mary have left?

In ∆XYZ, m∠X = 152, y = 15, and z = 19. Find side x and the measure of angle Y to the nearest tenth

solong [7]

The measure of the side $x$ is approximately 33 and the measure of angle $Y$ is approximately 12.321°.

<h3>How to find a missing angle in a triangle by law of sine and law of cosine</h3>

In this problem we must apply the law of cosine and the law of sine to determine the angle Y:

<h3>Law of cosine</h3>

$x = \sqrt{y^{2}+z^{2}-2\cdot y\cdot z\cdot \cos X}$

$x = \sqrt{15^{2}+19^{2}-2\cdot (15)\cdot (19)\cdot \cos 152^{\circ}}$

$x \approx 33$

$\frac{\sin Y}{y} = \frac{\sin X}{x}$

$Y = \sin^{-1}\left(\frac{y}{x}\cdot \sin X \right)$

$Y = \sin^{-1}\left(\frac{15}{33}\cdot \sin 152^{\circ} \right)$

$Y \approx 12.321^{\circ}$

The measure of the side $x$ is approximately 33 and the measure of angle $Y$ is approximately 12.321°. $\blacksquare$

To learn more on triangles, we kindly invite to check this verified question: brainly.com/question/25813512

7 0

2 years ago

What is the answer to this question?

lesya692 [45]

-160,25 are the coordinates

3 0

3 years ago

Shari has 1 ½ gallons of orange juice. She wants to serve the orange juice equally to 12 of her friends. How many ounces of juic

kotykmax [81]

Answer:

16 ounces each

Step-by-step explanation:

1 gallon equals 128 ounces so 1.5 gallons would be 192 ounces. Divide 192 by 12 and you'll get 16.

7 0

3 years ago

Lisa ate 1/8 of a pizza. Josh ate 21/2 times a much as Lisa. What fraction of the pizza did josh eat

Aliun [14]

Josh ate 5/2 of the pizza

3 0

3 years ago

Read 2 more answers

Find dy/dx by implicit differentiation.

kow [346]

dy/dx by implicit differentiation is cos(πx)/sin(πy)

<h3>How to find dy/dx by implicit differentiation?</h3>

Since we have the equation

(sin(πx) + cos(πy)⁸ = 17, to find dy/dx, we differentiate implicitly.

So, [(sin(πx) + cos(πy)⁸ = 17]

d[(sin(πx) + cos(πy)⁸]/dx = d17/dx

d[(sin(πx) + cos(πy)⁸]/dx = 0

Let sin(πx) + cos(πy) = u

So, du⁸/dx = 0

du⁸/du × du/dx = 0

Since,

du⁸/du = 8u⁷ and

du/dx = d[sin(πx) + cos(πy)]/dx

= dsin(πx)/dx + dcos(πy)/dx

= dsin(πx)/dx + (dcos(πy)/dy × dy/dx)

= πcos(πx) - πsin(πy) × dy/dx

So, du⁸/dx = 0

du⁸/du × du/dx = 0

8u⁷ × [ πcos(πx) - πsin(πy) × dy/dx] = 0

8[(sin(πx) + cos(πy)]⁷ × (πcos(πx) - πsin(πy) × dy/dx) = 0

Since 8[(sin(πx) + cos(πy)]⁷ ≠ 0

(πcos(πx) - πsin(πy) × dy/dx) = 0

πcos(πx) = πsin(πy) × dy/dx

dy/dx = πcos(πx)/πsin(πy)

dy/dx = cos(πx)/sin(πy)

So, dy/dx by implicit differentiation is cos(πx)/sin(πy)

Learn more about implicit differentiation here:

brainly.com/question/25081524

#SPJ1

6 0

2 years ago