1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tigry1 [53]
3 years ago
12

Write an expression for cos 68° using sine

Mathematics
1 answer:
Anettt [7]3 years ago
8 0

Answer:

sin22°

Step-by-step explanation:

Using the cofunction identity

cos x = sin (90 - x), then

cos68° = sin(90 - 68)° = sin22°

You might be interested in
The sum of 2 number is 42 and when you switch the order the difference is 5
Ksivusya [100]
So, x + y = 42 and y - x = 5;
Then, y = x + 5;
Finally, x + x + 5 = 42;
2x + 5 = 42;
2x = 37;
x = 18.5;
y = 18.5 + 5;
y = 23.5;
4 0
3 years ago
2. Which answer shows another way of writing the expression below?
maria [59]

Answer:

  • D. 6b - 2

Step-by-step explanation:

<u>Simplify the expression:</u>

  • 4(3b) – 2(3b + 1) =
  • 12b - 6b - 2 =
  • 6b - 2

Correct choice is D

6 0
2 years ago
Read 2 more answers
1. Which rule describes a translation that is 8 units to the right and 2 units up?
sineoko [7]
3rd one because it makes sense
7 0
3 years ago
Read 2 more answers
What's one third multiply 3
allsm [11]
Simple! 1/3 times 3 equals 3/3, or 1.
7 0
3 years ago
Read 2 more answers
Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w
siniylev [52]

Solution :

a). The level curves of the function :

$C(x,y) = e^{-(x^2+2y^2)/10^4}$

are actually the curves

$e^{-(x^2+2y^2)/10^4}=k$

where k is a positive constant.

The equation is equivalent to

$x^2+2y^2=K$

$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$

which is a family of ellipses.

We sketch the level curves for K =1,2,3 and 4.

If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$ and

$\triangledown C$ points in the direction of most rapid increase in concentration, which means $\triangledown C$ is tangent to the most rapid increase curve.

$r(t)=x(t)i+y(t)j$  is a parametrization of the most $\text{rapid increase curve}$ , then

$\frac{dx}{dt}=\frac{dx}{dt}i+\frac{dy}{dt}j$ is a tangent to the curve.

So then we have that $\frac{dr}{dt}=\lambda \triangledown C$

$\Rightarrow \frac{dx}{dt}=-\frac{2\lambda x}{10^4}e^{-(x^2+2y^2)/10^4}, \frac{dy}{dt}=-\frac{4\lambda y}{10^4}e^{-(x^2+2y^2)/10^4} $

∴ $\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{2y}{x}$

Using separation of variables,

$\frac{dy}{y}=2\frac{dx}{x}$

$\int\frac{dy}{y}=2\int \frac{dx}{x}$

$\ln y=2 \ln x$

⇒ y = kx^2 for some constant k

but we know that $y(x_0)=y_0$

$\Rightarrow kx_0^2=y_0$

$\Rightarrow k =\frac{y_0}{x_0^2}$

∴ The path of the shark will follow is along the parabola

$y=\frac{y_0}{x_0^2}x^2$

$y=y_0\left(\frac{x}{x_0}\right)^2$

7 0
2 years ago
Other questions:
  • X+2y = 5<br> 3х +6y = 15<br><br> Use the substitution method
    13·1 answer
  • Sherry bought 6 apples at 43¢ per apple. She then bought 4 oranges at 51¢ per orange. How much was her grocery bill?
    12·2 answers
  • WILL GIVE BRAINIEST NEED AN EXPERT AT MATH PLEASE!!!!!!!!!!!!!!
    11·1 answer
  • 7w = 87 ; w = 12 I need help
    11·2 answers
  • Solve the absolute value equation 3|7x|+2=17
    11·1 answer
  • A chord 20 inches long is 4 inches from the center
    7·1 answer
  • Find the value<br><br> a) x^2 when x = 5
    15·2 answers
  • Twice the sum of three times a number and eight translate this plz
    11·1 answer
  • PLEASE HELP DUE TODAY.
    12·1 answer
  • Find a solution to the linear equation y=6x−18 by filling in the boxes with a valid value of x and y.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!