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Gelneren [198K]
2 years ago
5

Find the value of x. 91° (7x)

Mathematics
2 answers:
7nadin3 [17]2 years ago
8 0

Answer:

13

Step-by-step explanation:

This angle is called a reflective angle so the angles equal eachother. So put them equal to eachother and solve.

91=7x

x= 91÷7

x=13

AnnyKZ [126]2 years ago
7 0

Answer:

x = 13

Step-by-step explanation:

7x = 91
91/7 = x
x = 13

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The population of a certain species of insects increases exponentially according to the model, P(0) = 952e0.12t where P is the n
NeX [460]
Answer:

A) 952 insects are in the original colony

B) 10494 insects are in the colony after 20 weeks

C) 25 weeks

Explanations:

The model representing the population of the species of insects

P(t)=952e^{0.12t}

An exponential growth is of the form:

P(t)=P_0e^{kt}

where P₀ is the original population

t is the time taken in weeks

Comparing the two equations:

P_0=\text{ 952}

952 insects are in the original colony

B. The number of insects that will be in the colony after 20 weeks

Substituting t = 20 into the function given

\begin{gathered} P=952e^{0.12(20)} \\ \text{P = }10494 \end{gathered}

C) If the population, P = 20000

\begin{gathered} 20000=952e^{0.12t} \\ e^{0.12t}=\text{ }\frac{20000}{952} \\ e^{0.12t}=21.008 \\ 0.12t\text{ = ln(21.008)} \\ 0.12t\text{ = }3.04 \\ t\text{ = }\frac{3.04}{0.12} \\ t\text{ = }25 \end{gathered}

8 0
1 year ago
Find the critical points of the surface f(x, y) = x3 - 6xy + y3 and determine their nature.​
Vedmedyk [2.9K]

Compute the gradient of f.

\nabla f(x,y) = \left\langle 3x^2 - 6y, -6x + 3y^2\right\rangle

Set this equal to the zero vector and solve for the critical points.

3x^2-6y = 0 \implies x^2 = 2y

-6x+3y^2=0 \implies y^2 = 2x \implies y = \pm\sqrt{2x}

\implies x^2 = \pm2\sqrt{2x}

\implies x^4 = 8x

\implies x^4 - 8x = 0

\implies x (x-2) (x^2 + 2x + 4) = 0

\implies x = 0 \text{ or } x-2 = 0 \text{ or } x^2 + 2x + 4 = 0

\implies x = 0 \text{ or } x = 2 \text{ or } (x+1)^2 + 3 = 0

The last case has no real solution, so we can ignore it.

Now,

x=0 \implies 0^2 = 2y \implies y=0

x=2 \implies 2^2 = 2y \implies y=2

so we have two critical points (0, 0) and (2, 2).

Compute the Hessian matrix (i.e. Jacobian of the gradient).

H(x,y) = \begin{bmatrix} 6x & -6 \\ -6 & 6y \end{bmatrix}

Check the sign of the determinant of the Hessian at each of the critical points.

\det H(0,0) = \begin{vmatrix} 0 & -6 \\ -6 & 0 \end{vmatrix} = -36 < 0

which indicates a saddle point at (0, 0);

\det H(2,2) = \begin{vmatrix} 12 & -6 \\ -6 & 12 \end{vmatrix} = 108 > 0

We also have f_{xx}(2,2) = 12 > 0, which together indicate a local minimum at (2, 2).

3 0
2 years ago
Which box-and-whisker plot shows the scores of ten students on a mathematics exam?
PIT_PIT [208]
I would need to see the box and whisker plot to answer this question.
7 0
4 years ago
Morty spent $54 on tulips and roses and bought a total of 14 flowers. If tulips cost $5 and roses $3
Tom [10]

Answer:

a) Let's define the variables:

t = number of tulips bought

r = number of roses bought

We know that each tulip costs $5, and each rose costs $3.

Then the total cost will be:

$5*t + $3*r

We know that Morty spent a total of $54, then we have the equation:

$5*t + $3*r = $54

We also know that he bought a total of 14 flowers, then:

r + t = 14

Then the system of equations is:

$5*t + $3*r = $54

r + t = 14

b) To solve the system, first, we need to isolate one of the variables in one of the equations. I will isolate r in the second one:

r = 14 - t

Now we can replace this into the other equation:

$5*t + $3*r = $54

$5*t + $3*(14 - t) = $54

Now we can solve this for t.

$5*t + $3*14 - $3*t = $54

$2*t + $42 = $54

$2*t = $54 - $42 = $12

t = $12/$2 = 6

t = 6

He bought 6 tulips.

Now we can use the equation r = 14 - t

r = 14 - 6 = 8

r = 8

He bought 8 roses.

4 0
3 years ago
The amount of $180 is what percentage of 135
Marizza181 [45]
75%

135x100= 13500
13500/180=75
5 0
3 years ago
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