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2 years ago

13

the angle between two radii of a circle is 130°. then the angle between the tangents at the end points of radius at their point

of intersection is

2 answers:

Triss [41]2 years ago

8 0

Answer:

the answer is =180° - 130° = 50°.

Step-by-step explanation:

Hope it helps

Elan Coil [88]2 years ago

5 0

Answer:

50 degrees

Step-by-step explanation:

the sum of all angles in a four-sided shape is 360 degrees.

our four points here are :

the center of the circle

the 2 points on the circle, where the 2 tangents touch the circle

the intersection point of the tangents (where they cross each other).

at the 2 points, where radius meets tangent, we have a right angle or 90 degrees. so, they together take already 180 degrees.

the angle at the center of the circle is 130 degrees.

so, all that is left for the angle at the tangent intersection point is

360 - 180 - 130 = 50 degrees

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Find the value of x!!

Wewaii [24]

Answer:

x=23°

Step-by-step explanation:

93°+(3x+18)°=180°

93°+3x+18°=180°

111°+3x=180°

3x=180°-111°

3x=69°

x=69°:3

x=23°

3 0

3 years ago

Read 2 more answers

Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer d

andrey2020 [161]

Answer:

The maximum value is 1/27 and the minimum value is 0.

Step-by-step explanation:

Note that the given function is equal to $(xyz)^2$ then it means that it is positive i.e $f(x,y,z)\geq 0$ .

Consider the function $F(x,y,z,\lambda)=x^2y^2z^2-\lambda (x^2+y^2+z^2-1)$

We want that the gradient of this function is equal to zero. That is (the calculations in between are omitted)

$\frac{\partial F}{\partial x} = 2x(y^2z^2 - \lambda)=0$

$\frac{\partial F}{\partial y} = 2y(x^2z^2 - \lambda)=0$

$\frac{\partial F}{\partial z} = 2z(x^2y^2 - \lambda)=0$

$\frac{\partial F}{\partial \lambda} = (x^2+y^2+z^2-1)=0$

Note that the last equation is our restriction. The restriction guarantees us that at least one of the variables is non-zero. We've got 3 options, either 1, 2 or none of them are zero.

If any of them is zero, we have that the value of the original function is 0. We just need to check that there exists a value for lambda.

Suppose that x is zero. Then, from the second and third equation we have that

$-2y\lambda = -2z\lambda$ . If lambda is not zero, then y =z. But, since $-2y\lambda=0$ and lambda is not zero, this implies that x=y=z=0 which is not possible. This proofs that if one of the variables is 0, then lambda is zero. So, having one or two variables equal to zero are feasible solutions for the problem.

Suppose that only x is zero, then we have the solution set $y^2+z^2=1$ .

If both x,y are zero, then we have the solution set $z^2=1$ . We can find the different solution sets by choosing the variables that are set to zero.

NOw, suppose that none of the variables are zero.

From the first and second equation we have that

$\lambda = y^2z^2 = x^2z^2$ which implies $x^2=y^2$

Also, from the first and third equation we have that

$\lambda = y^2z^2 = x^2y^2$ which implies $x^2=z^2$

So, in this case, replacing this in the restriction we have $3z^2=1$ , which gives as another solution set. On this set, we have $x^2=y^2=z^2=\frac{1}{3}$ . Over this solution set, we have that the value of our function is $\frac{1}{3^3}= \frac{1}{27}$

4 0

3 years ago

Divide fractions: 5/6 divided by 6/10 (leave as improper fraction if necessary)

tankabanditka [31]

Answer:

25/18

Step-by-step explanation:

5/6 / 6/10

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2 years ago

Adam is 4 years older than Tara. Five years ago the sum of their ages was 48. Use algebraic equations to represent the situation

lord [1]

Answer:

Tara is 27 and Adam is 31.

Step-by-step explanation:

Tara: x years old

Adam: x+4

Subtract the five years to get their current age

x-5 and x+4-5

x-5 and x-1

(x-5) + (x-1) = 48

x-5 + x-1 = 48

2x - 6 = 48

2x= 48+6

2x= 54

x= 27

Tara is 27 and Adam is 31

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3 years ago

When the product of 6 and the square of a number is increased by 5 times the number, the result is 4.

il63 [147K]

Let $x$ be the unknown number. Its square is $x^2$ . The product of 6 and the square of the number is $6x^2$ . Increase this by 5 and you get $6x^2+5$ .

If this has to equal 4, you have $6x^2+5=4$

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2 years ago

Read 2 more answers