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3 years ago

Add the equations. 3x - y = -1 - 3x + 3y= 27

Mathematics

1 answer:

harkovskaia [24]3 years ago

3 0

Step-by-step explanation:

3x - 3x -y + 3y = 27-1

2y = 26

y = 13 use this to find the value of x

3x - 13 = -1

3x = -1 + 13

3x = 12

x = 4

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Find the value of c, rounded to the nearest tenth <br> A. 11<br> B. 14.3<br> C. 37.6<br> D. 7.4

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Answer:

D. The correct value of c = 7.4

Step-by-step explanation:

According to Tangent-Secant theorem:

"When a tangent and a secant are drawn from one single external point to a circle, square of the length of tangent segment must be equal to the product of lengths of whole secant segment and the exterior portion of secant segment."

Here, the external length of tangent segment = 10

Also, the length of internal segment is 14 and c.

So, by the SECANT THEOREM:

$(10)^2 = 14 \times c\\\implies c = \frac{100}{14} = 7.14$

or, c = 7. 1428

Now, rounding off the value of c = 7. 14 to the nearest tenth, we get

c = 7. 4

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3 years ago

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3 years ago

What are the approximate values of the minimum and maximum points of f(x) = x5 − 10x3 + 9x on [-3,3]?

nika2105 [10]

Answer:

Minimum : -37 at x=2.4 and

Maximum = 37 at x=-2.4.

Step-by-step explanation:

Given:

$f(x)=x^5-10x^3+9x$ ; [-3,3]

Explanation:

In order to find minimum/maximum of a function, we need to find the first derivative of the function and then set it equal to 0 to get critical points.

Therefore,

$f'(x)=5x^4-30x^2+9$

Setting derivative equal to 0, we get

$5x^4-30x^2+9=0$

On applying quadratic formula, we get

x=2.4, -2.4, -0.7, 0.7.

So, those are critical points of the given function.

Plugging the values x=2.4, -2.4, -0.7, 0.7, -3 and 3 in above function, we get

f(2.4)=(2.4)^5-10(2.4)^3+9(2.4)= -37.01376 : Minimum.

f(-2.4)=(-2.4)^5-10(-2.4)^3+9(-2.4)= 37.01376 : Maximum.

f(0.7)=(0.7)^5-10(0.7)^3+9(0.7) = 3.03807

f(-0.7)=(-0.7)^5-10(-0.7)^3+9(-0.7) = -3.03807

f(-3)=(-3)^5-10(-3)^3+9(-3) =0

f(3)=(3)^5-10(3)^3+9(3) =0

Therefore the approximate values of the minimum and maximum points of f(x) = $x^5- 10x^3+ 9x$ on [-3,3] are:

Minimum : -37 at x=2.4 and

Maximum = 37 at x=-2.4.

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3 years ago