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stiv31 [10]
3 years ago
15

Estimate the slope of the tangent line of the function y(t)=\sqrt{(3t+1} at the point t=2.

Mathematics
1 answer:
Korvikt [17]3 years ago
7 0

Answer: 0.567

Step-by-step explanation:

y(t)=\sqrt{3t+1} \\\\y'(t)=\dfrac{3}{2\sqrt{3t+1} } \\\\y'(2)=\dfrac{3}{2\sqrt{3*2+1} } =\dfrac{3\sqrt{7} }{14} =0,56694670951384084082177480435127\approx{0.567}

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Triangle JKL has an area of in2 and a perimeter of in.
S_A_V [24]

Answer:

Area = 24 in²

Perimeter = 24in

Step-by-step explanation:

To find the area given the length of the 3 sides:

a= 8in

b= 6.4in + 3.6in= 10in

c= 6in

Add them together:

8in + 10in + 6in

= 24in²

To find the perimeter you do the same thing:

a= 8in

b= 10in

c= 6in

Add them together

=24in

DO <u>NOT</u> SQUARE THE ANSWER WHEN FINDING <u>PERIMETER</u>

5 0
3 years ago
You throw a ball up and its height h can be tracked using the equation h=2x^2-12x+20.
postnew [5]

<em><u>This problem seems to be wrong because no minimum point was found and no point of landing exists</u></em>

Answer:

1) There is no maximum height

2) The ball will never land

Step-by-step explanation:

<u>Derivatives</u>

Sometimes we need to find the maximum or minimum value of a function in a given interval. The derivative is a very handy tool for this task. We only have to compute the first derivative f' and have it equal to 0. That will give us the critical points.

Then, compute the second derivative f'' and evaluate the critical points in there. The criteria establish that

If f''(a) is positive, then x=a is a minimum

If f''(a) is negative, then x=a is a maximum

1)

The function provided in the question is

h(x)=2x^2-12x+20

Let's find the first derivative

h'(x)=4x-12

solving h'=0:

4x-12=0

x=3

Computing h''

h''(x)=4

It means that no matter the value of x, the second derivative is always positive, so x=3 is a minimum. The function doesn't have a local maximum or the ball will never reach a maximum height

2)

To find when will the ball land, we set h=0

2x^2-12x+20=0

Simplifying by 2

x^2-6x+10=0

Completing squares

x^2-6x+9+10-9=0

Factoring and rearranging

(x-3)^2=-1

There is no real value of x to solve the above equation, so the ball will never land.

This problem seems to be wrong because no minimum point was found and no point of landing exists

3 0
3 years ago
-3/2 + 3/7 find the sum. write your answer in simplest form.
DedPeter [7]

Answer: 1 1/14

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
4k + 12 = 52<br> using algbra
grigory [225]

Answer:

k=10

Step-by-step explanation:

4k + 12= 52

minus 12 on both sides

4k=40

now divide by 4

k=10

5 0
3 years ago
What are the relationships between inscribed, central, and circumscribed angles of a circle?
Delicious77 [7]

Answer:

Topics include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. Common Core: HSG-C.A.2

Step-by-step explanation:

PA BRAINLIEST

8 0
2 years ago
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