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slava [35]
3 years ago
10

Please help [photo attachment]

Mathematics
1 answer:
Alexxx [7]3 years ago
5 0
Absolute Zero, also I suggest cropping out your name and teacher for your safety :3 have an amazing day!
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At what point on the parabola y = 3x^2 + 2x is the tangent line parallel to the line<br> y = 10x −2?
oksian1 [2.3K]

Answer:

( \frac{4}{3} , 8 )

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 10x - 2 ← is in slope- intercept form

with slope m = 10

Parallel lines have equal slopes

then the tangent to the parabola with a slope of 10 is required.

the slope of the tangent at any point on the parabola is \frac{dy}{dx}

differentiate each term using the power rule

\frac{d}{dx} (ax^{n} ) = nax^{n-1} , then

\frac{dy}{dx} = 6x + 2

equating this to 10 gives

6x + 2 = 10 ( subtract 2 from both sides )

6x = 8 ( divide both sides by 6 )

x = \frac{8}{6} = \frac{4}{3}

substitute this value into the equation of the parabola for corresponding y- coordinate.

y = 3(\frac{4}{3} )² + 2

   = (3 × \frac{16}{9} ) + 2

   = \frac{16}{3} + \frac{8}{3}

   = \frac{24}{3}

   = 8

the point on the parabola with tangent parallel to y = 10x - 2 is ( \frac{4}{3} , 8 )

3 0
2 years ago
Which could be the dimensions of a rectangular prism whose surface area is greater than 140 square feet? Select three options. 0
olya-2409 [2.1K]

Answer:

I think the answers are...

B. 6 feet by 5 feet by 4 feet

C. 7 feet by 6 feet by 4 feet

D.  8 feet by 3 feet by 7 feet

(I'm so sorry if it's wrong)

Hope this Helps!

4 0
3 years ago
Read 2 more answers
Use the method from the Example to approximate the solution to the equations below to two decimal places.
STALIN [3.7K]

Answer:

x = 3.85

Step-by-step explanation:

Given equation:

6ˣ = 1,000

now,

on taking log both sides, we get

⇒ log(6ˣ) = log(1,000)

or

⇒ log(6ˣ) = log(10³)

now we know the property of log function that

log(aᵇ) = b × log(a)

thus, applying the above property, we get

⇒ x × log(6) = 3log(10)

or

⇒ x × log(2×3) = 3log(10)

now,

we have another property of log function as":

log(A) = log(A) + log(B)

therefore,

x × [log(2) + log(3)] = 3log(10)

also,

log(10) = 1

log(2) = 0.3010

log(3) = 0.4771

Thus,

⇒ x × [0.3010 + 0.4771 ] = 3 × 1

or

⇒ x × 0.7781 = 3

or

⇒ x = 3.85

3 0
3 years ago
48 cookies; 25 % decrease... Find the new amount given the original amount And the percent of change.
coldgirl [10]
48 cookies after 25 % decrease is as much as 75 % from 48:

75% from 48 =
= 75/100 * 48 =
= 3/4 * 48 =
= 3/1 * 12 =
= 3  * 12 =
= <u>36
</u>

I hope it will help you :)
7 0
3 years ago
What is the sum of the exterior angle measures for an irregular convex octagon?
Eva8 [605]
The sum of ext. angles on any convex polygon is always 360 degrees
4 0
3 years ago
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