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algol13
3 years ago
6

How to solve these question?

Mathematics
1 answer:
mart [117]3 years ago
7 0
3.) An extreme value refers to a point on the graph that is possibly a maximum or minimum. At these points, the instantaneous rate of change (slope) of the  graph is 0 because the line tangent to the point is horizontal. We can find the rate of change  by taking the derivative of the function.

y' = 2ax + b

Now that we where the derivative, we can set it equal to 0.

2ax + b = 0

We also know that at the extreme value, x = -1/2. We can plug that in as well.

2a (-\frac{1}{2} ) + b = 0

The 2 and one-half cancel each other out.

-a + b = 0

a = b

Now we know that a and b are the same number, and that ax^2 + bx + 10 = 0 at x = -1/2. So let's plug -1/2 in for x in the original function, and solve for a/b.

a(-0.5)^2 + a(-0.5) + 10 = 0

0.25a - 0.5a + 10 = 0

-0.25a = -10

a = 40

b = 40

To determine if the extrema is a minima or maxima, we need to go back to the derivative and plug in a/b.

80x + 40

Our critical number is x = -1/2. We need to plug a number that is less than -1/2  and a number that is greater than -1/2 into the derivative.

LESS THAN:
80(-1) + 40 =  -40

GREATER THAN:
80(0) + 40 = 40

The rate of change of the graph changes from negative  to positive at x = -1/2, therefore the extreme value is a minimum.

4.) If the quadratic function is symmetrical about x = 3, that means that the minimum or maximum must be at x = 3.

y' = 2ax + 1

2a(3) + 1 = 0

6a = -1

a = -1/6

So now plug the a value and x=3 into the original function to find the extreme value.

(-1/6)(3)^2 + 3 + 3 = 4.5

The extreme value is 4.5


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Leno4ka [110]

Answer:

97/113

Step-by-step explanation:

67 robots have legs only, 21 have wheels only, and 9 have both legs and wheels.  The total number of robots with legs and/or wheels is 97.

The probability is 97/113.

4 0
3 years ago
What is ✔️16 ? Raises cuadrada
aev [14]
If you are looking for √16, you are looking for the square root of 16. The square root of a number is defined by what number multiplied by itself will get you.
x^2 (a number squared) = 16.
√16 = x.
Let's try from numbers 1-5 for a square.
1x1 = 1
2x2 = 4
3x3 = 9
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5 0
2 years ago
Read 2 more answers
10) Find the measure of angle D. Hint: you must do two math problems to solve
NISA [10]

Answer:

Option A.) 43°

Step-by-step explanation:

Part 10)

step 1

Find the length of side EG

see the attached figure to better understand the problem

we know that

In the right triangle EGF

cos(65^o)=\frac{EG}{EF} ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

cos(65^o)=\frac{EG}{11}

solve for EG

EG=(11)cos(65^o)\\EG=4.65\ cm

step 2

Find the measure of angle D

In the right triangle DEG

tan(D)=\frac{EG}{DG} ----> by TOA (opposite side divided by adjacent side)

substitute the given values

tan(D)=\frac{4.65}{5}\\\\D=tan^{-1}(\frac{4.65}{5})=43^o

3 0
3 years ago
Please help i will give brainliest to first correct answer<br> (2 5/8 +4 8/17 )+( 9/17 +3 3/8 )
Serggg [28]

Answer:

11

Step-by-step explanation:

You don't need the parenthesis, so you get:

2 5/8 + 4 8/17 + 9/17 + 3 3/8

You combine the integer values and get:

9 + 5/8 + 8/17 + 9/17 + 3/8

You combine the fractions with the denom. of 8 and do the same with those with the denom. of 17 and get:

9 + 8/8 + 17/17

You simplify:

9 + 1 + 1 =

11

3 0
3 years ago
Read 2 more answers
What's the perpindicular line of y+5=4(x+12)
snow_tiger [21]
The slope of this line is
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5
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Perpendicular lines have opposite reciprocal slopes. To find an opposite reciprocal, multiply by
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Hence the opposite reciprocal of
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6 0
3 years ago
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