MATHEMATICS HIGH SCHOOL

If f(x)=8sin^6x - cos^2x. Find f'(\pi /4.

Answers

Answer 1
Answer: f'(x) = 48(sin(x))^5*cos(x)- 2cos(x)(-sin(x))
= 48(sin(x))^5*cos(x)+ 2cos(x)sin(x)

f'(π/4)= 48(sin(π/4))^5*cos(π/4)+ 2cos(π/4)sin(π/4)=7.

The final answer is 7.

Hope this helps~

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Fill in the common equivalents.
1.) 662/3% = ?/?

Answers

3% is the same as 0.03
Therefore, 662/3% = 662/0.03

Complete the equation of the graphed linear function in point-slope form.y – (–2) = ? (x – ?)

Answers

The point-slope form:
y-y_1=m(x-x_1)
m - slope
x₁, y₁ - the coordinates of a point

It passes through the points (1,-2) and (2,2).
(1,-2) \nx_1=1 \n y_1=-2 \n \n(2,2) \nx_2=2 \n y_2=2 \n \nm=(y_2-y_1)/(x_2-x_1)=(2-(-2))/(2-1)=(2+2)/(1)=4

\boxed{y-(-2)=4(x-1)}

Solve for m: 18d – 2m + 9k < 5k + 10.

Answers

Simple,

just go with the flow,

18d-2m+9k<5k+10
             -9k  -9k

18d-2m<-4k+10....

18d-2m<-4k+10
-18d      -18d

-2m<-18d-4k+10

Now, divide.. (but remember when dividing by a negative the sign gets flipped)

(-2m)/(-2) \ \textless \ (-18d-4k+10)/(-2)

Thus, m>9d+2k-5.

Your answer.. :D

Which measurement is equivalent to 80 cm?

8,000 mm
0.8 m
0.08 km
8 m

Answers

The answer is the second one, 0.8m





Hope it is helpful :)
0.8m is the answer because 0.1m is 10cm

Use cross products to demonstrate whether the two ratios are equivalent in this problem: 4 over 6 times 14 over 21

Answers

Determine if the two ratios are equivalent in this problem

The two ratios are equivalent

Given:

4 over 6 times 14 over 21

Times mean multiplication (×) in mathematics

Over means division (÷ or /) in mathematics

So,

4 over 6 times 14 over 21

= 4/6 × 14 / 21

Equate both ratio

4/6 = 14/21

cross product

(4 × 21) = (6 × 14)

84 = 84

Therefore, the two ratios are equivalent

Read more:

brainly.com/question/24425126
4/6 = 14/21When using cross product always multiply the left fractions numerator times the right side fractions denominator and the left side fractions denominator times the right side fractions numerator4×21 = 6×1484=84They are equivalent because they both equal 84

There are 10 vehicles in a parking lot: 3 SUVs and 7 trucks. What is the probability that any 7 randomly chosen parking spots have 2 SUVs and 5 trucks OR 3 SUVs and 4 trucks?

Answers

We have to calculate the probability that any randomly choosen parking spots have 2 SUVs and 5 trucks or 3 SUVs and 4 trucks. We will use the formula with combinations: P = ( 3C2 * 7C5 ) / ( 10C7) + ( 3C3 * 4C7) / ( 10C7). For example: 10C7 = 10! / 7!*(10-7)! = 10!/7!*3!= 10*9*8/3*2*1 = 120, etc. P = ( 3 * 21 ) / 120 + ( 1 * 35 ) / 120 = 63 / 120 + 35 / 120 = 98 / 120 = 0.8166. Answer: The probability is 0.8166 or 81.66%.
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