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3 years ago

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Let f be continuous on [0, a] and differentiable on (0, a), Prove that if f(a)=0 then there is at least one value of x in (0, a)

, such that f(x)= -xf'(x).(5marks) (%4h) 4

1 answer:

asambeis [7]3 years ago

6 0

Answer:

See picture attached

Step-by-step explanation:

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What is the measurement of BC to the nearest centimeter?

77julia77 [94]

Answer:

a 8

Step-by-step explanation:

You are given two sides and the included angle. Since you don't have any side and the opposite angle, you must use the law of cosines.

$a^2 = b^2 + c^2 - 2bc\cos A$

$a^2 = 5^2 + 11^2 - 2(5)(11)\cos 39^\circ$

$a^2 = 25 + 121 - 110\cos 39^\circ$

$a^2 = 60.51$

$a = 7.779$

Answer: a = 8 cm

7 0

3 years ago

Rename 4/7 as a percent. Round to the nearest tenth of a percent if necessary.

enyata [817]

Answer:

Part 1) Option C. 57.1%

Part 2) Option B. 70.9%

Part 3) Option C. 66 2/3 %

Part 4) Option A. About 16

Part 5) Option A. About $12

Part 6) Option B. About $9

Part 7) Option B. x/50=70/100

Part 8) Option B. 25%

Part 9) Option D. 800

Part 10) $1,770

Step-by-step explanation:

Part 1) Rename 4/7 as a percent

we know that

To rename a number as a percent, multiply the number by 100

so

(4/7)*100=400/7=57.1%

Part 2) Rename .709 as a percent

we know that

To rename a number as a percent, multiply the number by 100

so

0.709*100=70.9%

Part 3) If 1/3 is equivalent to 33 1/3% what percent is equivalent to 2/3?

we know that

33 1/3%=(33*3+1)/3 %=100/3 %

By proportion

(100/3 %)/(1/3)=x/(2/3)

x=200/3 %=66 2/3 %

Part 4) Alice plays basketball. In one game she shoots 21 free throws and makes 81.25% of them. Estimate how many she makes

To find the exact value multiply the total shoots by the percentage

21*(81.25/100)=17.06

so

<em>To find the estimate value</em>

21 shoots is about 20

81.25% is about 80%

so

20*(80/100)=16

the answer is about 16

Part 5) Estimate 48% of 23.95

To find the exact value multiply the number by the percentage

23.95*(48/100)=11.50

<em>To find the estimate value</em>

23.95 is about 24

48% is about 50%

so

24*(50/100)=12

Part 6) The bill at a restraint is $58.50 and Mrs. Johnson wants to leave a 15% tip. Approximately how much money

To find the exact value multiply the bill by the percentage

so

$58.50*(15/100)=$8.78

<em>To find the approximate value</em>

$58.50 is about $60

$60*(15/100)=$9

Part 7) Which proportion can be used to solve the following percent problem? What is 50% if 100% is 70?

using proportion

x/50=70/100

x=70*50/100

x=35

Part 8) What percent of 50 is 12.5?

using proportion

50/100%=12.5/x%

x=100*12.5/50

x=25%

Part 9) 50 Is 6.25% of what number?

using proportion

50/6.25%=x/100%

x=100*50/6.25

x=800

Part 10) Chris works at Higgins’ Automart and is selling a new Shelby Mustang for $59,000. If he earns a commission of 3%, how much money does he earn?

we know that

$59,000 ------> represent the 100%

using proportion

Find how much money represent 3% of the commission

59,000/100%=x/3%

so

X=$59,000*(3/100)=$1,770

4 0

3 years ago

What is 1.21 repeating as a fraction?

DochEvi [55]

$x=1.\overline{21}\\
100x=121.\overline{21}\\
100x-x=121.\overline{21}-1.\overline{21}\\
99x=120\\
x=\dfrac{120}{99}=\dfrac{40}{33}$

6 0

3 years ago

Read 2 more answers

6 Monica reads 15 pages of a mystery book in 9 minutes. What is

Ivan

Answer:

135

Step-by-step explanation:

15 x 9 = 135

3 0

3 years ago

Read 2 more answers

Plz Help.......

lana66690 [7]

Answer:

For product A, the product is increasing, for the bigger the number you plug into x (due to the fact that the numbers become bigger because of the time: year 1, year 2, etc)

Product A is 82% change rate, while

product B is 983.45/4 = 245.8625, 1756.16/3 = 585.3867

Product B is 245.8625/585.3867

product B is 42% change rate

Product A change rate is higher than Product B by 40%

Step-by-step explanation:

Hope this helped! :)

6 0

3 years ago