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3 years ago

The equation x^2+ (k - 3)x + (3 - 2k) = 0, where k is a constant, has two distinct real roots.

Mathematics

1 answer:

Lisa [10]3 years ago

4 0

Step-by-step explanation:

For quadratic equation ax^2 + bx + c = 0 to have two distinct real roots,

b^2 - 4ac must be positive.

b^2 - 4ac > 0

(k - 3)^2 - 4(3 - 2k) > 0

k^2 - 6k + 9 - 12 + 8k > 0

k^2 + 2k - 3 > 0

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A person stands 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 meters

In-s [12.5K]

Answer:

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

Step-by-step explanation:

Given that,

A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.

From Pythagorean Theorem,

(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+

Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.

∴y²= x²+10²

$\Rightarrow y=\sqrt{x^2+100}$

Differentiating with respect to t

$\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}$

$\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}$

Since the car driving towards the intersection at 13 m/s.

so, $\frac{dx}{dt}=-13$

$\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)$

Now

$\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)$

$=\frac{24\times (-13)}{\sqrt{676}}$

$=\frac{24\times (-13)}{26}$

= -12 m/s

Negative sign denotes the distance between the car and the person decrease.

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

8 0

3 years ago

Now that the party is over, it’s time to help your friend write the thank you notes. You have $24 to purchase and mail 32 thank

Tasya [4]

0.75 Jordan went to the pond and died soon

6 0

3 years ago

What is the value of 2 3/4 ➗ 3/4

Ivan

Answer:

3 2/3 is the answer

Step-by-step explanation:

Conversion a mixed number 2 3/

to a improper fraction: 2 3/4 = 2 3/

= 2 · 4 + 3/

= 8 + 3/

= 11/

To find new numerator:

a) Multiply the whole number 2 by the denominator 4. Whole number 2 equally 2 * 4/

= 8/

b) Add the answer from previous step 8 to the numerator 3. New numerator is 8 + 3 = 11

c) Write a previous answer (new numerator 11) over the denominator 4.

Two and three quarters is eleven quarters

Divide: 11/

: 3/

= 11/

· 4/

= 11 · 4/

4 · 3

= 44/

= 4 · 11 /

4 · 3

= 11/

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 3/

is 4/

) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step , cancel by a common factor of 4 gives 11/

so you simplify to get 3 2/3

8 0

3 years ago

The graph shows y in direct variation with x. Find the value of Y when X=-15

telo118 [61]

Y = 2x
y = 2*(-15) = -30 . . . . . selection A is appropriate

6 0

3 years ago

Gianna put $1000 in a savings account for 18 months, The interest on the account is 3.5%. How much will Gianna earn in interest?

zimovet [89]

Answer:

amount of interest = 52.5

amount at the end of the period = 1052.5

Step-by-step explanation:

use the formula for simple interest

PRT/100

P is the principle

R is the rate of interest charged

T is the Time taken

18 months = 1 years 6 months ( 1.5 years)

1000 * 3.5 * 1.5 = 5250

5250/100 = 52.5

the amount of interest = <u>52.5</u>

the amount she will have at the end of the period

= 1000 +52.5

= <u>1052.5</u>

8 0

3 years ago